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__________===== __________===== __________===== NOST Implementation of the Flexible Image Transport System (FITS) November 6, 1991 Draft Standard NOST 100-0.3b NASA/OSSA Office of Standards and Technology Code 933 NASA Goddard Space Flight Center Greenbelt MD 20771 USA The NASA/OSSA Office of Standards and Technology (NOST) has been established to serve the space science communities in evolving cost effective, interoperable data systems. The NOST performs a number of functions designed to facilitate the recognition, development, adoption, and use of standards by the space science communities. Approval of a NOST Standard requires verification by the NOST that the following requirements have been met: consensus of the technical panel, proper adjudication of the comments received from the targeted space and Earth science community, and conformance to the accreditation process. A NOST standard represents the consensus of the technical panel convened by the NASA/OSSA Office of Standards and Technology (NOST) of the National Space Science Data Center (NSSDC) of the National Aeronautics and Space Administration (NASA). Consensus is established when the NOST Accreditation Panel determines that substantial agreement has been reached by the Technical Panel. However, consensus does not necessarily imply that all members were in full agreement with every item in the standard. NOST standards are not binding as published; however, they may serve as a basis for mandatory standards when adopted by NASA or other organizations. A NOST standard may be revised at any time, depending on developments in the areas covered by the standard. Also, within five years from the date of its issuance, this standard will be reviewed by the NOST to determine whether it should 1) remain in effect without change, 2) be changed to reflect the impact of new technologies or new requirements, or 3) be retired or canceled. The Technical Panel that developed this standard consisted of the following members: Robert J. Hanisch, Chair Space Telescope Science Institute Barry M. Schlesinger, Secretary Hughes STX Lee E. Brotzman Hughes STX Edward Kemper Hughes STX Peter J. Teuben University of Maryland Michael E. Van Steenberg NASA Goddard Space Flight Center Wayne H. Warren Jr. Hughes STX Richard A. White NASA Goddard Space Flight Center This standard is published and maintained by the NOST. Send comments and orders for NOST documents to: NOST, Code 933, NASA Goddard Space Flight Center Greenbelt MD 20771 USA Internet: nost@nssdca.gsfc.nasa.gov DECNET: NSSDCA::NOST 301-286-3575 Contents Introduction vii 1 Overview 1 1.1 Purpose ...................................................... 1 1.2 Scope ........................................................ 1 1.3 Applicability ................................................ 1 1.4 Organization and Recommendations ............................. 2 2 References 3 3 Definitions, Acronyms, and Symbols 5 4 FITS File Organization 9 4.1 Overall ...................................................... 9 4.2 Individual FITS Structures ................................... 9 4.3 Primary Header and Data Array ................................ 9 4.3.1 Primary Header ......................................... 10 4.3.2 Primary Data Array ..................................... 10 4.4 Extensions ................................................... 10 4.4.1 Requirements for Conforming Extensions ................. 10 4.4.2 Standard Extensions .................................... 11 4.4.3 Order of Extensions .................................... 11 4.5 Special Records .............................................. 12 5 Headers 13 5.1 Card Images .................................................. 13 5.1.1 Syntax ................................................. 13 5.1.2 Components ............................................. 13 5.2 Keywords ..................................................... 14 5.2.1 Mandatory Keywords ..................................... 14 5.2.2 Other Reserved Keywords ................................ 17 5.2.3 Additional Keywords .................................... 21 5.3 Value ........................................................ 21 5.3.1 General Format Requirements ............................ 21 5.3.2 Fixed Format ........................................... 22 6 Data Representation 23 6.1 Characters ................................................... 23 6.2 Integers ..................................................... 23 6.2.1 Eight-bit .............................................. 23 6.2.2 Sixteen-bit ............................................ 23 6.2.3 Thirty-two-bit ......................................... 23 6.3 IEEE-754 Floating Point ...................................... 24 6.3.1 Thirty-two-bit Floating Point .......................... 24 6.3.2 Sixty-four-bit Floating Point .......................... 24 7 Random Groups Structure 27 7.1 Keywords ..................................................... 27 7.1.1 Mandatory Keywords ..................................... 27 7.1.2 Reserved Keywords ...................................... 29 7.2 Data Sequence ................................................ 30 7.3 Data Representation .......................................... 30 8 Standard Extensions 31 8.1 ASCII Tables Extension ....................................... 31 8.1.1 Mandatory Keywords ..................................... 31 8.1.2 Other Reserved Keywords ................................ 33 8.1.3 Data Sequence .......................................... 34 8.1.4 Fields ................................................. 34 8.1.5 Entries ................................................ 34 8.2 Other Standard Extensions .................................... 35 9 Restrictions on Changes 37 Appendixes A Draft Proposal for Binary Table Extension 39 A.1 Abstract ..................................................... 39 A.2 Introduction ................................................. 40 A.3 Binary Tables ................................................ 40 A.4 Table Header ................................................. 40 A.5 Conventions for Multidimensional Arrays ....................... 43 A.6 Table Data Records ............................................ 43 A.7 Example Binary Table Header ................................... 45 A.8 Acknowledgments by Authors of Draft Proposal .................. 47 A.9 Appendixes to Draft Proposal for Binary Tables Extension ...... 48 A.9.1 "Multidimensional Array" Convention .................... 48 A.9.2 "Variable Length Array" Facility ....................... 48 B Implementation on Physical Media 53 B.1 Block Size .................................................... 53 B.1.1 Nine-Track, Half-Inch Magnetic Tape .................... 53 B.1.2 Other Media ............................................ 53 B.2 Physical Properties of Media .................................. 54 B.3 Labeling ...................................................... 54 B.3.1 Tape ................................................... 54 B.3.2 Other Media ............................................ 54 B.4 FITS File Boundaries .......................................... 54 B.4.1 Magnetic Reel Tape ..................................... 54 B.4.2 Other Media ............................................ 54 B.5 Multiple Physical Volumes ..................................... 54 C Differences from IAU-endorsed Publications 55 D Summary of Keywords 61 E ASCII Text 63 F IEEE Special Formats 65 G Reserved Extension Type Names 67 H NOST Publications 71 Index 73 List of Tables 5.1 Principal mandatory keywords. ................................ 14 5.2 Interpretation of valid BITPIX value. ........................ 15 5.3 Mandatory keywords in conforming extensions. ................. 16 6.1 Content of 32-bit floating point bit positions. .............. 24 6.2 Content of 64-bit floating point bit positions. ............. 25 7.1 Mandatory keywords in primary header preceding random groups. 28 8.1 Mandatory keywords in ASCII tables extensions. .............. 32 8.2 Valid TFORMn format values in TABLE extensions. ............. 33 D.1 Mandatory FITS keywords ..................................... 61 D.2 Reserved FITS keywords ...................................... 62 D.3 General Reserved FITS keywords .............................. 62 E.1 ASCII character set ......................................... 64 F.1 IEEE special floating point formats ......................... 65 G.1 Reserved Extension Type Names ............................... 68 G.2 Status Codes ................................................ 69 H.1 NOST Publications ........................................... 71 List of Figures 4.1 Array data sequence ......................................... 11 Introduction The Flexible Image Transport System (FITS) evolved out of the recognition that a standard format was needed for transferring astronomical data from one installation to another. The original form, or Basic FITS [1], was designed for the transfer of images and consisted of a binary array, usually multidimensional, preceded by an ASCII text header with information describing the organization and contents of the array. The FITS concept was later expanded to accommodate more complex data formats. A new format for image transfer, random groups, was defined [2] in which the data would consist of a series of arrays, with each array accompanied by a set of associated parameters. These formats were formally endorsed by the International Astronomical Union (IAU) in 1982 [3]. Provisions for data structures other than simple arrays or groups were made later. These structures appear in extensions, each consisting of an ASCII header followed by the data whose organization it describes. A set of general rules governing such extensions [4] and a particular extension ASCII Tables [5], were endorsed by the IAU General Assembly in 1988 [6]. At the same General Assembly, an IAU FITS Working Group was formed with the mandate to maintain the existing FITS standards and to review, approve, and maintain future extensions to FITS, recommended practices for FITS, implementations, and the thesaurus of approved FITS keywords [7]. In 1989, the IAU Commission 5 FITS Working Group approved a formal agreement [8] for the representation of floating point numbers. FITS was originally designed and defined for 9-track half-inch magnetic tape. However, as improvements in technology have brought forward other data storage and data distribution media, it has generally been agreed that the FITS format is to be understood as a logical format and not defined in terms of the physical characteristics of any particular data storage medium or media. Section 1 Overview 1.1 Purpose This standard formally defines the implementation of the FITS format for data structuring and exchange to be used where applicable, as defined in Section 1.3. It is intended as a formal codification of the FITS format that has been endorsed by the IAU for transfer of astronomical data, fully consistent with all actions and endorsements of the IAU and the IAU Commission 5 FITS Working Group. Minor ambiguities and inconsistencies in FITS as described in the original papers are eliminated. The eventual goal is to submit this document to the IAU Commission 5 FITS Working Group for endorsement as a universal standard for FITS. 1.2 Scope This standard specifies the organization and content of FITS data sets, including the header and data for all standard FITS formats: Basic FITS, the random groups structure, and the ASCII tables extension. It also specifies minimum structural requirements for new extensions and general principles governing the creation of new extensions, giving as an example the draft proposal for a Binary Table Extension. For headers, it specifies the proper syntax for card images and defines required and reserved keywords. For data, it specifies character and value representations and the ordering of contents within the byte stream. It defines the general rules to which new extensions are required to conform. 1.3 Applicability The IAU has recommended that all astronomical computer facilities support FITS for the interchange of binary data. All spacecraft projects and astrophysics data archives under the management of the Astrophysics Division of the National Aeronautics and Space Administration are required to make processed data available to users in the FITS format defined by this standard, unless the Astrophysics Division specifically determines otherwise. This standard may also be used to define the format for data transport in other disciplines, as may be determined by the appropriate authorities. 1.4 Organization and Recommendations Following the definitions in Section 3, this document describes the overall organization of a FITS file, the contents of the first (primary) header and data, and the rules for creating new FITS extensions in Section 4. The next two sections provide additional details on the header and data, with a particular focus on the primary header. Section 5 provides details about header card image syntax and specifies those keywords required and reserved in a primary header. Section 6 describes how different data types are rep- resented in FITS. The following sections describe the headers and data of two standard FITS structures, the now to be deprecated random groups records (Section 7) and the only current standard extension, ASCII Tables (Section 8). Throughout the document, deprecation of structures or syntax is noted where relevant. Files containing deprecated features are valid FITS, but these features should not be used in new files; the old files using them remain standard because of the principle that no change in FITS shall cause a valid FITS file to become invalid. The Appendixes contain material that is not part of the standard. The first two provide illustrations of FITS practice. Appendix A provides an example of a conforming extension, the draft proposal for the Binary Table Extension[9]. The generally accepted recommendations for the expression of the logical FITS format on various physical media are provided in Appendix B as a guide to FITS practices. The next, Appendix C, lists the differences between this standard and the specifications of prior publications; it also identifies those ambiguities in the documents endorsed by the IAU on which this standard provides specific rules. The next four provide reference information: a tabular summary of the FITS keywords (Appendix D), a list of the ASCII character set and a subset designated ASCII text (Appendix E), the bit representation of the IEEE special values (Appendix F), and a list of the reserved extension type names (Appendix G). Section 2 References 1. Wells, D. C., Greisen, E. W., and Harten, R. H. 1981, "FITS: A Flexible Image Transport System," Astron. Astrophys. Suppl., 44, 363-370. 2. Greisen, E. W. and Harten, R. H. 1981, "An Extension of FITS for Small Arrays of Data," Astron. Astrophys. Suppl., 44, 371-374. 3. IAU. 1983, Information Bulletin No. 49. 4. Grosbol, P., Harten, R. H., Greisen, E. W., and Wells, D. C. 1988, "Generalized Extensions and Blocking Factors for FITS," Astron. Astrophys. Suppl., 73, 359-364. 5. Harten, R. H., Grosbol, P., Greisen, E. W., and Wells, D. C. 1988, "The FITS Tables Extension," Astron. Astrophys. Suppl., 73, 365-372. 6. IAU. 1988, Information Bulletin No. 61. 7. McNally, D., ed. 1988, Transactions of the IAU, Proceedings of the Twentieth General Assembly. (Dordrecht:Kluwer). 8. Wells, D. C. and Grosbol, P. 1990, "Floating Point Agreement for FITS." (available from the NOST FITS Support Office) 9. Cotton, W. D. and Tody, D. B. 1991 "Binary Table Extension to FITS: A Proposal", preprint. (access instructions available from the NOST FITS Support Office). 10. ANSI, 1978, "American National Standard for Information Processing: Programming Language FORTRAN," ANSI X3.9 - 1978 (ISO 1539). Published by American National Standards Institute, Inc., New York. 11. ANSI, 1977 "American National Standard for Information Processing: Code for Information Interchange," ANSI X3.4 - 1977 (ISO 646). Published by American National Standards Institute, Inc., New York. 12. IEEE, 1985, "American National Standard - IEEE Standard for Binary Float- ing Point Arithmetic". ANSI/IEEE 754-1985, Published by American National Standards Institute, Inc., New York. 13. ANSI, 1976, "American National Standard for Information Processing: Unrecorded Magnetic Tape," ANSI X3.40 - 1976, Published by American National Standards Institute, Inc., New York. 14. ANSI, 1978, "American National Standard for Information Processing: Magnetic Tape Labels and File Structure," ANSI X3.27 - 1978, Published by American National Standards Institute, Inc., New York. 15. "Going AIPS," National Radio Astronomy Observatory, Charlottesville, VA, 1990. 16. Munoz, J. R., "IUE Data in FITS Format," ESA IUE Newsletter 32, 12-45. Section 3 Definitions, Acronyms, and Symbols _ Used to designate an ASCII blank. AIPS Abbreviation of Astronomical Image Processing System. ANSI Abbreviation of American National Standards Institute. Array A sequence of data values, of zero or more dimensions. Array value The value of an element of an array in a FITS file, without the application of the associated linear transformation. ASCII Abbreviation of American National Standard Code for Information Interchange. ASCII blank Hexadecimal 20. ASCII character Any member of the 7-bit ASCII character set. ASCII text ASCII characters hexadecimal 20-7E. Basic FITS The FITS structure consisting of the primary header followed by a single primary data array. Bit A single binary digit. Byte A string of eight bits treated as a single entity. Card image A sequence of 80 bytes containing ASCII text, treated as a logical record. Conforming extension An extension whose keywords and organization adhere to the requirements for conforming extensions defined in Section 4.4.1 of this standard. Deprecate To express earnest disapproval of. This term is used to refer to obsolete structures that ought not to be used but remain valid. Entry A single value in a table. Extension A FITS HDU appearing after the primary HDU in a FITS file. Extension name The identifier used to distinguish a particular extension HDU from others of the same type, appearing as the value of the EXTNAME keyword. Extension type An extension format. Field A set of zero or more table entries collectively described by a single format. File A sequence of one or more records terminated by an end-of-file indicator appropriate to the medium. FITS Abbreviation of Flexible Image Transport System. FITS file A file with a format that conforms to the specifications in this document. FITS logical record A record of 23040 bits, corresponding to 2880 8-bit bytes within a FITS file. FITS structure One of the components of a FITS file: the primary HDU, the random groups records, an extension, or, collectively, the special records following the last extension. Floating point A number whose bit structure is composed of a mantissa and exponent, whose ASCII representation contains an explicit decimal point and may include a power-of-ten exponent. Group parameter value The value of one of the parameters preceding a group in the random groups structure, without the application of the associated linear transformation. Header A series of card images organized within one or more FITS Logical Records which describes structures and/or data which follow it in the FITS file. Header and Data Unit (HDU) A data structure consisting of a Header and the data the Header describes. Note that an HDU may consist entirely of a header with no data records. IAU Abbreviation of International Astronomical Union. IUE Abbreviation of International Ultraviolet Explorer. IEEE Abbreviation of Institute of Electrical and Electronic Engineers. IEEE NaN Abbreviation of IEEE Not-a-Number value. IEEE special values (-0, 1, NaN). Indexed keyword A keyword that is of the form of a fixed root with an appended integer count. Keyword The first eight bytes of a header card image. Mandatory keyword A keyword that must be used in all FITS files or a keyword required in conjunction with particular FITS structures. Matrix A data array of two or more dimensions. MIDAS Abbreviation of ESO-MIDAS, the European Southern Observatory Munich Image Data Analysis System. NOAO Abbreviation of National Optical Astronomy Observatories. NOST Abbreviation of NASA/OSSA Office of Standards and Technology. NRAO Abbreviation of National Radio Astronomy Observatory. Physical value The value in physical units represented by a member of an array and possibly derived from the array value using the associated, but optional, linear transformation. Picture element A single location within an image array. Pixel Abbreviation of "picture element". Primary data array The data array contained in the Primary HDU. Primary header The first header in a FITS file, containing information on the overall contents of the file as well as on the primary data array. Record A sequence of bits treated as a single logical entity. Reference point The point along a given coordinate axis, given in units of pixel number, at which a value and increment are defined. Reserved keyword An optional keyword that may be used only in the manner defined in this standard. Special records A series of 23040-bit (2880 8-bit byte) records, following the primary HDU, whose internal structure does not otherwise conform to that for the primary HDU or to that specified for a conforming extension in this standard. Standard extension A conforming extension whose header and data content are specified explicitly in this standard. Type name The value of the XTENSION keyword used to identify the type of the extension in the data following. Valid value A member of a data array or table corresponding to an actual physical quantity. Section 4 FITS File Organization 4.1 Overall A FITS file shall be composed of the following FITS structures, in the order listed: o Primary HDU o Random Groups structure (optional; allowed only if there is no primary data array) o Conforming Extensions (optional) o Other special records (optional) Each FITS structure shall consist of an integral number of FITS logical records. The primary HDU shall start with the first record of the FITS file. The first record of each subsequent FITS structure shall be the record immediately following the last record of the preceding FITS structure. The size of a FITS logical record shall be 23040 bits, corresponding to 2880 8-bit bytes. 4.2 Individual FITS Structures The primary HDU and every extension HDU shall consist of an integral number of header records consisting of ASCII text, which may be followed by an integral number of data records. The first record of data shall be the record immediately following the last record of the header. 4.3 Primary Header and Data Array The first component of a FITS file shall be the primary header. The primary header may, but need not be, followed by a primary data array. The presence or absence of a primary data array shall be indicated by the values of the NAXIS or NAXISn keywords in the primary header (Section 5.2.1.1). 4.3.1 Primary Header The header of a primary HDU shall consist of a series of card images in ASCII text. All header records shall consist of 36 card images. Card images without information shall be filled with ASCII blanks (hexadecimal 20). 4.3.2 Primary Data Array In FITS format, the primary data array shall consist of a single data array of 0-999 dimensions. The data values shall be a byte stream with no embedded fill or blank space. The first value shall be in the first position of the first primary data array record. The first value of each subsequent row of the array shall be in the position immediately following the last value of the previous row. Arrays of more than one dimension shall consist of a sequence such that the index along axis 1 varies most rapidly, that along axis 2 next most rapidly, and those along subsequent axes progressively less rapidly, with that along axis m, where m is the value of NAXIS, varying least rapidly; i.e., the elements of an array A(x1, x2, ..., xm ) shall be in the order shown in Figure 4.1. The index count along each axis shall begin with 1 and increment by 1 up to the value of the NAXISn keyword (Section 5.2.1.1), If the data array does not fill the final record, the remainder of the record shall be filled with zero values with the same data repre- sentation as the values in the array. For IEEE floating point data, values of +0. shall be used to fill the remainder of the record. 4.4 Extensions 4.4.1 Requirements for Conforming Extensions All extensions, whether or not further described in this standard, shall fulfill the following requirements to be in conformance with this FITS standard. 4.4.1.1 Identity Each extension type shall have a unique type name, specified in the header according to the syntax codified in Section 5.2.1.2. To preclude conflict, extension type names must be registered with the IAU Commission 5 FITS Working Group. The NOST shall maintain and provide a list of the registered extensions. A(1, 1, ..., 1), A(2, 1, ..., 1), ..., A(NAXIS1, 1, ..., 1), A(1, 2, ..., 1), A(2, 2, ..., 1), ..., A(NAXIS1, 2, ..., 1), ..., A(1, NAXIS2, ..., NAXISm), ..., A(NAXIS1, NAXIS2, ..., NAXISm) Figure 4.1: Arrays of more than one dimension shall consist of a sequence such that the index along axis 1 varies most rapidly and those along subsequent axes progressively less rapidly. Except for the location of the first element, array structure is independent of record structure. 4.4.1.2 Size Specification The total number of bits in the data of each extension shall be specified in the header for that extension, in the manner prescribed in Section 5.2.1.2. 4.4.1.3 Compatibility with Existing FITS Files No extension shall be constructed that invalidates existing FITS files. 4.4.2 Standard Extensions A standard extension shall be a conforming extension whose organization and content are completely specified in this standard. Only one FITS format shall be approved for each type of data organization. Each standard extension shall have a unique type name. 4.4.3 Order of Extensions An extension may follow the primary HDU (or random groups records if present) or another conforming extension. Standard extensions and other conforming extensions may appear in any order in a FITS file. 4.5 Special Records The first 8 bytes of special records must not contain the string "XTENSION". It is recommended that they not contain the string "SIMPLE ". The records must have the standard FITS 23040-bit record length. The contents of special records are not otherwise specified by this standard. Section 5 Headers 5.1 Card Images 5.1.1 Syntax Header card images shall consist of a keyword, an optional value, and an optional comment. If a value is present, column 9 shall contain an equal sign (hexadecimal 3D, "="), column 10 shall contain an ASCII blank (hexadecimal 20), and columns 11-80 shall be as specified in the remainder of Section 5.2. If no value is present, columns 9-80 may contain any ASCII text. Except where specifically stated otherwise in this standard, keywords may appear in any order. 5.1.2 Components 5.1.2.1 Keyword (bytes 1-8) The keyword shall be a left justified, 8-character, blank filled, ASCII string with no embedded blanks. All digits (hexadecimal 30 to 39,"0123456789") and upper case Latin alphabetic characters (hexadecimal 41 to 5A, "ABCDEFG HIJKLMN OPQRST UVWXYZ") are permitted; no lower case characters shall be used. The underscore (hexadecimal 5F, "_") and hyphen (hexadecimal 2D, "-") are also permitted. No other characters are permitted. For indexed keywords, the counter shall not have leading zeroes. 5.1.2.2 Value Indicator (bytes 9-10) This field shall contain an ASCII "= " for keywords with an associated value field. If there is no associated value field, this field may contain any ASCII text. 5.1.2.3 Value/Comment This field, when used, shall contain the value, if any, of the keyword, followed by optional comments. Separation of the value and comments by a slash (hexadecimal 2F, "/"), and a space between the value and the slash are strongly recommended. The value shall be the ASCII representation of a string or constant, in the format specified in Section 5.3. The value field must be written in a notation consistent with list-directed read operations in ANSI FORTRAN-77 [10]. The comment may contain any ASCII text. 5.2 Keywords 5.2.1 Mandatory Keywords Mandatory keywords are required as described in the remainder of this subsection. They may be used only as described in this standard. 5.2.1.1 Principal Principal mandatory keywords other than SIMPLE are required in all FITS headers. The SIMPLE keyword is required in all primary headers. The card images of any primary header must contain the keywords shown in Table 5.1 in the order given. 1 SIMPLE 2 BITPIX 3 NAXIS 4 NAXISn, n = 1,:: :, NAXIS ... (other keywords) ... last END Table 5.1: Principal mandatory keywords. The total number of bits in the primary data array, exclusive of fill that is needed after the data to complete the last record (Section 4.1), must be given by the following expression: NBITS = |BITPIX | x (NAXIS1 x NAXIS2 x ... x NAXISm ); (5.1) where NBITS is non-negative and the number of bits excluding fill, m is the value of NAXIS, and BITPIX and the NAXISn represent the values associated with those keywords. SIMPLE Keyword The value field shall contain a logical constant with the value T if the file conforms to this standard. This keyword is mandatory only for the primary header. A value of F signifies that the file does not conform to this standard in some significant way. BITPIX Keyword The value field shall contain an integer. The absolute value is used in computing the sizes of data structures. It shall specify the number of bits that represent a data value. The only valid values of BITPIX are given in Table 5.2. Value Data_Represented ________________________________________________________ 8 Character or unsigned binary integer 16 16-bit twos complement binary integer 32 32-bit twos complement binary integer -32 IEEE single precision floating point -64 IEEE double precision floating point ________________________________________________________ Table 5.2: Interpretation of valid BITPIX value. NAXIS Keyword The value field shall contain a non-negative integer no greater than 999, representing the number of axes in an ordinary data array. A value of zero signifies that no data follow the header in the HDU. NAXISn Keywords The value field of this indexed keyword shall contain a non- negative integer, representing the number of positions along axis n of an ordinary data array. The NAXISn must be present for all values n = 1, ..., NAXIS. A value of zero for any of the NAXISn signifies that no data follow the header in the HDU. If NAXIS is equal to 0, there should not be any NAXISn keywords. END Keyword This keyword has no associated value. Columns 9-80 shall be filled with ASCII blanks. 5.2.1.2 Conforming Extensions The use of extensions necessitates a single additional keyword in the primary header of the FITS file. EXTEND Keyword If the FITS file may contain extensions, a card image with the keyword EXTEND and the value field containing the logical value T must appear in the primary header immediately after the last NAXISn card image, or, if NAXIS=0, the NAXIS card image. The presence of this keyword with the value T in the primary header does not require that extensions be present. The card images of any extension header must use the keywords defined in Table 5.3 in the order specified. This organization is required for any conforming extension, whether or not further specified in this standard. 1 XTENSION 2 BITPIX 3 NAXIS 4 NAXISn, n = 1,:: :, NAXIS ... (other keywords, including ...) PCOUNT GCOUNT ... last END Table 5.3: Mandatory keywords in conforming extensions. The total number of bits in the extension data array exclusive of fill that is needed after the data to complete the last record (Section 4.1) such as that for the primary data array (Section 4.3.2) must be given by the following expression: NBITS = | BITPIX | x GCOUNT x (PCOUNT + NAXIS1 x NAXIS2 x ... x NAXISm ); (5.2) where NBITS is non-negative and the number of bits excluding fill, m is the value of NAXIS, and BITPIX, GCOUNT, PCOUNT, and the NAXISn represent the values associated with those keywords. XTENSION Keyword The value field shall contain a character string giving the name of the extension type. This keyword is mandatory for an extension header and must not appear in the primary header. For an extension that is not a standard extension, the type name must not be the same as that of a standard extension. The IAU Commission 5 FITS Working Group may specify additional type names that must be used only to identify specific types of extensions; the full list shall be available from the NOST. PCOUNT Keyword The value field shall contain an integer that shall be used in any way appropriate to define the data structure, consistent with equation 5.2. GCOUNT Keyword The value field shall contain an integer that shall be used in any way appropriate to define the data structure, consistent with equation 5.2. 5.2.2 Other Reserved Keywords These keywords are optional but may be used only as defined in this standard. These keywords apply to any FITS structure except where specifically further restricted. 5.2.2.1 Keywords Describing the History or Physical Construction of the HDU DATE Keyword The value field shall contain a character string giving the date on which the HDU was created, in the form DD/MM/YY, where DD shall be the day of the month, MM the month number, with January given by 01 and December by 12, and YY the last two digits of the year. Specification of the date using Universal Time is recommended. Copying of a FITS file does not require changing any of the keyword values in the file's HDUs. ORIGIN Keyword The value field shall contain a character string identifying the organization creating the FITS file. BLOCKED Keyword This keyword may be used only in the primary header. It shall appear within the first 36 card images of the FITS file. (Note: This keyword thus cannot appear if NAXIS is greater than 31, or if NAXIS greater than 30 and the EXTEND keyword is present.) Its presence with the required logical value of T advises that the physical block size of the FITS file on which it appears may be an integral multiple of the logical record length, and not necessarily equal to it. Physical block size and logical record length may be equal even if this keyword is present or unequal if it is absent. It is reserved primarily to prevent its use with other meanings. The issuance of this standard deprecates the BLOCKED keyword. 5.2.2.2 Keywords Describing Observations DATE-OBS Keyword The value field shall contain a character string giving the day on which the observations represented by the array were made, in the form DD/MM/YY, where DD shall be the day of the month, MM the month number, with January given by 01 and December by 12, and YY the last two digits of the year. Specification of the date using Universal Time is recommended. TELESCOP Keyword The value field shall contain a character string identifying the telescope used to acquire the data contained in the array. INSTRUME Keyword The value field shall contain a character string identifying the instrument used to acquire the data contained in the array. OBSERVER Keyword The value field shall contain a character string identifying who acquired the data associated with the header. This keyword is appropriate when the data describe the results of observations. OBJECT Keyword The value field shall contain a character string giving the name of the object observed. EQUINOX Keyword The value field shall contain a floating point number giving the equinox in years for the celestial coordinate system in which positions given in either the header or data are expressed. EPOCH Keyword The value field shall contain a floating point number giving the equinox in years for the celestial coordinate system in which positions given in either the header or data are expressed. This document deprecates the use of the EPOCH keyword and thus it shall not be used in FITS files created after the adoption of this standard; rather, the EQUINOX keyword shall be used. 5.2.2.3 Bibliographic Keywords AUTHOR Keyword The value field shall contain a character string identifying who compiled the information in the data associated with the header. This keyword is appropriate when the data originate in a published paper or are compiled from many sources. REFERENC Keyword The value field shall contain a character string citing a reference where the data associated with the header are published. 5.2.2.4 Commentary Keywords COMMENT Keyword This keyword shall have no associated value; columns 9-80 may contain any ASCII text. Any number of COMMENT card images may appear in a header. HISTORY Keyword This keyword shall have no associated value; columns 9-80 may contain any ASCII text. The text should contain a history of steps and procedures associated with the processing of the associated data. Any number of HISTORY card images may appear in a header. Keyword Field is Blank Columns 1-8 contain ASCII blanks. Columns 9-80 may contain any ASCII text. Any number of card images with blank keyword fields may appear in a header. 5.2.2.5 Array Keywords These keywords are used to describe the contents of an array, either alone or in a series of random groups. They are optional, but if they appear in the header describing an array or groups, they must be used as defined in this section of this standard. They shall not be used in headers describing other structures unless the meaning is the same as that for a primary or groups array. BSCALE Keyword This keyword shall be used, along with the BZERO keyword, when the array pixel values are not the true physical values, to transform the primary data array values to the true physical values they represent, using equation 5.3. The value field shall contain a floating point number representing the coefficient of the linear term in the scaling equation, the ratio of physical value to array value at zero offset. The default value for this keyword is 1.0. BZERO Keyword This keyword shall be used, along with the BSCALE keyword, when the array pixel values are not the true physical values, to transform the primary data array values to the true values. The value field shall contain a floating point number representing the physical value corresponding to an array value of zero. The default value for this keyword is 0.0. The transformation equation is as follows: physical value = BZERO + BSCALE x array value (5.3) BUNIT Keyword The value field shall contain a character string, describing the physical units in which the quantities in the array, after application of BSCALE and BZERO, are expressed. Use of the units defined in the IAU Style Manual [7] is recommended. BLANK Keyword This keyword shall be used only in headers with positive values of BITPIX (i.e. in arrays with integer data). Columns 1-8 contain the string, "BLANK " (ASCII blanks in columns 6-8). The value field shall contain an integer that specifies the representation of array values whose physical values are undefined. CTYPEn Keywords The value field shall contain a character string, giving the name of the coordinate represented by axis n. Where this coordinate represents a physical quantity, units defined in the IAU Style Manual [7] are recommended. CRPIXn Keywords The value field shall contain a floating point number, identifying the location of a reference point along axis n, in units of the axis index. This value is based upon a counter that runs from 1 to NAXISn with an increment of 1 per pixel. The reference point value need not be that for the center of a pixel nor lie within the actual data array. Use comments to indicate the location of the index point relative to the pixel. CRVALn Keywords The value field shall contain a floating point number, giving the value of the coordinate specified by the CTYPEn keyword at the reference point CRPIXn. CDELTn Keywords The value field shall contain a floating point number, giving the partial derivative of the coordinate specified by the CTYPEn keywords with respect to the pixel index, evaluated at the reference point CRPIXn, in units of the coordinate specified by the CTYPEn keyword. CROTAn Keywords This keyword is used to indicate a rotation from a standard coordinate system described by the CTYPEn to a different coordinate system in which the values in the array are actually expressed. Rules for such rotations are not further specified in this standard; the rotation should be explained in comments. The value field shall contain a floating point number, giving the rotation angle in degrees between axis n and the direction implied by the coordinate system defined by CTYPEn. DATAMAX Keyword The value field shall always contain a floating point number, regardless of the value of BITPIX. This number shall give the maximum valid physical value represented in the array, exclusive of any special values. DATAMIN Keyword The value field shall always contain a floating point number, regardless of the value of BITPIX. This number shall give the minimum valid physical value represented in the array, exclusive of any special values. 5.2.2.6 Extension Keywords These keywords are used to describe an extension. EXTNAME Keyword The value field shall contain a character string, to be used to distinguish among different extensions of the same type, i.e., with the same value of XTENSION, in a FITS file. EXTVER Keyword The value field shall contain an integer, to be used to distinguish among different extensions in a FITS file with the same type and name, i.e., the same values for XTENSION and EXTNAME. The values need not start with 1 for the first extension with a particular value of EXTNAME and need not be in sequence for subsequent values. If the EXTVER keyword is absent, the file should be treated as if the value were 1. EXTLEVEL Keyword The value field shall contain an integer, specifying the level in a hierarchy of extension levels of the extension header containing it. The value shall be 1 for the highest level; levels with a higher value of this keyword shall be subordinate to levels with a lower value. If the EXTLEVEL keyword is absent, the file should be treated as if the value were 1. 5.2.3 Additional Keywords 5.2.3.1 Requirements New keywords may be devised in addition to those described in this standard, so long as they are consistent with the generalized rules for keywords and do not conflict with mandatory or reserved keywords. 5.2.3.2 Restrictions No keyword in the primary header shall specify the presence of a specific extension in a FITS file; only the EXTEND keyword described in Section 5.2.1.2 shall be used to indicate the possible presence of extensions. No keyword in either the primary or extension header shall explicitly refer to the physical block size, other than the BLOCKED keyword of Section 5.2.2.1. 5.3 Value 5.3.1 General Format Requirements The value field must be written in a notation consistent with the list-directed read operations in ANSI FORTRAN-77 [10]. The structure shall be determined by the type of the variable. The fixed format is required for values of mandatory keywords and recommended for values of all others. This standard imposes no requirements on case sensitivity of character strings other than those explicitly specified. 5.3.2 Fixed Format 5.3.2.1 Character String If the value is a character string, column 11 shall contain a single quote (hexadecimal code 27, "'"); the string shall follow, starting in column 12, followed by a closing single quote (also hexadecimal code 27) that should not occur before column 20 and must occur in or before column 80. Proper interpretation of the FITS file should not require decoding any more than the first eight characters of a character string. The character string shall be composed only of ASCII text. A single quote is represented within a string as two successive single quotes, e.g., O'HARA = 'O''HARA'. Leading blanks are significant; trailing blanks are not. 5.3.2.2 Logical Variable If the value is a logical constant, it shall appear as a T or F in column 30. 5.3.2.3 Integer If the value is an integer, the ASCII representation shall appear right justified in columns 11-30. For a complex integer, the imaginary part shall be right justified in columns 31-50. 5.3.2.4 Real Floating Point Number If the value is a real floating point number, the ASCII representation shall appear in columns 11-30. Letters in the exponential form shall be upper case. The value shall be right justified, and the decimal point must appear. Note: The full precision of 64-bit values can not be expressed as a single value using the fixed format. 5.3.2.5 Complex Floating Point Number If the value is a complex floating point number, the ASCII representation of the real part shall appear in the same manner as a real floating point number (see above). The ASCII representation of the imaginary part shall appear in columns 31 - 50. Letters in the exponential form shall be upper case. The value shall be right justified, and the decimal point must appear. Note: The full precision of 64-bit values can not be expressed as a single value using the fixed format. Section 6 Data Representation Primary and extension data shall be represented in one of the formats described in this section. FITS data shall be interpreted to be a byte stream. Bytes are in order of decreasing significance. The byte that includes the sign bit shall be first, and the byte that has the ones bit shall be last. 6.1 Characters Each character shall be represented by one byte. A character shall be represented by its 7-bit ASCII [11] code in the low order seven bits in the byte. The high-order bit shall be zero. 6.2 Integers 6.2.1 Eight-bit Eight-bit integers shall be unsigned binary integers, contained in one byte. 6.2.2 Sixteen-bit Sixteen-bit integers shall be twos-complement signed binary integers, contained in two bytes. 6.2.3 Thirty-two-bit Thirty-two-bit integers shall be twos-complement signed binary integers, contained in four bytes. 6.3 IEEE-754 Floating Point Transmission of 32- and 64-bit floating point data within the FITS format shall use the ANSI/IEEE-754 standard [12]. BITPIX = -32 and BITPIX = -64 signify 32- and 64- bit IEEE floating point numbers, respectively; the absolute value of BITPIX is used for computing the sizes of data structures. The full IEEE set of number forms is allowed for FITS interchange, including all special values (e.g., the "Not-a-Number" cases). The order of the bytes will be sign and exponent first, followed by the mantissa bytes in order of decreasing significance. The BLANK keyword should not be used when BITPIX = -32 or -64. Use of the BSCALE and BZERO keywords is not recommended. 6.3.1 Thirty-two-bit Floating Point 6.3.1.1 Structure Table 6.1 describes the bit structure of 32-bit floating point standard numeric values. Bit Positions Content (first to last) ________________________________ 1 sign 2 - 9 exponent 10 - 32 mantissa ________________________________ Table 6.1: Content of 32-bit floating point bit positions. 6.3.1.2 Interpretation Standard numeric values of IEEE 32-bit floating point numbers are interpreted according to the following rule: value = (-1)sign x 2(exponent -127) x mantissa (6.1) The IEEE NaN (Not-a-Number) values shall be used to represent undefined values. All IEEE special values are recognized. 6.3.2 Sixty-four-bit Floating Point 6.3.2.1 Structure Table 6.2 describes the bit structure of 64-bit floating point standard numeric values. Bit Positions Content (first to last) _______________________________ 1 sign 2 - 12 exponent 13 - 64 mantissa _______________________________ Table 6.2: Content of 64-bit floating point bit positions. 6.3.2.2 Interpretation Standard numeric values for IEEE 64-bit floating point numbers are interpreted according to the following rule: value = (-1)sign x 2(exponent -1023) x mantissa (6.2) The IEEE NaN (Not-a-Number) values shall be used to represent undefined values. All IEEE special values are recognized. Section 7 Random Groups Structure Although it is standard FITS, the random groups structure has been used almost exclusively for applications in radio interferometry; outside this field, few FITS readers can read data in random groups format. A proposed binary tables extension will eventually be able to accommodate the structure described by random groups. While existing FITS files use the format, and it is therefore included in this standard, its use for future applications is deprecated by this document. 7.1 Keywords 7.1.1 Mandatory Keywords If the random groups format records follow the primary header, the card images of the primary header must use the keywords defined in Table 7.1 in the order specified. The total number of bits in the random groups records exclusive of the fill described in Section 7.2 must be given by the following expression: NBITS = | BITPIX | x GCOUNT x (PCOUNT + NAXIS2 x NAXIS3 x ... x NAXISm ); (7.1) where NBITS is non-negative and the number of bits excluding fill, m is the value of NAXIS, and BITPIX, GCOUNT, PCOUNT, and the NAXISn represent the values associated with those keywords. 7.1.1.1 SIMPLE Keyword The card image containing this keyword is structured in the same way as if a primary data array were present (Section 5.2.1). 1 SIMPLE 2 BITPIX 3 NAXIS 4 NAXIS1 5 NAXISn, n=2, ..., value of NAXIS ... (other keywords, which must include ...) GROUPS PCOUNT GCOUNT ... last END Table 7.1: Mandatory keywords in primary header preceding random groups. 7.1.1.2 BITPIX Keyword The card image containing this keyword is structured as prescribed in Section 5.2.1. 7.1.1.3 NAXIS Keyword The value field shall contain an integer ranging from 1 to 999, representing one more than the number of axes in each data array. 7.1.1.4 NAXIS1 Keyword The value field shall contain the integer 0, a signature of random groups format indi- cating that there is no primary data array. 7.1.1.5 NAXISn Keywords (n=2, ..., value of NAXIS) The value field shall contain an integer, representing the number of positions along axis n-1 of the data array in each group. 7.1.1.6 GROUPS Keyword The value field shall contain the logical constant T. The value T associated with this keyword implies that random groups records are present. 7.1.1.7 PCOUNT Keyword The value field shall contain an integer equal to the number of parameters preceding each group. 7.1.1.8 GCOUNT Keyword The value field shall contain an integer equal to the number of random groups present. 7.1.1.9 END Keyword The card image containing this keyword is structured as described in Section 5.2.1. 7.1.2 Reserved Keywords 7.1.2.1 PTYPEn Keywords The value field shall contain a character string giving the name of parameter n. If the PTYPEn keywords for more than one value of n have the same associated name in the value field, then the data value for the parameter of that name is to be obtained by adding the derived data values of the corresponding parameters. This rule provides a mechanism by which a random parameter may have more precision than the accompanying data array members; for example, by summing two 16-bit values with the first scaled relative to the other such that the sum forms a number of up to 32-bit precision. 7.1.2.2 PSCALn Keywords This keyword shall be used, along with the PZEROn keyword, when the nth FITS group parameter value is not the true physical value, to transform the group parameter value to the true physical values it represents, using equation 7.2. The value field shall contain a floating point number representing the coefficient of the linear term in equation 7.2, the scaling factor between true values and group parameter values at zero offset. The default value for this keyword is 1.0. 7.1.2.3 PZEROn Keywords This keyword shall be used, along with the PSCALn keyword, when the nth FITS group parameter value is not the true physical value, to transform the group parameter value to the physical value. The value field shall contain a floating point number, representing the true value corresponding to a group parameter value of zero. The default value for this keyword is 0.0. The transformation equation is as follows: physical value = PZEROn + PSCALn x group parameter value (7.2) 7.2 Data Sequence Random groups data shall consist of a set of groups. The number of groups shall be specified by the GCOUNT keyword in the associated header record. Each group shall consist of the number of parameters specified by the PCOUNT keyword followed by an array with the number of members GMEM given by the following expression: GMEM = (NAXIS2 x NAXIS3 x ... x NAXISm): (7.3) where GMEM is the number of members in the data array in a group, m is the value of NAXIS, and the NAXISn represent the values associated with those keywords. The first parameter of the first group shall appear in the first location of the first data record. The first element of each array shall immediately follow the last parameter associated with that group. The first parameter of any subsequent group shall imme- diately follow the last member of the array of the previous group. The arrays shall be organized internally in the same way as an ordinary primary data array. If the groups data do not fill the final record, the remainder of the record shall be filled with zero val- ues in the same way as a primary data array (Section 4.3.2). If random groups records are present, there shall be no primary data array. 7.3 Data Representation Permissible data representations are those listed in Section 6. Parameters and members of associated data arrays shall have the same representation. Should more precision be required for an associated parameter than for a member of a data array, the parameter shall be divided into two or more addends, represented by the same value for the PTYPEn keyword. The value shall be the sum of the physical values, which may have been obtained from the group parameter values using the PSCALn and PZEROn keywords. Section 8 Standard Extensions 8.1 ASCII Tables Extension Data shall appear as an ASCII Tables extension if the primary header of the FITS file has the keyword EXTEND set to T and the first keyword of that extension header has XTENSION= 'TABLE '. 8.1.1 Mandatory Keywords The card images in the header of an ASCII Tables Extension must use the keywords defined in Table 8.1 in the order specified. XTENSION Keyword The value field shall contain the character string 'TABLE '. BITPIX Keyword The value field shall contain the integer 8, denoting that the array contains ASCII characters. NAXIS Keyword The value field shall contain the integer 2, denoting that the included data array is two-dimensional: rows and columns. NAXIS1 Keyword The value field shall contain a non-negative integer, giving the number of ASCII characters in each row of the table. NAXIS2 Keyword The value field shall contain a non-negative integer, giving the number of rows in the table. PCOUNT Keyword The value field shall contain the integer 0. 1 XTENSION 2 BITPIX 3 NAXIS 4 NAXIS1 5 NAXIS2 6 PCOUNT 7 GCOUNT 8 TFIELDS ... (other keywords, which must include ...) TBCOLn, n=1,2,...,k where k is the value of TFIELDS TFORMn, n=1,2,...,k where k is the value of TFIELDS ... last END Table 8.1: Mandatory keywords in ASCII tables extensions. GCOUNT Keyword The value field shall contain the integer 1; the data records contain a single table. TFIELDS Keyword The value field shall contain a non-negative integer representing the number of fields in each row. The maximum permissible value is 999. TBCOLn Keywords The value field of this indexed keyword shall contain an integer specifying the column in which field n starts. The first column of a row is numbered 1. TFORMn Keywords The value field of this indexed keyword shall contain a character string describing the FORTRAN-77 [10] format in which field n is coded. The formats in Table 8.2 are permitted for encoding. Repetition of a format from one field to the next must be indicated by using separate pairs of TBCOLn and TFORMn keywords for each field; format repetition may not be indicated by prefixing the format by a number. END Keyword This keyword has no associated value. Columns 9-80 shall contain ASCII blanks. Field Value Data Type __________________________________________________________ Aw Character Iw Integer Fw.d Single precision real Ew.d Single precision real, exponential notation Dw.d Double precision real, exponential notation __________________________________________________________ Table 8.2: Valid TFORMn format values in TABLE extensions. 8.1.2 Other Reserved Keywords In addition to the mandatory keywords defined in section 8.1.1, these keywords may be used to describe the structure of an ASCII Tables data array. They are optional, but if they appear within an ASCII Tables extension header, they must be used as defined in this section of this standard. TSCALn Keywords This indexed keyword shall be used, along with the TZEROn key- word, when the quantity in field n does not represent a true physical quantity. The value field shall contain a floating point number representing the coefficient of the linear term in equation 8.1, which must be used to compute the true physical value of the field. The default value for this keyword is 1.0. This keyword may not be used for A-format fields. TZEROn Keywords This indexed keyword shall be used, along with the TSCALn key- word, when the quantity in field n does not represent a true physical quantity. The value field shall contain a floating point number representing the zero point for the true physical value of field n. The default value for this keyword is 0.0. This keyword may not be used for A-format fields. The transformation equation used to compute a true physical value from the quantity in field n is physical value = TZEROn + TSCALn x field value TNULLn Keywords The value field for this indexed keyword shall contain the character string that represents an undefined value for field n. The string is implicitly blank filled to the width of the field. TTYPEn Keywords The value field for this indexed keyword shall contain a character string, giving the name of field n. It is recommended that only letters, digits, and underscore (hexadecimal code 5F, "__") be used in the name. However, string comparisons with the values of TTYPEn keywords should not be case sensitive. The use of identical names for different fields should be avoided. TUNITn Keywords The value field shall contain a character string describing the phys- ical units in which the quantity in field n, after any application of TSCALn and TZEROn, is expressed. Use of the units defined in the IAU Style Manual [7] is recommended. 8.1.3 Data Sequence The table is constructed from a two-dimensional array of ASCII characters. The row length and the number of rows shall be those specified, respectively, by the NAXIS1 and NAXIS2 keywords of the associated header records. The number of characters in a row and the number of rows in the table shall determine the size of the character array. Every row in the array shall have the same number of characters. The first character of the first row shall be at the start of the record immediately following the last header record. The first character of subsequent rows shall follow immediately the character at the end of the previous row, independent of the record structure. The positions in the last data record after the last character of the last row of the data array shall be filled with ASCII blanks. 8.1.4 Fields Each row in the array shall consist of a sequence of fields, with one entry in each field. For every field, the FORTRAN-77 format of the information contained, location in the row of the beginning of the field and (optionally) the field name, shall be specified in keywords of the associated header records. A separate format keyword must be provided for each field. The location and format of fields shall be the same for every row. Fields may overlap. 8.1.5 Entries All data in an ASCII tables extension record shall be ASCII text in FORTRAN format. The only possible formats shall be those specified in Table 8.2. If values of -0 and +0 must be distinguished, then the sign character should appear in a separate field in character format. TNULLn keywords may be used to specify a character string that represents an undefined value in each field. The characters representing an undefined value may differ from field to field but must be the same within a field. Blanks within the fields are not to be interpreted as zeroes; zeroes must be given explicitly. 8.2 Other Standard Extensions At the effective date of this standard there are no other standard extensions. Section 9 Restrictions on Changes Any structure that is a valid FITS structure shall remain a valid FITS structure at all future times. Use of certain valid FITS structures may be deprecated by this or future FITS standard documents. Appendix A Draft Proposal for Binary Table Extension (This Appendix is not part of the NOST FITS Standard but is included for informa- tional purposes only.) This appendix contains a draft proposal for a Binary Table extension, type name "BINTABLE", developed by W. D. Cotton (NRAO) and D. Tody (NOAO), dated September 20, 1991. With their permission, that proposal [9] is reproduced nearly verbatim; the only changes are those required for stylistic consistency with the rest of this document. The BINTABLE extension has been developed from the earlier A3DTABLE extension implemented in AIPS by NRAO. It supports all features of the earlier, more limited extension. Binary tables are being used at a number of different installations and by NASA and NASA-supported projects. A limited subset, without the repeat count feature, has successfully been exchanged between AIPS and MIDAS, and full interoperability testing of the BINTABLE extension is in progress. However, much of the existing FITS-reading software cannot yet decode the format. The extension is now undergoing community review as part of the process leading to eventual consideration by the IAU Commission 5 FITS Working Group. Because it is becoming widely used, and because it illustrates an application of the rules for conforming extensions, the text of the proposal is included as the remainder of this Appendix. A.1 Abstract This paper describes the FITS binary tables which are a flexible and efficient means of transmitting a wide variety of data structures. Table rows may be a mixture of a number of numerical, logical and character data entries. In addition, each entry is allowed to be a single dimensioned array. Numeric data are kept in IEEE formats. A.2 Introduction The Flexible Image Transport System (FITS) [1], [2] has been used for a number of years both as a means of transporting data between computers and/or processing systems and as an archival format for a variety of astronomical data. The success of this system has resulted in the introduction of enhancements. In particular, considerable use has been made of the records following the "main" data file. Grosbol et al. [4] introduced a generalized header format for extension "files" following the "main" data file, but in the same physical file. Harten et al. [5] defined an ASCII table structure which could convey information that could be conveniently printed as a table. This paper generalizes the ASCII tables and defines an efficient means for conveying a wide variety of data structures as "extension" files. A.3 Binary Tables The binary tables are tables in the sense that they are organized into rows and columns. They are multi-dimensional since an entry, or set of values associated with a given row and column, can be an array of arbitrary size. These values are represented in a standardized binary form. Each row in the table contains an entry for each column. This entry may be one of a number of different data types, 8 bit unsigned integers, 16 or 32 bit signed integers, logical, character, bit, 32 or 64 bit floating point or complex values. The datatype and dimensionality are independently defined for each column but each row must have the same structure. Additional information associated with the table may be included in the table header as keyword/value pairs. The binary tables come after the "main" data file, if any, in a FITS file and follow the standards for generalized extension tables defined in [4]. The use of the binary tables requires the use of a single additional keyword in the main header: EXTEND (logical) if true (ASCII 'T') indicates that there may be extension files fol- lowing the data records and, if there are, that they conform to the generalized extension file header standards. A.4 Table Header The table header begins at the first byte in the first record following the last record of main data (if any) or following the last record of the previous extension file. The format of the binary table header is such that a given FITS reader can decide if it wants (or understands) it and can skip the table if not. A table header consists of one or more 2880 8-bit byte logical records each containing 36 80-byte "card images" in the form: keyword = value / comment where the keyword begins in column 1 and contains up to eight characters and the value begins in column 10 or later. Keyword/value pairs in binary table headers conform to standard FITS usage. The number of columns in the table is given by the value associated with keyword TFIELDS. The type, dimensionality, labels, units, blanking values, and display formats for entries in column nnn may be defined by the values associated with the keywords TFORMnnn, TTYPEnnn, TUNITnnn, TNULLnnn, and TDISPnnn. Of these only TFORMnnn is required but the use of TTYPEnnn is strongly recommended. An entry may be omitted from the table, but still defined in the header, by using a zero element count in the TFORMnnn entry. The required keywords XTENSION, BITPIX, NAXIS, NAXIS1, NAXIS2, PCOUNT, GCOUNT and TFIELDS must be in order; other keywords follow these in an arbitrary order. The required keywords in a binary table header record are: XTENSION (character) indicates the type of extension file, this must be the first keyword in the header. This is 'BINTABLE' for the binary tables. BITPIX (integer) gives the number of bits per "pixel" value. For binary tables this value is 8. NAXIS (integer) gives the number of "axes"; this value is 2 for binary tables. NAXIS1 (integer) gives the number of 8 bit bytes in each "row". This should correspond to the sum of the values defined in the TFORMnnn keywords. NAXIS2 (integer) gives the number of rows in the table. PCOUNT (integer) is used to tell the number of bytes following the regular portion of the table. These bytes are allowed but no meaning is attached to them in this document. PCOUNT should normally be 0 for binary tables (see however Section A.9.2). GCOUNT (integer) gives the number of groups of data defined as for the random group main data records. This is 1 for binary tables. TFIELDS (integer) gives the number of fields (columns) present in the table. TFORMnnn1 (character) gives the size and data type of field nnn. Allowed values of nnn range from 1 to the value associated with TFIELDS. Allowed values of TFORMnnn are of the form rL, rX, rI, rJ, rA, rE, rD, rB, rC, rM, or rP (logical, bit, 16-bit integers, 32- bitntegers, characters, single precision, double precision, unsigned bytes, complex pair of single precision values, double complex pair of double precision values and variable length array descriptor [64 bits]) where r=number of elements. If the element count is absent, it is assumed to be 1. A value of zero is allowed. Note: additional characters may follow the datatype code character but they are not defined in this document. The number of bytes determined from summing the TFORMnnn values should equal NAXIS1 but NAXIS1 should be used as the definition of the actual length of the row. END is always the last keyword in a header. The remainder of the FITS logical (2880- byte) record following the END keyword is blank filled. The optional standard keywords are: EXTNAME (character) can be used to give a name to the extension file to distinguish it from other similar files. The name may have a hierarchical structure giving its relation to other files (e.g., "map1.cleancomp") EXTVER (integer) is a version number which can be used with EXTNAME to identify a file. EXTLEVEL (integer) specifies the level of the extension file in a hierarchical structure. The default value for EXTLEVEL should be 1. TTYPEnnn (character) gives the label for field nnn. TUNITnnn (character) gives the physical units of field nnn. TSCALnnn (floating) gives the scale factor for field nnn. True_value = FITS_value * TSCAL + TZERO. Note: TSCALnnn and TZEROnnn are not defined for A, L, P, or X format fields. Default value is 1.0. TZEROnnn (floating) gives the offset for field nnn. (See TSCALnnn.) Default value is 0.0. TNULLnnn (integer) gives the undefined value for integer (B, I, and J) field nnn. Section A.6 discusses the conventions for indicating invalid data of other data types. NOTE: The "nnn" in keyword names indicates an integer index in the range 1 - 999. The integer is left justified with no leading zeroes, e.g. TFORM1, TFORM19, etc. TDISPnnn (character) gives the Fortran 90 format suggested for the display of field nnn. Each byte of bit and byte arrays will be considered to be a signed integer for purposes of display. The allowed forms are Aw, Lw, Iw.m, Bw.m (Binary, integers only), Ow.m (Octal, integers only), Zw.m (Hexadecimal, integers only) Fw.d, Ew.dEe, ENw.d, ESw.d, Gw.dEe, and Dw.dEe where w is the width of the displayed value in characters, m is the minimum number of digits possibly requiring leading zeroes, d is the number of digits to the right of the decimal, and e is the number of digits in the exponent. All entries in a field are displayed with a single, repeated format. If Fortran 90 formats are not available to a reader which prints a table then equivalent FORTRAN 77 formats may be substituted. Any TSCALnnn and TZEROnnn values should be applied before display of the value. Note that characters and logical values may be null (zero byte) terminated. TDIMnnn (character) This keyword is reserved for use by the convention described in Section A.9.1. THEAP (integer) This keyword is reserved for use by the convention described in Section A.9.2. AUTHOR (character) gives the name of the author or creator of the table. REFERENC (character) gives the reference for the table. Nonstandard keyword/value pairs adhering to the FITS keyword standards are al- lowed although a reader may chose to ignore them. A.5 Conventions for Multidimensional Arrays There is commonly a need to use data structures more complex than the one dimen- sional definition of the table entries defined for this table format. Multidimensional arrays, or more complex structures, may be implemented by passing dimensions or other structural information as either column entries or keywords in the header. Pass- ing the dimensionality as column entries has the advantage that the array can have variable dimension (subject to a fixed maximum size and storage usage). A convention is suggested in Section A.9.1. A.6 Table Data Records The binary table data records begin with the next logical record following the last header record. If the intersection of a row and column is an array then the elements of this array are contiguous and in order of increasing array index. Within a row, columns are stored in order of increasing column number. Rows are given in order of increasing row number. All 2880-byte logical records are completely filled with no extra bytes between columns or rows. Columns and rows do not necessarily begin in the first byte of a 2880-byte record. Note that this implies that a given word may not be aligned in the record along word boundaries of its type; words may even span 2880-byte records. The last 2880-byte record should be zero byte filled past the end of the valid data. If word alignment is ever considered important for efficiency considerations then this may be accomplished by the proper design of the table. The simplest way to accomplish this is to order the columns by data type (M, D, C, P, E, J, I, B, L, A, X) and then add sufficient padding in the form of a dummy column of type B with the number of elements such that the size of a row is either an integral multiple of 2880 bytes or an integral number of rows is 2880 bytes. The data types are defined in the following list (r is the number of elements in the entry): rL A logical value consists of an ASCII "T" indicating true and "F" indicating false. A null character (zero byte) indicates an invalid value. rX A bit array will start in the most significant bit of the byte and the following bits in the order of decreasing significance in the byte. Bit significance is in the same order as for integers. A bit array entry consists of an integral number of bytes with trailing bits zero. No explicit null value is defined for bit arrays but if the capability of blanking bit arrays is needed it is recommended that one of the following conventions be adopted: 1) designate a bit in the array as a validity bit, 2) add an L type column to indicate validity of the array or 3) add a second bit array which contains a validity bit for each of the bits in the original array. Such conventions are beyond the scope of this general format design and in general readers will not be expected to understand them. rB Unsigned 8-bit integer with bits in decreasing order of significance. Signed values may be passed with appropriate values of TSCALnnn and TZEROnnn. rI A 16-bit twos complement integer with the bits in decreasing order of significance. Unsigned values may be passed with appropriate values of TSCALnnn and TZEROnnn. rJ A 32-bit twos complement integer with the bits in decreasing order of significance. Unsigned values may be passed with appropriate values of TSCALnnn and TZEROnnn. rA Character strings are represented by ASCII characters in their natural order. A character string may be terminated before its explicit length by an ASCII NULL char- acter. An ASCII NULL as the first character will indicate an undefined string i.e. a NULL string. Legal characters are printable ASCII characters in the range ' ' (hex 20) to '"' (hex 7E) inclusive and ASCII NULL after the last valid character. Strings the full length of the field are not NULL terminated. rE Single precision floating point values are in IEEE 32-bit precision format in the order: sign bit, exponent and mantissa in decreasing order of significance. The IEEE NaN (not a number) values are used to indicate an invalid number; a value with all bits set is recognized as a NaN. All IEEE special values are recognized. rD Double precision floating point values are in IEEE 64-bit precision format in the order: sign bit, exponent and mantissa in decreasing order of significance. The IEEE NaN values are used to indicate an invalid number; a value with all bits set is recognized as a NaN. All IEEE special values are recognized. rC A Complex value consists of a pair of IEEE 32-bit precision floating point values with the first being the real and the second the imaginary part. If either word contains a NaN value the complex value is invalid. rM Double precision complex values. These consist of a pair of IEEE 64-bit precision floating point values with the first being the real and the second the imaginary part. If either word contains a NaN value the complex value is invalid. rP Variable length array descriptor. An element is equal in size to a pair of 32-bit integers (i.e., 64 bits). The anticipated use of this data type is described in Section A.9.2. Arrays of type P are not defined; the r field is permitted, but values other than 0 or 1 are undefined. For purposes of printing, an entry of type P should be considered equivalent to 2J. A.7 Example Binary Table Header The following is an example of a binary table header which has 19 columns using a number of different data types and dimensions. Columns labeled "IFLUX", "QFLUX", "UFLUX", "VFLUX", "FREQOFF", "LSRVEL" and "RESTFREQ" are arrays of dimension 2. Columns labeled "SOURCE" and "CALCODE" are character strings of length 16 and 4 respectively. The nonstandard keywords "NO_IF", VELTYP", and "VELDEF" also appear at the end of the header. The first two lines of numbers are only present to show card columns and are not part of the table header. 1 2 3 4 5 6 7 8 12345678901234567890123456789012345678901234567890123456789012345678901234567890 XTENSION= 'BINTABLE' / Extension type BITPIX = 8/ Binary data NAXIS = 2/ Table is a matrix NAXIS1 = 168/ Width of table row in bytes NAXIS2 = 5/ Number of rows in table PCOUNT = 0/ Random parameter count GCOUNT = 1/ Group count TFIELDS = 19/ Number of columns in each row EXTNAME = 'AIPS SU ' / AIPS source table EXTVER = 1/ Version number of table TFORM1 = '1I ' / 16-bit integer TTYPE1 = 'ID. NO. ' / Type (label) of column 1 TUNIT1 = ' ' / Physical units of column 1 TFORM2 = '16A ' / Character string TTYPE2 = 'SOURCE ' / Type (label) of column 2 TUNIT2 = ' ' / Physical units of column 2 TFORM3 = '1I ' / 16-bit integer TTYPE3 = 'QUAL ' / Type (label) of column 3 TUNIT3 = ' ' / Physical units of column 3 TNULL3 = 32767/ Undefined value for column 3 TFORM4 = '4A ' / Character string TTYPE4 = 'CALCODE ' / Type (label) of column 4 TUNIT4 = ' ' / Physical units of column 4 TFORM5 = '2E ' / Single precision array TTYPE5 = 'IFLUX ' / Type (label) of column 5 TUNIT5 = 'JY ' / Physical units of column 5 TFORM6 = '2E ' / Single precision array TTYPE6 = 'QFLUX ' / Type (label) of column 6 TUNIT6 = 'JY ' / Physical units of column 6 TFORM7 = '2E ' / Single precision array TTYPE7 = 'UFLUX ' / Type (label) of column 7 TUNIT7 = 'JY ' / Physical units of column 7 TFORM8 = '2E ' / Single precision array TTYPE8 = 'VFLUX ' / Type (label) of column 8 TUNIT8 = 'JY ' / Physical units of column 8 TFORM9 = '2D ' / Double precision array. TTYPE9 = 'FREQOFF ' / Type (label) of column 9 TUNIT9 = 'HZ ' / Physical units of column 9 TSCAL9 = 1.0D9/ Scaling factor of column 9 TZERO9 = 0.0/ Offset of column 9 TFORM10 = '1D ' / Double precision TTYPE10 = 'BANDWIDTH ' / Type (label) of column 10 TUNIT10 = 'HZ ' / Physical units of column 10 TFORM11 = '1D ' / Double precision TTYPE11 = 'RAEPO ' / Type (label) of column 11 TUNIT11 = 'DEGREES ' / Physical units of column 11 TFORM12 = '1D ' / Double precision TTYPE12 = 'DECEPO ' / Type (label) of column 12 TUNIT12 = 'DEGREES ' / Physical units of column 12 TFORM13 = '1D ' / Double precision TTYPE13 = 'EPOCH ' / Type (label) of column 13 TUNIT13 = 'YEARS ' / Physical units of column 13 TFORM14 = '1D ' / Double precision TTYPE14 = 'RAAPP ' / Type (label) of column 14 TUNIT14 = 'DEGREES ' / Physical units of column 14 TFORM15 = '1D ' / Double precision TTYPE15 = 'DECAPP ' / Type (label) of column 15 TUNIT15 = 'DEGREES ' / Physical units of column 15 TFORM16 = '2D ' / Double precision array TTYPE16 = 'LSRVEL ' / Type (label) of column 16 TUNIT16 = 'M/SEC ' / Physical units of column 16 TFORM17 = '2D ' / Double precision array TTYPE17 = 'RESTFREQ ' / Type (label) of column 17 TUNIT17 = 'HZ ' / Physical units of column 17 TDISP17 = 'D17.10 ' / Display format of column 17 TFORM18 = '1D ' / Double precision array TTYPE18 = 'PMRA ' / Type (label) of column 18 TUNIT18 = 'DEG/DAY ' / Physical units of column 18 TFORM19 = '1D ' / Double precision array TTYPE19 = 'PMDEC ' / Type (label) of column 19 TUNIT19 = 'DEG/DAY ' / Physical units of column 19 NO_IF = 2 VELTYP = 'LSR ' VELDEF = 'OPTICAL ' END A.8 Acknowledgments by Authors of Draft Proposal The authors would like to thank E. Greisen, D. Wells, P. Grosbol, B. Hanisch, E. Mandel, E. Kemper, S. Voels, B. Schlesinger, W. Pence and many others for invaluable discussions and suggestions. A.9 Appendixes to Draft Proposal for Binary Tables Extension A.9.1 "Multidimensional Array" Convention It is anticipated that binary tables will need to contain data structures more complex that those describable by the basic notation. Examples of these are multidimensional arrays and nonrectangular data structures. Suitable conventions may be defined to pass these structures using some combination of keyword/value pairs and table entries to pass the parameters of these structures. One case, multidimensional arrays, is so common that it is prudent to describe a simple convention. The "Multidimensional array" convention consists of the following: any column with a dimensionality of 2 or larger will have an associated character keyword TDIMnnn='(l,m,n,...)' where l, m, n,... are the dimensions of the array. The data is ordered such that the array index of the first dimension given (l) is the most rapidly varying and that of the last dimension given is the least rapidly varying. The size implied by the TDIMnnn keyword will equal the element count specified in the TFORMnnn key- word. The adherence to this convention will be indicated by the presence of a TDIMnnn keyword in the form described above. A character string is represented in a binary table by a one-dimensional character array, as described in section A.6. For example, a FORTRAN CHARACTER*20 variable could be represented in a binary table as a character array declared as TFORMn = '20A '. Arrays of character strings, i.e., multidimensional character arrays, may be represented using the TDIMnnn notation. If a column is an array of strings then each string may be null terminated. For example, if TFORMn='20A' and TDIMn='(5,4)' then the entry consists of 4 strings of up to 5 characters each of which may be null terminated. This convention is optional and will not preclude other conventions. This convention is not part of the proposed binary table definition. A.9.2 "Variable Length Array" Facility One of the most attractive features of binary tables is that any field of the table can be an array. In the standard case this is a fixed size array, i.e., a fixed amount of storage is allocated in each record for the array data whether it is used or not. This is fine so long as the arrays are small or a fixed amount of array data will be stored in each record, but if the stored array length varies for different records, it is necessary to impose a fixed upper limit on the size of the array that can be stored. If this upper limit is made too large excessive wasted space can result and the binary table mechanism becomes seriously inefficient. If the limit is set too low then it may become impossible to store certain types of data in the table. The "variable length array" construct presented here was devised to deal with this problem. Variable length arrays are implemented in such a way that, even if a table contains such arrays, a simple reader program which does not understand variable length arrays will still be able to read the main table (in other words a table containing variable length arrays conforms to the basic binary table standard). The implementation chosen is such that the records in the main table remain fixed in size even if the table contains a variable length array field, allowing efficient random access to the main table. Variable length arrays are logically equivalent to regular static arrays, the only differences being 1) the length of the stored array can differ for different records, and 2) the array data is not stored directly in the table records. Since a field of any datatype can be a static array, a field of any datatype can also be a variable length array (excluding type P, the variable length array descriptor itself, which is not a datatype so much as a storage class specifier). Conventions such as TDIMnnn apply equally to both to variable length and static arrays. A variable length array is declared in the table header with a special field datatype specifier of the form rPt(maxelem) where the "P" indicates the amount of space occupied by the array descriptor in the data record (64 bits), the element count "r" should be 0, 1, or absent, t is a character denoting the datatype of the array data (L, X, B, I, J, etc., but not P), and maxelem is a quantity guaranteed to be equal to or greater than the maximum number of elements of type t actually stored in a table record. There is no built-in upper limit on the size of a stored array; maxelem merely reflects the size of the largest array actually stored in the table, and is provided to avoid the need to preview the table when, for example, reading a table containing variable length elements into a database that supports only fixed size arrays. For example, TFORM8 = 'PB(1800)' / Variable length byte array indicates that field 8 of the table is a variable length array of type byte, with a maximum stored array length not to exceed 1800 array elements (bytes in this case). The data for the variable length arrays in a table is not stored in the actual data records; it is stored in a special data area, the heap, following the last fixed size data record. What is stored in the data record is an array descriptor. This consists of two 32 bit integer values: the number of elements (array length) of the stored array, followed by the zero-indexed byte offset of the first element of the array, measured from the start of the heap area. Storage for the array is contiguous. The array descriptor for field N as it would appear embedded in a data record is illustrated symbolically below. field N-1 ; - nelem offset " ; field N+1 If the stored array length is zero there is no array data, and the offset value is undefined (it should be set to zero). The storage referenced by an array descriptor must lie entirely within the heap area; negative offsets are not permitted. A binary table containing variable length arrays consists of three main segments, as follows: table header record storage area (data records) heap area (variable array data) The table header consists of one or more 2880 byte FITS logical records with the last record indicated by the keyword END somewhere in the record. The record storage area begins with the next 2880 byte logical record following the last header record and is NAXIS1*NAXIS2 bytes in length. The zero indexed byte offset of the heap measured from the start of the record storage area is given by the THEAP keyword in the header. If this keyword is missing the heap is assumed to begin with the byte immediately following the last data record, otherwise there may be a gap between the last stored record and the start of the heap. If there is no gap the value of the heap offset is NAXIS1*NAXIS2. The total length in bytes of the area following the last stored record (gap plus heap) is given by the PCOUNT keyword in the table header. For example, suppose we have a table containing 5 168 byte records, with a heap area 2880 bytes long, beginning at an offset of 2880, thereby aligning the record storage and heap areas on FITS record boundaries (this alignment is not necessarily recommended but is useful for our example). The data portion of the table consists of 2 2880 byte FITS records, 840 bytes of which are used by the 5 table records, hence PCOUNT is 2*2880-840, or 4920 bytes. NAXIS1 = 168 / Width of table row in bytes NAXIS2 = 5 / Number of rows in table PCOUNT = 4920 / Random parameter count ... THEAP = 2880 / Byte offset of heap area While the above description is sufficient to define the required features of the variable length array implementation, some hints regarding usage of the variable length array facility may also be useful. Programs which read binary tables should take care to not assume more about the physical layout of the table than is required by the specification. For example, there are no requirements on the alignment of data within the heap. If efficient runtime access is a concern one may want to design the table so that data arrays are aligned to the size of an array element. In another case one might want to minimize storage and forgo any efforts at alignment (by careful design it is often possible to achieve both goals). Variable array data may be stored in the heap in any order, i.e., the data for record N+1 is not necessarily stored at a larger offset than that for record N. There may be gaps in the heap where no data is stored. Pointer aliasing is permitted, i.e., the array descriptors for two or more arrays may point to the same storage location (this could be used to save storage if two or more arrays are identical). Byte arrays are a special case because they can be used to store a "typeless" data sequence. Since FITS is a machine independent storage format, some form of machine specific data conversion (byte swapping, floating point format conversion) is implied when accessing stored data with types such as integer and floating, but byte arrays are copied to and from external storage without any form of conversion. An important feature of variable length arrays is that it is possible that the stored array length may be zero. This makes it possible to have a column of the table for which, typically, no data is present in each stored record. When data is present the stored array can be as large as necessary. This can be useful when storing complex objects as records in a table. Accessing a binary table stored on a random access storage medium is straightforward. Since the data records in the main table are fixed in size they may be randomly accessed given the record number, by computing the offset. Once the record has been read in, any variable length array data may be directly accessed using the element count and offset given by the array descriptor stored in the data record. Reading a binary table stored on a sequential access storage medium requires that a table of array descriptors be built up as the main table records are read in. Once all the table records have been read, the array descriptors are sorted by the offset of the array data in the heap. As the heap data is read, arrays are extracted sequentially from the heap and stored in the affected records using the back pointers to the record and field from the table of array descriptors. Since array aliasing is permitted, it may be necessary to store a given array in more than one field or record. Variable length arrays are more complicated than regular static arrays and imply an extra data access per array to fetch all the data for a record. For this reason, it is recommended that regular static arrays be used instead of variable length arrays unless efficiency or other considerations require the use of a variable array. This facility is still undergoing trials and is not currently part of the main binary table definition. Appendix B Implementation on Physical Media (This Appendix is not part of the NOST FITS Standard, but is included as a guide to recommended practices) B.1 Block Size The block size (physical record length) for transport of data should, where possible, equal the logical record length or an integer blocking factor times this record length. Standard values of the blocking factor may be specified for each medium; if not otherwise specified, the expected value is unity. B.1.1 Nine-Track, Half-Inch Magnetic Tape For nine-track half-inch magnetic tapes conforming to the ANSI X3.40-1983 specifications [13], there should be from one to ten logical records per physical block. The BLOCKED keyword (section 5.2.2.1) may be used to warn that there may be more than one logical record per physical block. The last physical block of a FITS file should be truncated to the minimum number of FITS logical records required to hold the remaining data, in accordance with ANSI X3.27-1978 specifications [14]. With the issuance of this standard, the BLOCKED keyword is deprecated by this document. B.1.2 Other Media For media where the physical block size cannot be equal to or an integral multiple of the FITS logical record length of 23040-bits (2880 8-bit bytes), records should be written over multiple blocks as a byte stream. Conventions regarding the relation between physical block size and logical record length of FITS files have not been otherwise established for other media. B.2 Physical Properties of Media The arrangement of digital bits and other physical properties of any medium should be in conformance with the relevant national and/or international standard for that medium. B.3 Labeling B.3.1 Tape Tapes may be either ANSI standard labeled or unlabeled. Unlabeled tapes are preferred. B.3.2 Other Media Conventions regarding labels for physical media containing FITS files have not been established for other media. B.4 FITS File Boundaries B.4.1 Magnetic Reel Tape Individual FITS files are terminated by a tape-mark. B.4.2 Other Media For media where the physical record size cannot be equal to or an integral multiple of the standard FITS logical record length, a record of fewer than 23040 bits (2880 8-bit bytes) immediately following the end of the primary header, data, or an extension should be treated as an end-of-file. Otherwise, individual FITS files should be terminated by a delimiter appropriate to the medium, analogous to the tape end-of-file mark. If more than one FITS file appears on a physical structure, the appropriate end-of-file indicator should immediately precede the start of the primary headers of all files after the first. B.5 Multiple Physical Volumes Storage of a single FITS file on more than one unlabeled tape or on multiple units of any other medium is not universally supported in FITS. One possible way to handle multivolume unlabeled tape was suggested in [1]. Appendix C Differences from IAU-endorsed Publications (This Appendix is not part of the NOST FITS Standard but is included for informational purposes only.) Note: In this discussion, the term the FITS papers refers to [1], [2], [4], and [5], collectively, and the term Floating Point Agreement (FPA) refers to [8]. 1. Section 3 - Definitions, Acronyms, and Symbols Array value - This precise definition is not used in the original FITS papers. ASCII text - This permissible subset of the ASCII character set, used in many contexts, is not precisely defined in the FITS papers. Basic FITS - This definition includes the possibility of floating point data arrays, while the terminology in the FITS papers refers to FITS as described in [1], where only integer arrays were possible. Conforming Extension - This terminology is not used in the FITS papers. Deprecate - The concept of deprecation does not appear in the FITS FITS papers. FITS structure - This terminology is not used in the FITS papers in the precise way that it is in this standard. Header and Data Unit - This terminology is not used in the FITS papers. Indexed keyword - This terminology is not used in the original FITS papers. Physical value - This precise definition is not used in the original FITS papers. Reference point - This term replaces the reference pixel of the FITS papers. The new terminology is consistent with the fact that the array need not represent a digital image and that the reference point (or pixel) need not lie within the array. Reserved keyword - The FITS papers describe optional keywords but do not say explicitly that they are reserved. Standard Extension - This precise definition is new. The term standard extension is used in some contexts in the FITS papers to refer to what this standard defines as a standard extension and in others to refer to what this standard defines as a conforming extension. 2. Section 4.3.2 Primary Data Array Fill format - This specification is new. The FITS papers and the FPA do not precisely specify the format of data fill for the primary data array. 3. Section 4.4.1.1 Identity (of conforming extensions) The FITS papers specify that creators of new extension types should check with the FITS standards committee. This standard identifies the committee specifi- cally, introduces the role of the NOST as its agent, and mandates registration. 4. Section 5.1.2.1 Keyword (as header component) The specification of permissible keyword characters is new. The FITS papers do not precisely define the permissible characters for keywords. 5. Section 5.2.1.1 Principal (mandatory keywords) (a) NAXIS keyword - The requirement that the NAXIS keyword may not be negative is not explicitly specified in the FITS papers. (b) NAXISn keyword - The requirement that the NAXISn keyword may not be negative is not explicitly specified in the FITS papers. 6. Section 5.2.1.2 Conforming Extensions (a) NBITS - The requirement that NBITS may not be negative is not explicitly specified in the FITS papers. (b) XTENSION keyword - That this keyword may not appear in the primary header is only implied by the FITS papers; the prohibition is explicit in this standard. The FITS papers name a FITS standards committee as the keeper of the list of accepted extension type names. This standard specifically identifies the committee and introduces the role of the NOST as its agent. 7. Section 5.2.2 Other Reserved Keywords That the optional keywords defined in the FITS papers are to be reserved with the meanings and usage defined in those papers, as in the standard, is not explicitly stated in them. 8. Section 5.2.2.1 Keywords Describing the History... (a) DATE Keyword - The recommendation for use of Universal Time is not in the FITS papers. (b) BLOCKED keyword - The FITS papers require the BLOCKED keyword to appear in the first record of the primary header even though it cannot when the value of NAXIS exceeds the values described in the text. They do not address this contradiction. Deprecation of the BLOCKED keyword is new with this standard. 9. Section 5.2.2.2 Keywords Describing Observations (a) DATE-OBS Keyword - The recommendation for use of Universal Time is not in the FITS papers. (b) EQUINOX and EPOCH keywords - This standard replaces the EPOCH keyword with the more appropriately named EQUINOX keyword and deprecates the EPOCH name. 10. Section 5.2.2.4 Commentary keywords Keyword field is blank - Reference [1] contains the text "BLANK" to represent a blank keyword field. The standard clarifies the intention. 11. Section 5.2.2.5 Array keywords (a) BUNIT Keyword - The FITS papers recommend the use of SI units and identify other units standard in astronomy. This standard makes the recommendation more specific by referring to the IAU Style Manual [7]. (b) CTYPEn Keywords - This standard extends the recommendations on units to coordinate axes. (c) CRPIXn Keywords - This standard explicitly notes the ambiguity in the location of the index number relative to an image pixel. (d) CDELTn Keywords - The definition in the standard differs from that in the FITS papers in that it provides for the case where the spacing between index points varies over the grid. For the case of constant spacing, it is identical to the specification in the FITS papers. (e) DATAMAX and DATAMIN Keywords - The standard clarifies that the value refers to the physical value represented by the array, after any scaling, not the array value before scaling. The standard also notes that special values are not to be considered when determining the values of DATAMAX and DATAMIN, an issue not specifically addressed by the FITS papers or the FPA. 12. Section 5.3.2.1 Character String (fixed format) The standard explicitly describes how single quotes are to be coded into keyword values, a rule only implied by the FORTRAN-77 list-directed read requirements of the FITS papers. 13. Section 5.3.2.4 Real Floating Point Number (fixed format) The standard explicitly notes that the full precision of 64-bit values cannot be expressed as a single value using the fixed format. 14. Section 5.3.2.4 Complex Floating Point Number (fixed format) The standard explicitly notes that the full precision of 64-bit values cannot be expressed as a single value using the fixed format. 15. Section 7 Random Groups Structure The standard deprecates the Random Groups structure. 16. Section 7.1.2 Reserved keywords (random groups) That the optional keywords defined in the FITS papers are to be reserved with the meanings and usage defined in those papers, as in the standard, is not explicitly stated in them. 17. Section 7.1.2.2 PSCALn Keywords - The default value is explicitly specified in the standard, whereas in the FITS papers it is assumed by analogy with the BSCALE keyword. 18. Section 7.1.2.3 PZEROn Keywords - The default value is explicitly specified in the standard, whereas in the FITS papers it is assumed by analogy with the BZERO keyword. 19. Section 8.1 ASCII Tables Extension The name ASCII Tables is given to the Tables extension discussed in the FITS papers to distinguish it from binary tables. 20. Section 8.1.1 Mandatory Keywords (ASCII tables) (a) NAXIS1 keyword - The requirement that the NAXIS1 keyword may not be negative in an ASCII table header is not explicitly specified in the FITS papers. (b) NAXIS2 keyword - The requirement that the NAXIS2 keyword may not be negative in an ASCII table header is not explicitly specified in the FITS papers. (c) TFIELDS keyword - The requirement that the TFIELDS keyword may not be negative is not explicitly specified in the FITS papers. 21. Section 8.1.2 Other Reserved Keywords (ASCII tables) That the optional keywords defined in the FITS papers are to be reserved with the meanings and usage defined in those papers, as in the standard, is not explicitly stated in them. (a) TUNIT Keyword - The FITS papers do not explicitly recommend the use of any particular units for this keyword, although the reference to the BUNIT keyword may be considered an implicit extension of the recommendation for that keyword. This standard makes the recommendation more specific for the TUNIT keyword by referring to the IAU Style Manual [7]. (b) TSCALn Keyword - The prohibition against use in A-format fields is stronger than the statement in the FITS papers that the keyword "is not relevant". (c) TZEROn Keywords - The prohibition against use in A-format fields is stronger than the statement in the FITS papers that the keyword "is not relevant". 22. Section 9 Restrictions on Changes The concept of deprecation is not provided for in the FITS papers. 23. Appendix B Implementation on Physical Media Material in the FITS papers specifying the expression of FITS on specific physical media is not part of this Standard. Appendix D Summary of Keywords (This Appendix is not part of the NOST FITS Standard, but is included for convenient reference). Principal Conforming ASCII Table Random Groups Proposed Binary HDU Extension Extension Extension Table_Extension _______________________________________________________________________________ SIMPLE XTENSION XTENSION (1) SIMPLE XTENSION (2) BITPIX BITPIX BITPIX = 8 BITPIX BITPIX = 8 NAXIS NAXIS NAXIS = 2 NAXIS NAXIS = 2 NAXISn NAXISn NAXIS1 NAXIS1 = 0 NAXIS1 EXTEND (3) PCOUNT NAXIS2 NAXISn NAXIS2 END GCOUNT PCOUNT = 0 GROUPS PCOUNT = 0 END GCOUNT = 1 PCOUNT GCOUNT = 1 TFIELDS GCOUNT TFIELDS TBCOLn END TFORMn TFORMn END END _______________________________________________________________________________ 1 XTENSION= 'TABLE ' for the ASCII Table extension. 2 XTENSION= 'BINTABLE' for the proposed binary table extension. 3 Required only if extensions are present. Table D.1: Mandatory FITS keywords for the structures described in this document. Principal HDU Conforming ASCII Table Random Groups Binary Table General Array Extension Extension Extension Extension _______________________________________________________________________________ DATE BSCALE EXTNAME TSCALn PTYPEn TTYPEn ORIGIN BZERO EXTVER TZEROn PSCALn TUNITn BLOCKED BUNIT EXTLEVEL TNULLn PZEROn TNULLn AUTHOR BLANK TTYPEn TSCALn REFERENC CTYPEn TUNITn TZEROn COMMENT CRPIXn TDISPn HISTORY CROTAn TDIMn CRVALn THEAP DATE-OBS CDELTn TELESCOP DATAMAX INSTRUME DATAMIN OBSERVER OBJECT EQUINOX EPOCH _______________________________________________________________________________ Table D.2: Reserved FITS keywords for the structures described in this document. Note that the EPOCH and BLOCKED keywords are deprecated by this document. Production Bibliographic Commentary Observation Array ____________________________________________________________________ DATE AUTHOR COMMENT DATE-OBS BSCALE ORIGIN REFERENC HISTORY TELESCOP BZERO BLOCKED INSTRUME BUNIT OBSERVER BLANK OBJECT CTYPEn EQUINOX CRPIXn EPOCH CROTAn CRVALn CDELTn DATAMAX DATAMIN ____________________________________________________________________ Table D.3: General Reserved FITS keywords described in this document. Note that the EPOCH and BLOCKED keywords are deprecated by this document. Appendix E ASCII Text (This appendix is not part of the NOST FITS standard; the material in it is taken from the ANSI standard for ASCII [11] and is included here for informational purposes.) In the table below the first column is the decimal and the second column the hexadecimal value for the character in the third column. The characters hexadecimal 20 to 7E (decimal 32 to 126) constitute the subset referred to in this document as ASCII text. _______________________________________________________________________ | ASCII Control || ASCII Text | | dec hex char || dec hex char | dec hex char | dec hex char | ----------------------------------------------------------------------- | 0 00 NUL || 32 20 SP | 64 40 @ | 96 60 ` | | 1 01 SOH || 33 21 ! | 65 41 A | 97 61 a | | 2 02 STX || 34 22 " | 66 42 B | 98 62 b | | 3 03 ETX || 35 23 # | 67 43 C | 99 63 c | | 4 04 EOT || 36 24 $ | 68 44 D | 100 64 d | | 5 05 ENQ || 37 25 % | 69 45 E | 101 65 e | | 6 06 ACK || 38 26 & | 70 46 F | 102 66 f | | 7 07 BEL || 39 27 ' | 71 47 G | 103 67 g | | 8 08 BS || 40 28 ( | 72 48 H | 104 68 h | | 9 09 HT || 41 29 ) | 73 49 I | 105 69 i | | 10 0A LF || 42 2A * | 74 4A J | 106 6A j | | 11 0B VT || 43 2B + | 75 4B K | 107 6B k | | 12 0C FF || 44 2C , | 76 4C L | 108 6C l | | 13 0D CR || 45 2D - | 77 4D M | 109 6D m | | 14 0E SO || 46 2E . | 78 4E N | 110 6E n | | 15 0F SI || 47 2F / | 79 4F O | 111 6F o | | 16 10 DLE || 48 30 0 | 80 50 P | 112 70 p | | 17 11 DC1 || 49 31 1 | 81 51 Q | 113 71 q | | 18 12 DC2 || 50 32 2 | 82 52 R | 114 72 r | | 19 13 DC3 || 51 33 3 | 83 53 S | 115 73 s | | 20 14 DC4 || 52 34 4 | 84 54 T | 116 74 t | | 21 15 NAK || 53 35 5 | 85 55 U | 117 75 u | | 22 16 SYN || 54 36 6 | 86 56 V | 118 76 v | | 23 17 ETB || 55 37 7 | 87 57 W | 119 77 w | | 24 18 CAN || 56 38 8 | 88 58 X | 120 78 x | | 25 19 EM || 57 39 9 | 89 59 Y | 121 79 y | | 26 1A SUB || 58 3A : | 90 5A Z | 122 7A z | | 27 1B ESC || 59 3B ; | 91 5B [ | 123 7B - | | 28 1C FS || 60 3C < | 92 5C " | 124 7C _ | | 29 1D GS || 61 3D = | 93 5D ] | 125 7D " | | 30 1E RS || 62 3E > | 94 5E ^ | 126 7E " | | 31 1F US || 63 3F ? | 95 5F _ | 127 7F DEL | ----------------------------------------------------------------------- Table E.1: ASCII character set Appendix F IEEE Special Formats (The material in this Appendix is not part of this standard; it is taken from the IEEE- 754 floating point standard [12] for informational purposes). The table below displays the hexadecimal contents, most significant byte first, of the double and single precision IEEE special values. bytes are used. IEEE special value Double Precision Single Precision _________________________________________________________________ NaN (1) 7FFFFFFFFFFFFFFF FFFFFFFF -0 8000000000000000 80000000 +0 0000000000000000 00000000 +1 7FF0000000000000 7F800000 -1 FFF0000000000000 FF800000 underflow 7FEFFFFFFFFFFFFF 7F7FFFFF overflow 0010000000000000 00800000 _________________________________________________________________ 1 Referred to as the quiet NaN, as opposed to the signaling NaN Table F.1: IEEE special floating point formats Appendix G Reserved Extension Type Names (This Appendix is not part of the NOST FITS Standard, but is included for informational purposes) Type Name Status Reference Sponsor Comments ______________________________________________________________________________ 'A3DTABLE' L [15] NRAO Prototype binary table design supported in AIPS; superseded by BINTABLE, which supports all A3DTABLE features. 'BINTABLE' D [9] IAU Draft Proposal for NRAO binary table design. NOAO 'DUMP ' R none none Intended for binary dumps. 'FILEMARK' R none NRAO Intended for structure to represent equivalent of tape mark on other media. 'IMAGE ' R [16] IUE For including multidimensional matrices in extensions. 'TABLE ' S [5] IAU ASCII Tables. _______________________________________________________________________________ Table G.1: Reserved Extension Type Names Code Significance _______________________________________________________________________________ D Draft extension proposal for discussion by regional FITS committees. L Local FITS extension. P Proposed FITS extension approved by regional FITS committees but not by IAU FITS Working Group. R Reserved type name for which a full draft proposal has not been submitted. S Standard extension approved by IAU FITS Working Group and endorsed by the IAU. _______________________________________________________________________________ Table G.2: Status Codes Appendix H NOST Publications Document Title Date Status _______________________________________________________________________________ NOST 100-0.1 FITS Standard December, 1990 Draft Standard NOST 100-0.2 FITS Implementation Standard June, 1991 Revised Draft Standard NOST 100-0.3 FITS Implementation Standard December, 1991 Revised Draft Standard _______________________________________________________________________________ Table H.1: NOST Publications Index ', 22 /, 14 =, 13 A3DTABLE, 68 A3DTABLE, extension, 39 AIPS, 5, 39, 68 ANSI, 5 ANSI, ASCII, 4 ANSI, FORTRAN, 3, 14, 21, 43 ANSI, IEEE, 4, 24 ANSI, tapes, 4, 54 ANSI, X3.27-1978, 53 ANSI, X3.27-1978, 4 ANSI, X3.40-1983, 53 ANSI, X3.40-1976, 4 array value, 5, 7, 19, 55, 57 array, multidimensional, 10, 11 ASCII Tables, 3 ASCII tables, vii, 1, 2, 31, 40, 58, 67 ASCII, ANSI, 4 ASCII, character, 5, 23, 31, 34, 45, 63 ASCII, characters, 2 ASCII, text, vii, 2, 5, 9, 10, 13, 14, 18, 19, 22, 34, 55, 63 AUTHOR, 18, 43 Basic FITS, vii, 1, 5, 55 binary tables, 1-3, 27, 39, 61 BINTABLE, 41, 68 BINTABLE, extension, 39, 61, 67 bit array, 44 BITPIX, 15, 16, 19, 20, 24, 27, 28, 31, 41 BLANK, 19, 24, 57 BLOCKED, 17, 21, 53, 57, 62 BSCALE, 19, 24, 58 BUNIT, 19, 57, 59 byte order, 23, 24 BZERO, 19, 24, 58 case sensitivity, 21 CDELTn, 20, 57 character string, 21, 22, 45, 48, 57 COMMENT, 18 complex, 42 complex, floating point, 22, 45, 58 complex, integer, 22 conforming extension, 2, 5, 8-11, 15, 39, 55, 56 CROTAn, 20 CRPIXn, 20, 57 CRVALn, 20 CTYPEn, 20, 57 data, invalid, 42 DATAMAX, 20, 57 DATAMIN, 20, 57 DATE, 17, 57 DATE-OBS, 17, 57 deprecate, 2, 6, 17, 18, 27, 37, 53, 55, 57, 58 DUMP, 68 END, 15, 29, 32, 42 EPOCH, 18, 57, 62 EQUINOX, 18, 57 ESA, IUE Newsletter, 4 EXTEND, 16, 17, 21, 31, 40 extension, vii, 1, 2, 6, 8-11, 20, 21, 23, 39, 40, 54, 56, 67 extension, conforming, 2, 5, 8-11, 15, 39, 55, 56 extension, name, 6 extension, registration, 10, 56 extension, standard, 11, 16, 56 extension,standard, 8, 11, 31 EXTLEVEL, 21, 42 EXTNAME, 6, 20, 42 EXTVER, 21, 42 FILEMARK, 68 fill, 10, 13, 30, 33, 34, 56 FITS, structure, 2, 5-7, 9, 11, 17, 37, 55 FITS, Working Group, vii, 1, 10, 16, 39 floating point, 6, 10, 22, 45, 65 floating point, 64 bit, 24, 58 floating point, complex, 22, 45 floating point, FITS agreement, vii, 3, 55 floating point, format, 65 format, 32 format, data, vii, 23 format, extension, 6 format, fixed, 21 format, keywords, 21 format, standard, 1 format,fixed, 58 FORTRAN, ANSI manual, 3 FORTRAN-77, format, 32, 34 FORTRAN-77, list-directed read, 14, 21, 58 GCOUNT, 16, 17, 27, 29, 30, 32, 41 Going AIPS, 4 group parameter value, 6, 29, 30 GROUPS, 28 HDU, 6, 15, 17 HDU, extension, 9 HDU, primary, 8-10 HDU,extension, 6 HDU,primary, 6, 7, 9, 11 HISTORY, 19 i, 42 IAU, vii, 1-3, 6, 55, 68 IAU, 1988 General Assembly, vii IAU, Commission 5, vii, 1, 10, 16, 39 IAU, Style Manual, 3, 19, 34, 57, 59 IAU,Style Manual, 20 IEEE, 7, 39 IEEE, ANSI, 4 IEEE, floating point, 24, 25 IEEE, floating point +0.0, 10 IEEE, NaN, 7, 24, 25, 45 IEEE, special format, 65 IEEE, special values, 2, 7, 20, 24, 25, 45, 57 IMAGE, 68 INSTRUME, 18 integer value, 22, 44 integer value, 16 bit, 23 integer value, 32 bit, 23 integer value, 8 bit, 23 interferometry, 27 IUE, 6, 68 IUE, FITS, 4 keyword, indexed, 7, 13, 55 keyword, required, 1, 2, 7, 14-16, 27, 31, 56, 58 keyword, reserved, 1, 2, 7, 17, 29, 33, 56, 58, 59 keyword, valid characters, 13 logical, 42 logical value, 22, 44 MIDAS, 7, 39 multidimensional entries, 43, 48 NAXIS, 10, 15-17, 27, 28, 30, 31, 41, 56, 57 NAXIS1, 28, 31, 34, 41, 42, 50, 58 NAXIS2, 31, 34, 41, 50, 58 NAXISn, 10, 15, 16, 20, 27, 28, 30 NBITS, 15, 16, 27, 56 NOAO, 7, 68 NOST, 7, 10, 16, 56 NRAO, 7, 39, 68 OBJECT, 18 OBSERVER, 18 ORIGIN, 17 parameter, vii, 29, 30 PCOUNT, 16, 17, 27, 29-31, 41, 50 physical value, 7, 19, 20, 29, 30, 33, 55, 57 primary data array, 5, 7, 9, 10, 16, 19, 27, 28, 30, 56 primary header, 2, 5, 7, 9, 14-16, 21, 27, 54, 57 PSCALn, 29, 30, 58 PTYPEn, 29, 30 PZEROn, 29, 30, 58 quote, 22 random groups, vii, 1-3, 6, 9, 11, 19, 27, 58 random groups, array, vii, 30 REFERENC, 18, 43 reference point, 7, 20, 55 registration, extension, 10 scaling, data, 19, 29, 30, 33, 57 sign, bit, 23, 24 sign, character, 34 SIMPLE, 27 SIMPLE, in primary header, 14, 15 SIMPLE, in special records, 12 special records, 6, 8, 9, 12 standard extension, 8, 11, 16, 31, 56 TABLE, 31, 68 TABLE, extension, 31, 61 tape, 9-track half-inch, vii, 53 TBCOLn, 32 TDIMnnn, 43, 48, 49 TDISPnnn, 41, 43 TELESCOP, 18 TFIELDS, 32, 41, 58 TFORMn, 32, 41, 48 THEAP, 43, 50 TNULLn, 33, 34, 41, 42 TSCALn, 33, 34, 42-44, 59 TTYPEn, 33, 41, 42 TUNIT, 59 TUNITn, 34, 41, 42 TZEROn, 33, 34, 42-44, 59 units, 19, 20, 34, 57 Universal Time, 17, 57 value undefined, 34 value, invalid, 44 value, null, 44 value, undefined, 33, 42 XTENSION, 8, 12, 16, 20, 31, 41, 56