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- Newsgroups: rec.photo,rec.answers,news.answers
- Path: bloom-beacon.mit.edu!hookup!swrinde!sdd.hp.com!hpscit.sc.hp.com!hplextra!cello!jacobson
- From: jacobson@cello.hpl.hp.com (David Jacobson)
- Subject: Photographic Lenses FAQ
- Summary: This posting contains a list of Frequently Asked Questions
- about lenses. It is intended for photographers. It
- defines terms, gives a large number of formulas, discusses
- depth of field issues, diffraction, and lens aberrations.
- Message-ID: <1994Mar22.032803.25692@cello.hpl.hp.com>
- Supersedes: <1994Feb22.173331.14777@cello.hpl.hp.com>
- Approved: news-answers-request@MIT.EDU
- Date: Tue, 22 Mar 1994 03:28:03 GMT
- Expires: Fri, 22 Apr 1994 06:00:00 GMT
- Organization: Hewlett-Packard Laboratories
- Followup-To: rec.photo
- Lines: 282
- Xref: bloom-beacon.mit.edu rec.photo:44485 rec.answers:4566 news.answers:16723
-
- Archive-name: rec-photo/lenses/faq
- Last-modified 1994/02/10
- Version: 1.0
-
- Frequently Asked Questions regarding lenses.
- By David Jacobson
- jacobson@hpl.hp.com
-
-
- Q. What is the meaning of the symbols in the rest of this FAQ?
-
- A. f focal length
- So distance from front principal point to subject (object)
- Sfar distance from front principal point to farthest point in focus
- Sclose distance from front principal point to closest point in focus
- Si distance from rear principal point to film (image) plane
- M magnification
- N f-number or f-stop
- Ne effective f-number (corrected for bellows factor)
- c diameter of largest acceptable circle of confusion
- h hyperfocal distance
-
- See the technical notes at the end for more infomation on subject
- distances, more information on the meaning of f-number and
- limitations to be observed when applying these formulas to lenses in
- which the aperture does not appear the same size front and rear.
-
- Q. What meant by f-stop?
-
- A. The focal length of the lens divided by the diameter of the
- aperture (as seen from the front). It is also called an f-number.
- The brightness of the image on the film is inversely proportional
- to the f-number squared.
-
- Q. What is the basic formula for the conditions under which an image
- is in focus?
-
- A. There are several forms.
- 1/Si + 1/So = 1/f (Gaussian form)
- (Si-f)*(So-f) = f^2 (Newtonian form)
-
-
- Q. What is the formula for magnification?
-
- A. There are several forms.
- M = Si/So
- M = (Si-f)/f
- M = f/(So-f)
-
-
- Q. How do I correct for bellows factor?
-
- A. Ne = N*(1+M)
-
-
- Q. What is meant by circle of confusion?
-
- A. When a lens is defocused, a point in the subject gets rendered as
- a small circle, called the circle of confusion. If the circle of
- confusion is small enough, the image will look sharp. There is no one
- circle "small enough" for all circumstances, but rather it depends on
- how much the image will be enlarged, the quality of the rest of the
- system, and even the subject. Nevertheless, for 35mm work c=.03mm is
- generally agreed on as the diameter of the acceptable circle of
- confusion. Another rule of thumb is c=1/1730 of the diagonal of the
- frame, which comes to .025mm for 35mm film. (Zeiss and Sinar are
- known to be consistent with this rule.)
-
-
- Q. What is hyperfocal distance?
-
- A. The closest distance that is in acceptable focus when the lens is
- focused at infinity. (See below for a variant use of this term.)
-
- h = f^2/(N*c)
-
-
-
- Q. What are the closest and farthest points that will be in sharp
- focus?
-
- A. Sclose = h * So / (h + (So - f))
- Sfar = h * So / (h - (So - f))
-
- If the denominator is zero or negative, Sfar is infinity.
-
- Q. What is depth of field?
-
- A. It is convenient to think of a rear depth of field and a front
- depth of field. The rear depth of field is the distance from the
- subject to the farthest point that is sharp and the front depth of
- field is the distance from the closest point that is sharp to the
- subject. (Here we assume the lens is focused on the subject.)
- Sometimes the term depth of field is used for the combination of these
- two, i.e. the distance from the closest point that is sharp to the
- farthest point that is sharp.
-
- frontdepth = S - Sclose
- frontdepth = Ne*c/(M^2 * (1 + (So-f)/h))
- frontdepth = Ne*c/(M^2 * (1 + (N*c)/(f*M)))
-
- reardepth = Sfar - S
- reardepth = Ne*c/(M^2 * (1 - (So-f)/h))
- reardepth = Ne*c/(M^2 * (1 - (N*c)/(f*M)))
-
- In the last two, if the denominator is zero or negative, reardepth is
- infinity.
-
-
- Q. Where should I focus my lens so I will get everything from some
- close point to infinity in focus?
-
- A. At approximately the hyperfocal distance. More precisely, at
- So = h + f. In this condition the closest point that will be in focus
- is at half the subject distance. (Some authorities use this as the
- definition of hyperfocal distance.)
-
-
- Q. I have heard that the depth of field depends only the the f-stop and
- the magnification. Is this true?
-
- A. Yes, under some conditions. When the subject distance is small
- with respect to the hyperfocal distance, the front and rear depth of
- field are almost equal and depend only on the magnification and f-stop.
- As the subject distance approaches the hyperfocal distance, the front
- depth of field gets smaller and the rear depth gets larger, eventually
- extending to infinity.
-
-
- Q. I have heard that one should use a long lens to get a shallow depth
- of field and a short lens to get a large depth of field. Is this
- true?
-
- A. Assuming that you frame the subject the same way, using a long
- lens does not make the depth of field very much shorter. It does make
- the front and rear depths more even, but you probably didn't care
- about that very much. Using a short lens can make the rear depth of
- field very large, or even infinite. (See the previous question.) Now
- back to the long lens issue. Even though making the lens very long
- has little effect on the maximum distance behind the subject at which
- points still appear to be sharp, it has a big effect on how fuzzy very
- distant points appear. Specifically, if the lens is focused on some
- nearby point rendered with magnification M, a distant point at
- infinity will be rendered as a circle of diameter C, given by
-
- C = f M / N
-
- which shows that the distant background point will be fuzzed out in
- direct proportion to the focal length.
-
-
- Q. If I focus on some point, and then recompose with that point not
- in the center, will the focus be off?
-
- A. Yes, but maybe only a little bit. If the object is far enough
- away, the depth of field will cover the shift in distance.
-
- An approximate formula for the minimum distance such that the error
- will be covered by depth of field is given by
-
- d = w^2/(2 N c)
-
- where
- d = minimum distance to make the point be sharply rendered
- d is measured from the film plane
- w = distance image point on the film is from center of the image
-
- Thus for 35mm you can recompose the image moving the subject clear to
- the edge of the frame and still have it be sharp if the subject
- distance (at the center) was at least 5.4 meters (18 feet) divided by
- the f-number. See the technical notes at the end for a bunch of
- assumptions.
-
-
- Q. What is diffraction?
-
- A. When a beam of light passes through any aperture it spreads out.
- This effect limits how sharp a lens can possibly be.
-
-
- Q. What is the diffraction limit of a lens.
-
- A. A lens is diffraction limited at about 1500/N line pairs per mm.
-
-
- Q. What are aberrations?
-
- A. Aberrations are image defects that result from limitations in the
- way lenses can be designed. Better lenses have smaller aberrations,
- but aberrations can never be completely eliminated, just reduced.
-
- The classic aberrations are:
-
- * Spherical aberration. Light passing through the edge of the lens is
- focused at a different distance (closer in simple lenses) than light
- striking the lens near the center.
-
- * Coma. The distance from the axis at which an off-axis object point
- is rendered varies with the distance from the center of the lens at
- which the light passes. In other words, magnification varies with the
- distance from the center of the lens. Off axis points are rendered
- with tails, reminiscent of comets, hence the name.
-
- * Astigmatism. Off-axis points are blurred in their the radial or
- tangential direction, and focusing can reduce one at the expense
- of the other, but cannot bring both into focus at the same time.
- (Optometrists apply the word "astigmatism" to a defect in the human
- eye that causes *on-axis* points to be blurred along one axis or at 90
- degrees to that axis. That astigmatism is not quite the same as
- astigmatism in photographic lenses.)
-
-
- * Curvature of field. Points in a plane get focused sharply on a
- curved surface, rather than a plane (the film). Or equivalently, the
- set of points in the subject space that are sharp makes a curved
- surface rather than a plane. With a plane subject or a subject at
- infinite distance the net effect is that when the center is in focus
- the edges are out of focus, and if the edges are in focus the center
- is out of focus.
-
- * Distortion (pincushion and barrel). The image of a square object
- has sides that curve in or out. (This should not be confused with the
- natural perspective effects that become particularly noticeable with
- wide angle lenses.) This happens because the magnification is not a
- constant, but rather varies with the angle from the axis.
-
- * Chromatic aberration. The position (forward and back) of sharp focus
- varies with the wavelength.
-
- * Lateral color. The magnification varies with wavelength.
-
-
- Q. Can I eliminate these aberrations by stopping down the lens?
-
- A. The effect of all aberrations except distortion and lateral color
- is reduced by stopping down.
-
-
- Q. What are "elements" and "groups", and are more better?
-
- A. The number of elements is the number of pieces of glass used in the
- lens. If two or more are cemented together, that whole set is called
- a group. Thus a lens that has 8 elements in 7 groups has 8 pieces of
- glass with 2 cemented together. It is impossible to completely
- correct all aberrations. Each additional element the designer has at
- his/her disposal gives a few more degrees of freedom to design out an
- aberration. So one would expect a 4 element Tessar to be better than
- a 3 element Triotar. However, each element also reflects a little
- light, causing flare. So too many elements is not good either. Note
- that an unscrupulous manufacturer could slap together 13 pieces of
- glass and claim to have a 13 element lens, but it might be terrible.
- So by itself the number of elements is no guarantee of quality.
-
-
- Technical notes:
-
- The subject distance, So, as used in the formulas is measured from the
- subject to the lens's front principal point. On most cameras the
- focusing scale is calibrated to read the distance from the subject to
- the film plane. There is no easy way to precisely convert between the
- focusing scale distance and So.
-
- The formulas presented here all assume that the aperture looks the
- same size front and rear. If it does not, which is particularly
- common in wide angle lenses, use the front diameter and note that the
- formulas for bellows correction and depth of field will not be correct
- at macro distances. Formulas that are exact even with this condition
- are given in the lens tutorial, posted separately.
-
- The conditions under which the formula for the minimum distance at
- which the effect of focusing and recomponsing will be covered by depth
- of field are:
-
- 1. w is no more than the focal length of the lens. At the edge
- w=18mm for 35mm, so this will very seldom be a problem. 2. The
- lens's two nodal points are not very widely separated. But if the
- front nodal point is in front of the rear nodal point, which I think
- is the more common case, the formula is too conservative, so this is
- not a problem either. 3. The camera is rotated about the front nodal
- point. Almost always the camera will be rotated about an axis behind
- the front nodal point which again makes the formula too conservative.
- For guide number given assumes c=.03mm.
-