DR. PLASKETT'S DETAILED ACCOUNT of the acceptance tests for the great 82" mirror for the McDonald observatory, reprinted from Contributions from the McDonald Observatory, University of Texas, begun here last month, is concluded as follows:

The focal length of the completed mirror was carefully measured before the reductions of the final measures, as 319.656", or 811.928 cm; and with this focal length the intersections of the 12 zones used in the visual tests and the 15 in the Hartmann test were computed anew, and are given in Table I. On the left-hand side the units are inches and on the right centimeters, as the separation of the zones, which are those of the diaphragm used in the Hartmann test and the pitch of the screw used in measuring the photographs, are given in these units. The recomputation was necessary, as the difference between these positions and those for the focal length of 320" amounts to 0.005", or 0.12 mm, which is quite significant with so good a mirror as the 82".

The visual measures of the intersections of the pencils from the various zones were made on October 12 and October 14, immediately after the parabolizing was completed, and again on October 26 and November 1, after the mirror was aluminized. There were four independent sets of measures on October 12 and six each on the other three dates, equally divided between, and alternated by, Mr. Lundin and myself. The separation of the scratches was measured by dividers on a steel rule divided into fiftieths and hundredths of an inch. These measures, or rather the differences between the observed and the computed position

The results of these four measures are given in Table 2, where the first column contains the zone number, the second and third and the succeeding three pairs of columns give the Rs, the difference between the observed and computed positions of the zonal intersections, and their transformations into the curve of shape for the four dates. It will be noted that the values of R which, it must be remembered, are expressed in thousandths of an inch and are four times the longitudinal aberrations at the principal focus, vary somewhat on the different dates, being lower on October 12 and 26 than on October 14 and November 1. While the accidental errors of the means of the sets, varying from +/-0.003" to +/-0.004", and increasing from edge to center of the mirror, may account for a considerable fraction of the variation, there may be something systematic about the differences, such as temperature variations on the different dates, or change of figure produced by irregularities in the thickness of the aluminum coating.

So far as the latter effect is concerned, it may be dismissed as negligible, as there is no appreciable systematic difference in the run of the R's before the coating, on October 12 and 14, and after it, on October 25 and November 1. There may be, however, some evidence of a temperature effect on the figure of the 82" mirror. On October 12 and 25, when the variations in the Rs were somewhat smaller than in the other two measures, the decrease in temperature, taken from a thermograph near the mirror, between midnight and the time of the tests, about 11:00 A.M., was 1°.2F, while on October 14 the change was 2°F. However, on November 1 the temperature was constant within 0°.3F, so that, on the whole, a variation of figure with small temperature changes is not demonstrated.

We may, hence, consider that the variation in Rs are mainly accidental and use the mean values of the 22 different settings as best representing the figure of the mirror, and these means are given in the last three columns of Table 2. The mean Rs are all remarkably small, less than 0.004", or 0.001" at the principal focus, except for zones 6, 9, and, to a smaller extent, 11. These indicate only a very small deviation from a perfect figure, the maximum longitudinal aberration at the principal focus in the last column being 0.005", or 0.12 mm, as compared with the 0.4 mm allowed by the specifications. The total area of the three divergent zones is only 15 percent of the area of the surface, so the effect on the resultant image will be small. The maximum diameter of the circle of confusion, computed geometrically from the largest longitudinal aberrations, is 0.014 mm, as compared with the 0.05 mm of the specifications Furthermore, 85 percent of the light is concentrated in a diffusion disk of an average diameter less than one third the foregoing.

The R's from Table 2 are represented graphically in Figure 3, the scale divisions being in hundredths of an inch, although numbered in thousandths (these being used rather than millimeters since all the measures were more conveniently made in those units). The curves of shape computed from these Rs are given immediately below each curve of R, the units here being millionths of inches. The maximum departure from the mean paraboloid in the lowest curve is 0.0000007", considerably less than a twentieth of a wave.

The Hartmann Test: There remains one further test of the surface, the well-known Hartmann test, which was requested by the purchasers early in the negotiations, the diaphragm being made according to their specifications. The latter contains 60 holes, each about 38 mm in diameter, spaced along twelve radii 30° apart. The holes cover 1S zones of the surface twice, the two sets being 90° apart to determine the astigmatism. The radii of the zones are given in Table I in centimeters, successive zones being 5 on apart except that the distance between No. 1 and No. 2 is 4.5 cm. This diaphragm was placed directly over the aluminized mirror, which rested on the table of the polishing machine and was turned into a vertical position for both visual and photographic tests.

Several precautions were taken to insure reliable results on these tests. The principal difficulty encountered in my earlier tests of the 72" Victoria and the 69" Delaware mirrors had been temperature stratification in the Brashear testing chamber. This difficulty was much less troublesome at Cleveland, owing to the better temperature correction and to the tests being made in an open room instead of the closed 6' square tube at Allegheny. Nevertheless, it was still present, as the images of the zonal apertures on the plates were all elongated in the vertical direction. To overcome as much as possible such temperature difficulties, the mirror was always kept horizontal, except for the few minutes the photograph was being made, so that it must have been at practically constant temperature throughout. Four exposures were made in each set, the mirror being rotated 90° each time, so that the longitudinal aberrations and the astigmatism could be tested not only from the two sets of apertures on each plate but also from the horizontal sets only, on successive plates, in the hope of overcoming stratification effects.

The four plates yielded four determinations of theR's and four of the astigmatism. The average probable errors of the mean values, which, unlike the visual settings, did not increase in the inner zones, was +/- 0.21 mm, which, compared with the visual average of +/- 0.082, makes the photographic probable error over 2.5 times greater than the visual. The values of the photographic R's and of the longitudinal aberrations at the focus are given in the seventh and eighth columns of Table 1. These, reduced to the same scale as those of the visual tests, are shown graphically in the fifth group of Figure 3. Although these show a trend similar to the visual graphs, they are naturally, owing to the higher probable errors, considerably more ragged and are entitled to considerably less weight.

The principal value of the photographic method is its definite test of the presence of astigmatism. The mean differences between the longitudinal aberrations at the principal focus in two azimuths on the mirror 90° apart are given in the last column of Table 1. If not wholly due to accidental errors, as seems likely from those determined above, there is certainly no systematic trend of the signs, the algebraic mean being only +0.02 mm, and it may be safely said that the surface is free from astigmatism.

The Hartmann criterion T, obtained from the formula

where F_o is the focal length, F the longitudinal aberration at the principal focus, taken without regard to sign, and r the radius of any zone, simply gives the weighted mean value of the diameter of the geometrical confusion circle expressed in terms of F_o/100,000, while 2.0626T is its apparent diameter in seconds of arc. The values of T were computed for each of the four visual measures and for the single photographic test, and are given in Table 3. This was done for completeness only, as the value of T obtained from the mean of the 22 visual measures of R at the center of curvature (given in the last line of Table 3) is obviously of much greater weight and is taken as more truly representing the optical qualities of the mirror. The maximum diameter of the diffusion disk was calculated above as 0.014 mm, less than one third the 0.05 mm permitted by the specifications, but is nevertheless nearly four times larger than the average diameter of 0.00S9 mm in the last line Table 3. There is, however, such a small proportion of the total light entering into this expanded disk that, in comparison to the central condensation, it will be quite inappreciable.

It will be of interest to compare the optical qualities of the 82" mirror with those of other large reflecting surfaces which have been similarly tested. For this purpose the criterion T forms the best guide, as the errors or aberrations and the diameter of the geometrical diffusion disks are directly proportional to T. The following list comprises all those known to me, as the Mount Wilson 60" and 100" mirrors have had, to the best my knowledge, no measures of their aberrations published.

72-inch Victoria mirror¹ T = 0.12

69-inch Delaware mirror² T = 1.4

74-inch Toronto mirror³ T = .20

82-inch Texas mirror T = 0.050

Not only has the Texas mirror much smaller measured errors than any other, but such a relatively large proportion of the figuring was performed with large tools that the surface must be remarkably smooth and regular. This was, indeed, amply demonstrated by the Foucault and Ronchi tests, and it can be safely stated that the quality of the 82" mirror of the McDonald Observatory is unequaled by any mirror previously made and tested.

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