Abstract

Quantitative methods for examining and describing the surfaces of off-axis parabolic mirrors are given, together with practical suggestions for the most effective use of such mirrors. Included are tests with, and without, an optical flat. In each case the theory and experimental procedure are illustrated by application to a particular mirror. The quality of a mirror is given in terms of the minimum slit width that can be profitably used with it.

© 1946 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Amateur Telescope Making and Amateur Telescope Making Advanced, Sci. Am. (1937).
  2. John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., New York, 1945).
  3. E. Gaviola, J. Opt. Soc. Am. 26, 163 (1936).
    [Crossref]
  4. Two definitions: a. The principal radius: The distance from the mirror axis to the remote edge of the mirror. This radius passes through the geometric center of the mirror. b. f-number of an off-axis mirror: The f-number of the smallest symmetrical mirror from which the off-axis mirror can be cut. One might call the usual ratio, aperture diameter/focal length, the effective f-number of the mirror.

1937 (1)

Amateur Telescope Making and Amateur Telescope Making Advanced, Sci. Am. (1937).

1936 (1)

Gaviola, E.

Strong, John

John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., New York, 1945).

J. Opt. Soc. Am. (1)

Sci. Am. (1)

Amateur Telescope Making and Amateur Telescope Making Advanced, Sci. Am. (1937).

Other (2)

John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc., New York, 1945).

Two definitions: a. The principal radius: The distance from the mirror axis to the remote edge of the mirror. This radius passes through the geometric center of the mirror. b. f-number of an off-axis mirror: The f-number of the smallest symmetrical mirror from which the off-axis mirror can be cut. One might call the usual ratio, aperture diameter/focal length, the effective f-number of the mirror.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Ray diagrams to show the origin of parallax. A and B are views from above and C is an end view of A. In A the source, S, is displaced from the axis by the amount Δ Y; its image, I, is formed Δ Y on the opposite side of the axis. The points of reflection on the mirror surface are separated by 2Δ Y, the same as the separation of S and I. In B the reflected ray returns on the path of the incident ray and there is no parallax. The use of a pellicle, P, makes it possible to place the source at S.

Fig. 2
Fig. 2

An arrangement for avoiding the effects of parallax when testing for defects which are symmetrical to the mirror axis. A, as seen from the side; B, as seen from above; and C, as seen from the position of the tester. This is the most sensitive arrangement for detecting mirror defects.

Fig. 3
Fig. 3

An arrangement for minimizing the effect of defects symmetrical to the axis when the mirror is being used in an optical system employing a slit source. A, as seen from the side; B, as seen from above; and C, as seen from the end.

Fig. 4
Fig. 4

A graph showing the rate at which a mirror surface darkened as a knife-edge was moved through the image. The vertical scale is the percentage of the surface illuminated, the horizontal scale the motion of the knife-edge, left to right. Curve 2 is for the arrangement of Fig. 2; Curve 3 for the arrangement of Fig. 3.

Fig. 5
Fig. 5

In A is shown the relative positions of mirror, light source, and image for testing without a flat. The source and its image are approximately at the center of curvature of the mirror. In B is shown the manner in which rays pass through the image. Y0 is the point on the mirror from which the ray has been reflected; Xe of Eq. (6) is measured along the Y02/R scale. The line KE indicates the path followed by the knife-edge in obtaining the shadow pattern of Fig. 8. All dimensions are in inches.

Fig. 6
Fig. 6

Graph showing the position of the knife-edge to obtain last darkening at point Y0 on the mirror surface. The two experimental points at Y0 equal to 1.5 inches and 5.2 inches were used to locate the zero point on the parallel motion of the knife-edge. Both scales are in inches.

Fig. 7
Fig. 7

Two graphs showing the manner in which the position of last darkening is located from the experimental data. The two values are indicated in Fig. 6.

Fig. 8
Fig. 8

The curve A is the shadow pattern which should result when the knife-edge is moved through the image as shown in Fig. 5. The double curve is drawn to fit the experimental points when they deviate from the theoretical curve. Curve B is the shadow pattern for the spherical mirror before it was parabolized. In C is shown the shadow pattern obtained when the defect between Y0 equals 3 and 4 inches is examined with a flat, arrangement Fig. 2.

Fig. 11
Fig. 11

In each figure the circle represents the 6-inch mirror with an arc defect through the geometric center, as in Figs. 8 and 9. In A, arrangement of Fig. 2, the slit is perpendicular to the principal radius and on the axis which is 1 2 inch outside the mirror edge. In B, arrangement of Fig. 3, the ends of the defect would at worse broaden the image by 0.05 mm or a mean of about 0.02 mm. In C the axis is outside the mirror a distance equal to the radius. Assuming a defect of the same magnitude as that in A and B the broadening in C will be reduced to a mean of about 0.015 mm.

Fig. 9
Fig. 9

Shadow patterns when the knife-edge is placed for last darkening at Y0 equal to zero and to 5.7 inches. The smooth curves are the theoretical patterns, and the vertical lines the experimental points.

Fig. 10
Fig. 10

The relative thickness of metal, T, on a parabolized mirror as a function of the distance Y0 along the principal radius. The horizontal base line represents the original spherical surface, the solid curve the theoretically correct deposit, and the broken curve the actual thickness over the defective area of Figs. 8 and 9.

Fig. 12
Fig. 12

A shows a typical “doughnut” shadow pattern on a symmetrical on-axis parabolic mirror. The smaller circle represents a small off-axis mirror cut from the larger one. B is a graph showing completed parabolization for the 6-inch mirror of Fig. 8. The lower curve is for half-completion. Both scales of B are in inches.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

X = Y 2 / 2 R ,
d Y / d X = Y 0 / R .
Y Y 0 = ( Y 0 / R ) [ X ( Y 0 2 / 2 R ) ] ,
X = R + ( Y 0 2 / 2 R ) .
Δ X = Y 2 / R ,
X e = 3 Y 0 2 / R
Y e = ( Y 0 / R ) [ X e ( Y 0 2 / R ) ] .
Y e = 2 Y 0 3 / R 2 .
Y = ( Y 0 / R ) [ X e ( Y 0 2 / R ) ] .
T = Y 0 2 ( Y 2 Y 0 2 ) / 8 R 3 .