Abstract

A simple step-by-step method is given for deriving the shapes of wavefronts from data obtained with a wavefront shearing interferometer. No mathematics, other than arithmetic, is used. The result is the accurate deviation of the wavefront from a reference sphere that coincides with it at three chosen reference points. The method is intended primarily for the use of opticians in optical workshops, but is also quite practical for the final testing of optics for performance rating. A method is given by which an optician can evaluate an optical surface by comparing the interferogram produced by it and a known prism interferometer, with a drawing of the desired interferogram. This procedure is analogous to using test plates for visual inspection of optical surfaces.

© 1970 Optical Society of America

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References

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  1. J. B. Saunders, J. Res. Nat. Bur. Stand. 68C, 155 (1964).
    [CrossRef]
  2. J. B. Saunders, Appl. Opt. 6, 1581 (1967).
    [CrossRef] [PubMed]
  3. J. B. Saunders, J. Res. Nat. Bur. Stand. 65B, 239 (1961).
    [CrossRef]
  4. J. B. Saunders, R. J. Bruening, Astron. J. 73, 415 (1968).
    [CrossRef]
  5. Reference 1, Appendix A.
  6. W. J. Bates, Proc. Phys. Soc. 59, 946 (1967).

1968

J. B. Saunders, R. J. Bruening, Astron. J. 73, 415 (1968).
[CrossRef]

1967

W. J. Bates, Proc. Phys. Soc. 59, 946 (1967).

J. B. Saunders, Appl. Opt. 6, 1581 (1967).
[CrossRef] [PubMed]

1964

J. B. Saunders, J. Res. Nat. Bur. Stand. 68C, 155 (1964).
[CrossRef]

1961

J. B. Saunders, J. Res. Nat. Bur. Stand. 65B, 239 (1961).
[CrossRef]

Bates, W. J.

W. J. Bates, Proc. Phys. Soc. 59, 946 (1967).

Bruening, R. J.

J. B. Saunders, R. J. Bruening, Astron. J. 73, 415 (1968).
[CrossRef]

Saunders, J. B.

J. B. Saunders, R. J. Bruening, Astron. J. 73, 415 (1968).
[CrossRef]

J. B. Saunders, Appl. Opt. 6, 1581 (1967).
[CrossRef] [PubMed]

J. B. Saunders, J. Res. Nat. Bur. Stand. 68C, 155 (1964).
[CrossRef]

J. B. Saunders, J. Res. Nat. Bur. Stand. 65B, 239 (1961).
[CrossRef]

Appl. Opt.

Astron. J.

J. B. Saunders, R. J. Bruening, Astron. J. 73, 415 (1968).
[CrossRef]

J. Res. Nat. Bur. Stand.

J. B. Saunders, J. Res. Nat. Bur. Stand. 65B, 239 (1961).
[CrossRef]

J. B. Saunders, J. Res. Nat. Bur. Stand. 68C, 155 (1964).
[CrossRef]

Proc. Phys. Soc.

W. J. Bates, Proc. Phys. Soc. 59, 946 (1967).

Other

Reference 1, Appendix A.

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Figures (12)

Fig. 1
Fig. 1

Prism interferometers. (a) The angle α1 may be equal to α2. When α1 and α2 are equal (as when the two component prisms are cut from a common prism) the shear is obtained by a small rotation of one component prism relative to the other. The direction of shear is then perpendicular to the plane of the figure. (b) A beam dividing cube, cemented to the entrance face of the interferometer, permits locating the image of the source on-axis for the testing of concave mirrors, as shown in Figs. 2(b) and (d). The angular size of the acceptable cone of light is increased by using a beam divider cube that is larger than the interferometer, as shown in Fig. 1(d). (c) Spherical aberration is practically eliminated in the interferometer by cementing a plano-convex lens to its entrance face. Ideally, the center of curvature of the entrance face should be located at the center of the back (reflecting) face of the interferometer where is also located the zero order of interference. (d) Two prism interferometers cemented to one beam divider for simultaneous photographing of the wavefront, sheared in two directions, for recording rapidly changing effects such as are caused by temperature and pressure changes in fluids.

Fig. 2
Fig. 2

Optics for several types of tests. These are: (a) for testing camera lenses for objects at finite distances; (b) for testing lenses with one conjugate at infinity; (c) for testing microscope objectives; and (d) and (e) for testing concave mirrors with the source located on and slightly off axis, respectively.

Fig. 3
Fig. 3

Reference Points. (a)–(c) do not comply and (d)–(f) does comply with the definition of a family of points. (a) The direction of the line of points is not parallel to the direction of shear as required for this test. (b) The direction of the line is correct but the spacing is incorrect (not equal to the lateral shear). (c) One point is out of line. (d) The spacing is correct but the position of the family is not favorably chosen for this aperture. There are only five points located at three radial distances. (e) This position of the family is better than that for Fig. 1(d) since it provides an additional point and more zones are represented. (f) This position of the family is better than that for Fig. 1(e) since it provides the same number of points and each point represents a different zone of the wavefront.

Fig. 4
Fig. 4

Interferograms produced by prisms of different shear angles.

Fig. 5
Fig. 5

Changes in an interferogram caused by changing the distance from the objective to the prism.

Fig. 6
Fig. 6

An interferogram, showing reference points produced by equally spaced beads on a straight wire.

Fig. 7
Fig. 7

A graphical representation of the interferogram of Fig. 6.

Fig. 8
Fig. 8

Computed position of the wavefront relative to the lens, reference sphere, and reference points.

Fig. 9
Fig. 9

Photograph of interference fringes produced by a wavefront shearing interferometer and a parabolic mirror.

Fig. 10
Fig. 10

Family of curves representing the interferogram shown in Fig. 9.

Fig. 11
Fig. 11

Polishing machine used to polish off-axis parabolic mirrors.

Fig. 12
Fig. 12

Optical arrangement for testing off-axis parabolas without removal from the polishing machine.

Tables (2)

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Table II Typical Values (see Fig. 7).

Equations (2)

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P = P 1 X / X 1 + e 2 Φ 4 R X ( X 2 + Y 2 X 1 2 ) / λ ,
P = 0.045 X ( X 2 + Y 2 25 ) .

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