Abstract

A method of measuring the shape of high numerical aperture (NA <0.95), convex or concave, aspheric surfaces is described. The aspheric slope may be as large as 1200 waves/rad. The method is applied in two steps. First, a standard measurement is performed to obtain a reference surface. Second, the reproducibility of the fabrication of aspheric surfaces is tested by means of a holographic comparison method. The measuring error is smaller than 0.1 μm.

© 1978 Optical Society of America

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References

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  1. J. C. Wyant, V. P. Bennett, Appl. Opt. 11, 2833 (1972).
    [CrossRef] [PubMed]
  2. M. P. Rimmer, J. C. Wyant, Appl. Opt. 14, 142 (1975).
    [PubMed]
  3. P. L. Ruben, Appl. Opt. 15, 3080 (1976).
    [CrossRef] [PubMed]
  4. K. Snow, R. Vandewarker, Appl. Opt. 9, 822 (1970).
    [CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

The geometry of the asphere (solid line) given in the x′y′ frame and represented in polar coordinates (R,α) relative to the laboratory frame.

Fig. 2
Fig. 2

The air bearing displacement transducer scanning the rotating asphere.

Fig. 3
Fig. 3

The holographic interferometer for testing the reproducibility of the fabrication of aspheres; M1,2 are mirrors, B is the beam splitter, l1l5 are lenses, P is the photographic plate, S is the observing screen.

Fig. 4
Fig. 4

(a) The unique relation between different locations on the asphere and the corresponding locations on the hologram. (b) The phase shift of the aspheric wavefront resulting from a small axial displacement (1 μ) of the asphere. (c) The interference pattern resulting from the comparison test; the deviation from straight lines indicates deviation from the reference asphere.

Equations (10)

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f ( x , y ) = 0 asphere with respect to C .
f ( x u , y υ ) = 0 asphere with respect to O ,
x = R cos ( α ) ,
y = R sin ( α ) ,
R = R ref + Δ R ( α ; u , υ ) .
Δ ( Δ α ; u , υ ) Δ max ( Δ α ; u , υ ) Δ min ( Δ α ; u , υ ) ,
Δ max ( Δ α ; u , υ ) max [ Δ R ( α i + Δ α ; u , υ ) Δ R exp ( α i ) ]
Δ min ( Δ α ; u , υ ) min [ Δ R ( α i + Δ α ; u , υ ) Δ R exp ( α i ) ] .
δ ( α i ) = Δ R ( α i + Δ α f ; u f , υ f ) Δ R exp ( α i ) Δ min ( Δ α f ; u f , υ f )
Δ R ( α ; u , υ ) [ u cos ( α ) + υ sin ( α ) ] + n a n { [ R ref + Δ R ( α ; u , υ ) ] sin ( α ) υ } 2 n ,

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