Abstract

A variable shear lateral shearing interferometer consisting of two holographically produced crossed diffraction gratings is used to test nonrotationally symmetric wavefronts having aberrations greater than 100 wavelengths and slope variations of more than 400 wavelengths/diameter. Comparisons are made with results of Twyman-Green interferometric tests for wavefront aberrations of up to thirty wavelengths. The results indicate that small wavefront aberrations can be measured as accurately with the lateral-shear interferometer as with the Twyman-Green interferometer and that aberrations that cannot be measured at all with a Twyman-Green interferometer can be measured to about 1% accuracy or better.

© 1975 Optical Society of America

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References

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  1. M. P. Rimmer, Appl. Opt. 13, 623 (1974).
    [CrossRef] [PubMed]
  2. J. B. Saunders, R. J. Bruening, Astron. J. 73, 415 (1968).
    [CrossRef]
  3. D. Nyyssonen, J. M. Jerke, Appl. Opt. 12, 2061 (1973).
    [CrossRef] [PubMed]
  4. V. Ronchi, Appl. Opt. 3, 437 (1964).
    [CrossRef]
  5. A. Cornejo, D. Malacara, Appl. Opt. 9, 1897 (1970).
    [PubMed]
  6. M. V. R. K. Murty, A. Cornejo, J. Opt. Soc. Am. 63, 1312 (1973).
  7. J. C. Wyant, Appl. Opt. 12, 2057 (1973).
    [CrossRef] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 464.
  9. D. Dutton et al., Appl. Opt. 7, 125 (1968).
    [CrossRef] [PubMed]
  10. H. Sumita, Jap. J. Appl. Phys. 8, 1027 (1969).
    [CrossRef]

1974 (1)

1973 (3)

1970 (1)

1969 (1)

H. Sumita, Jap. J. Appl. Phys. 8, 1027 (1969).
[CrossRef]

1968 (2)

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

D. Dutton et al., Appl. Opt. 7, 125 (1968).
[CrossRef] [PubMed]

1964 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 464.

Bruening, R. J.

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

Cornejo, A.

M. V. R. K. Murty, A. Cornejo, J. Opt. Soc. Am. 63, 1312 (1973).

A. Cornejo, D. Malacara, Appl. Opt. 9, 1897 (1970).
[PubMed]

Dutton, D.

Jerke, J. M.

Malacara, D.

Murty, M. V. R. K.

M. V. R. K. Murty, A. Cornejo, J. Opt. Soc. Am. 63, 1312 (1973).

Nyyssonen, D.

Rimmer, M. P.

Ronchi, V.

Saunders, J. B.

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

Sumita, H.

H. Sumita, Jap. J. Appl. Phys. 8, 1027 (1969).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 464.

Wyant, J. C.

Appl. Opt. (6)

Astron. J. (1)

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

J. Opt. Soc. Am. (1)

M. V. R. K. Murty, A. Cornejo, J. Opt. Soc. Am. 63, 1312 (1973).

Jap. J. Appl. Phys. (1)

H. Sumita, Jap. J. Appl. Phys. 8, 1027 (1969).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 464.

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Figures (14)

Fig. 1
Fig. 1

LSI—LUPI interferometer.

Fig. 2
Fig. 2

Diffraction orders produced by two crossed gratings.

Fig. 3
Fig. 3

Introduction of tilt between sheared wavefronts.

Fig. 4
Fig. 4

LSI attachment to LUPI.

Fig. 5
Fig. 5

LUPI and LSI.

Fig. 6
Fig. 6

Experimental setup used to obtain nonsymmetric aspheric wavefront.

Fig. 7
Fig. 7

Aberration vs plate tilt.

Fig. 8
Fig. 8

LUPI interferograms: (a) plate tilt = 0°; (b) plate tilt = 15°.

Fig. 9
Fig. 9

LSI interferograms: (a) plate tilt = 0°, shear = 0.36; (b) plate tilt = 15°, shear = 0.63.

Fig. 10
Fig. 10

LSI interferograms for plate tilt of 20°: (a) shear = 0.09; (b) shear = 0.30.

Fig. 11
Fig. 11

LSI interferograms: plate tilt = 30°, shear = 0.09.

Fig. 12
Fig. 12

Contour plots for plate tilt of 0° (contour intervals = 0.1λ): (a) raytrace; (b) LUPI; (c) LSI.

Fig. 13
Fig. 13

Contour plots for plate tilt of 5° (contour intervals = 5λ): (a) raytrace; (b) LUPI; (c) LSI.

Fig. 14
Fig. 14

Estimated error vs aberration.

Tables (1)

Tables Icon

Table I RMS and Peak-to-Peak Values

Equations (16)

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percentage shear = 4 f n o tan θ sin ( α / 2 ) .
Δ = Δ 2 Δ 1 = x 2 tan θ ( sin α 2 j ˆ + cos α 2 k ˆ ) x 1 tan θ ( sin α 2 j ˆ + cos α 2 k ˆ ) = tan θ [ ( 2 x 1 + L ) sin α 2 j ˆ + L cos α 2 k ˆ ] ,
V = ( a α c ) T G ( a α c ) + ( b β c ) T G ( b β c ) .
c = Q 1 d ,
Q = α T G α + β T G β ,
d = α T G a + β T G b .
W ( r , θ ) = n = 0 k m = 0 n A n m R n n 2 m { sin cos } ( n 2 m ) θ ,
R n n 2 m = s = 0 m ( 1 ) s ( n s ) ! s ! ( m s ) ! ( n m s ) ! r n 2 s .
V = n = 0 k m = 0 n n m 2 ( n + 1 ) A n m 2 ,
W ( x , y ) = n = 0 k m = 0 n B n m x m y n m .
R n n 2 m { sin cos } ( n 2 m ) θ = i = 0 q j = 0 m k = 0 m j ( 1 ) i + j ( | 2 m n | 2 i + p ) ( m j k ) · ( n i ) ! j ! ( m j ) ! ( n m j ) ! x n 2 ( i + j + k ) p y 2 ( i + k ) + p ,
q = ( 2 m n ) / 2 for the cos terms and n even , q = [ ( n 2 m ) / 2 ] 1 for the sin terms and n even , q = ( 2 m n 1 ) / 2 for the cos terms and n odd , q = ( n 2 m 1 ) / 2 for the sin terms and n odd .
( i j ) = i ! / [ ( i j ) ! j ! ] .
B = H A ,
C n m = j = 1 k n ( j + m j ) S j B j + n , j + m , D n m = j = 1 k n ( j + n m j ) T j B j + n , m ,
α = H k 1 1 γ H k , β = H k 1 1 δ H k ,

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