Abstract

A new white light shear interferometer based on the use of superposition fringes is described (superposition fringe shear interferometer, SFSI). The SFSI enables one to test for plane waves; chromatic as well as all other aberrations can be measured. Test examples and the secondary spectrum of a microscope objective are given. By spectroscopically dispersing a slit section of the shear interferogram the chromatic aberrations can be displayed. The mean phase difference between the two interfering waves can be adjusted by tilting one of the two interferometer etalons. The whole setup is mechanically stable. Shear interferograms can be obtained by inserting an interference filter in the ray path.

© 1980 Optical Society of America

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References

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  1. V. Ronchi, Appl. Opt. 3, 437 (1964), and papers cited therein.
    [CrossRef]
  2. W. J. Bates, Proc. Soc. London 59, 940 (1947); R. L. Drew, Proc. Phys. Soc. London Sect. B 64, 1005 (1951).
    [CrossRef]
  3. Shearing interferometers have a common problem: the wave front to be tested is not only influenced by the lens to be tested but also by all the optical systems in the ray path in front of the shearing interferometer.
  4. J. D. Briers, Opt. Laser Technol. 4, 28 (1972); O. Bryngdahl, Prog. Opt. 4, 37 (1965).
    [CrossRef]
  5. E. Waetzmann, Ann. Phys. 39, 1042 (1912); M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
    [CrossRef]
  6. J. Schwider, Appl. Opt. 18, 2364 (1979).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).
  8. D. Malacara, A. Cornejo, Appl. Opt. 10, 679 (1971).
    [CrossRef]
  9. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 249.
  10. From Eq. (12) it follows that the sensitivity of the SFSI method concerning chromatic aberrations is proportional to the ratio shear/(back focus length)2 meaning that microscope objectives show the biggest effect.
  11. G. A. Boutry, Instrumental Optics (Hilger & Watts, London, 1961), p. 138.
  12. M. Herzberger, Opt. Acta 6, 197 (1959).
    [CrossRef]
  13. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]

1979

1974

1972

J. D. Briers, Opt. Laser Technol. 4, 28 (1972); O. Bryngdahl, Prog. Opt. 4, 37 (1965).
[CrossRef]

1971

1964

1959

M. Herzberger, Opt. Acta 6, 197 (1959).
[CrossRef]

1947

W. J. Bates, Proc. Soc. London 59, 940 (1947); R. L. Drew, Proc. Phys. Soc. London Sect. B 64, 1005 (1951).
[CrossRef]

1912

E. Waetzmann, Ann. Phys. 39, 1042 (1912); M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
[CrossRef]

Bates, W. J.

W. J. Bates, Proc. Soc. London 59, 940 (1947); R. L. Drew, Proc. Phys. Soc. London Sect. B 64, 1005 (1951).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Boutry, G. A.

G. A. Boutry, Instrumental Optics (Hilger & Watts, London, 1961), p. 138.

Brangaccio, D. J.

Briers, J. D.

J. D. Briers, Opt. Laser Technol. 4, 28 (1972); O. Bryngdahl, Prog. Opt. 4, 37 (1965).
[CrossRef]

Bruning, J. H.

Cornejo, A.

Gallagher, J. E.

Herriott, D. R.

Herzberger, M.

M. Herzberger, Opt. Acta 6, 197 (1959).
[CrossRef]

Malacara, D.

Ronchi, V.

Rosenfeld, D. P.

Schwider, J.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 249.

Waetzmann, E.

E. Waetzmann, Ann. Phys. 39, 1042 (1912); M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
[CrossRef]

White, A. D.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Ann. Phys.

E. Waetzmann, Ann. Phys. 39, 1042 (1912); M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
[CrossRef]

Appl. Opt.

Opt. Acta

M. Herzberger, Opt. Acta 6, 197 (1959).
[CrossRef]

Opt. Laser Technol.

J. D. Briers, Opt. Laser Technol. 4, 28 (1972); O. Bryngdahl, Prog. Opt. 4, 37 (1965).
[CrossRef]

Proc. Soc. London

W. J. Bates, Proc. Soc. London 59, 940 (1947); R. L. Drew, Proc. Phys. Soc. London Sect. B 64, 1005 (1951).
[CrossRef]

Other

Shearing interferometers have a common problem: the wave front to be tested is not only influenced by the lens to be tested but also by all the optical systems in the ray path in front of the shearing interferometer.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 249.

From Eq. (12) it follows that the sensitivity of the SFSI method concerning chromatic aberrations is proportional to the ratio shear/(back focus length)2 meaning that microscope objectives show the biggest effect.

G. A. Boutry, Instrumental Optics (Hilger & Watts, London, 1961), p. 138.

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Figures (14)

Fig. 1
Fig. 1

Schema of the SFSI for microscope objectives in a double pass arrangement: WL, white light source; S, slit; C, collimator (f = 500 mm); F.P., Fabry-Perot interferometer; SP, shear plate; MO, microscope objective; SM, spherical mirror; SC, spectroscope.

Fig. 2
Fig. 2

Spectrally dispersed section of a SFSI interferogram: on the left, interference pattern for an achromat; on the right, interferogram of an ideal plane wave in white light. Note the small fringe displacements due to λ-dependent phase jumps of the dielectric F.P. coatings.

Fig. 3
Fig. 3

Paraxial representation of the test situation: zλ, intercept distance for wavelength λ; za, adjusted intercept distance, distance of the center of curvature of the spherical mirror from the principal plane H; z0, achromatic intercept distance; ρ, radius of curvature of SM; r, radius of curvature of the wave front leaving the lens to be tested after reflection at SM.

Fig. 4
Fig. 4

SFSI spectrum of an achromat 25×/0.50; approximate fringe pattern Δz0 = 0.

Fig. 5
Fig. 5

SFSI spectrum of an achromat 25×/0.50; approximate fringe pattern Δz0 > 0.

Fig. 6
Fig. 6

SFSI spectrum of an achromat 25×/0.50; approximate fringe pattern Δz0 < 0.

Fig. 7
Fig. 7

Comparison of an intrafocal adjustment with an approximation of the SSP by Eq. (17): on the left, interferogram; on the right, computer plot.

Fig. 8
Fig. 8

SSP for an achromat 25×/0.50.

Fig. 9
Fig. 9

Comparison of actual spectra of a planachromat 25×/0.50 for different adjustment with computed spectra; left above, Δz0 = 0; 2t′ = 0; right above, Δz0 = 0; 2t′ = 20 μm; left middle, Δz0 = −4 μm; 2t′ = 0; right middle, Δz0 = −4 μm; 2t′ = 13.4 μm; left below, Δz0 = 13 μm; 2t′ = 0; right below, Δz0 = +13 μm; 2t′ = 10 μm.

Fig. 10
Fig. 10

SFSI spectrogram for the achromat compared with shear interferograms for different wavelengths.

Fig. 11
Fig. 11

Influence of spectral bandwidth on the contrast in the shear interferograms at λ = 436 nm: on the left, Δλ = 20 nm; on the right, Δλ = 2 nm.

Fig. 12
Fig. 12

SFSI spectrogram of a planapochromat 16×/0.20, ψ0 ≠ 0.

Fig. 13
Fig. 13

SFSI spectrogram of a planachromat 16×/0.20, ψ0 = 0, intrafocal adjustment (left), extrafocal adjustment (right).

Fig. 14
Fig. 14

Shear interferograms of a planachromat 16×/0.20: on the left, extrafocal; on the right, intrafocal, λ = 568 nm.

Equations (26)

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i = i 0 ( 1 + R N V cos Δ ¯ ) ,
P D = 2 t n 2 sin 2 α ,
P D F . P . P D shear 0.
2 t F . P . n F . P . N 2 t shear n shear 2 sin 2 α = 0.
t F . P . t shear cos α = 0 ,
s = t shear sin 2 α n shear 2 sin 2 α ,
s = 2 t shear sin α .
s = 2 t F . P . tan α .
W ( x , y ) = const exp [ i k 2 r ( x 2 + y 2 ) ] ,
Δ ψ = k 2 r [ ( x + s ) 2 + y 2 x 2 y 2 ] = k 2 r [ 2 x s + s 2 ] .
x = x 1 2 s , Δ ψ ( x ) = k r x s .
Δ ψ ( x ) = k r x s + ψ 0 .
f 2 = z z ,
z λ 2 = 2 ( z a z λ ) ( r + z λ ) ,
z a = z 0 + Δ z 0 .
1 r 2 z 0 2 ( SSP Δ z 0 ) .
Δ ψ ( x ) = 2 k x s z 0 2 ( SSP Δ z 0 ) + ψ 0 .
x ( λ ) = [ m ψ 0 ( λ ) 2 π ] z 0 2 2 s λ SSP Δ z 0 ;
z λ z 0 = SSP = a ( λ λ F ) ( λ λ c ) ,
x = [ m ψ 0 ( λ ) 2 π ] z 0 2 2 s λ a ( λ λ F ) ( λ λ c ) Δ z 0 .
Δ ψ ( x ) k r x s + 2 k s W ( x ) x ,
x = ( m 2 s λ W x ) z 0 2 2 s λ SSP Δ z 0 .
ψ 0 ( λ ) 2 π = 2 t λ = 2 λ ( t F . P . t shear cos α ) ,
ψ 0 ( λ ) 2 π = 2 λ t F . P . ( 1 cos α cos α 0 ) .
x = [ m 2 t F . P . λ ( 1 cos α cos α 0 ) ] z 0 2 2 s λ SSP Δ z 0 .
SSP = a 1 + a 2 λ + a 3 λ 2 + a 4 1 λ 2 λ 0 2 ,

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