Abstract

We describe a modification of the wedge-plate shear interferometer for collimation testing. The surface of the wedge plate is coated to increase the reflectivity such that multiple-beam interference takes place resulting in sharp fringes. In addition to sharpening the fringes also tend to split when the test beam is noncollimated. This splitting has been used as a test criterion for collimation testing. Experimental results are presented.

© 1995 Optical Society of America

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References

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  1. M. V. R. K. Murty, “The use of a single plane parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964).
    [Crossref]
  2. R. S. Sirohi, M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
    [Crossref] [PubMed]
  3. M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
    [Crossref]
  4. K. V. Sriram, P. Senthilkumaran, M. P. Kothiyal, R. S. Sirohi, “Double wedge plate interferometer for collimation testing: new configurations,” Appl. Opt. 32, 4199–4203 (1993).
    [Crossref] [PubMed]
  5. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
    [Crossref]
  6. G. Li, M. Zhao, J. Zhang, “Improved wedge-plate shearing interferometric technique for a collimation test,” Appl. Opt. 31, 4363–4364 (1992).
    [Crossref]
  7. D-Y. Xu, K. J. Rosenbruch, “Rotatable single wedge plate shearing interference technique for collimation testing,” Opt. Eng. 30, 391–396 (1991).
    [Crossref]
  8. R. S. Sirohi, T. Eiju, K. Matsuda, T. H. Barnes, “Multiple beam shear interferometry for optical testing,” Appl. Opt. (to be published).

1993 (2)

1992 (1)

1991 (1)

D-Y. Xu, K. J. Rosenbruch, “Rotatable single wedge plate shearing interference technique for collimation testing,” Opt. Eng. 30, 391–396 (1991).
[Crossref]

1988 (1)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[Crossref]

1987 (1)

1964 (1)

Barnes, T. H.

R. S. Sirohi, T. Eiju, K. Matsuda, T. H. Barnes, “Multiple beam shear interferometry for optical testing,” Appl. Opt. (to be published).

Eiju, T.

R. S. Sirohi, T. Eiju, K. Matsuda, T. H. Barnes, “Multiple beam shear interferometry for optical testing,” Appl. Opt. (to be published).

Kothiyal, M. P.

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[Crossref]

K. V. Sriram, P. Senthilkumaran, M. P. Kothiyal, R. S. Sirohi, “Double wedge plate interferometer for collimation testing: new configurations,” Appl. Opt. 32, 4199–4203 (1993).
[Crossref] [PubMed]

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[Crossref]

R. S. Sirohi, M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
[Crossref] [PubMed]

Li, G.

Matsuda, K.

R. S. Sirohi, T. Eiju, K. Matsuda, T. H. Barnes, “Multiple beam shear interferometry for optical testing,” Appl. Opt. (to be published).

Murty, M. V. R. K.

Rosenbruch, K. J.

D-Y. Xu, K. J. Rosenbruch, “Rotatable single wedge plate shearing interference technique for collimation testing,” Opt. Eng. 30, 391–396 (1991).
[Crossref]

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[Crossref]

Senthilkumaran, P.

Sirohi, R. S.

K. V. Sriram, P. Senthilkumaran, M. P. Kothiyal, R. S. Sirohi, “Double wedge plate interferometer for collimation testing: new configurations,” Appl. Opt. 32, 4199–4203 (1993).
[Crossref] [PubMed]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[Crossref]

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[Crossref]

R. S. Sirohi, M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
[Crossref] [PubMed]

R. S. Sirohi, T. Eiju, K. Matsuda, T. H. Barnes, “Multiple beam shear interferometry for optical testing,” Appl. Opt. (to be published).

Sriram, K. V.

Xu, D-Y.

D-Y. Xu, K. J. Rosenbruch, “Rotatable single wedge plate shearing interference technique for collimation testing,” Opt. Eng. 30, 391–396 (1991).
[Crossref]

Zhang, J.

Zhao, M.

Appl. Opt. (4)

Opt. Eng. (2)

D-Y. Xu, K. J. Rosenbruch, “Rotatable single wedge plate shearing interference technique for collimation testing,” Opt. Eng. 30, 391–396 (1991).
[Crossref]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[Crossref]

Opt. Laser Technol. (1)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[Crossref]

Other (1)

R. S. Sirohi, T. Eiju, K. Matsuda, T. H. Barnes, “Multiple beam shear interferometry for optical testing,” Appl. Opt. (to be published).

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Figures (6)

Fig. 1
Fig. 1

Generation of multiple beams in a coated wedge plate.

Fig. 2
Fig. 2

Intensity versus δ plots in reflection for Δδ = 0° and 7°.

Fig. 3
Fig. 3

Intensity versus δ plots in transmission for Δδ = 0° and 7°.

Fig. 4
Fig. 4

Collimation testing arrangement with a multiple-beam wedge-plate interferometer.

Fig. 5
Fig. 5

Interferograms in reflection for the point source located (a) inside, (b) at, and (c) outside the focus positions of the collimating lens: Δf = 500 μm and i = 25°.

Fig. 6
Fig. 6

Interferograms in transmission for the point source located (a) inside, (b) at, and (c) outside the focus positions of the collimating lens: Δf = 500 μm and i = 25°.

Tables (1)

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Table 1 Setting Sensitivity Measurements in Csollimation Testing

Equations (27)

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Δ W = W ( x , y ) - W ( x - Δ x , y ) = m λ ,
Δ W = W x Δ x = m λ .
W ( x , y ) = D ( x 2 + y 2 ) ,
D = Δ f 2 f 2 .
Δ W = 2 D x Δ x = m λ .
2 D x Δ x + y β = m λ ,
tan θ = - 2 D Δ x β .
a i exp ( j δ i ) ,
a 1 = r 1
a i = a t 1 t 1 r 1 ( i - 2 ) r 2 ( i - 1 )             for 2 i N
a i = a t 1 t 2 ( r 1 r 2 ) ( i - 1 ) ,
δ i = ( i - 1 ) δ 0 + 2 π λ W [ x - ( i - 1 ) Δ x , y ] ,
δ 0 = 2 π λ ( 2 μ t cot θ r + y β ) ,
2 π λ W [ x - ( i - 1 ) Δ x , y ] = δ w - ( i - 1 ) Δ x δ w ,
δ W = 2 π λ W ( x , y ) .
I R ( δ ) = a 2 ( 1 - R 1 R 2 ) 2 + 4 R 1 R 2 sin 2 ( δ / 2 ) × [ R 1 + R 2 ( R 1 + T 1 ) 2 + T 1 2 R 2 ( R 1 R 2 ) N - 1 - 2 R 1 R 2 ( R 1 + T 1 ) cos δ - 2 T 1 R 2 ( R 1 + T 1 ) × ( R 1 R 2 ) ( N - 1 ) / 2 cos ( N - 1 ) δ + 2 T 1 ( R 1 R 2 ) N / 2 cos N δ ] ,
I T ( δ ) = a 2 T 1 T 2 [ 1 + R 1 R 2 - 2 R 1 R 2 cos ( N δ ) ] 1 + R 1 R 2 - 2 R 1 R 2 cos ( δ ) ,
δ = δ 0 - Δ x δ W ( x , y ) .
2 π λ W [ x - ( i - 1 ) Δ x , y ] = δ W - ( i - 1 ) Δ x δ W + [ ( i - 1 ) Δ x ] 2 2 ! δ W ,
δ i = ( i - 1 ) δ 0 + δ W - ( i - 1 ) Δ x δ W + [ ( i - 1 ) Δ x ] 2 2 ! δ W = ( i - 1 ) δ + δ W + ( i - 1 ) 2 Δ x 2 2 δ W , δ i = δ W + ( i - 1 ) δ + ( i - 1 ) 2 Δ δ ,
Δ δ = ½ ( Δ x ) 2 δ W ,
I R ( δ ) = a 2 R 1 ( 1 - R 1 R 2 ) + T 1 2 R 2 ( 1 - R 1 R 2 ) 6 1 - R 1 R 2 - 2 R 1 R 2 T 1 n = 1 N = 1 ( R 1 R 2 ) n - 1 / 2 cos ( n δ + n 2 Δ δ ) + 2 R 1 R 2 T 1 2 p = 1 N - 1 R 1 p - 1 R 2 p n = 1 N - p ( R 1 R 2 ) ( n - 1 ) / 2 × cos [ n δ + [ ( n + p ) 2 - p 2 ] Δ δ ] ,
I T ( δ ) = a 2 [ T 1 T 2 1 - ( R 1 R 2 ) N 1 - R 1 R 2 + 2 T 1 T 2 p = 0 N - 1 n = 1 N - p × ( R 1 R 2 ) ( n / 2 + p ) cos { n δ + [ ( n + p ) 2 - p 2 ] Δ δ } ] ,
Δ δ = 1 2 2 π λ ( Δ x ) 2 W ( x , y ) .
Δ δ = 2 π λ D ( Δ x ) 2 .
Δ δ = π λ Δ f ( Δ x f ) 2
Δ f = λ π Δ δ ( f Δ x ) 2 .

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