Abstract

Some new configurations of a wedge-plate interferometer are described that use two wedge plates for collimation testing with a built-in reference unlike a single wedge plate for which an external reference is required. Theory and measurement results are presented.

© 1993 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 variable 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]

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)

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

1964 (1)

Kothiyal, M. P.

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]

Murty, M. V. R. K.

Rosenbruch, K. J.

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

Sirohi, R. S.

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]

Appl. Opt (1)

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

Appl. Opt. (1)

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]

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Figures (4)

Fig. 1
Fig. 1

Schematics of three different collimation testing configurations: (a) configuration A; (b) configuration B; (c) configuration C; W1 and W2, wedge plates; T, test beam; P, observation plane; BS, beam splitter; M, mirror.

Fig. 2
Fig. 2

Simulated interferograms of the double-wedge-plate interferometer for collimated beam illumination: (1) ϕ = 0, (b) ϕ = π.

Fig. 3
Fig. 3

Simulated fringe patterns for different defocusing values by using a double-wedge plate in configurations A2, B1, and C: (a) Δf = 25 μm, (b) Δf = 50 μm, (c) Δf = 100 μm.

Fig. 4
Fig. 4

Experimental fringe patterns obtained from a double-wedge-plate configuration for a collimating lens placed (a) inside, (b) at, and (c) outside the focus. Here f = 250 mm and Δf = 100 μm.

Tables (1)

Tables Icon

Table 1 Experimental Results for the Sensitivity of Collimation Setting for Different Focal Length Lensesa

Equations (36)

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Δ W = W ( x + Δ x , y ) W ( x , y ) = n λ,
Δ W = W x Δ x = n λ .
W ( x , y ) = D ( x 2 + y 2 ) ,
D = | Δ f | 2 f 2 .
Δ W = 2 D x Δ x + y β = n λ,
W 1 ( x , y ) = D ( x 2 + y 2 ) ,
W 2 ( x , y ) = D [ ( x + Δ x ) 2 + y 2 ] + y β + d ,
W 3 ( x , y ) = D [ ( x + Δ x ) 2 + y 2 ] + y β,
W 4 ( x , y ) = D [ ( x + 2 Δ x ) 2 + y 2 ] + 2 y β + d ,
A 1 ( x , y ) = a 1 exp [ i k D ( x 2 + y 2 ) ] ,
A 2 ( x , y ) = a 2 exp ( i k { D [ ( x + Δ x ) 2 + y 2 ] + y β + d } ) ,
A 3 ( x , y ) = a 3 exp ( i k { D [ ( x + Δ x ) 2 + y 2 ] + y β } ) ,
A 4 ( x , y ) = a 4 exp ( i k { D [ ( x + 2 Δ x ) 2 + y 2 ] + 2 y β + d } ) ,
A = A 1 + A 2 + A 3 + A 4 ;
I = A A * = a 1 2 + a 2 2 + a 3 2 + a 4 2 + 2 a 2 a 3 cos ( k d ) + 2 a 1 a 2 cos [ k ( 2 D x Δ x + y β + d ) ] + 2 a 1 a 3 cos [ k ( 2 D x Δ x + y β ) ] + 2 a 1 a 4 cos [ k ( 4 D x Δ x + 2 y β + d ) ] + 2 a 2 a 4 cos [ k ( 2 D x Δ x + y β ) ] + 2 a 3 a 4 cos [ k ( 2 D x Δ x + y β + d ) ] .
I = 4 a 2 { 1 + cos [ k ( 2 D x Δ x + y β + d ) ] } × { 1 + cos [ k ( 2 D x Δ x + y β ) ] }
A 1 ( x , y ) = a 1 exp [ i k D ( x 2 + y 2 ) ] ,
A 2 ( x , y ) = a 2 exp ( i k { D [ ( x + Δ x ) 2 + y 2 ] + y β + d } ) ,
A 3 ( x , y ) = a 3 exp ( i k { D [ ( x + Δ x ) 2 + y 2 ] y β } ) ,
A 4 ( x , y ) = a 4 exp ( i k { D [ ( x + 2 Δ x ) 2 + y 2 ] + d } ) ,
I = a 1 2 + a 2 2 + a 3 2 + a 4 2 + 2 a 1 a 2 cos [ k ( 2 D x Δ x + y β + d ) ] + 2 a 1 a 3 cos [ k ( 2 D x Δ x y β ) ] + 2 a 1 a 4 cos [ k ( 4 D x Δ x + d ) ] + 2 a 2 a 3 cos [ k ( 2 y β + d ) ] + 2 a 2 a 4 cos [ k ( 2 D x Δ x y β ) ] + 2 a 3 a 4 cos [ k ( 2 D x Δ x + y β + d ) ] .
I = 4 a 2 { 1 + cos [ k ( 2 D x Δ x + y β + d ) ] } × { 1 + cos [ k ( 2 D x Δ x y β ) ] } .
A 1 ( x , y ) = a 1 exp [ i k D ( x 2 + y 2 ) ] ,
A 2 ( x , y ) = a 2 exp ( i k { D [ ( x + Δ x ) 2 + y 2 ] + y β + d } ) ,
A 3 ( x , y ) = a 3 exp ( i k { D [ ( x Δ x ) 2 + y 2 ] + y β } ) ,
A 4 ( x , y ) = a 4 exp { i k [ D ( x 2 + y 2 ) + 2 y β + d ] } .
I = a 1 2 + a 2 2 + a 3 2 + a 4 2 + 2 a 1 a 2 cos [ k ( 2 D x Δ x + y β + d ) ] + 2 a 1 a 3 cos [ k ( 2 D x Δ x y β ) ] + 2 a 1 a 4 cos [ k ( 2 y β + d ) ] + 2 a 2 a 3 cos [ k ( 4 D x Δ x + d ) ] + 2 a 2 a 4 cos [ k ( 2 D x Δ x y β ) ] + 2 a 3 a 4 cos [ k ( 2 D x Δ x + y β + d ) ] ,
I = 4 a 2 { 1 + cos [ k ( 2 D x Δ x + y β + d ) ] } × { 1 + cos [ k ( 2 D x Δ x y β ) ] } .
A 1 ( x , y ) = a 1 exp [ i k D ( x 2 + y 2 ) ] ,
A 2 ( x , y ) = a 2 exp ( i k { D [ ( x + Δ x ) 2 + y 2 ] + y β + d } ) ,
A 3 ( x , y ) = a 3 exp ( i k { D [ ( x Δ x ) 2 + y 2 ] y β } ) ,
A 4 ( x , y ) = a 4 exp { i k [ D ( x + y 2 ) + d ] } ,
I = a 1 2 + a 2 2 + a 3 2 + a 4 2 + 2 a 1 a 2 cos [ k ( 2 D x Δ x + y β + d ) ] + 2 a 1 a 3 cos [ k ( 2 D x Δ x + y β ) ] + 2 a 1 a 4 cos ( k d ) + 2 a 2 a 3 cos [ k ( 4 D x Δ x + 2 y β + d ) ] + 2 a 2 a 4 cos [ k ( 2 D x Δ x + y β ) ] + 2 a 3 a 4 cos [ k ( 2 D x Δ x + y β + d ) ] ,
I = 4 a 2 { 1 + cos [ k ( 2 D x Δ x + y β + d ) ] } × { 1 + cos [ k ( 2 D x Δ x + y β ) ] } .
I 1 = a 2 r 4 ( 1 + 2 t 4 + t 8 ) + 2 a 2 r 4 ( t 2 + t 6 ) × { cos [ k ( 2 D x Δ x + y β + d ) ] + cos [ k ( 2 D x Δ x + y β ) ] } + 4 a 2 r 4 t 4 cos [ k ( 2 D x Δ x + y β + d ) ] × cos [ k ( 2 D x Δ x + y β ) ]
I 2 = a 2 r 4 ( 1 + 2 t 4 + t 8 ) + 2 a 2 r 4 ( t 2 + t 6 ) × { cos [ k ( 2 D x Δ x + y β + d ) ] + cos [ k ( 2 D x Δ x + y β ) ] } + 4 a 2 r 4 t 4 cos [ k ( 2 D x Δ x + y β + d ) ] × cos [ k ( 2 D x Δ x + y β ) ]

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