Abstract

A new real-time interferometer based on diffraction phenomena is discussed. It consists of a point-diffraction interferometer fabricated on a transmission grating. The real-time data-analysis capability is achieved by simultaneously introducing a phase shift (piston) on the three separate channels of diffracted interferograms. Mathematical analysis and preliminary observational results are included.

© 1984 Optical Society of America

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References

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  1. R. K. Crane, Appl. Opt. 8, 538 (1969).
  2. D. Malacara, I. Rizo, P. L. Morales, Appl. Opt. 8, 1746 (1969).
    [CrossRef] [PubMed]
  3. W. H. Stevenson, Appl. Opt. 9, 649 (1970).
    [CrossRef] [PubMed]
  4. J. H. Bruning, D. R. Harriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  5. G. E. Sommargren, J. Opt. Soc. Am. 65, 960 (1975).
    [CrossRef]
  6. J. W. Hardy, J. E. Lefebvre, C. L. Koliopoulos, J. Opt. Soc. Am. 67, 360 (1977).
    [CrossRef]
  7. J. C. Wyant, Appl. Opt. 14, 2622 (1975).
    [CrossRef] [PubMed]
  8. J. C. Wyant, Laser Focus 65(5), 65 (1982).
  9. R. N. Smartt, J. Strong, J. Opt. Soc. Am. 62, 737 (1972).
  10. R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 114(1975).R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 1, 351 (1975).
  11. C. Koliopoulos, O. Kwon, R. Shagam, J. C. Wyant, C. R. Hayslett, Opt. Lett. 3, 118 (1978).
    [CrossRef] [PubMed]

1982 (1)

J. C. Wyant, Laser Focus 65(5), 65 (1982).

1978 (1)

1977 (1)

1975 (3)

J. C. Wyant, Appl. Opt. 14, 2622 (1975).
[CrossRef] [PubMed]

G. E. Sommargren, J. Opt. Soc. Am. 65, 960 (1975).
[CrossRef]

R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 114(1975).R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 1, 351 (1975).

1974 (1)

1972 (1)

R. N. Smartt, J. Strong, J. Opt. Soc. Am. 62, 737 (1972).

1970 (1)

1969 (2)

Brangaccio, D. J.

Bruning, J. H.

Crane, R. K.

R. K. Crane, Appl. Opt. 8, 538 (1969).

Gallagher, J. E.

Hardy, J. W.

Harriott, D. R.

Hayslett, C. R.

Koliopoulos, C.

Koliopoulos, C. L.

Kwon, O.

Lefebvre, J. E.

Malacara, D.

Morales, P. L.

Rizo, I.

Rosenfeld, D. P.

Shagam, R.

Smartt, R. N.

R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 114(1975).R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 1, 351 (1975).

R. N. Smartt, J. Strong, J. Opt. Soc. Am. 62, 737 (1972).

Sommargren, G. E.

Steel, W. H.

R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 114(1975).R. N. Smartt, W. H. Steel, Jpn. J. Appl. Phys. Suppl. 1, 351 (1975).

Stevenson, W. H.

Strong, J.

R. N. Smartt, J. Strong, J. Opt. Soc. Am. 62, 737 (1972).

White, A. D.

Wyant, J. C.

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Figures (2)

Fig. 1
Fig. 1

Optical schematic of the new multichannel phaseshifted interferometer with magnified view of the relative pinhole position within a period of substrate grating.

Fig. 2
Fig. 2

Microscopic photographs of pinholes and corresponding interferograms for F/20 object beams. The diameter of the pinholes is 5 μm, and the grating spacing is 20 μm. (a) Xg = dg/4 (Δϕ = π/2). (b) Xg = 0 (Δϕ = 0). (c) Xg = dg/2 (Δϕ = π).

Equations (15)

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I ( x , y ) = I a + I b cos [ Φ ( x , y ) + δ ] ,
I A ( x , y ) = I a + I b cos [ ϕ ( x , y ) + π / 4 ] , I B ( x , y ) = I a + I b cos [ ϕ ( x , y ) + 3 π / 4 ] , I C ( x , y ) = I a + I b cos [ ϕ ( x , y ) + 5 π / 4 ] .
ϕ ( x , y ) = tan 1 [ I C ( x , y ) I B ( x , y ) I A ( x , y ) I B ( x , y ) ] .
t ( x , y ) = t p ( x , y ) t g ( x , y ) ,
t p ( x , y ) = t b + ( 1 t b ) × cyl { [ ( x x 0 ) 2 + ( y y 0 ) 2 ] 1 / 2 d } ,
t g ( x , y ) = 1 2 [ 1 + β cos 2 π ξ ( x x g ) ] ,
ξ > 1 / ( 2 λ F ) or d g < 2 λ F ,
U 0 ( x , y ) = cyl [ ( x 2 + y 2 ) 1 / 2 D ] exp [ i 2 π λ W ( x , y ) ] ,
U i ( x , y ) = t b cyl [ ( x 2 + y 2 ) 1 / 2 D ] exp [ i ϕ ( x , y ) ] + 1 2 t b β cyl { [ ( x s ) 2 + y 2 ] 1 / 2 D } × exp [ i ϕ ( x , y ) ] exp ( i 2 π ξ x g ) + 1 2 t b β cyl { [ ( x + s ) 2 + y 2 ] 1 / 2 D } × exp [ i ϕ ( x , y ) ] exp ( i 2 π ξ x g ) + ( 1 t b ) α [ 1 + β cos 2 π ξ ( x 0 x g ) ] × exp [ i 2 π ( x 0 x + y 0 y ) / λ f ] ,
ϕ ( x , y ) = ( 2 π / λ ) W ( x , y ) .
Δ ϕ ± = ± 2 π ξ x g .
I ( x , y ) = I 1 ( ) + I 2 ( ) cos [ ϕ ( x , y ) 2 π ξ x g ] , I 0 ( x , y ) = I 1 ( 0 ) + I 2 ( 0 ) cos [ ϕ ( x , y ) ] , I + ( x , y ) = I 1 ( + ) + I 2 ( + ) cos [ ( x , y ) + 2 π ξ x g ] ,
I 1 ( ) = I 1 ( + ) = I 1 , I 2 ( ) = I 2 ( + ) = I 2 ,
I 1 ( 0 ) = I 1 + ( 1 β 2 4 ) t b 2 , I 2 ( 0 ) = 2 β I 2 .
ϕ ( x , y ) = tan 1 × { I I + β [ 2 I 0 ( I + I + ) 2 + ( 1 β 2 4 ) t b 2 ] } .

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