Abstract

Two improved techniques of aberrationless phase difference amplification are presented. Both make use of double-exposure holographic interferometry. In contrast to the ordinary technique, not only the state of the tested object is changed between exposures but also the direction of the hologram fringes. This approach allows one to separate desired higher diffraction orders of the double-exposed hologram, to eliminate setup aberrations, and, consequently, to achieve an amplification of the phase difference given by the tested object alone.

© 1989 Optical Society of America

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References

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  1. O. Bryngdahl, A. W. Lohmann, “Interferograms Are Image Holograms,” J. Opt. Soc. Am. 58, 141–142 (1968).
    [CrossRef]
  2. O. Bryngdahl, “Longitudally Reversed Shearing Interferometry,” J. Opt. Soc. Am. 59, 142–146 (1969).
    [CrossRef]
  3. K. Matsumoto, M. Takashima, “Phase-Difference Amplification by Nonlinear Holograms,” J. Opt. Soc. Am. 60, 30–33 (1970).
    [CrossRef]
  4. K. S. Mustafin, V. A. Seleznev, E. I. Shtyrkov, “Use of the Nonlinear Properties of a Photoemulsion for Enhancing the Sensitivity of Holographic Interferometry,” Opt. Spectrosc. USSR 28, 638–647 (1970).
  5. D. Dameron, C. Vest, “Fringe Sharpening and Diffraction in Nonlinear Two-Exposure Holographic Interferometry,” J. Opt. Soc. Am. 66, 1418–1421 (1976).
    [CrossRef]
  6. C. Vest, Holographic interferometry (Wiley, New York, 1979).
  7. V. L. Afanaseva, L. T. Mustafina, V. A. Seleznev, “Method of Compensating Aberrations in Holographic Interferometry of Increased Sensitivity,” Opt. Spectrosc. USSR 37, 448–449 (1974).
  8. S. Toyooka, “Elimination of Wavefront Aberration of Optical Elements Used in Phase Difference Amplification,” Appl. Opt. 13, 2014–2018 (1974).
    [CrossRef] [PubMed]
  9. M. I. de la Rosa, A. M. de Frutos, “Phase Difference Amplification: Some Results,” Appl. Opt. 24, 2486–2487 (1985).
    [CrossRef] [PubMed]
  10. Z. Jaroszewicz, “Evaluation of Holographic Emulsion Movement using Phase Difference Amplification,” Opt. Laser Technol. 20, 251–254 (1988).
    [CrossRef]
  11. I. I. Komissarova, G. V. Ostrovskaya, V. N. Filippov, E. N. Shedova, “Holographic Plasma Interferometry in the Infrared Spectrum. II. Using Nonlinear Effects to Increase the Sensitivity,” Sov. J. Tech. Phys. 28, 156–162 (1983).
  12. C. H. F. Velzel, “Small Phase Difference in Holographic Interferometry,” Opt. Commun. 2, 289–291 (1970).
    [CrossRef]
  13. J. Schwider, “Isophotes and Enhancement of Phase Sensitivity Through Optical Filtering in Image Holography,” in Applications de l'holographie, J.-C. Vienot, J. Bulabois, J. Pasteur, Eds., (Comptes Rendus du Symposium International, Besancon1970).
  14. Z. Jaroszewicz, “Interferometric Testing of the Spacing Error of a Plane Diffraction Grating,” Opt. Commun. 60, 345–350 (1986).
    [CrossRef]

1988 (1)

Z. Jaroszewicz, “Evaluation of Holographic Emulsion Movement using Phase Difference Amplification,” Opt. Laser Technol. 20, 251–254 (1988).
[CrossRef]

1986 (1)

Z. Jaroszewicz, “Interferometric Testing of the Spacing Error of a Plane Diffraction Grating,” Opt. Commun. 60, 345–350 (1986).
[CrossRef]

1985 (1)

1983 (1)

I. I. Komissarova, G. V. Ostrovskaya, V. N. Filippov, E. N. Shedova, “Holographic Plasma Interferometry in the Infrared Spectrum. II. Using Nonlinear Effects to Increase the Sensitivity,” Sov. J. Tech. Phys. 28, 156–162 (1983).

1976 (1)

1974 (2)

V. L. Afanaseva, L. T. Mustafina, V. A. Seleznev, “Method of Compensating Aberrations in Holographic Interferometry of Increased Sensitivity,” Opt. Spectrosc. USSR 37, 448–449 (1974).

S. Toyooka, “Elimination of Wavefront Aberration of Optical Elements Used in Phase Difference Amplification,” Appl. Opt. 13, 2014–2018 (1974).
[CrossRef] [PubMed]

1970 (3)

C. H. F. Velzel, “Small Phase Difference in Holographic Interferometry,” Opt. Commun. 2, 289–291 (1970).
[CrossRef]

K. S. Mustafin, V. A. Seleznev, E. I. Shtyrkov, “Use of the Nonlinear Properties of a Photoemulsion for Enhancing the Sensitivity of Holographic Interferometry,” Opt. Spectrosc. USSR 28, 638–647 (1970).

K. Matsumoto, M. Takashima, “Phase-Difference Amplification by Nonlinear Holograms,” J. Opt. Soc. Am. 60, 30–33 (1970).
[CrossRef]

1969 (1)

1968 (1)

Afanaseva, V. L.

V. L. Afanaseva, L. T. Mustafina, V. A. Seleznev, “Method of Compensating Aberrations in Holographic Interferometry of Increased Sensitivity,” Opt. Spectrosc. USSR 37, 448–449 (1974).

Bryngdahl, O.

Dameron, D.

de Frutos, A. M.

de la Rosa, M. I.

Filippov, V. N.

I. I. Komissarova, G. V. Ostrovskaya, V. N. Filippov, E. N. Shedova, “Holographic Plasma Interferometry in the Infrared Spectrum. II. Using Nonlinear Effects to Increase the Sensitivity,” Sov. J. Tech. Phys. 28, 156–162 (1983).

Jaroszewicz, Z.

Z. Jaroszewicz, “Evaluation of Holographic Emulsion Movement using Phase Difference Amplification,” Opt. Laser Technol. 20, 251–254 (1988).
[CrossRef]

Z. Jaroszewicz, “Interferometric Testing of the Spacing Error of a Plane Diffraction Grating,” Opt. Commun. 60, 345–350 (1986).
[CrossRef]

Komissarova, I. I.

I. I. Komissarova, G. V. Ostrovskaya, V. N. Filippov, E. N. Shedova, “Holographic Plasma Interferometry in the Infrared Spectrum. II. Using Nonlinear Effects to Increase the Sensitivity,” Sov. J. Tech. Phys. 28, 156–162 (1983).

Lohmann, A. W.

Matsumoto, K.

Mustafin, K. S.

K. S. Mustafin, V. A. Seleznev, E. I. Shtyrkov, “Use of the Nonlinear Properties of a Photoemulsion for Enhancing the Sensitivity of Holographic Interferometry,” Opt. Spectrosc. USSR 28, 638–647 (1970).

Mustafina, L. T.

V. L. Afanaseva, L. T. Mustafina, V. A. Seleznev, “Method of Compensating Aberrations in Holographic Interferometry of Increased Sensitivity,” Opt. Spectrosc. USSR 37, 448–449 (1974).

Ostrovskaya, G. V.

I. I. Komissarova, G. V. Ostrovskaya, V. N. Filippov, E. N. Shedova, “Holographic Plasma Interferometry in the Infrared Spectrum. II. Using Nonlinear Effects to Increase the Sensitivity,” Sov. J. Tech. Phys. 28, 156–162 (1983).

Schwider, J.

J. Schwider, “Isophotes and Enhancement of Phase Sensitivity Through Optical Filtering in Image Holography,” in Applications de l'holographie, J.-C. Vienot, J. Bulabois, J. Pasteur, Eds., (Comptes Rendus du Symposium International, Besancon1970).

Seleznev, V. A.

V. L. Afanaseva, L. T. Mustafina, V. A. Seleznev, “Method of Compensating Aberrations in Holographic Interferometry of Increased Sensitivity,” Opt. Spectrosc. USSR 37, 448–449 (1974).

K. S. Mustafin, V. A. Seleznev, E. I. Shtyrkov, “Use of the Nonlinear Properties of a Photoemulsion for Enhancing the Sensitivity of Holographic Interferometry,” Opt. Spectrosc. USSR 28, 638–647 (1970).

Shedova, E. N.

I. I. Komissarova, G. V. Ostrovskaya, V. N. Filippov, E. N. Shedova, “Holographic Plasma Interferometry in the Infrared Spectrum. II. Using Nonlinear Effects to Increase the Sensitivity,” Sov. J. Tech. Phys. 28, 156–162 (1983).

Shtyrkov, E. I.

K. S. Mustafin, V. A. Seleznev, E. I. Shtyrkov, “Use of the Nonlinear Properties of a Photoemulsion for Enhancing the Sensitivity of Holographic Interferometry,” Opt. Spectrosc. USSR 28, 638–647 (1970).

Takashima, M.

Toyooka, S.

Velzel, C. H. F.

C. H. F. Velzel, “Small Phase Difference in Holographic Interferometry,” Opt. Commun. 2, 289–291 (1970).
[CrossRef]

Vest, C.

Appl. Opt. (2)

J. Opt. Soc. Am. (4)

Opt. Commun. (2)

C. H. F. Velzel, “Small Phase Difference in Holographic Interferometry,” Opt. Commun. 2, 289–291 (1970).
[CrossRef]

Z. Jaroszewicz, “Interferometric Testing of the Spacing Error of a Plane Diffraction Grating,” Opt. Commun. 60, 345–350 (1986).
[CrossRef]

Opt. Laser Technol. (1)

Z. Jaroszewicz, “Evaluation of Holographic Emulsion Movement using Phase Difference Amplification,” Opt. Laser Technol. 20, 251–254 (1988).
[CrossRef]

Opt. Spectrosc. USSR (2)

K. S. Mustafin, V. A. Seleznev, E. I. Shtyrkov, “Use of the Nonlinear Properties of a Photoemulsion for Enhancing the Sensitivity of Holographic Interferometry,” Opt. Spectrosc. USSR 28, 638–647 (1970).

V. L. Afanaseva, L. T. Mustafina, V. A. Seleznev, “Method of Compensating Aberrations in Holographic Interferometry of Increased Sensitivity,” Opt. Spectrosc. USSR 37, 448–449 (1974).

Sov. J. Tech. Phys. (1)

I. I. Komissarova, G. V. Ostrovskaya, V. N. Filippov, E. N. Shedova, “Holographic Plasma Interferometry in the Infrared Spectrum. II. Using Nonlinear Effects to Increase the Sensitivity,” Sov. J. Tech. Phys. 28, 156–162 (1983).

Other (2)

C. Vest, Holographic interferometry (Wiley, New York, 1979).

J. Schwider, “Isophotes and Enhancement of Phase Sensitivity Through Optical Filtering in Image Holography,” in Applications de l'holographie, J.-C. Vienot, J. Bulabois, J. Pasteur, Eds., (Comptes Rendus du Symposium International, Besancon1970).

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Figures (6)

Fig. 1
Fig. 1

Optical arrangements of the rotating hologram method. Top, for exposing crossed hologram, and bottom for phase difference amplification. PW, plane wave (λ = 0.6328 μm); M1,M2 mirrors; BS1, BS2 semitransparent mirrors; Ob, tested object; H, crossed hologram plane; L1, L2 lenses of spatial filtering unit; f, focal length; F, filtering mask; I, image plane.

Fig. 2
Fig. 2

Optical arrangements of the variable direction reference beam method. Top, for exposing crossed hologram, and bottom for phase difference amplification. RB2, second reference beam.

Fig. 3
Fig. 3

Spectrum of the crossed hologram.

Fig. 4
Fig. 4

Phase difference amplification in absence of the object under test. (4,−4), and (−4,4) diffraction order beams are superposed.

Fig. 5
Fig. 5

Interferogram of a nonperfect plane–parallel plate: (a) an ordinary interferogram taken in Mach–Zehnder interferometer T = 1; (b) interferogram with (2,−2) and (−2,2) diffraction order beams from the crossed hologram, T = 4; (c) with (4,−4) and (−4,4) diffraction order beams from the crossed hologram, T = 8.

Fig. 6
Fig. 6

Interferogram of the interferometer aberrations: (a) interferogram of a uniform field, T = 1; (b) interferogram with (2,2) and (−2,−2) diffraction order beams from the crossed hologram, T = 8; (c) with (4,4) and (−4,−4) diffraction order beams from the crossed hologram, T = 16.

Equations (23)

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U r ( x , y ) = exp { ik [ δ r ( x , y ) x sin θ r ] } U t ( x , y ) = exp { ik [ δ t ( x , y ) + x sin θ t ] } ,
I 1 ( x , y ) = 2 + 2 cos { k [ δ t ( x , y ) δ r × ( x , y ) + x ( sin θ t + sin θ r ) ] } .
I 2 ( x , y ) = 2 + 2 cos { k [ δ t ( x , y ) δ r × ( x , y ) + ϕ ( x , y ) + x ( sin θ t + sin θ r ) ] } ,
t ( x , y ) = ν , μ = N + N exp { ik ν [ δ t ( x , y ) δ r ( x , y ) + ϕ ( x , y ) + D sy ( y , x ) ( sin θ t + sin θ r ) + x ( sin θ t + sin θ r ) ] } × exp { ik μ [ + δ t ( y , x ) δ r ( y , x ) D sx ( y x ) ( sin θ t + sin θ r ) y ( sin θ t + sin θ r ) ] } .
U ( m , o ) ( x , y ) = exp ( ik { m [ δ t ( x , y ) δ r ( x , y ) + ϕ ( x , y ) + D sy × ( y , x ) ( sin θ t + sin θ r ) + x ( sin θ t + sin θ r ) ] + W [ mf ( sin θ t + sin θ r ) , 0 ] + ( 1 n o ) h 1 ( y , x ) + ( n o 1 ) h 2 ( y + ( m / n o ) × ( sin θ t + sin θ r ) Δ , x ) } ) ,
I 1 k ( x , y ) = 2 + 2 cos ( k { 2 m [ δ t ( x , y ) δ r ( x , y ) + ϕ ( x , y ) + D sy × ( y , x ) ( sin θ t + sin θ r ) + x ( sin θ t + sin θ r ) + Δ ( sin θ t + sin θ r ) ( n o 1 n o ) h 2 ( y , x ) x ] + W [ mf ( sin θ t + sin θ r ) , 0 ] W [ mf ( sin θ t + sin θ r ) , 0 ] } ) ,
( n o 1 ) h 2 [ y + ( m / n o ) ( sin θ t + sin θ r ) Δ , x ] ( n o 1 ) h 2 ( y , x ) + m Δ ( sin θ t + sin θ r ) ( n o 1 n o ) h 2 ( y , x ) x .
I k ( x , y ) = 2 + 2 cos ( k 2 m { ϕ ( x , y ) + ( sin θ t + sin θ r ) × ( D sy ( y , x ) D sx ( x , y ) ) + Δ ( sin θ t + sin θ r ) × ( n o 1 n o ) [ h 2 ( y , x ) x h 2 ( x , y ) x ] } ) .
T < τ d / 2 [ | D s | max + Δ ( n o 1 n o ) | h 2 | max ] ,
U r ( x , y , z ) = exp { ik [ z + δ r ( x , y ) ] } U t ( x , y , z ) = exp { ik [ z + δ t ( x , y ) ] } .
U r ( x , y , z ) = exp ( ik { z + δ r [ x tan θ r × ( z + d 1 ) , y ] x sin θ r } ) ,
I 1 ( x , y ) = 2 + 2 cos { k [ δ t ( x , y ) δ r × ( x , y ) + tan θ r d 1 δ r x + x sin θ r ] } .
U r ( x , y , z ) = exp ( ik { z + δ r [ x , y tan θ r × ( z + d 1 ) ] y sin θ r } ) ,
I 2 ( x , y ) = 1 + cos { k [ δ t ( x , y ) + ϕ ( x , y ) δ r ( x , y ) + tan θ r d 1 × δ r y + y sin θ r ] } .
t ( x , y ) = ν , μ = N + N exp { ik ν [ δ t ( x , y ) δ r ( x , y ) + tan θ r d 1 δ r x + D sx ( x , y ) sin θ r + x sin θ r ] } exp { ik μ × [ δ t ( x , y ) δ r ( x , y ) + ϕ ( x , y ) + tan θ r d 1 × δ r y + D sy ( x , y ) sin θ r + y sin θ r ] } .
t p ( x , y ) = μ = N + N exp ( ik μ { ϕ ( x , y ) + sin θ r [ D sy ( x , y ) D sx ( x , y ) ] + tan θ r d 1 ( δ r y δ r x ) + ( y x ) sin θ r } ) .
U r 1 ( x , y , z ) = exp { ik [ sin θ r m ( x y ) + δ r × ( x + m tan θ r d , y m tan θ r d ) ] } .
U r 1 ( x , y , z ) U mm ( x , y ) = exp ( ik { m ϕ ( x , y ) + δ r ( x , y ) + sin θ r m [ D sy ( x , y ) D sx ( x , y ) ] } ) .
I 1 k = 2 + 2 cos { k [ m ϕ ( x , y ) + δ r ( x , y ) + sin θ r m × ( D sy ( x , y ) D sx ( x , y ) ) δ r 2 ( x Δ r 2 , y ) + sin θ r 2 x ] } ,
I 2 k = 2 + 2 cos { k { m ϕ ( x , y ) + δ r × ( x , y ) + sin θ r m [ D sy ( x , y ) D sx ( x , y ) ] δ r 2 ( x Δ r 2 , y ) + sin θ r 2 x } } ,
I k = 2 + 2 cos ( k { 2 m ϕ ( x , y ) + 2 sin θ r m × [ D sy ( x , y ) D sx ( x , y ) ] } ) .
T < τ d / 2 | D s | max .
I k = 2 + 2 cos ( k { 4 m [ δ t ( x , y ) δ r ( x , y ) ] + 2 sin θ r m × [ D sy ( x , y ) D sx ( x , y ) ] } ) .

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