Abstract

Two holograms are used. A first hologram is recorded by the light that passes through the phase object with an ordinary off-axis holographic system. A second hologram is recorded by the light that passes through the deformed object and is diffracted by the first hologram and processed nonlinearly. Phase difference amplification is performed by the superposition of two higher harmonic waves from the second hologram. In a resultant interferogram of eight-fold phase difference amplification, phase change, due to only the deformation of the object, is amplified; and wavefront aberration, caused by poor quality of an optical system and by inhomogeneity of the object, is completely eliminated.

© 1974 Optical Society of America

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References

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  1. K. Matsumoto, T. Ose, Seisan-Kenkyu 19, 18 (1967).
  2. O. Bryngdahl, J. Opt. Soc. Am. 59, 142 (1969).
    [CrossRef]
  3. K. Matsumoto, M. Takashima, J. Opt. Soc. Am. 60, 30 (1970).
    [CrossRef]
  4. O. Bryngdahl, A. W. Lohmann, J. Opt. Soc. Am. 58, 141 (1968).
    [CrossRef]
  5. K. S. Pennington, J. S. Harper, Appl. Opt. 9, 1643 (1970).
    [CrossRef] [PubMed]
  6. H. Okayama, K. Nakatsuka, Y. Emori, Oyo Butsuri 40, 1209 (1971).

1971

H. Okayama, K. Nakatsuka, Y. Emori, Oyo Butsuri 40, 1209 (1971).

1970

1969

1968

1967

K. Matsumoto, T. Ose, Seisan-Kenkyu 19, 18 (1967).

Bryngdahl, O.

Emori, Y.

H. Okayama, K. Nakatsuka, Y. Emori, Oyo Butsuri 40, 1209 (1971).

Harper, J. S.

Lohmann, A. W.

Matsumoto, K.

K. Matsumoto, M. Takashima, J. Opt. Soc. Am. 60, 30 (1970).
[CrossRef]

K. Matsumoto, T. Ose, Seisan-Kenkyu 19, 18 (1967).

Nakatsuka, K.

H. Okayama, K. Nakatsuka, Y. Emori, Oyo Butsuri 40, 1209 (1971).

Okayama, H.

H. Okayama, K. Nakatsuka, Y. Emori, Oyo Butsuri 40, 1209 (1971).

Ose, T.

K. Matsumoto, T. Ose, Seisan-Kenkyu 19, 18 (1967).

Pennington, K. S.

Takashima, M.

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Figures (6)

Fig. 1
Fig. 1

Optical arrangement for making two holograms and for phase difference amplification. BS, beam splitter; M1, M2, and M3, mirrors; MO, microscope objectives having a filtering pinhole; CL, collimator lenses; O, phase object under test; H1 and H2, holograms; L, lens; F, filtering mask; S, screen.

Fig. 2
Fig. 2

Electron micrographs of the surface of the first hologram processed (a) with ordinary developing and bleaching solutions; and (b) with precautions of annealing, prehardening, and drying of the plate to reduce the shrinkage of the emulsion and the scattering noise.

Fig. 3
Fig. 3

Fraunhofer diffraction patterns from the second hologram made with waves reconstructed by the first hologram; according to the following processes: (a) the frist hologram was processed with no precautions, and its surface figure is shown in Fig. 2(a); (b) the first hologram was processed with precautions, and its surface figure is shown in Fig. 2(b).

Fig. 4
Fig. 4

Holographic interferogram obtained with conventional holographic method showing inhomogeneity of the glass plates.

Fig. 5
Fig. 5

Two-beam interferogram to estimate wavefront aberration inherent in the optical system.

Fig. 6
Fig. 6

Interferogram with amplified phase difference that was generated by the index change of air around an electrically heated tungsten wire that was stretched vertically and held between two glass plates: (a) interferogram with zero-order and 1st-order diffracted waves from the second hologram; (b) with ±2nd-order diffracted waves; and (c) with ±4th-order diffracted waves.

Equations (21)

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U t = exp i k [ δ t ( x , y ) + x sin θ t ] ,
U r = exp i k [ δ r ( x , y ) + x sin θ r ] ,
I 1 = | U t + U r | 2 = 2 + 2 cos k [ δ t ( x , y ) δ r ( x , y ) + x ( sin θ t sin θ r ) ] .
T 1 = 2 e i k δ p + exp i k [ δ t δ r + δ p + δ s + x ( sin θ t sin θ r ) ] + exp i k [ δ t δ r δ p + δ s + x ( sin θ t sin θ r ) ] .
T 1 ( U t + U r ) = 2 exp i k ( δ t + δ p + x sin θ t ) + 2 exp i k ( δ r + δ p + x sin θ r ) + exp i k [ 2 δ t δ r + δ p + δ s + x ( 2 sin θ t sin θ r ) ] + exp i k ( δ t + δ p + δ s + x sin θ t ) + exp i k ( δ r + δ p δ s + x sin θ r ) + exp i k [ δ t + 2 δ r + δ p δ s x ( sin θ t 2 sin θ r ) ] .
ψ t = exp i k [ φ ( x , y ) + δ r ( x , y ) + δ p ( x , y ) δ s ( x , y ) + x sin θ r ] .
ψ r = exp i k [ δ r ( x , y Δ y α ) + δ p ( x , y Δ y α ) + x sin θ r + y sin α ] ,
Δ y α = M 2 H 2 ¯ tan α , Δ y α = H 1 H 2 ¯ tan α .
I 2 = | ψ t + ψ r | 2 = 2 + 2 cos k [ φ ( x , y ) + δ r ( x , y ) δ r ( x , y Δ y α ) + δ p ( x , y ) δ p ( x , y Δ y α ) δ s ( x , y ) y sin α ] .
T 2 = m = exp i m k [ φ ( x , y ) + δ r ( x , y ) δ r ( x , y Δ y α ) + δ p ( x , y ) δ p ( x , y Δ y α ) δ s ( x , y ) y sin α ] ,
ψ t = exp i k [ δ r ( x , y ) + δ p ( x , y ) δ s ( x , y ) + x sin θ r ] ,
T 2 ψ t = m = exp i k { m [ φ ( x , y ) + δ r ( x , y ) δ r ( x , y Δ y α ) + δ p ( x , y ) δ p ( x , y Δ y α ) δ s ( x , y ) y sin α ] + δ r ( x , y ) + δ p ( x , y ) δ s ( x , y ) + x sin θ r } .
T 2 ψ r = m = exp i k { m [ φ ( x , y ) + δ r ( x , y ) δ r ( x , y Δ y α ) + δ p ( x , y ) δ p ( x , y Δ y α ) δ s ( x , y ) y sin α ] + δ r ( x , y Δ y β ) + δ p ( x , y Δ y β ) + x sin θ r + y sin β } ,
Δ y β = M 2 H 2 ¯ tan β , Δ y β = H 1 H 2 ¯ tan β .
μ y sin α = ν y sin α + y sin β .
I s = 1 + cos k { ( μ + ν ) [ φ ( x , y ) + δ r ( x , y ) δ r ( x , y Δ y α ) + δ p ( x , y ) δ p ( x , y Δ y α ) δ s ( x , y ) ] δ r ( x , y ) + δ r ( x , y Δ y β ) δ p ( x , y ) + δ p ( x , y Δ y β ) + δ s ( x , y ) } .
( μ + ν ) α = β .
Δ y β = M 2 H 2 ¯ β = ( μ + ν ) M 2 H 2 ¯ α = ( μ + ν ) Δ y α .
δ r ( x , y ) δ r ( x , y Δ y α ) = [ ( δ r ) / ( y ) ] Δ y α , δ r ( x , y ) δ r ( x , y Δ y β ) = [ ( δ r ) / ( y ) ] Δ y β = ( μ + ν ) [ ( δ r ) / ( y ) ] Δ y α .
( μ + ν ) [ δ r ( x , y ) δ r ( x , y Δ y α ) ] δ r ( x , y ) + δ r ( x , y Δ y β ) = 0.
I s = 1 + cos k [ ( μ + ν ) φ ( x , y ) ( μ + ν 1 ) δ s ( x , y ) ] .

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