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References

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  1. R. K. Erf, Holographic Nondestructive Testing (Academic, New York, 1974).
  2. H. K. Lin, R. L. Kurtz, Opt. Eng. 16, 176 (1977);K. A. Stetson, Appl. Opt. 14, 2256 (1975);V. F. Bellani, A. Sona, Appl. Opt. 13, 1337 (1974);C. A. Sciammarella, J. A. Gilbert, Appl. Opt. 12, 1951 (1973);N. Abramson, Appl. Opt. 16, 2521 (1977).
    [CrossRef] [PubMed]
  3. C. Roychoudhuri, Bol. Inst. Tonantzintla 1, 259 (1975);C. Roychoudhuri, R. Machorro, M. Cervantes, Bol. Inst. Tonantzintla 2, 55 (1976).
  4. C. Roychoudhuri, R. Machorro, 18th Congress of Mexican Physical Society, Bulletin no. 4 (Mexico1975), p. 95.
  5. P. M. Boone, in Engineering Uses of Coherent Optics, E. R. Robertson, Ed. (Cambridge U. P., London, 1976), pp. 81–98;P. M. Boone, L. C. De Backer, Optik 37, 61 (1973);P. M. Boone, Opt. Technol. 4, 162 (1972);J. W. C. Gates, Opt. Technol. 1, 246 (1969);J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
    [CrossRef]
  6. E. Archbold, A. E. Ennos, Opt. Acta 19, 253 (1972).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1977

H. K. Lin, R. L. Kurtz, Opt. Eng. 16, 176 (1977);K. A. Stetson, Appl. Opt. 14, 2256 (1975);V. F. Bellani, A. Sona, Appl. Opt. 13, 1337 (1974);C. A. Sciammarella, J. A. Gilbert, Appl. Opt. 12, 1951 (1973);N. Abramson, Appl. Opt. 16, 2521 (1977).
[CrossRef] [PubMed]

1975

C. Roychoudhuri, Bol. Inst. Tonantzintla 1, 259 (1975);C. Roychoudhuri, R. Machorro, M. Cervantes, Bol. Inst. Tonantzintla 2, 55 (1976).

1972

E. Archbold, A. E. Ennos, Opt. Acta 19, 253 (1972).
[CrossRef]

Archbold, E.

E. Archbold, A. E. Ennos, Opt. Acta 19, 253 (1972).
[CrossRef]

Boone, P. M.

P. M. Boone, in Engineering Uses of Coherent Optics, E. R. Robertson, Ed. (Cambridge U. P., London, 1976), pp. 81–98;P. M. Boone, L. C. De Backer, Optik 37, 61 (1973);P. M. Boone, Opt. Technol. 4, 162 (1972);J. W. C. Gates, Opt. Technol. 1, 246 (1969);J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
[CrossRef]

Ennos, A. E.

E. Archbold, A. E. Ennos, Opt. Acta 19, 253 (1972).
[CrossRef]

Erf, R. K.

R. K. Erf, Holographic Nondestructive Testing (Academic, New York, 1974).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Kurtz, R. L.

H. K. Lin, R. L. Kurtz, Opt. Eng. 16, 176 (1977);K. A. Stetson, Appl. Opt. 14, 2256 (1975);V. F. Bellani, A. Sona, Appl. Opt. 13, 1337 (1974);C. A. Sciammarella, J. A. Gilbert, Appl. Opt. 12, 1951 (1973);N. Abramson, Appl. Opt. 16, 2521 (1977).
[CrossRef] [PubMed]

Lin, H. K.

H. K. Lin, R. L. Kurtz, Opt. Eng. 16, 176 (1977);K. A. Stetson, Appl. Opt. 14, 2256 (1975);V. F. Bellani, A. Sona, Appl. Opt. 13, 1337 (1974);C. A. Sciammarella, J. A. Gilbert, Appl. Opt. 12, 1951 (1973);N. Abramson, Appl. Opt. 16, 2521 (1977).
[CrossRef] [PubMed]

Machorro, R.

C. Roychoudhuri, R. Machorro, 18th Congress of Mexican Physical Society, Bulletin no. 4 (Mexico1975), p. 95.

Roychoudhuri, C.

C. Roychoudhuri, Bol. Inst. Tonantzintla 1, 259 (1975);C. Roychoudhuri, R. Machorro, M. Cervantes, Bol. Inst. Tonantzintla 2, 55 (1976).

C. Roychoudhuri, R. Machorro, 18th Congress of Mexican Physical Society, Bulletin no. 4 (Mexico1975), p. 95.

Bol. Inst. Tonantzintla

C. Roychoudhuri, Bol. Inst. Tonantzintla 1, 259 (1975);C. Roychoudhuri, R. Machorro, M. Cervantes, Bol. Inst. Tonantzintla 2, 55 (1976).

Opt. Acta

E. Archbold, A. E. Ennos, Opt. Acta 19, 253 (1972).
[CrossRef]

Opt. Eng.

H. K. Lin, R. L. Kurtz, Opt. Eng. 16, 176 (1977);K. A. Stetson, Appl. Opt. 14, 2256 (1975);V. F. Bellani, A. Sona, Appl. Opt. 13, 1337 (1974);C. A. Sciammarella, J. A. Gilbert, Appl. Opt. 12, 1951 (1973);N. Abramson, Appl. Opt. 16, 2521 (1977).
[CrossRef] [PubMed]

Other

R. K. Erf, Holographic Nondestructive Testing (Academic, New York, 1974).

C. Roychoudhuri, R. Machorro, 18th Congress of Mexican Physical Society, Bulletin no. 4 (Mexico1975), p. 95.

P. M. Boone, in Engineering Uses of Coherent Optics, E. R. Robertson, Ed. (Cambridge U. P., London, 1976), pp. 81–98;P. M. Boone, L. C. De Backer, Optik 37, 61 (1973);P. M. Boone, Opt. Technol. 4, 162 (1972);J. W. C. Gates, Opt. Technol. 1, 246 (1969);J. Tsujiuchi, N. Takeya, K. Matsuda, Opt. Acta 16, 709 (1969).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (4)

Fig. 1
Fig. 1

The holographic arrangement to study object motion at the Fourier transform plane. O—object plane; L1—Fourier transform lens, f1 = 21 cm; F(H)—hologram plane that is also the Fourier plane corresponding to O; L2—imaging lens, f2 = 21 cm; O′—image plane conjugate to O, one uses movable aperture in this plane to isolate object points or lines; F′—the imaged Fourier plane conjugate to F(H).

Fig. 2
Fig. 2

Fringes due to pure rigid body translation along X (a) and Z (b) axes recorded at the Fourier plane F of Fig. 1. δx ≃ 0.13 mm and δz ≃ 2 mm.

Fig. 3
Fig. 3

Fringes due to tilt or rotation about the Y axis recorded at the image Fourier plane F′ of Fig. 1 for different positions of a 1-mm slit parallel to the Y axis in the O′ plane: (a) slit on Y axis; (b) slit on X1; and (c) slit on X2 > X1. Rotation θy ≃ 5°.

Fig. 4
Fig. 4

Fringes due to in-plane rotation (about the Z axis) of the object, recorded at the image Fourier plane F′ of Fig. 1 for different positions of a 1-mm2 aperture in the O′ plane: (a) aperture on the Y axis at a distance of 5 mm from the Z axis of rotation; (b) aperture at 45° angle from the Y axis at a 12-mm distance from the Z axis; and (c) aperture on the X axis at a 9-mm distance from the Z axis. Rotation θz ≃ 1.3°.

Equations (6)

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I lat ( ξ , η ) = | u ( ξ , η ) + u ( ξ , η ) exp ( i k ξ δ x / f ) | 2 = 2 | u ( ξ , η ) | [ 1 + cos ( k ξ δ x / f ) ] .
δ x = λ f / δ ξ .
I long ( ξ , η ) = 2 | u ( ξ , η ) | 2 [ 1 + cos k ( ξ 2 + η 2 ) δ z / 2 f 2 ] .
δ z = n ( λ f 2 / 2 r n 2 ) .
I gen 2 { 1 + cos k [ ξ δ x + η δ y f + ( ξ 2 + η 2 ) δ z 2 f 2 ] } .
I z rot 2 { 1 + cos [ k ( ξ δ x + η δ y ) / f ] } .

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