Abstract

A new method for recording holograms using incoherent light is described. The method is based on optical propagation through birefringent crystals. Optical methods for the reconstruction of such a hologram are also presented.

© 1985 Optical Society of America

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References

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  1. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  2. G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977).
  3. G. Cochran, J. Opt. Soc. Am. 56,1513 (1966).
    [CrossRef]
  4. H. R. Worthington, J. Opt. Soc. Am. 56,1397 (1966).
    [CrossRef]
  5. G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
    [CrossRef]
  6. A. W. Lohmann, J. Opt. Soc. Am. 55,1555 (1965).
    [CrossRef]
  7. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 20.
  8. R. W. Ditchburn, Light (Wiley Interscience, New York, 1963), Chap. XVI.
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. XIV.
  10. E. N. Leith, B. J. Chang, Appl. Opt. 12, 1957 (1973).
    [CrossRef] [PubMed]
  11. J. B. De Velis, G. O. Reynolds, Theory and Applications of Holography (Addison-Wesley, Reading, Mass., 1967), Chap. 5.

1973

1966

1965

A. W. Lohmann, J. Opt. Soc. Am. 55,1555 (1965).
[CrossRef]

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. XIV.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 20.

Chang, B. J.

Cochran, G.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 20.

De Velis, J. B.

J. B. De Velis, G. O. Reynolds, Theory and Applications of Holography (Addison-Wesley, Reading, Mass., 1967), Chap. 5.

Ditchburn, R. W.

R. W. Ditchburn, Light (Wiley Interscience, New York, 1963), Chap. XVI.

Leith, E. N.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 20.

Lohmann, A. W.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Restrick, R. C.

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
[CrossRef]

Reynolds, G. O.

J. B. De Velis, G. O. Reynolds, Theory and Applications of Holography (Addison-Wesley, Reading, Mass., 1967), Chap. 5.

Rogers, G. L.

G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977).

Stroke, G. W.

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. XIV.

Worthington, H. R.

Appl. Opt.

Appl. Phys. Lett.

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
[CrossRef]

J. Opt. Soc. Am.

Other

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 20.

R. W. Ditchburn, Light (Wiley Interscience, New York, 1963), Chap. XVI.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Chap. XIV.

J. B. De Velis, G. O. Reynolds, Theory and Applications of Holography (Addison-Wesley, Reading, Mass., 1967), Chap. 5.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977).

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Figures (4)

Fig. 1
Fig. 1

Propagation of light in a birefringent crystal.

Fig. 2
Fig. 2

Experimental demonstration of the formation of conoscopic holograms, (a) Hologram of a single point source, (b) Hologram of two point sources.

Fig. 3
Fig. 3

Coherent reconstruction.

Fig. 4
Fig. 4

Experimental demonstration of coherent reconstruction. (a) Reconstruction of the hologram shown in Fig. 2(b). (b) Reconstruction of the same hologram through a high-pass spatial filter for contrast improvement.

Equations (23)

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n E ( ϑ ) n O + Δ n sin 2 ϑ .
Δ φ = ( 2 π / λ ) ( L / cos ϑ ) Δ n sin 2 ϑ ( 2 π L / λ ) Δ n ϑ 2 , ϑ 1 .
I ( R , P ) = I ( P ) cos 2 [ Δ φ ( P , R ) / 2 ] = 0.5 I ( P ) + 0.5 I ( P ) cos [ Δ φ ( P , R ) ] .
I ( R ) = υ I ( R , P ) d P = υ I ( P ) T ( R , P ) d P ,
ϑ 2 [ ( x x ) 2 + ( y y ) 2 ] / z 2 ,
I ( R , P ) = I ( P ) T ( P , R ) = I ( P ) × ( 0.5 + 0.5 cos { 2 π L Δ n [ ( x x ) 2 + ( y y ) 2 ] / z 2 λ } ) .
F = L Δ n sin 2 ϑ 0 / λ ( L Δ n A 2 ) / λ z 0 2 ,
I ( R , P ) = I ( P ) ( 0.5 + 0.5 cos { 2 π [ ( x x ) 2 + ( y y ) 2 ] / λ EQ z } ) ,
λ EQ = λ z / Δ n L A 2 / F z 0 .
I ( P ) = s I ( R ) T ( P , R ) d S .
I ( P ) = s υ I ( P ) T ( P , R ) T ( P , R ) d V d S .
Δ x = ( 1.22 λ EQ z 0 ) / 2 A = 1.22 λ z 0 2 / Δ n A L = ( 1.22 A 2 z 0 ) / 2 A F z 0 = 0.61 A / F .
Δ z = 0.5 Δ x ( z 0 / A ) = 0.61 ( z 0 / 2 F ) .
l 1 = 2 × 61 / Δ x = ( 2 F / A ) .
SBP = 1.64 l 1 G = 1.64 ( 2 F / A ) mA = 3.38 mF .
Δ λ / λ = ( 1 / F ) .
a R = exp ( j φ R ) = exp [ j ( 2 π / λ ) ( x 2 + y 2 ) / 2 z M ] .
μ = λ EQ ( z 0 ) / λ .
A G ( R ) = exp ( j φ R ) s I ( P ) T ( P , R ) d S = s I ( P ) exp ( j φ ) d S + bias ,
φ = ( 2 π / λ ) { [ ( x x ) 2 + ( y y ) 2 ] z 0 / z 2 μ + ( x 2 + y 2 ) / 2 z M } . = ( x 2 + y 2 ) / 2 z G + ( x x G + y y G ) / z G + phase term
( 2 z G ) 1 = ( μ z 2 / z 0 ) 1 + ( 2 z M ) 1 , x G = x ( z G z 0 / μ z 2 ) , y G = y ( z G z 0 / μ z 2 ) .
( 2 z G ) 1 = ( μ z 2 / z 0 ) 1 + ( μ z 0 ) 1 = μ ( z 0 / z 2 + z 0 ) .
z G = 2 μ z , x G = 2 μ x , y G = 2 μ y .

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