Abstract

In a previous paper, several theoretical expressions were derived for calculating the ratio of the light flux in a holographic image of a uniform but extended source to that of a direct image of the source itself, account being taken of the sensitometric characteristics of the photographic material. The present paper is an experimental extension of this work. In particular, comparisons are made between theoretical curves and experimental data for variations of (1) the average density of the hologram, (2) the ratio of object-beam to reference-beam irradiances, and (3) the angular extent of the object. The performance of certain photographic developers is also discussed.

© 1968 Optical Society of America

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References

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  1. F. G. Kaspar and R. L. Lamberts, J. Opt. Soc. Am. 58, 970 (1968). All notations in the present paper are identical with those in this earlier publication.
    [Crossref]
  2. The theoretical curve of 12Ki vs Ta was calculated from Eq. (19b) in Ref. 1, namely, 12Ki=g′2(E0)[E02/(1+R02)2], where g′(E0) is the slope of the sensitometric curve at the average exposure, E0.
  3. A. A. Friesem, A. Kozma, and G. F. Adams, Appl. Opt. 6, 851 (1967).
    [Crossref] [PubMed]
  4. Note that a pure sine wave with 21% modulation gives the same ratio of standard deviation to average exposure; that is, 0.21÷(2)12=0.15.
  5. R. L. Lamberts, J. Soc. Motion Picture Television Engrs. 71, 635 (1962).
  6. A. VanderLugt and R. H. Mitchel, J. Opt. Soc. Am. 57, 372 (1967).
    [Crossref]
  7. Equation (25) is K1 = 0.377 [g′(ζ0)]2. In this equation, g′ is the slope of the Ta vs logE curve, and ζ0 is the average of logE.
  8. Equation (31) reads(total diffracted image flux)/(zero-order flux) = 0.497[g′(ζ0)]2R02.In this case, g′ is the slope of the D vs logE curve, ζ0 is the average of logE, and R02 is the beam-balance ratio.
  9. See the expansion of Eq. (20), Ref. 1, and note that the quantity [ζ(x) − ζ0] is equal to log{1+R2(x)+2R(x) cos[kξx− ϕ(x)]}.

1968 (1)

1967 (2)

1962 (1)

R. L. Lamberts, J. Soc. Motion Picture Television Engrs. 71, 635 (1962).

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Soc. Motion Picture Television Engrs. (1)

R. L. Lamberts, J. Soc. Motion Picture Television Engrs. 71, 635 (1962).

Other (5)

Equation (25) is K1 = 0.377 [g′(ζ0)]2. In this equation, g′ is the slope of the Ta vs logE curve, and ζ0 is the average of logE.

Equation (31) reads(total diffracted image flux)/(zero-order flux) = 0.497[g′(ζ0)]2R02.In this case, g′ is the slope of the D vs logE curve, ζ0 is the average of logE, and R02 is the beam-balance ratio.

See the expansion of Eq. (20), Ref. 1, and note that the quantity [ζ(x) − ζ0] is equal to log{1+R2(x)+2R(x) cos[kξx− ϕ(x)]}.

The theoretical curve of 12Ki vs Ta was calculated from Eq. (19b) in Ref. 1, namely, 12Ki=g′2(E0)[E02/(1+R02)2], where g′(E0) is the slope of the sensitometric curve at the average exposure, E0.

Note that a pure sine wave with 21% modulation gives the same ratio of standard deviation to average exposure; that is, 0.21÷(2)12=0.15.

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Figures (11)

Fig. 1
Fig. 1

Equipment used for making and photometering holograms. LP denotes lens–pinhole combination, D is diffuse object, RB is reference beam, H is hologram, L is lens, D′ is image formed by lens, and PM is photomultiplier tube.

Fig. 2
Fig. 2

Image-to-object radiance ratio vs amplitude transmittance. Curve a is theoretical, b is experimental, and c is Ta vs E. Beam-balance ratio is 1:89.

Fig. 3
Fig. 3

Same as Fig. 2, except beam-balance ratio is 1:22.

Fig. 4
Fig. 4

Same as Fig. 2, except beam-balance ratio is 1:7.6.

Fig. 5
Fig. 5

MTF for Kodak spectroscopic plates, type 649F.

Fig. 6
Fig. 6

Same as Fig. 2, except spatial frequency is 140 cycles/mm.

Fig. 7
Fig. 7

Total diffracted image flux divided by specularly transmitted flux as a function of density (open circles and solid curves). Dashed curve is theoretical. Also included is D vs logE curve with transposed axes.

Fig. 8
Fig. 8

Image-to-object radiance ratio vs beam-balance ratio (open circles). Dashed curve is theoretical. Solid curve through the dark circles is proportional to absolute image radiance. Theoretical curve for this is shown dashed.

Fig. 9
Fig. 9

Photographs of holographic image showing flare for beam-balance ratios. a, 1:2; b, 1:7.6.

Fig. 10
Fig. 10

Image-to-object radiance ratio vs object (image) area for constant beam-balance ratio.

Fig. 11
Fig. 11

Ta vs logE curves for Kodak spectroscopic plates, type 649F, processed in Kodak developers as follows: a is D-19, 8 min at 68°F; b is D-8, 2 1 2 min at 68°F; c is Kodak HRP developer, 5 min at 68°F; d is D-165, 14 min at 68°F.

Equations (2)

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( 2 E A E B ) 1 2 / E 0 = ( 2 E A 2 R 0 2 ) 1 2 / E 0 = ( 2 R 0 2 ) 1 2 / ( 1 + R 0 2 ) .
diffracted image flux transmitted zero-order flux = diffracted image flux flux from object × flux from object flux from ref . beam × 1 T a 2 .