Abstract

The linear recording of a Fourier transform hologram of a 2-D object using a pseudorandom diffuser is described. The recording condition is determined by two parameters: (1) intensity ratio of the reference-to-object beam; and (2) exposure energy of the reference beam, which is estimated from the shape of the power spectrum of the diffuser and the exposure-to-amplitude transmittance curve of the recording medium. The estimating process of the recording condition is confirmed by a computer simulation and an experiment. The effect of the dynamic range of the recording medium on the reconstructed image is also discussed.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964).
    [CrossRef]
  2. C. B. Burckhardt, Appl. Opt. 9, 695 (1970).
    [CrossRef] [PubMed]
  3. Y. Takeda, Y. Oshida, Y. Miyamura, Appl. Opt. 11, 818 (1972).
    [CrossRef] [PubMed]
  4. W. J. Dallas, Appl. Opt. 12, 1179 (1973).
    [CrossRef] [PubMed]
  5. S. Yonezawa, Opt. Commun. 19, 370 (1976).
    [CrossRef]
  6. Y. Torii, Opt. Commun. 24, 175 (1978).
    [CrossRef]
  7. M. Kato, Y. Nakayama, T. Suzuki, Appl. Opt. 14, 1093 (1975).
    [CrossRef] [PubMed]
  8. M. Kato, I. Sato, Y. Nakayama, in Proceedings, Tenth Congress of the International Commission for Optics, Palacky University, Olomouc Czech Technical University, Prague, 25– 29, Aug. 1975.
  9. Y. Nakayama, M. Kato, J. Opt. Soc. Am. 69, 1367 (1979).
    [CrossRef]
  10. Y. Nakayama, M. Kato, J. Opt. Soc. Am. 70, 1382 (1980).
    [CrossRef]
  11. Y. Nakayama, M. Kato, Appl. Opt. 20, 2178 (1981).
    [CrossRef] [PubMed]
  12. A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
    [CrossRef]
  13. M. C. King, Appl. Opt. 11, 791 (1972).
    [CrossRef] [PubMed]

1981

1980

1979

1978

Y. Torii, Opt. Commun. 24, 175 (1978).
[CrossRef]

1976

S. Yonezawa, Opt. Commun. 19, 370 (1976).
[CrossRef]

1975

1973

1972

1970

1966

1964

Burckhardt, C. B.

Dallas, W. J.

Kato, M.

Y. Nakayama, M. Kato, Appl. Opt. 20, 2178 (1981).
[CrossRef] [PubMed]

Y. Nakayama, M. Kato, J. Opt. Soc. Am. 70, 1382 (1980).
[CrossRef]

Y. Nakayama, M. Kato, J. Opt. Soc. Am. 69, 1367 (1979).
[CrossRef]

M. Kato, Y. Nakayama, T. Suzuki, Appl. Opt. 14, 1093 (1975).
[CrossRef] [PubMed]

M. Kato, I. Sato, Y. Nakayama, in Proceedings, Tenth Congress of the International Commission for Optics, Palacky University, Olomouc Czech Technical University, Prague, 25– 29, Aug. 1975.

King, M. C.

Kozma, A.

Leith, E. N.

Miyamura, Y.

Nakayama, Y.

Y. Nakayama, M. Kato, Appl. Opt. 20, 2178 (1981).
[CrossRef] [PubMed]

Y. Nakayama, M. Kato, J. Opt. Soc. Am. 70, 1382 (1980).
[CrossRef]

Y. Nakayama, M. Kato, J. Opt. Soc. Am. 69, 1367 (1979).
[CrossRef]

M. Kato, Y. Nakayama, T. Suzuki, Appl. Opt. 14, 1093 (1975).
[CrossRef] [PubMed]

M. Kato, I. Sato, Y. Nakayama, in Proceedings, Tenth Congress of the International Commission for Optics, Palacky University, Olomouc Czech Technical University, Prague, 25– 29, Aug. 1975.

Oshida, Y.

Sato, I.

M. Kato, I. Sato, Y. Nakayama, in Proceedings, Tenth Congress of the International Commission for Optics, Palacky University, Olomouc Czech Technical University, Prague, 25– 29, Aug. 1975.

Suzuki, T.

Takeda, Y.

Torii, Y.

Y. Torii, Opt. Commun. 24, 175 (1978).
[CrossRef]

Upatnieks, J.

Yonezawa, S.

S. Yonezawa, Opt. Commun. 19, 370 (1976).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Schematic models of 2-D diffusers.

Fig. 2
Fig. 2

Normalized forms of the power spectra: (a) six-level WMD and (b) eight-level WMD. M indicates the degree of modulation. The WMD reduces to the CPRD when M = 0 and to the PRD when M = 1. The horizontal scale ξ is calculated for P = 25 μm, λ = 488 nm, and f = 70 mm.

Fig. 3
Fig. 3

Theoretical curves of (a) ratio EPP/EB of the difference between maximum and minimum energy to their average energy in the hologram plane and (b) energy ratio EB/ER of average to reference beam to intensity ratio IR/IO of reference-to-object beam for a 1-D model with DH = 1.37-mm hologram size: A, 3-L-PRD; B, 6-L-WMD (M = 0.5); C, 6-L-CPRD; D, 4-L-PRD; E, 8-L-WMD (M = 0.5); and F, 8-L-CPRD.

Fig. 4
Fig. 4

Theoretical curves of (a) EPP/EB and (b) EB/ER vs IR/IO for a 2-D model with DH = 1.37 mm; the symbols A–F are the same as in Fig. 3.

Fig. 5
Fig. 5

Curve of amplitude transmittance T vs exposure E for silver halide emulsion. The insertion is density D vs exposure E. Emax and Emin are maximum and minimum energy on the linear region, respectively; EB denotes the medial energy, namely, the operating-bias point.

Fig. 6
Fig. 6

Schematic of holographic system used in the simulation: (a) recording and (b) reconstruction. Distance XR between the point source of the reference and the object is selected to be 3XO/2. The hologram size is DH.

Fig. 7
Fig. 7

Amplitude transmittance distributions of two simulated objects: (a) uniformly transparent pattern and (b) rectangular pattern.

Fig. 8
Fig. 8

Irradiance distribution in the hologram recording plane calculated by a computer for the six-level CPRD and the two objects: (a) uniformly transparent pattern and (b) rectangular pattern. The parameters used in the simulation are the same as in Fig. 2.

Fig. 9
Fig. 9

Curves of (a) EPP/EB and (b) EB/ER vs IR/IO obtained by simulation: ○ and ● are 4-L-PRD; △ and ▲ are 6-L-CPRD; □ and ■ are 6-L-WMD, wherein open and closed symbols are associated with the uniformly transparent and rectangular patterns, respectively.

Fig. 10
Fig. 10

Plots of SNR (solid line) and diffraction efficiency η (broken line) against DR for (a) 4-L-PRD, (b) 6-L-CPRD, and (c) 6-L-WMD: △, IR/IO = 17, Dev 9′; ○, IR/IO = 22, Dev 3′; and ●, IR/IO = 5, Dev 3′. Dashed lines show the SNR calculated in an ideal holographic system. Other parameters are the same as in Fig. 2.

Fig. 11
Fig. 11

Original phase levels of the 6-L-CPRD (lower solid line), irradiance distributions of the objects (broken line), and their normalized images (upper solid line) obtained by a computer simulation of linear hologram recording for different dynamic ranges: (a) DR = 40 dB; (b) DR = 20 dB; and (c) DR = 30 dB. The recording process is simulated assuming IR/IO = 22, ER = 0.54 and Dev 3′, and the hologram size DH is 1.37 mm. Other parameters are the same as in Fig. 2.

Fig. 12
Fig. 12

Original phase levels of the 6-L-CPRD (lower solid line), irradiance distributions of the objects (broken line), and their normalized images (upper solid line) obtained by a computer simulation of nonlinear hologram recording for different dynamic ranges: (a) DR = 40 dB; (b) DR = 20 dB; and (c) DR = 30 dB. The recording process is simulated assuming IR/IO = 5, ER = 0.34 and Dev 3′, and the hologram size DH is 1.37 mm. Other parameters are the same as in Fig. 2.

Fig. 13
Fig. 13

Schematic diagram of the experimental arrangement: (a) recording optical system and (b) measurement system of the SNR of the reconstructed image: M, mirror; B.S., beam splitter; F, density filter; F.T.L., Fourier transform lens and; Hm, hologram.

Fig. 14
Fig. 14

Characteristic of amplitude transmittance T vs exposure E for Sakura HRP-T. The emulsion was exposed by 488-nm light and developed by Kodak D-19 developer held at 19°C for 3 min.

Fig. 15
Fig. 15

Characteristic of the square root of diffraction efficiency η vs amplitude of energy distribution of interference pattern Ei for Sakura HRP-T. Area size and spatial frequency of the interference pattern are 2 × 2 mm and 1000 lines/mm, respectively. The emulsion processing is the same as in Fig. 14.

Fig. 16
Fig. 16

Three examples of reconstructed images: (a) 2-L-RD with L = 34 μm, IR/IO = 30, ER = 12.8 μJ/cm2,4-mm diam hologram size; (b) 4-L-PRD with L = 34 μm, IR/IO = 30, ER = 12.8 μJ/cm2, 4-mm diam hologram size; and (c) 6-L-CPRD with Lm = Ls = 25 μm, IR/IO = 30, ER = 13.2 μJ/cm2, 3-mm diam hologram size.

Fig. 17
Fig. 17

Irradiance distributions detected by a photomultiplier with a 50- × 50-μm aperture scanning on the widest line in the reconstructed images: (a), (b), and (c) are associated with the (a), (b), and (c) shown in Fig. 16, respectively. The SNR calculated from these distributions are 11 dB for (a), 15 dB for (b) and 16 dB for (c).

Fig. 18
Fig. 18

Signal-to-noise ratio against (a) intensity ratio IR/IO of reference-to-object beam for the recording conditions shown in Tables III and IV and (b) energy ER of reference beam for IR/IO = 30. E0 indicates the values of ER listed in Table III: △, 6-L-CPRD; ○, 4-L-PRD, and □, 2-L-RD.

Tables (4)

Tables Icon

Table I Examples of the Pseudorandom Phase Sequence

Tables Icon

Table II R/O Constants of the Diffuser for Five Hologram Sizes DH

Tables Icon

Table III Optimum Recording Conditions for the 4-L-PRD and the 6-L-CPRD

Tables Icon

Table IV ER and EPP/EB in the Cases of IR/IO = 10 and 40 for the 4-L-PRD and the 6-L-CPRD

Equations (32)

Equations on this page are rendered with MathJax. Learn more.

( I R I O ) 1 = β α R ,
R = D H D H / 2 D H / 2 I ( ξ ) d ξ .
I ( ξ , ζ ) = α I ( ξ ) I ( ζ ) ,
( I R I O ) 2 = β α R 2 ,
E P P E B = 4 ( β ) 1 / 2 β + 1 ,
E B E R = 1 + 1 β ,
β = { ( I R / I O ) 1 R , ( 1 D ) ( I R / I O ) 2 R 2 , ( 2 D ) .
ϕ x , y = ϕ x + ϕ y .
DR = 20 log E max E min Δ E ,
( η ) 1 / 2 E i 0.6 , ( E i < 1.0 μ J / cm 2 ) ( η ) 1 / 2 E i , ( 1.0 E i 20 μ J / cm 2 ) .
2 3 π
4 3 π
2 3 π
2 3 π
4 3 π
2 3 π
1 2 π
3 2 π
3 2 π
1 2 π
2 3 π
1 3 π
5 3 π
4 2 π
2 3 π
1 3 π
1 4 π
1 2 π
1 4 π
7 4 π
3 2 π
5 4 π

Metrics