Abstract

Analog-to-digital (A-D) conversion of intensity transmittance (or reflectance) can be accomplished through nonlinear coherent optical image processing. Theoretically speaking, for any given positive integer N, 2N discrete levels of transmittance (or reflectance) can be digitized into binary form simultaneously via pure optical means, involving the proper design and fabrication of a specific halftone screen. The digital outputs of the N bit-planes are selected at the Fourier plane by spatial filtering the (2n − 1)th diffraction order, where n = 1, 2, ⋯, and N, respectively. The specific halftone screen must have (2N − 1) gray levels, and it should be emphasized that only a single halftone photograph is required for the optical A-D conversion. The general principle of this new method and a preliminary experimental result of an eight-level A-D conversion are described in this paper.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Kato, J. W. Goodman, Opt. Commun. 8, 378 (1973).
    [CrossRef]
  2. H. Kato, J. W. Goodman, J. Opt. Soc. Am. 63, 1306A (1973).
  3. A. A. Sawchuk, S. R. Dashiell, in Proceedings IEEE International Computing Conference (April1975), p. 73;also Opt. Commun. 15, 66 (1975).
  4. T. C. Strand, Opt. Commun. 15, 60 (1975).
    [CrossRef]
  5. H. K. Liu, J. W. Goodman, J. L.-H. Chan, Appl. Opt. 15, 2394 (1976).
    [CrossRef] [PubMed]
  6. H. K. Liu, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
    [CrossRef]
  7. H. K. Liu, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 83–17 (1976).
  8. A. Lohmann, T. C. Strand, Erlangen-Nurnberg; private communication.
  9. S. R. Dashiell, A. A. Sawchuk, Appl. Opt. 16, 2279 (1977).
    [CrossRef] [PubMed]

1977 (1)

1976 (3)

H. K. Liu, J. W. Goodman, J. L.-H. Chan, Appl. Opt. 15, 2394 (1976).
[CrossRef] [PubMed]

H. K. Liu, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

H. K. Liu, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 83–17 (1976).

1975 (1)

T. C. Strand, Opt. Commun. 15, 60 (1975).
[CrossRef]

1973 (2)

H. Kato, J. W. Goodman, Opt. Commun. 8, 378 (1973).
[CrossRef]

H. Kato, J. W. Goodman, J. Opt. Soc. Am. 63, 1306A (1973).

Chan, J. L.-H.

Dashiell, S. R.

S. R. Dashiell, A. A. Sawchuk, Appl. Opt. 16, 2279 (1977).
[CrossRef] [PubMed]

A. A. Sawchuk, S. R. Dashiell, in Proceedings IEEE International Computing Conference (April1975), p. 73;also Opt. Commun. 15, 66 (1975).

Goodman, J. W.

H. K. Liu, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 83–17 (1976).

H. K. Liu, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

H. K. Liu, J. W. Goodman, J. L.-H. Chan, Appl. Opt. 15, 2394 (1976).
[CrossRef] [PubMed]

H. Kato, J. W. Goodman, Opt. Commun. 8, 378 (1973).
[CrossRef]

H. Kato, J. W. Goodman, J. Opt. Soc. Am. 63, 1306A (1973).

Kato, H.

H. Kato, J. W. Goodman, J. Opt. Soc. Am. 63, 1306A (1973).

H. Kato, J. W. Goodman, Opt. Commun. 8, 378 (1973).
[CrossRef]

Liu, H. K.

H. K. Liu, J. W. Goodman, J. L.-H. Chan, Appl. Opt. 15, 2394 (1976).
[CrossRef] [PubMed]

H. K. Liu, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 83–17 (1976).

H. K. Liu, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

Lohmann, A.

A. Lohmann, T. C. Strand, Erlangen-Nurnberg; private communication.

Sawchuk, A. A.

S. R. Dashiell, A. A. Sawchuk, Appl. Opt. 16, 2279 (1977).
[CrossRef] [PubMed]

A. A. Sawchuk, S. R. Dashiell, in Proceedings IEEE International Computing Conference (April1975), p. 73;also Opt. Commun. 15, 66 (1975).

Strand, T. C.

T. C. Strand, Opt. Commun. 15, 60 (1975).
[CrossRef]

A. Lohmann, T. C. Strand, Erlangen-Nurnberg; private communication.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

H. Kato, J. W. Goodman, J. Opt. Soc. Am. 63, 1306A (1973).

Nouv. Rev. Opt. (1)

H. K. Liu, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

Opt. Commun. (2)

H. Kato, J. W. Goodman, Opt. Commun. 8, 378 (1973).
[CrossRef]

T. C. Strand, Opt. Commun. 15, 60 (1975).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. K. Liu, J. W. Goodman, Proc. Soc. Photo-Opt. Instrum. Eng. 83, 83–17 (1976).

Other (2)

A. Lohmann, T. C. Strand, Erlangen-Nurnberg; private communication.

A. A. Sawchuk, S. R. Dashiell, in Proceedings IEEE International Computing Conference (April1975), p. 73;also Opt. Commun. 15, 66 (1975).

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 (6)

Fig. 1
Fig. 1

Diagram of a coherent optical imaging system.

Fig. 2
Fig. 2

A microphotograph showing the scale of calibration (top) and one period of the specific halftone screen (bottom) designed for the eight-level A-D conversion of intensity transmittance. The discrete screen transmittances in the same period, T 1 s through T 8 s  , are also indicated.

Fig. 3
Fig. 3

(a) The normalized diffraction outputs for the first, third, and seventh diffraction orders. (b) The normalized digital outputs of the three bit-planes corresponding to the outputs of (a).

Fig. 4
Fig. 4

Measured intensity transmittance over a linear width of 5 cm in the gray scale.

Fig. 5
Fig. 5

Polaroid photographs of the first, third, and seventh diffraction order outputs at the image plane of the coherent optical imaging system.

Fig. 6
Fig. 6

The densitometer measured intensity transmittances along a horizontal line of the same location of the negatives of the photographic recordings of the outputs of the three bit-planes as shown in Fig. 5.

Equations (10)

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

T s ( x ) = T s ( x + a )  ,
T s ( x ) = T 2 N s [ u ( x ) u ( x a / 2 ) ] + T 2 N 1 s ( u ( x a / 2 ) u { x a / 2 a / [ 2 ( 2 N 1 ) ] } ) + T 2 N 2 s ( u { x a / 2 a / [ 2 ( 2 N 1 ) ] } u [ x a / 2 a / ( 2 N 1 ) ] ) + T 2 N n s ( u { x a / 2 ( n 1 ) a / [ 2 ( 2 N 1 )  ] } u ( x a / 2 n a / [ 2 ( 2 N 1 ) ] } ) + T 1 s { u [ x a / 2 ( 2 N 1 1 ] a / ( 2 N 1 ) ] u ( x a ) }  ,
u ( x ) = 1 , x 0 , = 0 , x < 0.
T s ( x ) = T 2 N s [ u ( x ) u ( x a / 2 ) ] + n = 1 2 N 1 T 2 N n s    ( u { x a / 2 ( n 1 ) a / [ 2 ( 2 N 1 ) ] } u { x a / 2 n a / [ 2 ( 2 N 1 ) ] } ) .
T p ( x , y ) = ( T 2 N p ,   T 2 N 1 p , , T 2 p ,   T 1 p )  ,
1 T max p T i p > T j p T min p 0.
T i p T 2 N i + 1 s > E t ( P τ ) 1 > T i p    T 2 N i s  ,
x i a / 2 + ( i 1 ) a / ( 2 N + 1 2 ) x 0 ,
I n ( x i / a ) = a 2 ( n π λ f ) 2 sin 2 ( n π x i / a ) = I n    max sin 2 ( n π x i / a ) .
T s ( x ) = T 8 s [ u ( x ) u ( x a / 2 ) ]  + T 7 s [ u ( x a / 2 ) u ( x 4 a / 7 ) ] +  + T 1 s [ u ( x 13 a / 14 ) u ( x a ) ]  ,

Metrics