Abstract

Pulse modulation of electronic time signals is a well-proven concept, particularly in the context of data communications and computers. We suggest that pulse modulation of spatial optical signals might be another fruitful concept. The optical components and optical methods for performing the necessary operations for spatial pulse modulation are available. We demonstrate this experimentally by encoding a two-dimensional analog signal (an image) into a one-dimensional pulse signal. This might be of interest in connection with picture transmission over electronic channels, with cinematography, and with holography.

© 1971 Optical Society of America

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References

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  1. K. Biedermann, Opt. Acta 17, 111 (1970).
  2. M. Marquet, J. Tsujiuchi, Opt. Acta 8, 267 (1961).
    [CrossRef]
  3. B. M. Oliver, J. R. Pierce, C. E. Shannon, Proc. IRE 36, 1324 (1948).
    [CrossRef]
  4. E. M. Deloraine, A. H. Reeves, IEEE Spectrum56 (May1965).
    [CrossRef]
  5. R. M. Stuart, U.S. Patent2,969,531 (1959/1961).
  6. M. P. Battaglia, SPIE J. 8, 175 (1970).
  7. K. S. Pennington, P. M. Will, G. L. Shelton, J. Opt. Soc. Am. 60, 710A (1970).
  8. O. Bryngdahl, J. Opt. Soc. Am. 60, 1546A (1970).
  9. R. L. Lamberts, C. G. Higgins, Photogr. Sci. Eng. 10, 209 (1966); J. D. Kuehler, H. R. Kerby, Proc. Fall Joint Comp. Conf. (1966), p. 735; L. F. Shew, J. G. Blanchard, IEEE Conf. on Laser Eng. and Appl., Washington, D.C. (1969).
  10. A. Kozma, D. L. Kelly, Appl. Opt. 4, 387 (1965).
    [CrossRef]
  11. B. R. Brown, A. W. Lohmann, D. P. Paris, H. W. Werlich, Appl. Opt. 5, 967 (1966); Appl. Opt. 6, 1139, 1739 (1967); Appl. Opt. 7, 651 (1968); IBM J. Res. Dev. 13, 160 (1969).
    [CrossRef] [PubMed]
  12. J. H. Altman, H. J. Zweig, Photogr. Sci. Eng. 7, 173 (1963).
  13. A. W. Lohmann, IBM Tech. Discl. Bull. 7, 624 (1964).
  14. R. L. Hallows, R. J. Klensch, IEEE Spectrum 5, No. 10 (Oct.1968).
    [CrossRef]

1970 (4)

M. P. Battaglia, SPIE J. 8, 175 (1970).

K. S. Pennington, P. M. Will, G. L. Shelton, J. Opt. Soc. Am. 60, 710A (1970).

O. Bryngdahl, J. Opt. Soc. Am. 60, 1546A (1970).

K. Biedermann, Opt. Acta 17, 111 (1970).

1968 (1)

R. L. Hallows, R. J. Klensch, IEEE Spectrum 5, No. 10 (Oct.1968).
[CrossRef]

1966 (2)

B. R. Brown, A. W. Lohmann, D. P. Paris, H. W. Werlich, Appl. Opt. 5, 967 (1966); Appl. Opt. 6, 1139, 1739 (1967); Appl. Opt. 7, 651 (1968); IBM J. Res. Dev. 13, 160 (1969).
[CrossRef] [PubMed]

R. L. Lamberts, C. G. Higgins, Photogr. Sci. Eng. 10, 209 (1966); J. D. Kuehler, H. R. Kerby, Proc. Fall Joint Comp. Conf. (1966), p. 735; L. F. Shew, J. G. Blanchard, IEEE Conf. on Laser Eng. and Appl., Washington, D.C. (1969).

1965 (2)

E. M. Deloraine, A. H. Reeves, IEEE Spectrum56 (May1965).
[CrossRef]

A. Kozma, D. L. Kelly, Appl. Opt. 4, 387 (1965).
[CrossRef]

1964 (1)

A. W. Lohmann, IBM Tech. Discl. Bull. 7, 624 (1964).

1963 (1)

J. H. Altman, H. J. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

1961 (1)

M. Marquet, J. Tsujiuchi, Opt. Acta 8, 267 (1961).
[CrossRef]

1948 (1)

B. M. Oliver, J. R. Pierce, C. E. Shannon, Proc. IRE 36, 1324 (1948).
[CrossRef]

Altman, J. H.

J. H. Altman, H. J. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

Battaglia, M. P.

M. P. Battaglia, SPIE J. 8, 175 (1970).

Biedermann, K.

K. Biedermann, Opt. Acta 17, 111 (1970).

Brown, B. R.

Bryngdahl, O.

O. Bryngdahl, J. Opt. Soc. Am. 60, 1546A (1970).

Deloraine, E. M.

E. M. Deloraine, A. H. Reeves, IEEE Spectrum56 (May1965).
[CrossRef]

Hallows, R. L.

R. L. Hallows, R. J. Klensch, IEEE Spectrum 5, No. 10 (Oct.1968).
[CrossRef]

Higgins, C. G.

R. L. Lamberts, C. G. Higgins, Photogr. Sci. Eng. 10, 209 (1966); J. D. Kuehler, H. R. Kerby, Proc. Fall Joint Comp. Conf. (1966), p. 735; L. F. Shew, J. G. Blanchard, IEEE Conf. on Laser Eng. and Appl., Washington, D.C. (1969).

Kelly, D. L.

Klensch, R. J.

R. L. Hallows, R. J. Klensch, IEEE Spectrum 5, No. 10 (Oct.1968).
[CrossRef]

Kozma, A.

Lamberts, R. L.

R. L. Lamberts, C. G. Higgins, Photogr. Sci. Eng. 10, 209 (1966); J. D. Kuehler, H. R. Kerby, Proc. Fall Joint Comp. Conf. (1966), p. 735; L. F. Shew, J. G. Blanchard, IEEE Conf. on Laser Eng. and Appl., Washington, D.C. (1969).

Lohmann, A. W.

Marquet, M.

M. Marquet, J. Tsujiuchi, Opt. Acta 8, 267 (1961).
[CrossRef]

Oliver, B. M.

B. M. Oliver, J. R. Pierce, C. E. Shannon, Proc. IRE 36, 1324 (1948).
[CrossRef]

Paris, D. P.

Pennington, K. S.

K. S. Pennington, P. M. Will, G. L. Shelton, J. Opt. Soc. Am. 60, 710A (1970).

Pierce, J. R.

B. M. Oliver, J. R. Pierce, C. E. Shannon, Proc. IRE 36, 1324 (1948).
[CrossRef]

Reeves, A. H.

E. M. Deloraine, A. H. Reeves, IEEE Spectrum56 (May1965).
[CrossRef]

Shannon, C. E.

B. M. Oliver, J. R. Pierce, C. E. Shannon, Proc. IRE 36, 1324 (1948).
[CrossRef]

Shelton, G. L.

K. S. Pennington, P. M. Will, G. L. Shelton, J. Opt. Soc. Am. 60, 710A (1970).

Stuart, R. M.

R. M. Stuart, U.S. Patent2,969,531 (1959/1961).

Tsujiuchi, J.

M. Marquet, J. Tsujiuchi, Opt. Acta 8, 267 (1961).
[CrossRef]

Werlich, H. W.

Will, P. M.

K. S. Pennington, P. M. Will, G. L. Shelton, J. Opt. Soc. Am. 60, 710A (1970).

Zweig, H. J.

J. H. Altman, H. J. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

Appl. Opt. (2)

IBM Tech. Discl. Bull. (1)

A. W. Lohmann, IBM Tech. Discl. Bull. 7, 624 (1964).

IEEE Spectrum (2)

R. L. Hallows, R. J. Klensch, IEEE Spectrum 5, No. 10 (Oct.1968).
[CrossRef]

E. M. Deloraine, A. H. Reeves, IEEE Spectrum56 (May1965).
[CrossRef]

J. Opt. Soc. Am. (2)

K. S. Pennington, P. M. Will, G. L. Shelton, J. Opt. Soc. Am. 60, 710A (1970).

O. Bryngdahl, J. Opt. Soc. Am. 60, 1546A (1970).

Opt. Acta (2)

K. Biedermann, Opt. Acta 17, 111 (1970).

M. Marquet, J. Tsujiuchi, Opt. Acta 8, 267 (1961).
[CrossRef]

Photogr. Sci. Eng. (2)

R. L. Lamberts, C. G. Higgins, Photogr. Sci. Eng. 10, 209 (1966); J. D. Kuehler, H. R. Kerby, Proc. Fall Joint Comp. Conf. (1966), p. 735; L. F. Shew, J. G. Blanchard, IEEE Conf. on Laser Eng. and Appl., Washington, D.C. (1969).

J. H. Altman, H. J. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

Proc. IRE (1)

B. M. Oliver, J. R. Pierce, C. E. Shannon, Proc. IRE 36, 1324 (1948).
[CrossRef]

SPIE J. (1)

M. P. Battaglia, SPIE J. 8, 175 (1970).

Other (1)

R. M. Stuart, U.S. Patent2,969,531 (1959/1961).

Cited By

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Figures (16)

Fig. 1
Fig. 1

Analog modulation. Original, AM, and PhMf signals.

Fig. 2
Fig. 2

Pulse modulation. Original, PAM, PWM, PPM, and two PAM interlaced signals.

Fig. 3
Fig. 3

Noise removal for binary signals. Original signal, signal plus noise, signal after hardclipping.

Fig. 4
Fig. 4

Photographic response. Amplitude transmittance T and amplitude fluctuations ΔT vs exposure E.

Fig. 5
Fig. 5

The encoder. Object OBJ, lenses L, grating G1, output slit with one-dimensional signal S(X).

Fig. 6
Fig. 6

Transmittance of fine-slit grating.

Fig. 7
Fig. 7

The encoding process. The object F (outlines only), superposed by tilted grating, y integrated into S(X).

Fig. 8
Fig. 8

Encoding experiment: (a) grating M, (b) superposed by object IA, yielding IE, (c) y integrating IE, yielding S.

Fig. 9
Fig. 9

The decoder. One-dimensional signal S(X), lenses L, grating G2, low-pass filter FILT, final image IMG.

Fig. 10
Fig. 10

Decoding experiment: (a) one-dimensional signal S(X), (b) superposed by grating M, yielding ID, (c) through low-pass filter into image IB.

Fig. 11
Fig. 11

The decoding process. The one-dimensional signal S(X) spread out in y direction, superposed by tilted grating, yielding ID (in bold lines).

Fig. 12
Fig. 12

Frequency spectra in the encoder.

Fig. 13
Fig. 13

Frequency spectrum in the decoder before lowpass filter.

Fig. 14
Fig. 14

Influence of the grating angle ϕ in the encoder. Top row, one-dimensional signals; bottom row, corresponding decoded images; ϕ increasing from left to right.

Fig. 15
Fig. 15

Misalignment of the grating in the decoder. In the first three images ID the angle ϕ was too small, too large, and negative, respectively. In the fourth image, ϕ was correct but the grating shifted by d/2.

Fig. 16
Fig. 16

Multichannel encoder. Grating G1 and object OBJ are in contact. Each text line is imaged into its own 1–D channel slit Sm(x).

Equations (21)

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S ( X ) = 1 H - H / 2 + H / 2 I A ( x , y ) M ( x , y ) d y ,
I ˜ A ( ν , μ ) = I A ( x , y ) exp [ - 2 π i ( x ν + y μ ) ] d x d y .
Δ ν 0 Δ ν T ( 2 cos ϕ / d ) - Δ ν 0             Δ ν 0 cos ϕ / d
sin ϕ / d 1 / H , or ϕ ϕ 0 , sin ϕ 0 = d / H .
Δ μ 0 ( N / d ) sin ϕ .
I A ( x , y ) = 0 for y > H / 2.
I A ( x , y ) = Σ ( n ) I n ( X ) exp 2 π i n y / H rect ( y / H ) , rect ( y / H ) = 1 if y H / 2 ,             0 if y > H / 2.
M ( X ) = Σ ( m ) A m exp ( 2 π i m x / d ) , A m = W sinc ( m W ) ,             sinc Z - sin ( π Z ) / ( π Z ) .
M ( x , y ) = M 0 ( x cos ϕ 0 + y sin ϕ 0 ) , H tan ϕ 0 = d / cos ϕ 0 ,             H sin ϕ 0 = d , M ( x , y ) = Σ ( m ) A m exp [ 2 π i m ( x cos ϕ / d + y / H ) ] .
I E ( x , y ) = Σ Σ A m I n ( x ) exp { 2 π i [ m × cos ϕ / d + ( n + m ) y / H ] } .
S ( X ) = 1 H I E d y = Σ ( n ) A - n I n ( x ) exp ( - 2 π i n × cos ϕ / d )
I D ( x , y ) = rect ( y / H ) Σ Σ A m A - n I n exp { 2 π i [ ( m - n ) × cos ϕ / d + m y / H ] } .
I ˜ D ( ν , μ ) = H Σ Σ A m A - n I n [ ν - ( m - n ) cos ϕ / d ] sinc ( H μ - m ) , I ˜ n ( ν ) = I n ( x ) exp ( - 2 π i ν x ) d x ,
F ˜ ( ν ) = rect ( ν / Δ ν F ) ,             Δ ν 0 ν F ( 2 cos ϕ / d ) - Δ ν 0 , F ˜ ( ν ) I ˜ D ( ν , μ ) = H Σ A n A - n n I ˜ ( ν ) sinc ( H μ - n ) = I ˜ B ( ν , μ ) .
I B ( x , y ) = Σ A n A - n I n ( X ) exp ( 2 π i n y / H ) rect ( y / H ) ,
I n ( X ) = 0 for n > N / 2 , A n A - n = const for η N / 2.
A n 2 = W 2 sinc 2 ( n W ) = const if n 1 2 W ,             N W = 1 ,
L 0 ( X ) = Σ ( n ) rect ( x - n d ) d exp [ i x ( x - n d ) 2 / λ f ] , L 0 ( X ) = Σ ( m ) A m exp ( 2 π i m x / d ) , A m = 1 d - d / 2 + d / 2 L 0 exp ( - 2 π i m x / d ) d x , A m 2 λ f d 2             if m < d 2 / 2 λ f , A m 2 0             if m > d 2 / 2 λ f .
N = d 2 / λ f ,             A m 2 1 / N for m N / 2.
S W A = Δ x 0 y 0 / δ x 0 δ y 0 , Δ y 0 = H , δ x 0 = d / cos ϕ , δ y 0 = W d / sin ϕ , H sin ϕ = d , S W A = ( Δ x 0 / W d ) cos ϕ .
S W S = Δ x s / δ x s ,             Δ x s = Δ x 0 ,             δ x s = W d / cos ϕ , S W S = ( Δ x 0 / W d ) cos ϕ = S W A .

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