Abstract

A technique of encoding an extended incoherent source for image subtraction is presented. The source encoding is obtained from the coherence requirement for image subtraction operation. Since the coherence requirement is a point–pair concept for image subtraction the encoding can take place by spatial sampling an extended incoherent source with narrow slit apertures. The basic advantage of the source encoding is to increase the available light power for the processing operation, so that the inherent difficulty of obtaining a very small incoherent source can be alleviated. Experimental results obtained with this encoded incoherent source are given. Comparisons with the results obtained by processing technique are also provided.

© 1981 Optical Society of America

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  1. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).
  2. K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
    [CrossRef]
  3. S. H. Lee, S. K. Yao, A. G. Milnes, J. Opt. Soc. Am. 60, 1037 (1970).
    [CrossRef]
  4. D. Z. Zhao, C. K. Chiang, H. K. Lin, Opt. Lett. 6, 490 (1981).
    [CrossRef] [PubMed]
  5. J. F. Ebersole, Opt. Eng. 14, 436 (1975).
    [CrossRef]
  6. F. T. S. Yu, Opt. Commun. 27, 23 (1978).
    [CrossRef]
  7. F. T. S. Yu, Appl. Opt. 17, 3571 (1978).
    [CrossRef] [PubMed]
  8. S. L. Zhuang, T. H. Chao, F. T. S. Yu, Opt. Lett. 6, 109 (1981).
    [CrossRef]
  9. F. T. S. Yu, S. L. Zhuang, T. H. Chao, J. Opt. (in press).
  10. F. T. S. Yu, A. M. Tai, Appl. Opt. 18, 2705 (1979).
    [CrossRef]
  11. F. T. S. Yu, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 9 (1980).
  12. S. T. Wu, F. T. S. Yu, Opt. Lett. 6, 452 (1981).
    [PubMed]
  13. M. Born, E. Wolf, Principle of Optics (Pergamon, New York, 1964).
  14. F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, 1973).
  15. M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).
  16. P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 68, 559 (1978).
    [CrossRef]
  17. P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 68, 721 (1978).
    [CrossRef]

1981

1980

F. T. S. Yu, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 9 (1980).

1979

1978

1975

J. F. Ebersole, Opt. Eng. 14, 436 (1975).
[CrossRef]

1970

1969

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

1965

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).

Beran, M. J.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Born, M.

M. Born, E. Wolf, Principle of Optics (Pergamon, New York, 1964).

Bromley, K.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

Brumm, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).

Bryant, J. F.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

Chao, T. H.

S. L. Zhuang, T. H. Chao, F. T. S. Yu, Opt. Lett. 6, 109 (1981).
[CrossRef]

F. T. S. Yu, S. L. Zhuang, T. H. Chao, J. Opt. (in press).

Chavel, P.

Chiang, C. K.

Ebersole, J. F.

J. F. Ebersole, Opt. Eng. 14, 436 (1975).
[CrossRef]

Funkhouser, A.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).

Gabor, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).

Lee, S. H.

Lin, H. K.

Lowenthal, S.

Milnes, A. G.

Monahan, M. A.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

Parrent, G. B.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Restrick, R.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).

Stroke, G. W.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).

Tai, A. M.

Thompson, B. J.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principle of Optics (Pergamon, New York, 1964).

Wu, S. T.

Yao, S. K.

Yu, F. T. S.

S. T. Wu, F. T. S. Yu, Opt. Lett. 6, 452 (1981).
[PubMed]

S. L. Zhuang, T. H. Chao, F. T. S. Yu, Opt. Lett. 6, 109 (1981).
[CrossRef]

F. T. S. Yu, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 9 (1980).

F. T. S. Yu, A. M. Tai, Appl. Opt. 18, 2705 (1979).
[CrossRef]

F. T. S. Yu, Opt. Commun. 27, 23 (1978).
[CrossRef]

F. T. S. Yu, Appl. Opt. 17, 3571 (1978).
[CrossRef] [PubMed]

F. T. S. Yu, S. L. Zhuang, T. H. Chao, J. Opt. (in press).

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, 1973).

Zhao, D. Z.

Zhuang, S. L.

S. L. Zhuang, T. H. Chao, F. T. S. Yu, Opt. Lett. 6, 109 (1981).
[CrossRef]

F. T. S. Yu, S. L. Zhuang, T. H. Chao, J. Opt. (in press).

Appl. Opt.

Appl. Phys. Lett.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

F. T. S. Yu, Opt. Commun. 27, 23 (1978).
[CrossRef]

Opt. Eng.

J. F. Ebersole, Opt. Eng. 14, 436 (1975).
[CrossRef]

Opt. Lett.

Phys. Lett.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 123 (1965).

Proc. Soc. Photo-Opt. Instrum. Eng.

F. T. S. Yu, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 9 (1980).

Other

M. Born, E. Wolf, Principle of Optics (Pergamon, New York, 1964).

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, 1973).

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

F. T. S. Yu, S. L. Zhuang, T. H. Chao, J. Opt. (in press).

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Figures (5)

Fig. 1
Fig. 1

Young’s experiments with an extended source.

Fig. 2
Fig. 2

Image subtraction with an encoded extended incoherent source: S mercury arc lamp; MS, multislit mask; O1 and O2 object transparencies; G, diffraction grating; L, transform lens.

Fig. 3
Fig. 3

Coherence function obtained with multislit source encoding, where x = x 2 - x 2 and s/d = 1.5.

Fig. 4
Fig. 4

Image subtraction; continuous tone object: (a) and (b) input object transparencies; (c) subtracted image obtained with an incoherent technique; (d) subtracted image obtained with a coherent technique.

Fig. 5
Fig. 5

Image subtraction parking lot: (a), (b) input object transparencies; (c) subtracted image obtained with an incoherent technique.

Tables (2)

Tables Icon

Table I Spatial Coherence Requirement for Single-Slit Mask

Tables Icon

Table II Temporal Coherence Requirements

Equations (25)

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S [ λ / ( 2 h 0 ) ] R ,
r 1 - r 2 = ( r 1 - r 2 ) + m λ ,
d = m [ λ R / ( 2 h 0 ) ] .
μ 3 ( x 3 , x 3 ) = μ 2 ( x 2 , x 2 ) f ( x 2 ) f * ( x 2 ) K 2 ( x 2 , x 3 ) × K 2 * ( x 2 , x 3 ) d x 2 d x 2 ,
f ( x 2 ) = O 1 ( x 2 - h 0 ) + O 2 ( x 2 + h 0 ) ,
K 2 ( x 2 , x 3 ) = exp ( i 2 π x 2 x 3 λ f )
μ 3 ( x 3 , x 3 ) = μ 2 ( x 2 , x 2 ) [ O 1 ( x 2 - h 0 ) + O 2 ( x 2 + h 0 ) ] × [ O 1 * ( x 2 - h 0 ) + O 2 * ( x 2 + h 0 ) ] × exp ( i 2 π x 2 x 2 - x 3 x 2 λ f ) d x 2 d x 2 ,
μ 3 ( x 3 , x 3 ) = [ exp ( i 2 π h 0 λ f x 3 ) - exp ( - i 2 π h 0 λ f x 3 ) ] × [ exp ( - i 2 π h 0 λ f x 3 ) - exp ( i 2 π h 0 λ f x 3 ) ] μ 3 ( x 3 , x 3 ) ,
I ( x 4 ) = μ 3 ( x 3 , x 3 ) exp ( i 2 π x 3 - x 3 λ f x 4 ) d x 3 d x 3 ,
I ( x 4 ) = μ ( x 2 , x 2 ) [ O 1 ( x 2 - h 0 ) + O 2 ( x 2 + h 0 ) ] [ O 1 * ( x 2 - h 0 ) + O 2 * ( x 2 + h 0 ) ] · [ δ ( x 2 + x 4 + h 0 ) δ ( x 2 + x 4 + h 0 ) + δ ( x 2 + x 4 - h 0 ) δ ( x 2 + x 4 - h 0 ) - δ ( x 2 + x 4 + h 0 ) δ ( x 2 + x 4 - h 0 ) - δ ( x 2 + x 4 - h 0 ) δ ( x 2 + x 4 + h 0 ) ] d x 2 d x 2 ,
I ( x 4 ) = μ ( o ) [ O 1 ( - x 4 ) 2 + O 2 ( - x 4 ) 2 ] - μ ( 2 h 0 ) O 1 ( - x 4 ) O 2 * ( - x 4 ) - μ * ( 2 h 0 ) O 1 * ( - x 4 ) O 2 ( - x 4 ) + μ ( o ) [ O 1 ( - x 4 - 2 h o ) ] 2 + O 2 ( - x 4 + 2 h 0 ) 2 ] ,
I 0 ( - x 4 ) = μ ( 2 h 0 ) O 1 ( x 4 ) - O 2 ( x 4 ) 2 + [ 1 - μ ( 2 h 0 ) ] [ O 1 ( x 4 ) 2 + O 2 ( x 4 ) 2 ] ,             for ϕ = 0.
I 0 ( - x 4 ) O 1 ( x 4 ) - O 2 ( x 4 ) 2 ,             for μ ( 2 h 0 ) 1.
μ ( x 2 , x 2 ) = S ( x 1 ) K 1 ( x 1 , x 2 ) K 1 ( x 1 , x 2 ) d x 1 ,
K 1 ( x 1 , x 2 ) = exp i [ 2 π x 1 x 2 λ f + ( x 2 - x 1 b f ) ] ,
K 1 ( x 1 , x 2 ) exp { i [ 2 π x 1 x 2 λ f + ( x 2 ) ] } .
μ ( x 2 , x 2 ) = exp i [ ( x 2 ) - ( x 2 ) ] × S ( x 1 ) exp [ i 2 π x 1 λ f ( x 2 - x 2 ) ] d x 1 .
S ( x 1 ) = rect ( x 1 / s ) ,
μ ( x 2 - x 2 ) = sinc π s λ f ( x 2 - x 2 ) ,
μ ( 2 h 0 ) = sinc ( 2 π s d ) .
S ( x 1 ) = n = 1 N rect ( x - n d s ) ,
μ ( x ) = sin ( N π d x λ f ) , N sin ( π d x λ f ) sinc ( π s λ f x ) ,
μ ( x ) = sin ( N π x h 0 ) N sin ( π x h 0 ) sinc ( π s x d h 0 ) ,
[ ( p m f Δ λ ) / 2 π ] d ,
Δ λ λ 2 π h 0 p m ,

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