Abstract

A technique of restoration of smeared photographic images by white light optical processing is described. It is well known that the image quality and the degree of restoration obtainable by coherent optical processing techniques are severely limited by artifact noise. This new technique offers a lower artifact noise and possibly a higher degree of restoration. We stress that this incoherent restoration technique applies to 2-D objects, although the operation to be performed must be 1-D.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Tsujiuchi, “Correction of Optical Image by Compensation of Aberration and Spatial Frequency Filtering,” in Progress in Optics, Vol. 2 (North-Holland, Amsterdam, 1963).
    [CrossRef]
  2. G. W. Stroke, R. G. Zech, Phys. Lett., E. Wolf, Ed. 25, 89 (1967).
    [CrossRef]
  3. G. W. Stroke, F. Furrer, D. R. Lamberty, Opt. Commun. 1, 141 (1969).
    [CrossRef]
  4. F. T. S. Yu, Appl. Opt. 8, 53 (1969).
    [CrossRef] [PubMed]
  5. J. Tsujiuchi, T. Honda, T. Fukaya, Opt. Commun. 1, 379 (1970).
    [CrossRef]
  6. F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, Mass., 1973), Chap. 9.
  7. F. T. S. Yu, Optics and Information Theory (Wiley-Interscience, New York, 1976), Chap. 7.
  8. F. T. S. Yu, Opt. Commun., to be published (1978). (1978).
  9. A. W. Lohmann, D. P. Paris, Appl. Opt. 7, 651 (1968).
    [CrossRef] [PubMed]
  10. S. K. Case, R. Alferness, Appl. Phys. 10, 41 (1976).
    [CrossRef]
  11. E. N. Leith, B. Chang, Appl. Opt. 12, 1957 (1973).
    [CrossRef] [PubMed]
  12. E. N. Leith, J. Roth, Appl. Opt. 16, 2565 (1977).
    [CrossRef] [PubMed]

1977 (1)

1976 (1)

S. K. Case, R. Alferness, Appl. Phys. 10, 41 (1976).
[CrossRef]

1973 (1)

1970 (1)

J. Tsujiuchi, T. Honda, T. Fukaya, Opt. Commun. 1, 379 (1970).
[CrossRef]

1969 (2)

G. W. Stroke, F. Furrer, D. R. Lamberty, Opt. Commun. 1, 141 (1969).
[CrossRef]

F. T. S. Yu, Appl. Opt. 8, 53 (1969).
[CrossRef] [PubMed]

1968 (1)

Alferness, R.

S. K. Case, R. Alferness, Appl. Phys. 10, 41 (1976).
[CrossRef]

Case, S. K.

S. K. Case, R. Alferness, Appl. Phys. 10, 41 (1976).
[CrossRef]

Chang, B.

Fukaya, T.

J. Tsujiuchi, T. Honda, T. Fukaya, Opt. Commun. 1, 379 (1970).
[CrossRef]

Furrer, F.

G. W. Stroke, F. Furrer, D. R. Lamberty, Opt. Commun. 1, 141 (1969).
[CrossRef]

Honda, T.

J. Tsujiuchi, T. Honda, T. Fukaya, Opt. Commun. 1, 379 (1970).
[CrossRef]

Lamberty, D. R.

G. W. Stroke, F. Furrer, D. R. Lamberty, Opt. Commun. 1, 141 (1969).
[CrossRef]

Leith, E. N.

Lohmann, A. W.

Paris, D. P.

Roth, J.

Stroke, G. W.

G. W. Stroke, F. Furrer, D. R. Lamberty, Opt. Commun. 1, 141 (1969).
[CrossRef]

G. W. Stroke, R. G. Zech, Phys. Lett., E. Wolf, Ed. 25, 89 (1967).
[CrossRef]

Tsujiuchi, J.

J. Tsujiuchi, T. Honda, T. Fukaya, Opt. Commun. 1, 379 (1970).
[CrossRef]

J. Tsujiuchi, “Correction of Optical Image by Compensation of Aberration and Spatial Frequency Filtering,” in Progress in Optics, Vol. 2 (North-Holland, Amsterdam, 1963).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, Appl. Opt. 8, 53 (1969).
[CrossRef] [PubMed]

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, Mass., 1973), Chap. 9.

F. T. S. Yu, Optics and Information Theory (Wiley-Interscience, New York, 1976), Chap. 7.

F. T. S. Yu, Opt. Commun., to be published (1978). (1978).

Zech, R. G.

G. W. Stroke, R. G. Zech, Phys. Lett., E. Wolf, Ed. 25, 89 (1967).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. (1)

S. K. Case, R. Alferness, Appl. Phys. 10, 41 (1976).
[CrossRef]

Opt. Commun. (2)

J. Tsujiuchi, T. Honda, T. Fukaya, Opt. Commun. 1, 379 (1970).
[CrossRef]

G. W. Stroke, F. Furrer, D. R. Lamberty, Opt. Commun. 1, 141 (1969).
[CrossRef]

Other (5)

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, Mass., 1973), Chap. 9.

F. T. S. Yu, Optics and Information Theory (Wiley-Interscience, New York, 1976), Chap. 7.

F. T. S. Yu, Opt. Commun., to be published (1978). (1978).

J. Tsujiuchi, “Correction of Optical Image by Compensation of Aberration and Spatial Frequency Filtering,” in Progress in Optics, Vol. 2 (North-Holland, Amsterdam, 1963).
[CrossRef]

G. W. Stroke, R. G. Zech, Phys. Lett., E. Wolf, Ed. 25, 89 (1967).
[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 (7)

Fig. 1
Fig. 1

Solid curve represents the Fourier spectrum of a linear smeared point image and shaded area represents the restored Fourier spectrum. qn = 2πny, n = 1,2,3, …, Δq; the restored spatial bandwidth Tm; maximum transmittance of the restored spectrum.

Fig. 2
Fig. 2

Amplitude filter function.

Fig. 3
Fig. 3

Phase filter function.

Fig. 4
Fig. 4

An incoherent optical processor I; incoherent point source g(x,y); input transparency T(x); diffraction grating L1 and L2; transform lenses H1(q); spatial filter.

Fig. 5
Fig. 5

Sketch of the output diffraction of the restored images.

Fig. 6
Fig. 6

Determination of wavelength spread over the spatial filter.

Fig. 7
Fig. 7

Dash and solid curves represent the Fourier spectrum of a linear smeared point image for λ0 and for λ > λ0, respectively, where λ0 is the wavelength of the spatial filter.

Equations (36)

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

G ( q ) = S ( q ) D ( q ) ,
H ( q ) = 1 / [ D ( q ) ] ,
g ( y ) = { 1 , for Δ y 2 y Δ y 2 0 , otherwise ,
G ( q ) = Δ y sin ( g Δ y / 2 ) q Δ y / 2 .
H ( q ) = q Δ y / 2 sin ( q Δ y / 2 ) .
t ( q ) = 1 2 { 1 + cos [ ϕ ( q ) + β 0 q ] } ,
ϕ ( q ) = { π , for q n < q < q n + 1 , n = ± 1 , ± 3 , ± 5 , , 0 , otherwise ,
H 1 ( q ) = A ( q ) t ( q ) = 1 2 A ( q ) + 1 4 [ H ( q ) exp ( i β 0 q ) + H * ( q ) exp ( i β 0 q ) ] ,
H ( q ) = A ( q ) exp [ i ϕ ( q ) ]
g ( x , y ) T ( x ) = g ( x , y ) [ 1 + cos p 0 x ] ,
E ( p , q ) = C g ( x , y ) [ 1 + cos p 0 x ] × exp [ i ( p x + q y ) ] d x d y d λ ,
E ( p , q ; λ 0 ) = C 1 G ( p , q ) + C 2 G ( p p 0 , q ) + C 2 G ( p + p 0 , q ) ,
G ( p , q ) = g ( x , y ) exp [ i ( p x + q y ) ] d x d y ,
E ( α , β ; λ 0 ) = C 1 G ( α , β ) + C 2 G { α [ ( λ 0 f ) / ( 2 π ) ] p 0 , β } + C 2 G { α + [ ( λ 0 f ) / ( 2 π ) ] p 0 , β } ,
α = ± [ ( λ 0 f ) / ( 2 π ) ] p 0 ,
G ( α , β ) = { G ( α , β ) , ( α 2 + β 2 ) 1 / 2 γ , 0 , otherwise ,
α = α 0 = [ ( λ 0 f ) / ( 2 π ) ] p 0 ,
E ( α , β ) = Δ λ G ( α λ f 2 π p 0 , β ) H 1 ( β ) d λ ,
f ( x , y ) = G ( α λ f 2 π p 0 , β ) H 1 ( β ) × exp [ i 2 π λ f ( α x + β y ) ] d α d β d λ ,
f ( x , y ) λ Δ G ( α λ 0 f 2 π p 0 , β ) H 1 ( β ) × exp [ i 2 π λ 0 f ( α x + β y ) ] d α d β .
E ( α , β ) Δ λ G { α [ ( λ 0 f ) / ( 2 π ) ] p 0 , β } H 1 ( β ) .
E ( p , q ) Δ λ G ( p p 0 , q ) H 1 ( q ) ,
E ( p , q ) 1 2 Δ λ G ( p p 0 , q ) A ( q ) + 1 4 Δ λ [ G ( p p 0 , q ) H ( q ) exp ( i β 0 q ) + G ( p p 0 , q ) H * ( q ) exp ( i β 0 q ) ] ,
f ( x , y ) 1 2 Δ λ [ g ( x , y ) exp ( i p 0 x ) * a ( y ) + 1 4 g ( x , y ) × exp ( i p 0 x ) * h ( y + β 0 ) + 1 4 g ( x , y ) exp ( i p 0 x ) * h ( y β 0 ) ] ,
s ( x , y ) = G ( p , q ) H ( q ) exp [ i ( p x + q y ) ] d p d q ,
f ( x , y ) 1 2 Δ λ { g ( x , y ) exp ( i p 0 x ) * a ( y ) + 1 4 exp ( i p 0 x ) [ s ( x , y + β 0 ) + s ( x , y β 0 ) ] } .
D ( T m ) = Δ q [ G ( q ) H ( q ) / Δ y ] d q T m Δ q × 100 % ,
α 1 = [ ( λ 0 f ) / ( 2 π ) ] ( p 0 + Δ p ) ,
α 2 = [ ( λ 0 f ) / ( 2 π ) ] ( p 0 Δ p ) ,
λ 1 = λ 0 [ ( p 0 + Δ p ) / ( p 0 Δ p ) ] ,
λ 2 = λ 0 [ ( p 0 Δ p ) / ( p 0 + Δ p ) ] .
Δ λ = λ 1 λ 2 = λ 0 4 p 0 Δ p p 0 2 ( Δ p ) 2 .
Δ λ λ 0 [ ( 4 Δ p ) / p 0 ] , p 0 Δ p .
= Σ shaded area Σ solid area × 100 % .
α 1 = ( 600 × 10 6 ) ( 250 ) ( 1000 + 25 ) = 153.75 mm , α 2 = ( 600 × 10 6 ) ( 250 ) ( 1000 25 ) = 146.25 mm .
λ 1 = 6000 1000 + 25 1000 25 = 6307.7 Å , λ 2 = 6000 1000 25 1000 + 25 = 5707.3 Å .

Metrics