Abstract

A source-encoding technique is utilized to achieve image superresolution. The method overcomes several drawbacks of previous methods and shows a new approach for further study of practical applications of the superresolution technology.

© 1991 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984).
  2. D. Casasent, Optical Data Processing (Springer-Verlag, New York, 1978).
    [Crossref]
  3. S. H. Lee, Optical Information Processing (Springer-Verlag, New York, 1981).
    [Crossref]
  4. S. L. Zhuang, F. T. S. Yu, “Apparent transfer function for partially coherent optical information processing,” Appl. Phys. B 28, 359–364 (1982).
    [Crossref]
  5. F. T. S. Yu, S. L. Zhuang, S. T. Wu, “Source encoding for partially coherent optical processing,” Appl. Phys. B 27, 99–105 (1982).
    [Crossref]
  6. S. L. Zhuang, F. T. S. Yu, “Coherence requirements for partially coherent optical processing,” Appl. Opt. 21, 2587–2592 (1982).
    [Crossref] [PubMed]
  7. F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise performance of a white-light optical signal processor. I. Temporally partially coherent illumination,” J. Opt. Soc. Am. A. 1, 489–495 (1984).
    [Crossref]
  8. S. L. Zhuang, T. H. Chao, F. T. S. Yu, “Smeared-photographic-image deblurring utilizing white-light-processing technique,” Opt. Lett. 6, 102–107 (1981).
    [Crossref] [PubMed]
  9. F. T. S. Yu, S. L. Zhuang, T. H. Chao, M. S. Dymek, “Real-time white light spatial frequency and density pseudocolor encoder,” Appl. Opt. 19, 2986–2992 (1980).
    [Crossref] [PubMed]
  10. F. T. S. Yu, Y. W. Zhang, S. L. Zhuang, “Coherence requirement for partially coherent correlation detection,” Appl. Phys. B 30, 23–28 (1983).
    [Crossref]

1984 (1)

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise performance of a white-light optical signal processor. I. Temporally partially coherent illumination,” J. Opt. Soc. Am. A. 1, 489–495 (1984).
[Crossref]

1983 (1)

F. T. S. Yu, Y. W. Zhang, S. L. Zhuang, “Coherence requirement for partially coherent correlation detection,” Appl. Phys. B 30, 23–28 (1983).
[Crossref]

1982 (3)

S. L. Zhuang, F. T. S. Yu, “Apparent transfer function for partially coherent optical information processing,” Appl. Phys. B 28, 359–364 (1982).
[Crossref]

F. T. S. Yu, S. L. Zhuang, S. T. Wu, “Source encoding for partially coherent optical processing,” Appl. Phys. B 27, 99–105 (1982).
[Crossref]

S. L. Zhuang, F. T. S. Yu, “Coherence requirements for partially coherent optical processing,” Appl. Opt. 21, 2587–2592 (1982).
[Crossref] [PubMed]

1981 (1)

1980 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984).

Casasent, D.

D. Casasent, Optical Data Processing (Springer-Verlag, New York, 1978).
[Crossref]

Chao, T. H.

Dymek, M. S.

Lee, S. H.

S. H. Lee, Optical Information Processing (Springer-Verlag, New York, 1981).
[Crossref]

Shaik, K. S.

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise performance of a white-light optical signal processor. I. Temporally partially coherent illumination,” J. Opt. Soc. Am. A. 1, 489–495 (1984).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984).

Wu, S. T.

F. T. S. Yu, S. L. Zhuang, S. T. Wu, “Source encoding for partially coherent optical processing,” Appl. Phys. B 27, 99–105 (1982).
[Crossref]

Yu, F. T. S.

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise performance of a white-light optical signal processor. I. Temporally partially coherent illumination,” J. Opt. Soc. Am. A. 1, 489–495 (1984).
[Crossref]

F. T. S. Yu, Y. W. Zhang, S. L. Zhuang, “Coherence requirement for partially coherent correlation detection,” Appl. Phys. B 30, 23–28 (1983).
[Crossref]

S. L. Zhuang, F. T. S. Yu, “Coherence requirements for partially coherent optical processing,” Appl. Opt. 21, 2587–2592 (1982).
[Crossref] [PubMed]

S. L. Zhuang, F. T. S. Yu, “Apparent transfer function for partially coherent optical information processing,” Appl. Phys. B 28, 359–364 (1982).
[Crossref]

F. T. S. Yu, S. L. Zhuang, S. T. Wu, “Source encoding for partially coherent optical processing,” Appl. Phys. B 27, 99–105 (1982).
[Crossref]

S. L. Zhuang, T. H. Chao, F. T. S. Yu, “Smeared-photographic-image deblurring utilizing white-light-processing technique,” Opt. Lett. 6, 102–107 (1981).
[Crossref] [PubMed]

F. T. S. Yu, S. L. Zhuang, T. H. Chao, M. S. Dymek, “Real-time white light spatial frequency and density pseudocolor encoder,” Appl. Opt. 19, 2986–2992 (1980).
[Crossref] [PubMed]

Zhang, Y. W.

F. T. S. Yu, Y. W. Zhang, S. L. Zhuang, “Coherence requirement for partially coherent correlation detection,” Appl. Phys. B 30, 23–28 (1983).
[Crossref]

Zhuang, S. L.

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise performance of a white-light optical signal processor. I. Temporally partially coherent illumination,” J. Opt. Soc. Am. A. 1, 489–495 (1984).
[Crossref]

F. T. S. Yu, Y. W. Zhang, S. L. Zhuang, “Coherence requirement for partially coherent correlation detection,” Appl. Phys. B 30, 23–28 (1983).
[Crossref]

F. T. S. Yu, S. L. Zhuang, S. T. Wu, “Source encoding for partially coherent optical processing,” Appl. Phys. B 27, 99–105 (1982).
[Crossref]

S. L. Zhuang, F. T. S. Yu, “Coherence requirements for partially coherent optical processing,” Appl. Opt. 21, 2587–2592 (1982).
[Crossref] [PubMed]

S. L. Zhuang, F. T. S. Yu, “Apparent transfer function for partially coherent optical information processing,” Appl. Phys. B 28, 359–364 (1982).
[Crossref]

S. L. Zhuang, T. H. Chao, F. T. S. Yu, “Smeared-photographic-image deblurring utilizing white-light-processing technique,” Opt. Lett. 6, 102–107 (1981).
[Crossref] [PubMed]

F. T. S. Yu, S. L. Zhuang, T. H. Chao, M. S. Dymek, “Real-time white light spatial frequency and density pseudocolor encoder,” Appl. Opt. 19, 2986–2992 (1980).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (3)

F. T. S. Yu, Y. W. Zhang, S. L. Zhuang, “Coherence requirement for partially coherent correlation detection,” Appl. Phys. B 30, 23–28 (1983).
[Crossref]

S. L. Zhuang, F. T. S. Yu, “Apparent transfer function for partially coherent optical information processing,” Appl. Phys. B 28, 359–364 (1982).
[Crossref]

F. T. S. Yu, S. L. Zhuang, S. T. Wu, “Source encoding for partially coherent optical processing,” Appl. Phys. B 27, 99–105 (1982).
[Crossref]

J. Opt. Soc. Am. A. (1)

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise performance of a white-light optical signal processor. I. Temporally partially coherent illumination,” J. Opt. Soc. Am. A. 1, 489–495 (1984).
[Crossref]

Opt. Lett. (1)

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1984).

D. Casasent, Optical Data Processing (Springer-Verlag, New York, 1978).
[Crossref]

S. H. Lee, Optical Information Processing (Springer-Verlag, New York, 1981).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

One-dimensional partially coherent optical processing system.

Fig. 2
Fig. 2

Principle of superresolution described in this paper.

Fig. 3
Fig. 3

Curve of μ(l) versus l.

Fig. 4
Fig. 4

Encoded-source system.

Fig. 5
Fig. 5

(a) Radiating intensity distribution of the encoded source; (b) mutual intensity distribution at the front surface of the object.

Fig. 6
Fig. 6

Images of No. 2 from the resolution chart: (a) incoherent illumination, (b) illumination with the encoded source.

Fig. 7
Fig. 7

Images of the integrated-circuit mask: (a) incoherent illumination, (b) illumination with the encoded source.

Equations (20)

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O ( x ) = δ ( x l 2 ) + δ ( x + l 2 ) .
J 4 ( x 1 , x 2 λ ) = + + J ( x 1 , x 2 , λ ) [ δ ( x 1 l 2 ) + δ ( x 1 + l 2 ) ] * [ δ ( x 2 l 2 ) + δ ( x 2 + l 2 ) ] × K c x 1 , x 1 , λ ) * K ( x 2 , x 2 , λ ) d x 1 d x 2 ,
I ( x ) = sinc 2 [ Δ H ( x l 2 ) f λ ] + sinc 2 [ Δ H ( x + l 2 ) f λ ] + 2 μ ( l ) sinc [ Δ H ( x l 2 ) f λ ] sinc [ Δ H ( x + l 2 ) f λ ] ,
sinc 2 [ Δ H ( x l 2 ) f λ ] + sinc 2 [ Δ H ( x + l 2 ) f λ ] .
2 μ ( l ) sinc [ Δ H ( x l 2 ) f λ ] sinc [ Δ H ( x + l 2 ) f λ ]
μ ( l ) = μ ( l ) ,
μ ( 0 ) μ ( l ) ,
1 [ μ ( l ) ] 0 ,
μ ( l ) d c + c sinc [ Δ H l f λ ] 2 sinc 2 [ Δ H l f λ ] 2 sinc 2 [ Δ H l f λ ] 2 c sinc [ Δ H l f λ ] .
γ 1 ( χ 0 ) = rect ( x 0 h ) * comb ( x 0 d 2 d ) ,
γ 2 ( β ) = [ rect ( β D ) exp ( i k β 2 2 f ) ] * comb ( β D ) .
J 1 ( x 1 x 2 ) = c + γ 1 ( x 0 ) γ 1 ( x 0 ) * × { + γ 2 ( β ) exp [ i π ( β x 0 ) 2 d 0 λ + i π ( x 1 β ) 2 d 1 λ ] d β } * × { + γ 2 ( β ) exp [ i π ( β x 0 ) 2 d 0 λ + i π ( x 2 β ) 2 d 1 λ ] d β } d x 0 ,
J 1 ( x 1 , x 2 ) = c l m n a ( l ) h / 2 a ( l ) + h / 2 exp ( i π m n λ ) × { [ C ( ω + n 1 ) C ( ω n 1 ) ] i [ S ( ω + n 1 ) S ( ω n 1 ) ] } * × { [ C ( ω + m 2 ) C ( ω m 2 ) ] i [ S ( ω + m 2 ) S ( ω m 2 ) ] } d x 0 ,
C ( ω ) = 0 ω cos ( π 2 τ 2 ) d τ , S ( ω ) = 0 ω sin ( π 2 τ 2 ) d τ , a ( l ) = x 0 d 2 l d 2 , ω ± m n = ( 1 d 0 + 1 d 1 1 f ) 1 / 2 ( m D ± D 2 + m D f x 0 d 0 x n d 1 1 d 0 + 1 d 1 1 f ) , m n = D ( m 2 n 2 ) f x 2 2 x 1 2 d 1 + [ 2 x 0 ( x 2 x 1 ) d 0 d 1 D ( m + n ) ( x 2 x 1 ) + D ( m n ) ( x 2 x 1 ) d 1 f 2 x 0 D ( m n ) d 0 f + D 2 ( m 2 n 2 ) f 2 + x 2 2 x 1 2 d 1 ] / ( 1 d 0 + 1 d 1 1 f ) .
J 1 ( x 1 x 2 ) = c l a ( l ) h / 2 a ( l ) + h / 2 exp [ i 2 π x 0 ( x 2 x 1 ) f ] × { [ C ( ω + 1 ) C ( ω 1 ) i [ S ( ω + 1 ) S ( ω 1 ) ] } * × { [ C ( ω + 2 ) C ( ω 2 ) i [ S ( ω + 2 ) S ( ω 2 ) ] } d x 0 ,
ω ± n = 1 d 1 ( ± D 2 d 1 x 0 + f x n f ) .
μ ( l ) = sin ( N l d π f λ ) N sin ( l d π f λ ) sinc ( h l f λ ) ,
l = ± n f λ d , n = 0 , 1 , 2
l = ± n f λ N d , n / N k ,
μ ( l ) = 0 .

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