Abstract

We develop a phase-space representation (termed phase-space imager) suitable for analysis and design of imaging systems that use large illumination apertures (partially coherent illumination). The representation, developed from the transmission cross-coefficient model, falls in the general Cohen class of distributions and elegantly captures the bilinear nature of image formation in partially coherent systems. It uses only the requisite number of dimensions and leads to an efficient algorithm for calculating images. Computed partially coherent images of a double slit and a two-dimensional sinusoidal spoke are presented.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. H. Hopkins, Proc. R. Soc. London Ser A 217, 408 (1953).
    [CrossRef]
  2. C. J. R. Sheppard and A. Choudhury, J. Mod. Opt. 24, 1051 (1977).
  3. L. Cohen, Time-Frequency Analysis (Prentice Hall, 1995).
  4. M. J. Bastiaans, in Advances in Information Optics and Photonics, A.T.Friberg and R.Dändliker, eds. (SPIE Press, 2008), vol. PM183, pp. 27-56,.
    [CrossRef]
  5. J. Ojeda-Castañeda and E. E. Sicre, J. Mod. Opt. 31, 255 (1984).
  6. R. Castañeda, Appl. Opt. 47, E53 (2008).
    [CrossRef] [PubMed]
  7. S. B. Mehta and C. J. R. Sheppard, Opt. Express 16, 19462 (2008).
    [CrossRef] [PubMed]
  8. A. M. Goodbody, Proc. Phys. Soc. London Sect. B 70, 361 (1957).
    [CrossRef]
  9. H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. London Sect. B 63, 737 (1950).
    [CrossRef]

2008 (2)

1984 (1)

J. Ojeda-Castañeda and E. E. Sicre, J. Mod. Opt. 31, 255 (1984).

1977 (1)

C. J. R. Sheppard and A. Choudhury, J. Mod. Opt. 24, 1051 (1977).

1957 (1)

A. M. Goodbody, Proc. Phys. Soc. London Sect. B 70, 361 (1957).
[CrossRef]

1953 (1)

H. H. Hopkins, Proc. R. Soc. London Ser A 217, 408 (1953).
[CrossRef]

1950 (1)

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. London Sect. B 63, 737 (1950).
[CrossRef]

Barham, P. M.

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. London Sect. B 63, 737 (1950).
[CrossRef]

Bastiaans, M. J.

M. J. Bastiaans, in Advances in Information Optics and Photonics, A.T.Friberg and R.Dändliker, eds. (SPIE Press, 2008), vol. PM183, pp. 27-56,.
[CrossRef]

Castañeda, R.

Choudhury, A.

C. J. R. Sheppard and A. Choudhury, J. Mod. Opt. 24, 1051 (1977).

Cohen, L.

L. Cohen, Time-Frequency Analysis (Prentice Hall, 1995).

Goodbody, A. M.

A. M. Goodbody, Proc. Phys. Soc. London Sect. B 70, 361 (1957).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Proc. R. Soc. London Ser A 217, 408 (1953).
[CrossRef]

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. London Sect. B 63, 737 (1950).
[CrossRef]

Mehta, S. B.

Ojeda-Castañeda, J.

J. Ojeda-Castañeda and E. E. Sicre, J. Mod. Opt. 31, 255 (1984).

Sheppard, C. J. R.

S. B. Mehta and C. J. R. Sheppard, Opt. Express 16, 19462 (2008).
[CrossRef] [PubMed]

C. J. R. Sheppard and A. Choudhury, J. Mod. Opt. 24, 1051 (1977).

Sicre, E. E.

J. Ojeda-Castañeda and E. E. Sicre, J. Mod. Opt. 31, 255 (1984).

Appl. Opt. (1)

J. Mod. Opt. (2)

C. J. R. Sheppard and A. Choudhury, J. Mod. Opt. 24, 1051 (1977).

J. Ojeda-Castañeda and E. E. Sicre, J. Mod. Opt. 31, 255 (1984).

Opt. Express (1)

Proc. Phys. Soc. London Sect. B (2)

A. M. Goodbody, Proc. Phys. Soc. London Sect. B 70, 361 (1957).
[CrossRef]

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. London Sect. B 63, 737 (1950).
[CrossRef]

Proc. R. Soc. London Ser A (1)

H. H. Hopkins, Proc. R. Soc. London Ser A 217, 408 (1953).
[CrossRef]

Other (2)

L. Cohen, Time-Frequency Analysis (Prentice Hall, 1995).

M. J. Bastiaans, in Advances in Information Optics and Photonics, A.T.Friberg and R.Dändliker, eds. (SPIE Press, 2008), vol. PM183, pp. 27-56,.
[CrossRef]

Supplementary Material (2)

» Media 1: MOV (2677 KB)     
» Media 2: MOV (915 KB)     

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 (3)

Fig. 1
Fig. 1

A scanning-based (light propagation from right to left) or wide-field (light propagation from left to right) partially coherent imaging system is described by intensity distribution in the condenser pupil and amplitude distribution in the objective pupil. Labels in italics indicate terms used for the scanning microscope.

Fig. 2
Fig. 2

Simulating the effects of coherence of illumination on resolvability of a double slit: a snapshot from Media 1 (2.6 MB) at S = 1 . See the text for details.

Fig. 3
Fig. 3

Computed images of a sinusoidal spoke target under bright field microscope: (a) ideal image, (b) a snapshot from a sequence (Media 2) (914 KB) of par tially coherent images computed for different condenser sizes.

Equations (7)

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

W t ( m , x ) = T ( m + m 2 ) T ( m m 2 ) e 2 π i m . x d m ,
I ( x ) = T ( m 1 ) T ( m 2 ) C ( m 1 , m 2 ) × e 2 π i ( m 1 m 2 ) . x d m 1 d m 2 .
C ( m 1 , m 2 ) = | P c ( ξ ) | 2 P o ( m 1 + ξ ) P o ( m 2 + ξ ) d ξ
I ( x ) = T ( m + m 2 ) T ( m m 2 ) C ( m , m ) × e 2 π i m . x d m d m .
I ( x ) = Ψ ( m , x ; C ) d m ,
Ψ ( m , x ; C ) = T ( m + m 2 ) T ( m m 2 ) C ( m , m ) × e 2 π i m . x d m
C ( m , m ) = | P c ( ξ ) | 2 P o ( m + m 2 + ξ ) P o ( m m 2 + ξ ) d ξ .

Metrics