Abstract

It has long been known that image plane holography with low-coherence illumination achieves optical sectioning of a volume object. A method is analyzed that is similar to image plane holography, but the interferometric arrangement utilizes the interference between two object-bearing beams instead of the basic object and reference beams.

© 2004 Optical Society of America

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References

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  1. T. Wilson, ed., Confocal Microscopy (Academic, New York, 1990).
  2. C. Sheppard, M. Roy, M. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43, 1493–1502 (2004).
    [CrossRef] [PubMed]
  3. E. N. Leith, W. C. Chien, K. D. Mills, B. D. Athey, D. S. Dilworth, “Optical sectioning by holographic coherence imaging: a generalized analysis,” J. Opt. Soc. Am. A 20, 380–387 (2003).
    [CrossRef]
  4. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. 56, 1463–1472 (1966).
    [CrossRef]
  5. A. Lohmann, “Incoherent optical processing of complex data,” Appl. Opt. 16, 261–268 (1977).
    [CrossRef] [PubMed]
  6. D. Gorlitz, F. Lanzl, “Methods of zero-order noncoherent spatial filtering,” Opt. Commun. 30, 68–70 (1977).
    [CrossRef]
  7. A. Lohmann, W. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 1141–1144 (1978).
    [CrossRef] [PubMed]
  8. W. Stoner, “Incoherent optical processing via spatially offset pupil masks,” Appl. Opt. 17, 2454–2459 (1978).
    [CrossRef] [PubMed]
  9. E. N. Leith, D. Angell, S. Leon, L. Shentu, C. P. Kuei, “Optical processing and holography with incoherent light,” in Optical Testing and Metrology, C. Glover, ed., Proc. SPIE661, 2–8 (1986).
    [CrossRef]
  10. E. N. Leith, D. K. Angell, “Generalization of some incoherent spatial filtering techniques,” Appl. Opt. 25, 499–502 (1986).
    [CrossRef] [PubMed]
  11. E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217–219 (1977).
    [CrossRef]
  12. B. J. Chang, J. S. Chang, E. N. Leith, “Imaging through scattering media with an achromatic interferometer,” Opt. Lett. 4, 118–120 (1979).
    [CrossRef] [PubMed]

2004

2003

1986

1979

1978

1977

E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217–219 (1977).
[CrossRef]

A. Lohmann, “Incoherent optical processing of complex data,” Appl. Opt. 16, 261–268 (1977).
[CrossRef] [PubMed]

D. Gorlitz, F. Lanzl, “Methods of zero-order noncoherent spatial filtering,” Opt. Commun. 30, 68–70 (1977).
[CrossRef]

1966

Angell, D.

E. N. Leith, D. Angell, S. Leon, L. Shentu, C. P. Kuei, “Optical processing and holography with incoherent light,” in Optical Testing and Metrology, C. Glover, ed., Proc. SPIE661, 2–8 (1986).
[CrossRef]

Angell, D. K.

Athey, B. D.

Chang, B. J.

B. J. Chang, J. S. Chang, E. N. Leith, “Imaging through scattering media with an achromatic interferometer,” Opt. Lett. 4, 118–120 (1979).
[CrossRef] [PubMed]

E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217–219 (1977).
[CrossRef]

Chang, J. S.

Chien, W. C.

Dilworth, D. S.

Gorlitz, D.

D. Gorlitz, F. Lanzl, “Methods of zero-order noncoherent spatial filtering,” Opt. Commun. 30, 68–70 (1977).
[CrossRef]

Kuei, C. P.

E. N. Leith, D. Angell, S. Leon, L. Shentu, C. P. Kuei, “Optical processing and holography with incoherent light,” in Optical Testing and Metrology, C. Glover, ed., Proc. SPIE661, 2–8 (1986).
[CrossRef]

Lanzl, F.

D. Gorlitz, F. Lanzl, “Methods of zero-order noncoherent spatial filtering,” Opt. Commun. 30, 68–70 (1977).
[CrossRef]

Leith, E. N.

Leon, S.

E. N. Leith, D. Angell, S. Leon, L. Shentu, C. P. Kuei, “Optical processing and holography with incoherent light,” in Optical Testing and Metrology, C. Glover, ed., Proc. SPIE661, 2–8 (1986).
[CrossRef]

Lohmann, A.

Lukosz, W.

Mills, K. D.

Rhodes, W.

Roy, M.

Sharma, M.

Shentu, L.

E. N. Leith, D. Angell, S. Leon, L. Shentu, C. P. Kuei, “Optical processing and holography with incoherent light,” in Optical Testing and Metrology, C. Glover, ed., Proc. SPIE661, 2–8 (1986).
[CrossRef]

Sheppard, C.

Stoner, W.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

D. Gorlitz, F. Lanzl, “Methods of zero-order noncoherent spatial filtering,” Opt. Commun. 30, 68–70 (1977).
[CrossRef]

E. N. Leith, B. J. Chang, “Image formation with an achromatic interferometer,” Opt. Commun. 23, 217–219 (1977).
[CrossRef]

Opt. Lett.

Other

E. N. Leith, D. Angell, S. Leon, L. Shentu, C. P. Kuei, “Optical processing and holography with incoherent light,” in Optical Testing and Metrology, C. Glover, ed., Proc. SPIE661, 2–8 (1986).
[CrossRef]

T. Wilson, ed., Confocal Microscopy (Academic, New York, 1990).

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Figures (9)

Fig. 1
Fig. 1

Two-beam interferometer containing imaging or image processing systems in each beam. (a) A generalized interferometer, (b) a grating interferometer with gratings as beam splitters and combiners.

Fig. 2
Fig. 2

Optical system taken outside the interferometer showing three arrangements: (a) object and imaging systems before the interferometer (toward source), (b) interferometer between two imaging systems, (c) interferometer after the imaging system.

Fig. 3
Fig. 3

System for a simplified analysis showing a Fourier component of spatial frequency f n from an out-of-plane signal.

Fig. 4
Fig. 4

Rays deviated by spatial frequency f n still coincide.

Fig. 5
Fig. 5

As in Fig. 4, but without the paraxial approximation.

Fig. 6
Fig. 6

Plot of curves showing the sectioning capability for a representative out-of-plane component of spatial frequency f n = 100 lines/mm. The curves were produced from Eqs. (8)–(10) and integrated over the extended source. NA, numerical aperture.

Fig. 7
Fig. 7

As in Figs. 4 and 5, but for reflection, showing that the beams reflected by a Fourier component become widely separated at the recording plane (plane containing signal s).

Fig. 8
Fig. 8

Plot of curves showing sectioning capability for the reflection case. NA, numerical aperture.

Fig. 9
Fig. 9

Experimental results for the transmission case with parameters as given in the text.

Equations (9)

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

I=|s1 * h1|2+|s2 * h2|2+2 Res1 * h1 ×s2 * h2* expj4πfgx,
uupper=expj2πfs+fgxexpjkd1-1/2λ2×fs+fg2exp-j4πfgxexpjkd-z×1-1/2λ2fs-fg2expj2πfnx×expjkz1-1/2λ2fs+fn-fg2,
ulower=expj2πfs-fgxexpjkd1-1/2λ2×fs-fg2expj4πfgxexpjkd-z×1-1/2λ2fs+fg2expj2πfnx×expjkz1-1/2λ2fs+fn+fg2.
I=1+cos4πfgx-4πλzfnfg.
I=1+cos2π2fg-fnx-πλzfn2+2fgfn-2fsfn.
I=1+cos4πfgx-Δϕ,
Δϕz, fs, fn=6πλ3zfnfgfs2+fsfn.
I=1+cos2π2fg-fnx-Δϕ,
I=1+cos4πfgx+Δϕ,

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