Abstract

We study the three-dimensional (3-D) imaging properties of an optical heterodyne scanning image processor. The image processor is a two-pupil optical system capable of 3-D imaging coherently or incoherently, depending on the detection scheme used. We derive the imaging properties in terms of the two pupils and then show an important 3-D imaging application in scanning holography by deriving its 3-D point spread functions and compare them with conventional 3-D imaging systems.

© 2003 Optical Society of America

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  1. W. Lukosz, “Properties of linear low-pass filters for nonnegative signals,” J. Opt. Soc. Am. 52, 827–829 (1962).
    [CrossRef]
  2. A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 1141–1150 (1978).
    [CrossRef] [PubMed]
  3. W. Stoner, “Incoherent optical processing via spatially offset pupil masks,” Opt. Appl. 17, 2454–2466 (1978).
    [CrossRef]
  4. T.-C. Poon, A. Korpel, “Optical transfer function of an acousto-optic heterodyning image processor,” Opt. Lett. 4, 317–319 (1979).
    [CrossRef] [PubMed]
  5. T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 621–627 (1985).
    [CrossRef]
  6. J. N. Mait, “Pupil-function design for complex incoherent spatial filtering,” J. Opt. Soc. Am. A 4, 1185–1193 (1987).
    [CrossRef]
  7. G. Indebetouw, T.-C. Poon, “Novel approaches of incoherent image processing with emphasis on scanning methods,” Opt. Eng. 31, 2159–2167 (1992).
    [CrossRef]
  8. T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
    [CrossRef]
  9. T.-C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
    [CrossRef]
  10. T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
    [CrossRef]
  11. T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
    [CrossRef]
  12. P. Klysubun, G. Indebetpow, T. Kim, T.-C. Poon, “Accuracy of 3-D remote target location using scanning holographic correlation,” Opt. Commun. 184, 357–366 (2000).
    [CrossRef]
  13. G. Indebetouw, P. Klysubun, T. Kim, T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
    [CrossRef]
  14. G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics, 7th ed. p. 695-ff, (Cambridge University, Edinburgh, U.K., 1999), pp. 699–703.
  16. B. J. Thompson, “Image formation with partially coherent light,” in Progress in Optics, (E. Wolf, ed.), North-Holland, Amsterdam, 1969), Vol. 2.
    [CrossRef]
  17. T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing With Matlab (Elsevier Science, Oxford, U.K., 2001).
  18. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  19. B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
    [CrossRef]

2002 (1)

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

2000 (2)

P. Klysubun, G. Indebetpow, T. Kim, T.-C. Poon, “Accuracy of 3-D remote target location using scanning holographic correlation,” Opt. Commun. 184, 357–366 (2000).
[CrossRef]

G. Indebetouw, P. Klysubun, T. Kim, T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
[CrossRef]

1997 (1)

1996 (1)

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

1995 (1)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

1992 (1)

G. Indebetouw, T.-C. Poon, “Novel approaches of incoherent image processing with emphasis on scanning methods,” Opt. Eng. 31, 2159–2167 (1992).
[CrossRef]

1990 (1)

T.-C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

1988 (1)

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

1987 (1)

1985 (1)

T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 621–627 (1985).
[CrossRef]

1979 (1)

1978 (2)

A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 1141–1150 (1978).
[CrossRef] [PubMed]

W. Stoner, “Incoherent optical processing via spatially offset pupil masks,” Opt. Appl. 17, 2454–2466 (1978).
[CrossRef]

1962 (1)

Banerjee, P. P.

T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing With Matlab (Elsevier Science, Oxford, U.K., 2001).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. p. 695-ff, (Cambridge University, Edinburgh, U.K., 1999), pp. 699–703.

Doh, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Indebetouw, G.

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

G. Indebetouw, P. Klysubun, T. Kim, T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
[CrossRef]

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

G. Indebetouw, T.-C. Poon, “Novel approaches of incoherent image processing with emphasis on scanning methods,” Opt. Eng. 31, 2159–2167 (1992).
[CrossRef]

T.-C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

Indebetpow, G.

P. Klysubun, G. Indebetpow, T. Kim, T.-C. Poon, “Accuracy of 3-D remote target location using scanning holographic correlation,” Opt. Commun. 184, 357–366 (2000).
[CrossRef]

Kim, T.

P. Klysubun, G. Indebetpow, T. Kim, T.-C. Poon, “Accuracy of 3-D remote target location using scanning holographic correlation,” Opt. Commun. 184, 357–366 (2000).
[CrossRef]

G. Indebetouw, P. Klysubun, T. Kim, T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
[CrossRef]

Klysubun, P.

G. Indebetouw, P. Klysubun, T. Kim, T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
[CrossRef]

P. Klysubun, G. Indebetpow, T. Kim, T.-C. Poon, “Accuracy of 3-D remote target location using scanning holographic correlation,” Opt. Commun. 184, 357–366 (2000).
[CrossRef]

Korpel, A.

Lohmann, A. W.

Lukosz, W.

Mait, J. N.

Park, J.

T.-C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

Poon, T.-C.

P. Klysubun, G. Indebetpow, T. Kim, T.-C. Poon, “Accuracy of 3-D remote target location using scanning holographic correlation,” Opt. Commun. 184, 357–366 (2000).
[CrossRef]

G. Indebetouw, P. Klysubun, T. Kim, T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
[CrossRef]

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

G. Indebetouw, T.-C. Poon, “Novel approaches of incoherent image processing with emphasis on scanning methods,” Opt. Eng. 31, 2159–2167 (1992).
[CrossRef]

T.-C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 621–627 (1985).
[CrossRef]

T.-C. Poon, A. Korpel, “Optical transfer function of an acousto-optic heterodyning image processor,” Opt. Lett. 4, 317–319 (1979).
[CrossRef] [PubMed]

T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing With Matlab (Elsevier Science, Oxford, U.K., 2001).

Rhodes, W. T.

Schilling, B.

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Shinoda, K.

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Stoner, W.

W. Stoner, “Incoherent optical processing via spatially offset pupil masks,” Opt. Appl. 17, 2454–2466 (1978).
[CrossRef]

Storrie, B.

Suzuki, Y.

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Thompson, B. J.

B. J. Thompson, “Image formation with partially coherent light,” in Progress in Optics, (E. Wolf, ed.), North-Holland, Amsterdam, 1969), Vol. 2.
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. p. 695-ff, (Cambridge University, Edinburgh, U.K., 1999), pp. 699–703.

Wu, M.

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (1)

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Appl. (1)

W. Stoner, “Incoherent optical processing via spatially offset pupil masks,” Opt. Appl. 17, 2454–2466 (1978).
[CrossRef]

Opt. Commun. (2)

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

P. Klysubun, G. Indebetpow, T. Kim, T.-C. Poon, “Accuracy of 3-D remote target location using scanning holographic correlation,” Opt. Commun. 184, 357–366 (2000).
[CrossRef]

Opt. Eng. (3)

T.-C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

G. Indebetouw, T.-C. Poon, “Novel approaches of incoherent image processing with emphasis on scanning methods,” Opt. Eng. 31, 2159–2167 (1992).
[CrossRef]

Opt. Lett. (2)

Proc. IEEE (1)

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

Other (4)

M. Born, E. Wolf, Principles of Optics, 7th ed. p. 695-ff, (Cambridge University, Edinburgh, U.K., 1999), pp. 699–703.

B. J. Thompson, “Image formation with partially coherent light,” in Progress in Optics, (E. Wolf, ed.), North-Holland, Amsterdam, 1969), Vol. 2.
[CrossRef]

T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing With Matlab (Elsevier Science, Oxford, U.K., 2001).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (5)

Fig. 1
Fig. 1

Conventional 4-f 3-D imaging system.

Fig. 2
Fig. 2

Two-pupil heterodyne scanning processor.

Fig. 3
Fig. 3

Electronic demodulation system.

Fig. 4
Fig. 4

Optical scanning holographic recording of a 3-point source.

Fig. 5
Fig. 5

(a) Holographic reconstruction when i d (x, y) - ji Q (x, y) is used for constructing a complex transmittance for SLM display, (b) holographic reconstruction when i d (x, y) + ji Q (x, y) is used for constructing a complex transmittance for SLM display.

Equations (26)

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ψx, y; xm, ym   P1x, y; z+z0expjω0t +P2x, y; z+z0expj×ω0+ΩtTx+x, y+y; z ×expj k0fxxm+yym ×dxdy exp-j k0z2f2×xm2 +ym2dzMxm, ym,
ix, y   |ψx, y; xm, ym|2dxmdym,
iΩx, y   P1x, y; z+z0P2*x, y; z+z0 ×exp-jΩt+P2x, y; z+z0 ×P1*x, y; z+z0 ×expjΩtexpj k0fxmx-x +ymy-yexp-j k0z-z2f2 ×xm2+ym2Tx+x, y+y; z ×T*x+x, y+y; z ×|Mxm, ym|2 ×dxdydxdydzdzdxmdym.
ix, y   P1x, y; z+z0expjω0t +P2x, y; z+z0expjω0+Ωt ×|Tx+x, y+y; z|2dzdxdy.
iΩx, y  Re P1*x, y; z+z0P2x, y; z+z0 ×|Tx+x, y+y; z|2dxdydz × expjΩt,
iΩx, y  ReiΩpx, yexpjΩt=|iΩpx, y|cosΩt+θ,
idx, y-jiqx, y=iΩpx, y.
iΩpx, y= p1x, y * hx, y; z+z0*×exp-jk0z+z0Tx+x, y+y; z|2×dxdydz.
iΩpx, y * hx, y; z=exp-jk0z0×p1*-x, -y * hx, y; z-z0 ** |Tx, y; z|2×exp-jk0z,
iΩp*x, y * h*x, y; z=expjk0z0×p1-x, -y*h*x, y; z-z0 ** |Tx, y; z|2×expjk0z.
IPSFx, y, z=p1*-x, -y * hx, y; z-z0,
IPSFx, y, z=p1-x, -y * h*x, y; z-z0,
iΩpx, y * hx, y; z=hx, y; z-z0+exp-jk0z1hx, y; z-z1-z0+exp-jk0z1hx+x1, y; z-z1-z0.
iΩp*x, y * h*x, y; z=h*x, y; z-z0+expjk0z1h*x, y; z-z1-z0+expjk0z1h*x+x1, y; z-z1-z0,
iΩδx, y   P1x, y; z+z0P2*x, y; z+z0 ×exp-jΩt+P2x, y; z+z0 ×P1*x, y; z+z0expjΩt ×Tx+x, y+y; zT*x+x, y +y; zdxdydxdydzdz.
iΩδx, y  Re P2x, y; z+z0Tx+x, y +y; zdxdydz P1*x, y; z +z0T*x+x, y+y; zdxdydz ×expjΩt,
iΩδx, y  ReiΩpδx, yexpjΩt,
CPSFx, y, z=p2-x, -y * h*x, y; z-z0.
 P1x, y; z+z0P2*x, y; z+z0exp-jΩt+P2x, y; z+z0P1*x, y; z+z0expjΩt×Tx+x, y+y; zT*x+x, y+y; zΓx-x, y-y, z-zdxdydxdydzdz,
Γx-x, y-y, z-z= |Mxm, ym|2×expj k0fxmx-x+ymy-y×exp-j k0z-z2f2xm2+ym2dxmdym.
Γx-x, y-y, z-z= expj k0fxmx-x+ymy-y×exp-j k0z-z2f2xm2+ym2dxmdym.
Γx-x, y-y, z-z1z-z×expjk0x-x2+y-y22z-zδx-x, y-y; z-z.
iΩx,y  Re P1*x, y; z+z0P2x, y; z+z0 ×|Tx+x, y +y; z|2dxdydz expjΩt,
g1x, y * g2x, y= g1x, y×g2x-x, y-ydxdy.
g1x, y, z ** g2x, y, z= g1x, y, z×g2x-x, y-y,z-zdxdydz.
hx, y; z=exp-jk0zjk02πzexp-j k02zx2+y2.

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