Abstract

A three-dimensional (3-D) optical image-recognition technique is proposed and studied. The proposed technique is based on two-pupil optical heterodyne scanning and is capable of performing 3-D image recognition. A hologram of the 3-D reference object is first created and then is used to modulate spatially one of the pupils of the optical system; the other pupil is a point source. A 3-D target object to be recognized is then scanned in two dimensions by optical beams modulated by the two pupils. The result of the two-dimensional scan pattern effectively displays the correlation of the holographic information of the 3-D reference object and that of the 3-D target object. A strong correlation peak results if the two pieces of the holographic information are matched. We analyze the proposed technique and thereby lay a theoretical foundation for optical implementations of the idea. Finally, computer simulations are performed to verify the proposed idea.

© 1999 Optical Society of America

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  1. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
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    [CrossRef] [PubMed]
  3. Special issue on Advances in Recognition Technique, Opt. Eng. 37(1), 1998.
  4. Special issue on Spatial Light Modulators: Research, Development, and Application, Appl. Opt. 37(32), 1998.
  5. W. W. Stoner, W. J. Miceli, F. A. Horrigan, “One-dimensional to two-dimensional transformations in signal correlation,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 21–30 (1981).
    [CrossRef]
  6. W. T. Rhodes, “The falling raster in optical signal processing,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 11–20 (1981).
    [CrossRef]
  7. A. E. Siegman, “Two-dimensional calculations using one-dimensional arrays, or ‘Life on the Skew,’Comput. Phys.Nov./Dec. 74–75 (1988).
  8. J. Hofer-Alfeis, R. Bamler, “Three- and four-dimensional convolution by coherent optical filtering,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. SPIE373, 77–87 (1981).
    [CrossRef]
  9. J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964–966 (1997).
    [CrossRef] [PubMed]
  10. E. Paquet, P. Garcia-Martinez, J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
    [CrossRef]
  11. Y. B. Karasik, “Evaluation of three-dimensional convolution by use of two-dimensional filtering,” Appl. Opt. 36, 7397–7401 (1997).
    [CrossRef]
  12. T.-C. Poon, A. Korpel, “Optical transfer function of an acousto-optic heterodyning image processor,” Opt. Lett. 4, 317–319 (1979).
    [CrossRef] [PubMed]
  13. 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]
  14. A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 11451–1151 (1978).
    [CrossRef]
  15. G. Indebetouw, T.-C. Poon, “Novel approaches of incoherent image processing with emphasis on scanning methods,” Opt. Eng. 31, 2159–2167 (1992).
    [CrossRef]
  16. D. Gorlitz, F. Lanzl, “Method of zero-order noncoherent filtering,” Opt. Commun. 20, 68–72 (1977).
    [CrossRef]
  17. W. T. Rhodes, “Bipolar point spread function synthesis by phase switching,” Appl. Opt. 16, 265–267 (1977).
    [CrossRef] [PubMed]
  18. A. W. Lohmann, “Incoherent optical processing of complex data,” Appl. Opt. 16, 261–263 (1977).
    [CrossRef] [PubMed]
  19. W. Stoner, “Edge enhancement with incoherent optics,” Appl. Opt. 16, 1451–1453 (1997).
    [CrossRef]
  20. E. N. Leith, D. K. Angell, “Generalization of some incoherent spatial filtering techniques,” Appl. Opt. 25, 499–502 (1986).
    [CrossRef] [PubMed]
  21. T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
    [CrossRef]
  22. A. Korpel, Acousto-Optics (Marcel Dekker, New York, 1997).
  23. P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Richard D. Irwin, Inc., Homewood, Ill., 1991).

1998 (3)

Special issue on Advances in Recognition Technique, Opt. Eng. 37(1), 1998.

Special issue on Spatial Light Modulators: Research, Development, and Application, Appl. Opt. 37(32), 1998.

E. Paquet, P. Garcia-Martinez, J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

1997 (3)

1996 (1)

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

1988 (1)

A. E. Siegman, “Two-dimensional calculations using one-dimensional arrays, or ‘Life on the Skew,’Comput. Phys.Nov./Dec. 74–75 (1988).

1986 (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 (1)

A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 11451–1151 (1978).
[CrossRef]

1977 (3)

1966 (1)

1964 (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Angell, D. K.

Bamler, R.

J. Hofer-Alfeis, R. Bamler, “Three- and four-dimensional convolution by coherent optical filtering,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. SPIE373, 77–87 (1981).
[CrossRef]

Banerjee, P. P.

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Richard D. Irwin, Inc., Homewood, Ill., 1991).

Garcia, J.

E. Paquet, P. Garcia-Martinez, J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

Garcia-Martinez, P.

E. Paquet, P. Garcia-Martinez, J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

Goodman, J. W.

Gorlitz, D.

D. Gorlitz, F. Lanzl, “Method of zero-order noncoherent filtering,” Opt. Commun. 20, 68–72 (1977).
[CrossRef]

Hofer-Alfeis, J.

J. Hofer-Alfeis, R. Bamler, “Three- and four-dimensional convolution by coherent optical filtering,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. SPIE373, 77–87 (1981).
[CrossRef]

Horrigan, F. A.

W. W. Stoner, W. J. Miceli, F. A. Horrigan, “One-dimensional to two-dimensional transformations in signal correlation,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 21–30 (1981).
[CrossRef]

Indebetouw, G.

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

Karasik, Y. B.

Korpel, A.

Lanzl, F.

D. Gorlitz, F. Lanzl, “Method of zero-order noncoherent filtering,” Opt. Commun. 20, 68–72 (1977).
[CrossRef]

Leith, E. N.

Lohmann, A. W.

A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 11451–1151 (1978).
[CrossRef]

A. W. Lohmann, “Incoherent optical processing of complex data,” Appl. Opt. 16, 261–263 (1977).
[CrossRef] [PubMed]

Miceli, W. J.

W. W. Stoner, W. J. Miceli, F. A. Horrigan, “One-dimensional to two-dimensional transformations in signal correlation,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 21–30 (1981).
[CrossRef]

Paquet, E.

E. Paquet, P. Garcia-Martinez, J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

Poon, T.-C.

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

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Richard D. Irwin, Inc., Homewood, Ill., 1991).

Rhodes, W. T.

A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 11451–1151 (1978).
[CrossRef]

W. T. Rhodes, “Bipolar point spread function synthesis by phase switching,” Appl. Opt. 16, 265–267 (1977).
[CrossRef] [PubMed]

W. T. Rhodes, “The falling raster in optical signal processing,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 11–20 (1981).
[CrossRef]

Rosen, J.

Shinoda, K.

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

Siegman, A. E.

A. E. Siegman, “Two-dimensional calculations using one-dimensional arrays, or ‘Life on the Skew,’Comput. Phys.Nov./Dec. 74–75 (1988).

Stoner, W.

Stoner, W. W.

W. W. Stoner, W. J. Miceli, F. A. Horrigan, “One-dimensional to two-dimensional transformations in signal correlation,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 21–30 (1981).
[CrossRef]

Suzuki, Y.

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

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Weaver, C. S.

Wu, M.

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

Appl. Opt. (8)

Comput. Phys. (1)

A. E. Siegman, “Two-dimensional calculations using one-dimensional arrays, or ‘Life on the Skew,’Comput. Phys.Nov./Dec. 74–75 (1988).

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

J. Opt. (1)

E. Paquet, P. Garcia-Martinez, J. Garcia, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

J. Opt. Soc. Am. A (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]

Opt. Commun. (1)

D. Gorlitz, F. Lanzl, “Method of zero-order noncoherent filtering,” Opt. Commun. 20, 68–72 (1977).
[CrossRef]

Opt. Eng. (2)

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

Special issue on Advances in Recognition Technique, Opt. Eng. 37(1), 1998.

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 (5)

A. Korpel, Acousto-Optics (Marcel Dekker, New York, 1997).

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Richard D. Irwin, Inc., Homewood, Ill., 1991).

J. Hofer-Alfeis, R. Bamler, “Three- and four-dimensional convolution by coherent optical filtering,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. SPIE373, 77–87 (1981).
[CrossRef]

W. W. Stoner, W. J. Miceli, F. A. Horrigan, “One-dimensional to two-dimensional transformations in signal correlation,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 21–30 (1981).
[CrossRef]

W. T. Rhodes, “The falling raster in optical signal processing,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fineup, B. E. A. Saleh, eds., Proc. SPIE373, 11–20 (1981).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Two-pupil optical heterodyne scanning system. BPF@Ω, bandpass filter tuned at the frequency Ω; AOFS, acousto-optic frequency shifter.

Fig. 2
Fig. 2

Parallel processing for obtaining the in-phase and the quadrature-phase information of the scanned signal simultaneously. LPF, low-pass filter.

Fig. 3
Fig. 3

(a) Three-dimensional reference object R, with L x = L y = 1 cm and Δz = 1 cm. (b) Holograms of the 3-D reference object of (a) (the scanned area is 1 cm × 1 cm): Shown are the cosine FZP hologram (upper image) and the sine FZP hologram (lower image). A bias has been added to the holograms to avoid plotting negative values. (c) Correlation output (0.4 cm × 0.4 cm) when the target object O is matched with the reference object R.

Fig. 4
Fig. 4

(a) Three-dimensional target object O. (b) Holograms of the 3-D target object of (a): Shown are the cosine FZP (upper image) and the sine FZP (lower image) holograms. (c) Correlation output when the target object of (a) is scanned. The reference object is shown in Fig. 3(a).

Fig. 5
Fig. 5

(a) Three-dimensional target object O. (b) Holograms of the 3-D target object in (a): Shown are the cosine FZP (upper image) and the sine FZP (lower image) holograms. (c) Correlation output when the target object in (a) is scanned. The reference object is shown in Fig. 3(a).

Fig. 6
Fig. 6

Correlation output when the 3-D target object and the 3-D reference object are displaced along the depth (z) direction; otherwise the object and the reference are the same.

Fig. 7
Fig. 7

Optical system capable of extracting the depth difference between the 3-D target object and the 3-D reference object. Otherwise the two objects are the same.

Fig. 8
Fig. 8

Correlation outputs as observed by the CCD camera when the camera is translating along the z direction. The two 3-D objects are different in depth by 25 cm, but otherwise they are the same. Note the strong correlation peak at z = 25 cm.

Equations (42)

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icx, y; z=Re-1{|Γo|2×OTFΩ}=Re|Γox, y; z|2  hΩx, y; z,
isx, y; z=Im-1{|Γo|2×OTFΩ}=Im|Γox, y; z|2  hΩx, y; z,
OTFΩkx, ky; z=expj z2k0kx2+ky2× p1*x, yp2x+fk0 kx, y+fk0 ky×expj zfxkx+ykydxdy,
icx, y=Re -1{|Γox, y; z|2×OTFΩ}dz=Re |Γox, y; z|2  hΩx, y; zdz,
isx, y=Im -1{|Γox, y; z|2×OTFΩ}dz=Im |Γox, y; z|2  hΩx, y; zdz.
OTFΩkx, ky; z=exp-j z2k0kx2+ky2=OTFoshkx, ky; z,
Hx, y=Re -1{|Γox, y; z|2OTFoshkx, ky; z}dz=Re -1|Γox, y; z|2×exp-j z2k0kx2+ky2dz
Hx, y=Re |Γo|2  h*x, y; zdz,
Hsinx, y=Re hx, y; z  |Γo|2dz= k02πzsink02zx2+y2  |Γo|2dz,
Hcosx, y=Im hx, y; z  |Γo|2dz= k02πzcosk02zx2+y2  |Γo|2dz=k02πz0cosk02z0x-x02+y-y02,
OTFΩkx, ky; z=exp-j z2k0kx2+ky2×p1*-fk0 kx, -fk0 ky.
icx, y=Re -1Ox, y; z×exp-j z2k0kx2+ky2×p1*-fk0 kx, -fk0 kydz,
p1-fk0 kx, -fk0 ky= Rx, y; z×exp-j z2k0kx2+ky2dz.
icx, y=Re-1 Ox, y; z×exp-j z2k0kx2+ky2dz× Rx, y; zexp-j z2k0kx2+ky2dz*.
icx, y=Re -1Rx, y; z×exp-j z2k0kx2+ky2dz  -1Ox, y; z×exp-j z2k0kx2+ky2dz=ReHRx, y  HOx, y,
isx, y=ImHRx, y  HOx, y.
p1-fk0 kx, -fk0 ky= hx, y; z Rx, y; zkx,kydz.
p1x, y= hx, y; z Rx, y; zkx=-k0x/f,ky=-k0y/fdz= hx, y; z Rx, y; zdzkx=-k0x/f,ky=-k0y/f.
HRx, y=Hcosx, y+jHsinx, y hx, y; z  Rx, y; zdz,
tx, y=Re hx, y; z  Rx, y; zdz  hx, y; z  Ox, y; zdz.
icx, y=ReHRx, y   hx, y; z Ox-Δx, y-Δy; z-Δzdz=ReHRx, y   hx, y; z+Δz Ox-Δx, y-Δy; zdz.
icx, y=ReHRx, y   hx, y; z Ox-Δx, y-Δy; zdz h*x, y; Δz=ReHRx, y HOx-Δx, y-Δy h*x, y; Δz.
isx, y=ImHRx, y  HOx-Δx, y-Δy h*x, y; Δz.
Cx, y=icx, y+jisx, y=HRx, y  HOx-Δx, y-Δy h*x, y; Δz.
P1zk0xf, k0yfexpjω0t+P2zk0xf, k0yf×expjω0+Ωt,
Pizk0xf, k0yf=Pik0xf, k0yf  hx, y; z, i=1, 2.
Pik0xf, k0yf= pix, y×expj k0fxx+yydxdy=pix, yk0x/f,k0y/f,
hx, y; z=jk02πzexp-j k02zx2+y2,
g1x, y  g2x, y= g1x, yg2x-x, y-ydxdy.
ix, y; z=AP1zk0xf, k0yfexpjω0t+P2zk0xf, k0yfexpjω0+Ωt×Γox+x, y+y; z2dxdy.
iΩx, y; z=ReA P1z*k0xf, k0yfP2zk0xf, k0yf×|Γox+x, y+y; z|2dxdy expjΩt,
iΩx, y=ReiΩpx, y; zexpjΩt,
iΩpx, y; z=A P1z*k0xf, k0yfP2zk0xf, k0yf×|Γox+x, y+y; z|2dxdy
gx, y  hx, y= g*x, yhx+x, y+ydxdy,
iΩpx, y; z=P1zk0xf, k0yfP2z*k0xf, k0yf |Γox, y; z|2.
OTFΩkx, ky; z=iΩpx, y; z|Γox, y; z|2.
OTFΩkx, ky; z=*P1zk0xf, k0yfP2z*k0xf, k0yf.
OTFΩkx, ky; z=expj z2k0kx2+ky2× p1*x, yp2x+fk0 kx, y+fk0 ky×expj zfxkx+ykydxdy.
iΩx, y; z=ReiΩpx, y; zexpjΩt=Re-1{|Γox, y; z|2OTFΩkx, ky; z}×expjΩt.
iΩx, y; z=Re|Γox, y; z|2  hΩx, y; zexpjΩt.
icx, y; z=Re(-1{|Γo|2OTFΩ})=Re|Γo|2  hΩx, y; z,
isx, y; z=Im(-1{|Γo|2OTFΩ})=Im|Γo|2  hΩx, y; z,

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