Abstract

A computer-generated hologram consisting of N × N resolution cells produces a reconstructed image consisting of N × N sampling points. Since the width of the primary peaks in the point-spread function is twice the pitch of the sampling points, the intensity at intermediate points between the sampling points depends on the interference between the sampling points. Carefully controlling the complex amplitudes of the sampling points makes it possible to control the intensity not only at the sampling points but also at the intermediate points; the intensity of the reconstructed image can be controlled at 2N × 2N points. Preliminary experiments demonstrating the generation of high-density intensity patterns were performed.

© 1999 Optical Society of America

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References

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1996

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

1995

1994

1993

M. D. Levenson, “Wavefront engineering for photolithography,” Phys. Today 46(7), 28–36 (1993).
[CrossRef]

1992

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Comm. 94, 491–496 (1992).
[CrossRef]

1987

1986

1982

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1828–1836 (1982).
[CrossRef]

1980

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

1976

1974

1973

1972

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1970

1967

Akahori, H.

Allebach, J. P.

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

Gallagher, N. C.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Glückstad, J.

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

Hall, T. J.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Comm. 94, 491–496 (1992).
[CrossRef]

Itoh, M.

Kirk, A. G.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Comm. 94, 491–496 (1992).
[CrossRef]

Lee, W.-H.

Levenson, M. D.

M. D. Levenson, “Wavefront engineering for photolithography,” Phys. Today 46(7), 28–36 (1993).
[CrossRef]

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1828–1836 (1982).
[CrossRef]

Liu, B.

Lohmann, A. W.

Paris, D. P.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Seldowitz, M. A.

Simpson, R. A.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1828–1836 (1982).
[CrossRef]

Sweeney, D. W.

Viswanathan, N. S.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1828–1836 (1982).
[CrossRef]

Yatagai, T.

Yoshikawa, N.

Appl. Opt.

IEEE Trans. Electron Devices

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1828–1836 (1982).
[CrossRef]

Opt. Comm.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Comm. 94, 491–496 (1992).
[CrossRef]

Opt. Commun.

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

Opt. Eng.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

Opt. Lett.

Optik

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Phys. Today

M. D. Levenson, “Wavefront engineering for photolithography,” Phys. Today 46(7), 28–36 (1993).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Optimization of a phase-only CGH that generates a continuous image: (a) phase distribution of the phase-only CGH optimized by the Gerchberg–Saxton algorithm with 128 × 128 sample points, (b) reconstructed image calculated with a 128 × 128 matrix, (c) reconstructed image calculated with a 512 × 512 matrix.

Fig. 2
Fig. 2

Reconstruction of CGH: (a) CGH consisting of cells, (b) reconstruction.

Fig. 3
Fig. 3

Interference between sampling points of CGH’s reconstructed image.

Fig. 4
Fig. 4

Examples of high-density intensity pattern generation: (a), (b), (c), and (d) are target complex-amplitude distributions of reconstructed images for patterns A, B, C, and D; (e), (f), (g), and (h) are the intensity distributions corresponding to (a), (b), (c), and (d), respectively. a = exp(iπ/3), b = exp(i2π/3).

Fig. 5
Fig. 5

Diffraction plane divided into a signal area S and a dummy area D. The dummy area contains zero-order light Z and a conjugate image C.

Fig. 6
Fig. 6

Amplitude-only CGH patterns optimized by fast simulated annealing algorithm: (a), (b), (c), and (d) correspond to patterns A, B, C, and D, respectively.

Fig. 7
Fig. 7

Experimentally generated high-density intensity patterns: (a), (b), (c), and (d) are the measured intensity distributions of patterns A, B, C, and D, respectively. The gray scale is inverted. (e), (f), (g), and (h) are the three-dimensional representations of the intensity distributions (a), (b), (c), and (d), respectively.

Fig. 8
Fig. 8

Intensity distributions calculated by computer: (a), (b), (c), and (d) are the calculated intensity distributions of patterns A, B, C, and D, respectively. The gray-scale is inverted.

Fig. 9
Fig. 9

Generation of a complicated intensity pattern: (a) optimized binary-amplitude CGH, (b) experimentally obtained intensity distribution; (c) three-dimensional representation of (b), (d) calculated intensity distribution. The gray-scale is inverted in (b) and (d).

Fig. 10
Fig. 10

Cross section of high-density intensity distributions of pattern A at different reconstruction distances: (a) 0.92f, (b) 0.94f, (c) 0.96f, (d) 0.98f, (e) f, (f) 1.02f, (g) 1.04f, (h) 1.06f, (i) 1.08f.

Tables (1)

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Table 1 Amplitude and Phase Errors in the Diffraction Generated by the Optimized GCH’s

Equations (6)

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ux, y=k=-N/2N/2-1l=-N/2N/2-1 gkl rectx/a-k, y/a-l.
gkl=m=-N/2N/2-1n=-N/2N/2-1 Gmn expi2πkm+ln/N.
Uνx, νy=a2 sincaνx, aνyk=-N/2N/2-1l=-N/2N/2-1 gkl×exp-i2πakνx+lνy,
Uνx, νy=a2 sincaνx, aνym=-N/2N/2-1n=-N/2N/2-1 Gmn×k=-N/2N/2-1l=-N/2N/2-1exp-i2πaνx-m/Nak+νy-n/Nal=a2 sincaνx, aνym=-N/2N/2-1n=-N/2N/2-1 Gmn×Fνx-m/Na, νy-n/Na,
Fνx, νy=expiπaνx+νysinπNaνxsinπNaνy/sinπaνxsinπaνy.
et=m,nS |Umnt-cOmn|2,

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