Abstract

Diffractive optical elements able to generate zero-order (on-axis) distributions with phase as well as amplitude distributions are described. The proposed elements are surface relief plates, i.e., phase-only elements, that are based on the concept of computer-generated masks followed by common etching processes. The encoding method assumes fixed spatial partitioning of the cell and a phase-only value allocated to each subelement. The reconstructed amplitude and phase distributions contain imperfections (noise) resulting from the encoding process. Methods of error reduction and improvements are provided.

© 1997 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).
  2. A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).
    [CrossRef]
  3. B. R. Brown, A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969 (1966).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1749 (1967).
    [CrossRef] [PubMed]
  5. W. H. Lee, “Sampled Fourier transform hologram generated by computer,” Appl. Opt. 9, 639–643 (1970).
    [CrossRef] [PubMed]
  6. C. B. Burkhardt, “A simplification of Lee’s method of generating holograms by computer,” Appl. Opt. 9, 1949 (1970).
  7. C. K. Hsueh, A. A. Sawchuck, “Computer-generated double phase holograms,” Appl. Opt. 17, 3874–3883 (1978).
    [CrossRef] [PubMed]
  8. N. C. Gallagher, J. A. Bucklew, “Nondetour phase digital holograms: an analysis: errata,” Appl. Opt. 19, 4266–4272 (1980).
    [CrossRef] [PubMed]
  9. R. M. Matic, E. W. Hensen, “Nondetour computer-generated holograms: an improvement variation,” Appl. Opt. 21, 2304–2305 (1982).
    [CrossRef]
  10. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [CrossRef]
  11. J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  12. J. P. Kirk, A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1024–1028 (1971).
    [CrossRef]
  13. J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 487–498 (1991).
    [CrossRef]

1985 (1)

1982 (1)

1980 (1)

1978 (1)

1971 (1)

J. P. Kirk, A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1024–1028 (1971).
[CrossRef]

1970 (2)

1969 (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

1967 (1)

1966 (1)

1964 (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).
[CrossRef]

Brown, B. R.

Bucklew, J. A.

Burkhardt, C. B.

Florence, J. M.

J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 487–498 (1991).
[CrossRef]

Gallagher, N. C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

Hensen, E. W.

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Horner, J. L.

Hsueh, C. K.

Jones, A. L.

J. P. Kirk, A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1024–1028 (1971).
[CrossRef]

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Juday, R. D.

J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 487–498 (1991).
[CrossRef]

Kirk, J. P.

J. P. Kirk, A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1024–1028 (1971).
[CrossRef]

Lee, W. H.

Leger, J. R.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Lohmann, A. W.

Matic, R. M.

Paris, D. P.

Sawchuck, A. A.

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).
[CrossRef]

Appl. Opt. (8)

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

J. P. Kirk, A. L. Jones, “Phase-only complex-valued spatial filter,” J. Opt. Soc. Am. 61, 1024–1028 (1971).
[CrossRef]

Other (2)

J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. SPIE1558, 487–498 (1991).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

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Figures (7)

Fig. 1
Fig. 1

Top view of one cell (m, n).

Fig. 2
Fig. 2

Etching profile of cell (m, n).

Fig. 3
Fig. 3

Top view of one cell; 1-D symmetrical structure.

Fig. 4
Fig. 4

Top view of one cell; 2-D symmetrical structure.

Fig. 5
Fig. 5

(a) 1-D top-hat object to be encoded, (b) obtained reconstruction for original method, (c) obtained reconstruction using 1-D symmetrical structure.

Fig. 6
Fig. 6

(a) 2-D image to be encoded, (b) obtained reconstruction for original method, (c) obtained reconstruction using 2-D symmetrical structure.

Fig. 7
Fig. 7

(a) 2-D image to be encoded, (b) obtained reconstruction for original method, (c) obtained reconstruction using 2-D symmetrical structure.

Tables (1)

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Table 1 Accuracy Predictor for Basic Approach, Including Improvements

Equations (26)

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Hνx, νy=mnrectνyδνrect2νxδν * expiϕm,n1δνx-m+14δν×δνy-n+12δν+expiϕm,n2×δνx-m+34δνδνy-n+12δν,
hx, y=--Hνx, νyexpi2πxνx+yνydνxdνy.
hx, y=δν22expi2πyδν2expi2πxδν4sincδνx2×sincδνymnexpiϕm,n1+expiϕm,n2×expi2πx12δνexpi2πδνxm+yn,
sincx=sinπxπx.
δνx  1, δνy  1,
sincδνx, sincδνy1, expi2πxδν, expi2πyδν1.
hx, yδν22mnexpiϕm,n1+expiϕm,n2×expi2πδνxm+yn.
Hmδν, nδν=Am,n expiϕm,n.
hx, yδν2mnHmδν, nδν×expi2πxm+ynδν.
hx, y=δν2mncosϕm,n1-ϕm,n22×expiϕm,n1+ϕm,n22expi2πxm+ynδν.
Am,n=cosϕm,n1-ϕm,n22,
ϕm,n=ϕm,n1+ϕm,n22.
ϕm,n1=ϕm,n+cos-1Am,n,
ϕm,n2=ϕm,n-cos-1Am,n.
expi2πxδν2=1, expiϕm,n1+expi2πxδν2expiϕm,n22=1,
expi2πxδν2=i, expiϕm,n1+expi2πxδν2expiϕm,n22=1+i2,
AP=expi2πxδν2.
P=Umaxumax.
AP=expi2πXmaxδν2=expi2π14P.
Hνx, νy=mnrectνyδνrect4νxδν * expiϕm,n1δνx-m+18δν+δνx-m+78δν+expiϕm,n2×δνx-m+38δν+δνx-m+58δν×δνy-n+12δν.
hx, y=δν24expi2πyδν2expi2πxδν2sincδνx4×sincδνymnexpiϕm,n1×exp-i2π38δν+expi2π38δν+expiϕm,n2exp-i2πx18δν+expi2π18δνexpi2πδνxm+yn.
hx, yδν22mnexpiϕm,n1cos2πx38δν+expiϕm,n2cos2πx18δν×expi2πδνxm+yn.
AP=cosπ/8pcos3π/8p.
Hνx,νy=mnrect4νyδνrect4νxδν*expiϕm,n1δνx-m+18δν+δνx-m+78δν+expiϕm,n2×δνx-m+38δν+δνx-m+58δν×δνy-m+38δν+δνy-m+58δν+expiϕm,n2×δνx-m+18δν+δνx-m+78δν+expiϕm,n1δνx-m+38δν+δνx-m+58δνδνy-m+18δν+δνy-m+78δν.
hx, yδν22mnexpiϕm,n1cos2πx38δν×cos2πy18δν+cos2πx18δνcos2πy38δν+expiϕm,n2cos2πx38δνcos2πy38δν+cos2πx18δνcos2πy18δν×expi2πδνxm+yn.
AP=cos3π/8p+cosπ/8p2cos3π/8pcosπ/8p.

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