Abstract

We present a straightforward method to design multilevel phase-only diffractive optical elements with a locally improved signal-to-noise ratio in the reconstruction. The method is generally applicable to all unidirectional design schemes, such as direct search, simulated annealing, or genetic optimization. As the shape and the location of the desired low noise areas are supplied by a bit map file the method allows for the design of basically any two-dimensional low noise area. The improvement in the signal-to-noise ratio that may be achieved is considerable but also entails reduced diffraction efficiency. The suggested method is applied to different beam-splitter design examples. All examples are calculated with the scalar diffraction approximation in the far field.

© 2002 Optical Society of America

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References

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  1. J. Turunen, F. Wyrowski, “Introduction to diffractive optics,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowski, eds. (Wiley-VCH, Weinheim, Germany, 1997), pp. 28–34.
  2. J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995).
    [CrossRef]
  3. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
    [CrossRef] [PubMed]
  4. M. Clark, R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
    [CrossRef]
  5. V. Boutenko, R. Chevallier, “Second order direct binary search algorithm for the synthesis of computer-generated holograms,” Optics Commun. 125, 43–47 (1996).
    [CrossRef]
  6. L. Legeard, P. Réfrégier, P. Ambs, “Multicriteria optimality for iterative encoding of computer-generated holograms,” Appl. Opt. 36, 7444–7449 (1997).
    [CrossRef]
  7. M. P. Dames, R. J. Dowling, P. McKee, D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 30, 2685–2691 (1991).
    [CrossRef] [PubMed]
  8. A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Commun. 94, 491–496 (1992).
    [CrossRef]
  9. N. Yoshikawa, T. Yatagai, “Phase optimization of a kinoform by simulated annealing,” Appl. Opt. 33, 863–868 (1994).
    [CrossRef] [PubMed]
  10. G. Yang, “The performance analysis of the genetic algorithm for the optimum design of diffractive optical elements and its comparison to simulated annealing,” Optik 111, 133–137 (2000).
  11. P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
    [CrossRef]
  12. F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
    [CrossRef]
  13. J. N. Mait, “Fourier array generators,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 293–323.
  14. M. Meister, R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
    [CrossRef]
  15. F. Wyrowski, “Characteristics of diffractive optical elements/digital holograms,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 2–10 (1990).
  16. U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
    [CrossRef] [PubMed]

2002 (1)

M. Meister, R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

2000 (2)

G. Yang, “The performance analysis of the genetic algorithm for the optimum design of diffractive optical elements and its comparison to simulated annealing,” Optik 111, 133–137 (2000).

P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

1997 (1)

1996 (2)

M. Clark, R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[CrossRef]

V. Boutenko, R. Chevallier, “Second order direct binary search algorithm for the synthesis of computer-generated holograms,” Optics Commun. 125, 43–47 (1996).
[CrossRef]

1995 (1)

1994 (1)

1992 (2)

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

U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
[CrossRef] [PubMed]

1991 (2)

1987 (1)

Allebach, J. P.

Ambs, P.

Birch, P.

P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Boutenko, V.

V. Boutenko, R. Chevallier, “Second order direct binary search algorithm for the synthesis of computer-generated holograms,” Optics Commun. 125, 43–47 (1996).
[CrossRef]

Bryngdahl, O.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Budgett, D.

P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Chatwin, C.

P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Chevallier, R.

V. Boutenko, R. Chevallier, “Second order direct binary search algorithm for the synthesis of computer-generated holograms,” Optics Commun. 125, 43–47 (1996).
[CrossRef]

Clark, M.

M. Clark, R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[CrossRef]

Dames, M. P.

Dowling, R. J.

Farsari, M.

P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[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. Commun. 94, 491–496 (1992).
[CrossRef]

Kirk, A. G.

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

Krackhardt, U.

Legeard, L.

Mait, J. N.

McKee, P.

Meister, M.

M. Meister, R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

Réfrégier, P.

Seldowitz, M. A.

Smith, R.

M. Clark, R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[CrossRef]

Streibl, N.

Sweeney, D. W.

Turunen, J.

J. Turunen, F. Wyrowski, “Introduction to diffractive optics,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowski, eds. (Wiley-VCH, Weinheim, Germany, 1997), pp. 28–34.

Winfield, R. J.

M. Meister, R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

Wood, D.

Wyrowski, F.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

F. Wyrowski, “Characteristics of diffractive optical elements/digital holograms,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 2–10 (1990).

J. Turunen, F. Wyrowski, “Introduction to diffractive optics,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowski, eds. (Wiley-VCH, Weinheim, Germany, 1997), pp. 28–34.

Yang, G.

G. Yang, “The performance analysis of the genetic algorithm for the optimum design of diffractive optical elements and its comparison to simulated annealing,” Optik 111, 133–137 (2000).

Yatagai, T.

Yoshikawa, N.

Young, R.

P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

M. Clark, R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[CrossRef]

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

M. Meister, R. J. Winfield, “Novel approaches to direct search algorithms for the design of diffractive optical elements,” Opt. Commun. 203, 39–49 (2002).
[CrossRef]

Opt. Lasers Eng. (1)

P. Birch, R. Young, M. Farsari, C. Chatwin, D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Optics Commun. (1)

V. Boutenko, R. Chevallier, “Second order direct binary search algorithm for the synthesis of computer-generated holograms,” Optics Commun. 125, 43–47 (1996).
[CrossRef]

Optik (1)

G. Yang, “The performance analysis of the genetic algorithm for the optimum design of diffractive optical elements and its comparison to simulated annealing,” Optik 111, 133–137 (2000).

Rep. Prog. Phys. (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Other (3)

J. N. Mait, “Fourier array generators,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 293–323.

F. Wyrowski, “Characteristics of diffractive optical elements/digital holograms,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 2–10 (1990).

J. Turunen, F. Wyrowski, “Introduction to diffractive optics,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowski, eds. (Wiley-VCH, Weinheim, Germany, 1997), pp. 28–34.

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Figures (8)

Fig. 1
Fig. 1

The central diffraction order of the reference target pattern. The signal spots are white while the frame (the desired low-noise area) is indicated by the gray tone. Outside the frame, the intensity is allowed to vary freely.

Fig. 2
Fig. 2

Simulated performance of the DOEs obtained using Eq. (3) with different weights w while α = 0.7. The target pattern is shown in Fig. 1. An optimum with still reasonable diffraction efficiency seems to be reached between w = 1000 and w = 5000.

Fig. 3
Fig. 3

DOEs synthesized without a frame (c) and with a weighted frame (d) (w = 2000) and the corresponding simulated far field reconstructions (a, b) above. The target is shown in Figure 1. One observes a dark region around the signal spots in (b). This is the low-noise area created by the frame. The contrast in the reconstructions is increased to uncover the noise. Despite the visual impression the intensity of the noise is more than one order of magnitude less than the signal.

Fig. 4
Fig. 4

Central order of the simulated far field reconstruction of an asymmetric beam splitter with a triangular frame around the signal spots (see also Table 3). The boundaries of the square frame used for the design in Table 3 are superimposed. The intensities are severely compressed to reveal the low-noise area.

Fig. 5
Fig. 5

Central order of a simulated far-field reconstruction of a 3 × 5 beam splitter with a square frame around the signal spots and an additional external frame. The frames are highlighted by white lines. The intensities are severely compressed to reveal the low-noise regions. The corresponding DOE consists of 120 × 120 square pixels at three phase levels. The arrows indicate the line of the intensity scan in Fig. 6.

Fig. 6
Fig. 6

Intensity scan along the line in reconstruction Fig. 5. The values are given with respect to the largest signal sample I max. L is the full width of the oval as indicated in Fig. 5. The average noise inside L is less than one tenth the noise outside.

Fig. 7
Fig. 7

Part of the beam-splitter target bit map with the central frame and the additional spike suppression pixels painted in a darker color. These pixels are added at locations where one would suspect replicated signal spots.

Fig. 8
Fig. 8

Intensity scans along the same row in the simulated reconstruction of two DOEs synthesized according to the target Fig. 1. The standard frame DOE was obtained with the frame shown in Fig. 1 while the pixel matrix DOE was synthesized with additional frame spots as shown in Fig. 7. The data are normalized by the maximal intensity I max. The high-intensity data are clipped.

Tables (4)

Tables Icon

Table 1 DOE Performance in Dependence of the Scale Factor αa

Tables Icon

Table 2 DOE Performance with a Weighted Merit Functiona

Tables Icon

Table 3 Performance of DOE Synthesized with Different Framesa

Tables Icon

Table 4 Influence of the Spike Suppression Framea

Equations (8)

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

C=iS,FIi-αUi2, Ui=0 if iF, 0<α<1.
η=iS Ii.
C=iSIi-αUi2+w iF Ii2,w>0.
S/N=iS IiiF Ii.
SNR=10 log10miniSIimaxiFIi.
erms=1maxiIiiIi-ηUi2s1/2, iS.
C=iSIi-αUi2+wImax,F2, w>1
C=iSIi-αUi2+wiF Ii41/2, w>1.

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