Abstract

To provide screens for laser projection that improve contrast, a spectrally selective reflecting filter was designed by using genetic algorithms to overcome the problem of unknown starting values. Colormetrics rather than fixed targets were used for evaluation. Various selective filters were deposited upon glass as well as upon solid and flexible plastic substrates by reactive mid-frequency magnetron sputtering. For process control, in situ spectroscopic ellipsometry was applied.

© 2002 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  17. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
  18. M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
    [CrossRef]

2000 (1)

C. Deter, “Laser projection technology: image display of the future,” LaserOpto 32, 76–82 (2000).

1999 (1)

M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
[CrossRef]

1996 (2)

1992 (2)

1990 (1)

1988 (1)

J. A. Dobrowolski, “Computer design of optical coatings,” Thin Solid Films 163, 97–110 (1988).
[CrossRef]

1986 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1978 (1)

1953 (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Combinatorial minimization,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Chaton, P.

P. Chaton, P. Pinston, J. P. Gaillard, “Synthesis of optical coatings using a simulated annealing algorithm,” in Optical Interference Coatings, F. Abeles, ed. Proc. SPIE2254, 73–80 (1994).

DeBell, G. W.

Deter, C.

C. Deter, “Laser projection technology: image display of the future,” LaserOpto 32, 76–82 (2000).

Dobrowolski, J. A.

Furman, S. A.

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, Gif-sur-Yvette, France, 1992), pp. 108–151.

Gaillard, J. P.

P. Chaton, P. Pinston, J. P. Gaillard, “Synthesis of optical coatings using a simulated annealing algorithm,” in Optical Interference Coatings, F. Abeles, ed. Proc. SPIE2254, 73–80 (1994).

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Heistermann, J.

J. Heistermann, Genetische Algorithmen (Teubner, Stuttgart, Germany, 1994).

Kao, C.-Y.

J.-M. Yang, C.-Y. Kao, “An evolutionary algorithm for synthesizing optical thin-film designs,” in PPSN-Parallel Problem Solving from Nature, A. E. Eiben, T. Bäck, H.-P. Schwefel, M. Schoenauer, eds. (Springer-Verlag, Berlin, 1998), pp. 947–956.

Kemp, R. A.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Li, L.

Lowe, D.

Malkomes, N.

M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
[CrossRef]

Matthée, T.

M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
[CrossRef]

Metropolis, N.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Combinatorial minimization,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Pinston, P.

P. Chaton, P. Pinston, J. P. Gaillard, “Synthesis of optical coatings using a simulated annealing algorithm,” in Optical Interference Coatings, F. Abeles, ed. Proc. SPIE2254, 73–80 (1994).

Richter, U.

M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
[CrossRef]

Rosenbluth, A. W.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Combinatorial minimization,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Rosenbluth, M. N.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Combinatorial minimization,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Staedler, T.

M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
[CrossRef]

Sullivan, B. T.

Teller, A. H.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Combinatorial minimization,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Teller, E.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Combinatorial minimization,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, “Thin-film coatings design using second-order optimization methods,” in Thin Films for Optical Systems, K.-H. Guenther, ed. Proc. SPIE1782, 156–164 (1993).

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, Gif-sur-Yvette, France, 1992), pp. 108–151.

Trubetskov, M. K.

A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, “Thin-film coatings design using second-order optimization methods,” in Thin Films for Optical Systems, K.-H. Guenther, ed. Proc. SPIE1782, 156–164 (1993).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Vergöhl, M.

M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
[CrossRef]

Yang, J.-M.

J.-M. Yang, C.-Y. Kao, “An evolutionary algorithm for synthesizing optical thin-film designs,” in PPSN-Parallel Problem Solving from Nature, A. E. Eiben, T. Bäck, H.-P. Schwefel, M. Schoenauer, eds. (Springer-Verlag, Berlin, 1998), pp. 947–956.

Appl. Opt. (7)

J. Chem. Phys. (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Combinatorial minimization,” J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

LaserOpto (1)

C. Deter, “Laser projection technology: image display of the future,” LaserOpto 32, 76–82 (2000).

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Thin Solid Films (2)

J. A. Dobrowolski, “Computer design of optical coatings,” Thin Solid Films 163, 97–110 (1988).
[CrossRef]

M. Vergöhl, N. Malkomes, T. Staedler, T. Matthée, U. Richter, “Ex situ and in situ spectroscopic ellipsometry of MF- and DC-sputtered TiO2 and SiO2 films for process control,” Thin Solid Films 351, 42–47 (1999).
[CrossRef]

Other (6)

J. Heistermann, Genetische Algorithmen (Teubner, Stuttgart, Germany, 1994).

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

J.-M. Yang, C.-Y. Kao, “An evolutionary algorithm for synthesizing optical thin-film designs,” in PPSN-Parallel Problem Solving from Nature, A. E. Eiben, T. Bäck, H.-P. Schwefel, M. Schoenauer, eds. (Springer-Verlag, Berlin, 1998), pp. 947–956.

A. V. Tikhonravov, M. K. Trubetskov, “Thin-film coatings design using second-order optimization methods,” in Thin Films for Optical Systems, K.-H. Guenther, ed. Proc. SPIE1782, 156–164 (1993).

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, Gif-sur-Yvette, France, 1992), pp. 108–151.

P. Chaton, P. Pinston, J. P. Gaillard, “Synthesis of optical coatings using a simulated annealing algorithm,” in Optical Interference Coatings, F. Abeles, ed. Proc. SPIE2254, 73–80 (1994).

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Figures (12)

Fig. 1
Fig. 1

Left, flow chart of the calculation of the generic selective algorithm. Starting with a randomly generated population, several operations were repeatedly performed on individuals A–D until a good design was found. Step B denotes two different processes occurring at the same time; film thicknesses were modified by the procedure of metamutation, whereas layer materials were modified by the process of simple mutation. Right, schematics of (top) the XO recombination operator and of (bottom) the median XO recombination operator. For more details refer to the text.

Fig. 2
Fig. 2

Achievable contrast improvement versus total film thickness. Rectangulars, filter designs calculated with the genetic algorithm. Obviously the increase in contrast improvement is greater for thinner films and fewer layers and seems to saturate for greater thicknesses and more layers. The solid curve is meant as a guide for the eye.

Fig. 3
Fig. 3

Reflectance spectra of a nine-layer filter system for 0° and 20° angles of incidence and a total film thickness below 1.75 µm, which has been set as the maximum tolerable film thickness for flexible substrates. The contrast improvement over that of a white screen is k ≈ 2.5. Dashed and dotted-dashed curves are guides for the eye.

Fig. 4
Fig. 4

Reflectance spectra of a 20-layer filter system for 0° and 20° angles of incidence. Total film thickness is ∼4.2 µm, and the contrast improvement is k = 3.55.

Fig. 5
Fig. 5

Index profile of the nine-layer filter design corresponding to the reflectance plot in Fig. 3.

Fig. 6
Fig. 6

Index profile of the nine-layer filter design corresponding to the reflectance plot in Fig. 4.

Fig. 7
Fig. 7

Changes in the reflectance spectra of a 20-layer filter design with increasing angles of incidence (0°, 20°, and 40°).

Fig. 8
Fig. 8

Changes in the reflectance spectra of a 20-layer filter design as they occur for three kinds of high-refractive material.

Fig. 9
Fig. 9

Illustration of the coating setup: (1) coating chamber, (2) double magnetron (PK-500 TwinMag), (3) dc magnetron (PK-500), (4) spectroscopic in situ ellipsometer, (5) five-axis substrate holder (maximum of four substrates), (6) base rotation for multilayer depositions, (7) samples, (8) optical emission spectroscopy monitor, (9) λ probe, (10) photometer. A mass spectrometer (not shown) is also included.

Fig. 10
Fig. 10

Design evolution through the process of deposition and reengineering. Back to front, progression of the initial design to the final complete filter.

Fig. 11
Fig. 11

Comparison of the final spectra as calculated from in situ ellipsometric measurements and as measured by ex situ spectral photometry. Excellent agreement of ex situ and in situ acquired data is shown.

Fig. 12
Fig. 12

Comparison of the design after deposition with reengineering and the original (calculated) design. Deposition tolerances lead to a reduction of achievable contrast improvement (original design, k ≈ 2.75; design after reengineering, k ≈ 2.5).

Tables (1)

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Table 1 Changes in Contrast Improvement krealistic as the Angle of Incidence of the Ambient Light Is Varied while the Incidence of the Laser Light Remains Normal to the Screena

Equations (4)

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k=13Yi=r,g,b Ri,
Y=380780 SλλRλyλdλ
k=1Y3i=r,g,b RiCσR,
krealistic=1Y40°3i=r,g,b Ri,0°.

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