Abstract

Phase gratings with deep rectangular grooves have been successfully used in the zero diffraction order as transmission color filters. They form the basis of the ZOD microimage system for recording color images as surface-relief structures. ZOD images can be inexpensively replicated by hot embossing in a transparent sheet of plastic and read-out using conventional slide projectors or microfilm viewers. In this paper we use rigorous diffraction theory to derive optimum grating parameters for gratings with periods d < 2 μm to produce the three subtractive primary colors, cyan, magenta, and yellow, and also green. The theoretical results are in good agreement with the experiment.

© 1978 Optical Society of America

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References

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  1. K. Knop, Opt. Commun. 18, 298 (1976).
    [CrossRef]
  2. K. Knop, “Diffractive Subtractive Color Filtering Technique,” U.S. Patent3,957,354, issued 18May1976.
  3. M. T. Gale, J. Kane, K. Knop, J. Appl. Photogr. Eng. 4, 41 (1978).
  4. K. Knop, “Simplified and Improved Diffractive Subtractive Color Filtering Technique,” U.S. Patent4,057,326, issued 8November1977.
  5. K. Knop, “Rigorous Diffraction Theory for Dielectric Gratings with Deep Rectangular Grooves,” J. Opt. Soc. Am., Sept.1978 issue, in press.
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 8.6.
  7. European Standard C.E.I. 13: 67 (1967).
  8. R. W. G. Hunt, The Reproduction of Colour (Fountain Press, London, 1975).

1978

M. T. Gale, J. Kane, K. Knop, J. Appl. Photogr. Eng. 4, 41 (1978).

1976

K. Knop, Opt. Commun. 18, 298 (1976).
[CrossRef]

1967

European Standard C.E.I. 13: 67 (1967).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 8.6.

Gale, M. T.

M. T. Gale, J. Kane, K. Knop, J. Appl. Photogr. Eng. 4, 41 (1978).

Hunt, R. W. G.

R. W. G. Hunt, The Reproduction of Colour (Fountain Press, London, 1975).

Kane, J.

M. T. Gale, J. Kane, K. Knop, J. Appl. Photogr. Eng. 4, 41 (1978).

Knop, K.

M. T. Gale, J. Kane, K. Knop, J. Appl. Photogr. Eng. 4, 41 (1978).

K. Knop, Opt. Commun. 18, 298 (1976).
[CrossRef]

K. Knop, “Diffractive Subtractive Color Filtering Technique,” U.S. Patent3,957,354, issued 18May1976.

K. Knop, “Simplified and Improved Diffractive Subtractive Color Filtering Technique,” U.S. Patent4,057,326, issued 8November1977.

K. Knop, “Rigorous Diffraction Theory for Dielectric Gratings with Deep Rectangular Grooves,” J. Opt. Soc. Am., Sept.1978 issue, in press.
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 8.6.

European Standard C.E.I.

European Standard C.E.I. 13: 67 (1967).

J. Appl. Photogr. Eng.

M. T. Gale, J. Kane, K. Knop, J. Appl. Photogr. Eng. 4, 41 (1978).

Opt. Commun.

K. Knop, Opt. Commun. 18, 298 (1976).
[CrossRef]

Other

K. Knop, “Diffractive Subtractive Color Filtering Technique,” U.S. Patent3,957,354, issued 18May1976.

R. W. G. Hunt, The Reproduction of Colour (Fountain Press, London, 1975).

K. Knop, “Simplified and Improved Diffractive Subtractive Color Filtering Technique,” U.S. Patent4,057,326, issued 8November1977.

K. Knop, “Rigorous Diffraction Theory for Dielectric Gratings with Deep Rectangular Grooves,” J. Opt. Soc. Am., Sept.1978 issue, in press.
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 8.6.

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Figures (11)

Fig. 1
Fig. 1

Typical projector optics: when used with a periodic grating structure in the object plane, only the light diffracted into the zero order is transmitted onto the screen.

Fig. 2
Fig. 2

Square-wave phase grating as used to produce colors in the zero diffraction order. The grating parameters are: d = grating constant, a = depth, b = aspect ratio, n = refractive index.

Fig. 3
Fig. 3

Gamut of color which can be covered by the primary colors defined in Table II (dashed line). The color range attained with the coarse gratings defined in Table I is also plotted (solid line). G: Chromaticity of the green primary as realized by a single square-wave grating in the two-grating scheme.

Fig. 4
Fig. 4

Range of grating parameters where optimum primary colors exist. A color is considered optimum if its transmittance curve has maxima exceeding 80% and minima below 5%.

Fig. 5
Fig. 5

Grating depths a required to generate the primary colors for a given grating period d = 1.4 μm vs. aspect ratio b. Solid lines indicate good and dashed lines acceptable colors. The black dots show the optimum depths for coarse gratings.

Fig. 6
Fig. 6

Same as Fig. 4 but for d = 1.7 μm.

Fig. 7
Fig. 7

Same as Fig. 4 but for d = 2 μm.

Fig. 8
Fig. 8

Calculated transmittance for light polarized parallel (EP) and perpendicular (HP) to the grating lines for a set of primary colors. Cyan, magenta, and yellow are required for the three-grating scheme and green in addition for the two-grating scheme. The corresponding grating parameters are given in Table II.

Fig. 9
Fig. 9

Experimental transmittance curves for a typical set of primary colors, corresponding to the calculated set of Fig. 8 (Table II).

Fig. 10
Fig. 10

Transmittance for the best magenta primary color which could be found in theory (top) and experiment (bottom). Both are not optimum, having a transmission maxima in the blue < 80%.

Fig. 11
Fig. 11

From top to bottom: Experimental transmittance of original cyan grating, of the complementary grating structure, and of the complement of the complementary grating which has again the same grating parameters as the original grating. Bottom curve shows transmittance as calculated from Formula (1) (scalar theory) using the grating parameters measured in the SEM.

Tables (2)

Tables Icon

Table I Optimum Grating Parameters for Coarse Gratings with b = 0.5 and d ≫ λ

Tables Icon

Table II Optimum Grating Parameters for Fine Gratings d < 5λ

Equations (3)

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t ( λ ) = cos 2 [ π ( n 1 ) a / λ ] .
t min = ( 2 b 1 ) 2 .
0.1 b 0.9 , 0.7 d / λ 5 , 1 a / λ 7.

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