Abstract

Special phase gratings are described by means of which the red, green, and blue color components of colored objects are generated side by side around the optical axis in the image plane of a lens. An analysis of these color separation gratings is given, and theoretical and experimental results for some grating samples are presented.

© 1978 Optical Society of America

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References

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  1. M. T. Gale, K. Knop, Appl. Opt. 15, 2189 (1976); M. T. Gale, Opt. Commun. 18, 292 (1976); K. Knop, Opt. Commun. 18, 298 (1976).
    [CrossRef] [PubMed]
  2. H. Dammann, Optik 31, 95 (1969).
  3. D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).

1976 (1)

1969 (1)

H. Dammann, Optik 31, 95 (1969).

Dammann, H.

H. Dammann, Optik 31, 95 (1969).

Gale, M. T.

Judd, D. B.

D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).

Knop, K.

Wyszecki, G.

D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).

Appl. Opt. (1)

Optik (1)

H. Dammann, Optik 31, 95 (1969).

Other (1)

D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).

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Figures (12)

Fig. 1
Fig. 1

Desired phase-grating structures for different wavelengths λ. Only three grating periods are shown here.

Fig. 2
Fig. 2

Variable overphasing of the phase structure of Fig. 1(a). Only one grating period is shown. It is λb = λ1.

Fig. 3
Fig. 3

General form of a multilevel dielectric structure within one grating period, the width of which is normalized to 1.

Fig. 4
Fig. 4

Calculated spectral curves for different cases of overphasing based on the phase-grating structure of Fig. 2. It is φ 1 ( λ b ) = 2 3 π + 2 · 2 π , φ 2 ( λ b ) = 4 3 π + 4 · 2 π for Fig . 4 ( a ) , φ 1 ( λ b ) = 2 3 π + 1 · 2 π , φ 2 ( λ b ) = 4 3 π + 2 · 2 π for Fig . 4 ( b ) , φ 1 ( λ b ) = 2 3 π + 3 · 2 π , φ 2 ( λ b ) = 4 3 π + 6 · 2 π for Fig . 4 ( c ) .

Fig. 5
Fig. 5

Calculated spectral curves for different cases based on quaternary phase-grating structures. It is n = constant, and φ 1 ( λ b ) = π 2 + 2 · 2 π , φ 2 ( λ b ) = π + 4 · 2 π , φ 3 ( λ b ) = 3 2 π + 6 · 2 π for Fig . 5 ( a ) , φ 1 ( λ r ) = 2 · 2 π , φ 3 ( λ r ) = 4 · 2 π , φ 3 ( λ r ) = 6 · 2 π for Fig . 5 ( b ) .

Fig. 6
Fig. 6

Required spectral sensitivity curves (solid lines) and main parts of the calculated spectral curves from Fig. 5(b) (dashed, dashed–dotted, and dotted lines). Both sets of curves are shown in a normalized form for comparison.

Fig. 7
Fig. 7

Chromaticity coordinates of the color stimuli corresponding to the spectral curves of Figs. 4 and 5 assuming the equal-energy spectrum as illuminant. Figure 7(a) corresponds to the curves of Figs. 4(a), 4(b), 4(c), and the three cases are marked by crosses denoted by ⓐ, ⓑ, and ⓒ. Figure 7(b) corresponds to the curves of Figs. 5(a) and 5(b).

Fig. 8
Fig. 8

Realizing the grating structure of Fig. 2 by a sandwich of two binary grating structures.

Fig. 9
Fig. 9

Measured spectral curves generated by a grating structure designed after Fig. 2.

Fig. 10
Fig. 10

Comparison of calculated and measured spectral curves for a grating structure as shown in Fig. 2. For the calculated curves, 3% dispersion of n is assumed.

Fig. 11
Fig. 11

Optical setup for color separation by a phase grating.

Fig. 12
Fig. 12

Experimental result of color separation by a phase grating. The colored object (top) is split into the green image (zeroth diffraction order) and the red and blue components corresponding to the two first diffraction orders. The interrelated structures within the green and blue images are caused by the film recording process of the colored object. For a color print of this figure see the cover of this 1 August issue of Applied Optics.

Equations (20)

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φ 1 ( λ 1 ) = ( 2 / 3 ) π + 4 π = ( 14 / 3 ) π , φ 2 ( λ 1 ) = ( 4 / 3 ) π + 8 π = ( 28 / 3 ) π .
φ 1 ( λ ) = 2 π ( n 1 ) d 1 λ , φ 2 ( λ ) = 2 π ( n 1 ) d 2 λ ,
φ 1 ( λ 2 ) = φ 1 ( λ 1 ) λ 1 λ 2 , φ 2 ( λ 2 ) = φ 2 ( λ 1 ) λ 1 λ 2 , φ 1 ( λ 3 ) = φ 1 ( λ 1 ) λ 1 λ 3 , φ 2 ( λ 3 ) = φ 2 ( λ 1 ) λ 1 λ 3 .
λ 1 / λ 2 = λ b / λ r = 5 / 7 , λ 1 / λ 3 = λ b / λ g = 6 / 7 ,
φ 1 ( λ g ) = 14 / 3 · π · 6 / 7 = 4 π , φ 2 ( λ g ) = 28 / 3 · π · 6 / 7 = 8 π , φ 1 ( λ r ) = 14 / 3 · π · 5 / 7 = ( 4 / 3 ) π + 2 π , φ 2 ( λ r ) = 28 / 3 · π · 5 / 7 = ( 2 / 3 ) π + 6 π .
φ 1 ( λ g ) 0 , φ 2 ( λ g ) 0 , φ 1 ( λ r ) ( 4 / 3 ) π , φ 2 ( λ r ) ( 2 / 3 ) π ,
( n 1 ) d 1 = ( 7 / 3 ) λ b = 2 λ g = ( 5 / 3 ) λ r , ( n 1 ) d 2 = ( 14 / 3 ) λ b = 4 λ g = ( 10 / 3 ) λ r .
φ k ( λ ) = 2 π ( n 1 ) [ ( d k ) / λ ] ( k = 1,2 , , N ) .
a q ( λ ) = | k = 0 k = N ξ k ξ k + 1 exp [ i φ k ( λ ) ] exp ( 2 π i q ξ ) d ξ | 2 .
N = 2 , φ 1 ( λ b ) = 14 3 π , φ 2 ( λ b ) = 28 3 π , ξ 1 = 1 3 , ξ 2 = 2 3 ,
a 0 ( λ ) = a 1 ( λ ) = 0 for λ = λ b = 450 nm , a 1 ( λ ) = a 1 ( λ ) = 0 for λ = λ g = 525 nm , a 1 ( λ ) = a 0 ( λ ) = 0 for λ = λ r = 630 nm ,
υ 1 = 2 , υ 2 = 4 for Fig . 4 ( a ) , υ 1 = 1 , υ 2 = 2 for Fig . 4 ( b ) , υ 1 = 3 , υ 2 = 6 for Fig . 4 ( c ) ,
φ 1 ( λ b ) = π 2 + 2 · 2 π , φ 2 ( λ b ) = π + 4 · 2 π , φ 3 ( λ b ) = 3 2 π + 6 · 2 π ,
ξ 1 = 0.25 , ξ 2 = 0.5 , ξ 3 = 0.75.
λ b = λ g 4 π π / 2 + 4 π = 8 9 λ g = 467 nm , λ r = λ g 4 π ( 3 / 2 ) π + 2 π = 8 7 λ g = 600 nm .
d 1 ( 14 / 3 ) λ b , d 2 ( 28 / 3 ) λ b .
d 1 2.1 μ m , d 2 4.2 μ m .
a q ( λ ) m = radiant energy at wavelength λ in diffraction order q sum of radiant energy at wavelength λ in all diffraction orders .
φ 1 ( λ b ) = 2 3 π + 2 · 2 π , φ 2 ( λ b ) = 4 3 π + 4 · 2 π for Fig . 4 ( a ) , φ 1 ( λ b ) = 2 3 π + 1 · 2 π , φ 2 ( λ b ) = 4 3 π + 2 · 2 π for Fig . 4 ( b ) , φ 1 ( λ b ) = 2 3 π + 3 · 2 π , φ 2 ( λ b ) = 4 3 π + 6 · 2 π for Fig . 4 ( c ) .
φ 1 ( λ b ) = π 2 + 2 · 2 π , φ 2 ( λ b ) = π + 4 · 2 π , φ 3 ( λ b ) = 3 2 π + 6 · 2 π for Fig . 5 ( a ) , φ 1 ( λ r ) = 2 · 2 π , φ 3 ( λ r ) = 4 · 2 π , φ 3 ( λ r ) = 6 · 2 π for Fig . 5 ( b ) .

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