## Abstract

A pair of planar reflection gratings is proposed and discussed for
use in a color-splitting and imaging system, such as a projection-type
color-scanner head. Red, green, and blue light reflected from a
color subject are split by a color-splitting grating lens and imaged by
an image-correction grating, consisting of three segments, onto
three line sensors arranged in parallel. The phase-shift function
of the image-correction grating was optimized for each color by
numerical iteration with the ray-tracing method to suppress aberrations
resulting from the wide view angle and the three different wavelengths.
Gratings were designed and fabricated, and aberration suppression was
experimentally confirmed.

© 2001 Optical Society of America

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### Equations (3)

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(1)
$${\left[{x}^{2}+{\left(y+{f}_{\mathrm{IN}}sin{\mathrm{\theta}}_{\mathrm{IN}}\right)}^{2}+{\left({f}_{\mathrm{IN}}cos{\mathrm{\theta}}_{\mathrm{IN}}\right)}^{2}\right]}^{1/2}+{\left({x}^{2}+{y}^{2}+{{f}_{\mathrm{CS}}}^{2}\right)}^{1/2}=m{\mathrm{\lambda}}_{\mathrm{CS}}+\mathrm{constant}.$$
(2)
$$\frac{2\mathrm{\pi}}{\mathrm{\lambda}}\left(cos{\mathrm{\theta}}_{\mathrm{IN}}+cos{\mathrm{\theta}}_{\mathrm{DF}}\right){d}_{\mathrm{CS}}=\mathrm{\pi},$$
(3)
$${\mathrm{\varphi}}_{\mathrm{IC}}=\frac{2\mathrm{\pi}}{\mathrm{\lambda}}\left\{{\left[x_{\mathrm{IC}}{}^{2}+{\left({y}_{\mathrm{IC}}-{y}_{P}\right)}^{2}+z_{P}{}^{2}\right]}^{1/2}-{\left[x_{\mathrm{IC}}{}^{2}+{\left({y}_{\mathrm{IC}}-{y}_{Q}\right)}^{2}+z_{Q}{}^{2}\right]}^{1/2}+\sum _{i=0}^{8}\sum _{j=0}^{8-1}{C}_{\mathit{ij}}{{x}_{\mathrm{IC}}}^{i}{{y}_{\mathrm{IC}}}^{j}\right\},$$