## Abstract

Pseudoscopic (inverted depth) images that keep a continuous parallax were shown to be possible by use of a double diffraction process intermediated by a slit. One diffraction grating directing light to the slit acts as a wavelength encoder of views, while a second diffraction grating decodes the projected image. The process results in the enlargement of the image under common white light illumination up to infinite magnification at a critical point. We show that this point corresponds to another simple-symmetry object–observer system. Our treatment allows us to explain the experience by just dealing with main ray directions.

© 2006 Optical Society of America

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### Equations (8)

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(1)
$$\mathrm{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{i}-\mathrm{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{d}=\lambda \nu ,$$
(2)
$${\theta}_{i}=\mathrm{arcsin}\left[\frac{(X-{X}_{i})}{\sqrt{{(X-{X}_{i})}^{2}+{Z}^{2}}}\right],$$
(3)
$$\frac{(X-{X}_{i})}{\sqrt{{(X-{X}_{i})}^{2}+{Z}^{2}}}-\frac{{X}_{i}}{\sqrt{{X}_{i}^{2}+{Z}_{R}^{2}}}=\lambda \nu .$$
(4)
$${\theta}_{i}={\theta}_{i}(X,Z,{Z}_{R},\nu ,\lambda ),$$
(5)
$$\mathrm{\Delta}\theta ={\theta}_{i}(X,Z,{X}_{B},{Z}_{B},{Z}_{R},\nu ,{\lambda}_{M})-{\theta}_{i}(X,Z,{Z}_{A},{Z}_{A},{Z}_{R},\nu ,{\lambda}_{m}).$$
(6)
$${\theta}_{i}=\mathrm{arcsin}\phantom{\rule{0.2em}{0ex}}\lambda \nu ,$$
(7)
$$\mathrm{\Delta}\theta =\mathrm{arcsin}\phantom{\rule{0.2em}{0ex}}{\lambda}_{M}\nu -\mathrm{arcsin}\phantom{\rule{0.2em}{0ex}}{\lambda}_{m}\nu $$
(8)
$$\mathrm{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{i}-\mathrm{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{d}=\lambda \nu /\sqrt{1-{\phi}^{2}}.$$