## Abstract

This paper proposes a new computer generated hologram (CGH) method that considers the reflectance distribution on object surfaces and reflected images. The reflectance distributions are generated from phase differences determined by the shape of the object surface, which is constructed by using the Blinn and Torrance–Sparrow reflection models. Moreover, the reflected images are adapted when they are mapped onto metallic objects such as mirrors. Incorporating these two characteristics of reflection means that CGHs can express metallic objects realistically. Computer simulations and computational and optical reconstructed experiments were carried out. These results show the potential of the proposed method for showing metallic objects.

© 2009 Optical Society of America

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### Equations (14)

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(1)
$${g}_{I}(\xi ,\eta )=A(\xi ,\eta ),$$
(2)
$${g}_{R}(\xi ,\eta )={g}_{I}(\xi ,\eta )\mathrm{exp}[-j\varphi (\xi ,\eta )],$$
(3)
$${g}_{R}(\xi ,\eta )={g}_{I}(\xi ,\eta )s(\xi ,\eta ),$$
(4)
$$u(x,y)={\widehat{g}}_{R}(\xi ,\eta )\otimes h(\xi ,\eta ),$$
(5)
$$D(\theta )=\mathrm{exp}[-(\theta /m{)}^{2}],$$
(6)
$${g}_{R}(\xi ,\eta )={g}_{I}(\xi ,\eta )\mathrm{exp}[-j2{\varphi}_{M}(\xi ,\eta )],$$
(7)
$${\varphi}_{M(k)}(\xi )={\varphi}_{M(k)}({\xi}_{k0})+\frac{2\pi}{\lambda}(\xi -{\xi}_{k0})\mathrm{tan}{\theta}_{\xi (k)},$$
(8)
$${\varphi}_{M}(\xi )=\sum _{k}^{{M}_{\xi}}{\varphi}_{M(k)}(\xi ),$$
(9)
$${\varphi}_{M(k)}(\xi )=\{\begin{array}{c}{\varphi}_{M(k)}({\xi}_{k0})+\frac{2\pi}{\lambda}(\xi -{\xi}_{k0})\mathrm{tan}{\theta}_{\xi (k)}\\ {\xi}_{k0}\le \xi <{\xi}_{(k+1)0}\\ 0\phantom{\rule[-0.0ex]{1em}{0.0ex}}\text{otherwise}\end{array}\mathrm{.}$$
(10)
$${G}_{V}^{\prime}({f}_{x},{f}_{y})={G}_{V}({f}_{x},{f}_{y})\mathrm{exp}[-j2\pi (-\mathrm{\Delta}z){f}_{z}],$$
(11)
$${U}_{V}({f}_{x},{f}_{y})={G}_{V}^{\prime}({f}_{x},{f}_{y})\mathrm{exp}[-j2\pi {z}_{0}{f}_{z}],$$
(12)
$$={G}_{V}({f}_{x},{f}_{y})\mathrm{exp}[-j2\pi ({z}_{0}-\mathrm{\Delta}z){f}_{z}],$$