## Abstract

This paper presents a novel pixel-level resolution 3D profilometry technique that only needs binary phase-shifted structured patterns. This technique uses four sets of three phase-shifted binary patterns to achieve the phase error of less than 0.2%, and only requires two sets to reach similar quality if the projector is slightly defocused. Theoretical analysis, simulations, and experiments will be presented to verify the performance of the proposed technique.

© 2011 Optical Society of America

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### Equations (12)

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(1)
$${I}_{1}(x,y)={I}^{\prime}(x,y)+{I}^{\prime \prime}(x,y)\mathrm{cos}(\varphi -2\pi /3),$$
(2)
$${I}_{2}(x,y)={I}^{\prime}(x,y)+{I}^{\prime \prime}(x,y)\mathrm{cos}(\varphi ),$$
(3)
$${I}_{3}(x,y)={I}^{\prime}(x,y)+{I}^{\prime \prime}(x,y)\mathrm{cos}(\varphi +2\pi /3).$$
(4)
$$\varphi (x,y)={\mathrm{tan}}^{-1}[\sqrt{3}({I}_{1}-{I}_{3})/(2{I}_{2}-{I}_{1}-{I}_{3})].$$
(5)
$$\mathrm{\Phi}(x,y)=2\pi \times k(x,y).$$
(6)
$$y(x)=\{\begin{array}{ll}0& x\in [(2n-1)\pi ,2n\pi )\\ 1& x\in [2n\pi ,(2n+1)\pi )\end{array}\mathrm{.}$$
(7)
$$y(x)=0.5+\sum _{k=0}^{\infty}\frac{2}{(2k+1)\pi}\mathrm{sin}[(2k+1)x].$$
(8)
$${I}_{1}^{k}(x,y)={I}^{\prime}(x,y)+{I}^{\prime \prime}(x,y)\{\mathrm{cos}(\varphi -2\pi /3)\phantom{\rule{0ex}{0ex}}+\mathrm{cos}[(2k+1)(\varphi -2\pi /3)]/(2k+1)\},$$
(9)
$${I}_{2}^{k}(x,y)={I}^{\prime}(x,y)+{I}^{\prime \prime}(x,y)\{\mathrm{cos}(\varphi )\phantom{\rule{0ex}{0ex}}+\mathrm{cos}[(2k+1)\varphi ]/(2k+1)\},$$
(10)
$${I}_{3}^{k}(x,y)={I}^{\prime}(x,y)+{I}^{\prime \prime}(x,y)\{\mathrm{cos}(\varphi +2\pi /3)\phantom{\rule{0ex}{0ex}}+\mathrm{cos}[(2k+1)(\varphi +2\pi /3)]/(2k+1)\}.$$
(11)
$${\varphi}^{k}(x,y)={\mathrm{tan}}^{-1}[\sqrt{3}({I}_{1}^{k}-{I}_{3}^{k})/(2{I}_{2}^{k}-{I}_{1}^{k}-{I}_{3}^{k})].$$
(12)
$$\mathrm{\Delta}{\mathrm{\Phi}}^{k}(x,y)={\mathrm{\Phi}}^{k}(x,y)-\mathrm{\Phi}(x,y).$$