## Abstract

We proposed a general algorithm for phase-shifting shadow moiré by an iterative self-tuning algorithm. In our proposed system, the grating is translated in equal distance to introduce phase shifts across the field of view. The proposed algorithm produces accurate phase information with five interferograms and can calibrate the precise phase step during the process of the height demodulation. Compared with the traditional method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase-shift shadow moiré when reconstructing surfaces from fringe patterns. Numerical simulations and optical experiments show that the proposed method can eliminate the nonuniform phase-shift error and possesses a superior performance to existing typical phase-shifting algorithms.

© 2011 Optical Society of America

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### Equations (10)

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(1)
$${I}_{n}(x,y)=A(x,y)+B(x,y)\mathrm{cos}[\varphi (x,y)+n\delta (x,y)],\phantom{\rule{0ex}{0ex}}(n=-2,-1,0,1,2),$$
(2)
$$\delta (x,y)=2\pi d\mathrm{\Delta}h/[p(h+z(x,y))],$$
(3)
$${\delta}^{s}=2\pi d\mathrm{\Delta}h/ph>\delta .$$
(4)
$$\varphi =a\text{\hspace{0.17em}}\mathrm{tan}(\frac{{I}_{2}-{I}_{4}}{2{I}_{3}-{I}_{1}-{I}_{5}}\mathrm{sin}({\delta}^{e})).$$
(5)
$$\widehat{z}=\frac{ph\varphi}{2\pi d-p\varphi}.$$
(6)
$$\mathrm{\Delta}{h}^{c}=p(h+\widehat{z}){\delta}^{e}/2\pi d.$$
(7)
$${\delta}^{u}=2\pi d\mathrm{\Delta}{h}^{c}/p(h+\widehat{z}).$$
(8)
$$\mathrm{max}(|{z}^{q}-{z}^{q-1}|)<\epsilon ,$$
(9)
$$p=0.05\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mm},\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}d=100\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mm},\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}h=160\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{mm}.$$
(10)
$${h}_{1}-{h}_{2}=\mathrm{\Delta}h,$$