## Abstract

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moiré topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

© 1982 Optical Society of America

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### Equations (9)

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(1)
$$g(x,y)=a(x,y)+b(x,y)\hspace{0.17em}\text{cos}[2\pi {f}_{0}x+\varphi (x,y)],$$
(2)
$${g}_{0}(x,y)=a(x,y)+b(x,y)\hspace{0.17em}\text{cos}[\varphi (x,y)],$$
(3)
$$g(x,y)=a(x,y)+c(x,y)\hspace{0.17em}\text{exp}(2\pi i{f}_{0}x)+c*(x,y)\hspace{0.17em}\text{exp}(-2\pi i{f}_{0}x),$$
(4)
$$c(x,y)=(\xbd)b(x,y)\hspace{0.17em}\text{exp}[i\varphi (x,y)],$$
(5)
$$G(\text{f},\text{y})=A(f,y)+C(f-{f}_{0},y)+C*(f+{f}_{0},y),$$
(6)
$$\text{log}[c(x,y)]=\text{log}[(\xbd)b(x,y)]+i\varphi (x,y).$$
(7)
$${\varphi}_{c}(x,y)={\varphi}_{d}(x,y)+{\varphi}_{o}(x,y).$$
(8)
$$\mathrm{\Delta}{\varphi}_{d}({x}_{i},y)={\varphi}_{d}({x}_{i},y)-{\varphi}_{d}({x}_{i-1},y)$$
(9)
$${\varphi}_{o}(x,y)={{\varphi}_{o}}^{x}(x,y)-{{\varphi}_{o}}^{x}({x}_{L},y)+{{\varphi}_{o}}^{x}({x}_{L},y).$$