## Abstract

A technique observing contour lines of an object by the use of moiré is developed. Shadow of an equispaced plane grating is projected onto an object by a point source and observed through the grating. The resulting moiré is a contour line system showing equal depth from the plane of grating if the light source and the observing point lie on a plane parallel to the grating. A technique to wash away the unwanted aliasing moiré optimization of contour line spacing and visibility and the results of the application are described.

© 1970 Optical Society of America

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### Equations (12)

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(1)
$${T}_{Q}=\frac{1}{2}\left[1+\text{cos}2\pi \left(\u220a+y\right)/{s}_{0}\right],$$
(2)
$${I}_{s}=\frac{1}{2}\left\{1+\text{cos}2\pi \left[\left(\u220a+{y}_{Q}\right)/{s}_{0}+\xi /{s}^{\prime}\right]{I}_{0}\right\},$$
(3)
$$\xi =\left(y-{y}_{R}\right)\phantom{\rule{0.2em}{0ex}}\text{cos}\theta -\left(x-{x}_{R}\right)\phantom{\rule{0.2em}{0ex}}\text{sin}\theta .$$
(4)
$$\begin{array}{l}{I}_{M}=\{1+\text{cos}2\pi [\left(\u220a+{y}_{Q}\right)/{s}_{0}+\left(y-{y}_{R}\right)\phantom{\rule{0.2em}{0ex}}\text{cos}\theta /{s}^{\prime}\\ \phantom{\rule{1em}{0ex}}-\left(x-{x}_{R}\right)\phantom{\rule{0.2em}{0ex}}\text{sin}\theta /{s}^{\prime}]+\text{cos}2\pi \left(\u220a+y\right)/{s}_{0}\\ \phantom{\rule{0.6em}{0ex}}+\text{cos}2\pi \frac{1}{2}[\left({y}_{Q}-{y}_{R}\right)/{s}_{0}+\left(y-{y}_{R}\right)\phantom{\rule{0.2em}{0ex}}\left(\text{cos}\theta /{s}^{\prime}-1/{s}_{0}\right)\\ \phantom{\rule{0.8em}{0ex}}-\left(x-{x}_{R}\right)\phantom{\rule{0.2em}{0ex}}\text{sin}\theta /{s}^{\prime}]+\text{cos}2\pi \{[\left(2\u220a+{y}_{Q}+{y}_{R}\right)/{s}_{0}\\ \phantom{\rule{0.4em}{0ex}}+\left(y-{y}_{R}\right)\phantom{\rule{0.2em}{0ex}}\left(\text{cos}\theta /{s}^{\prime}+1/{s}_{0}\right)-\left(x-{x}_{R}\right)\phantom{\rule{0.2em}{0ex}}\text{sin}\theta /{s}^{\prime}]/2\}{I}_{0}/4.\end{array}$$
(5)
$${I}_{p}=\frac{1}{8}\left[1+\text{cos}2\pi \left({y}_{Q}-{y}_{R}\right)/{s}_{0}\right]{I}_{0}.$$
(6)
$${y}_{Q}-{y}_{R}=\left[{l}_{E}d-\left({l}_{E}-{l}_{s}\right){y}_{R}\right]h/{l}_{E}\left({l}_{s}+h\right),$$
(7)
$${y}_{Q}-{y}_{R}=hd/\left(l+h\right),$$
(8)
$$h=lN/\left(d/{s}_{0}-N\right).$$
(9)
$$h\approx l{s}_{0}N/d.$$
(10)
$$h={s}_{0}N\phantom{\rule{0.2em}{0ex}}\text{cot}\phi ,$$
(11)
$$\begin{array}{l}{f}_{1}\left(x,y\right)=I\Delta h\\ {f}_{2}\left(x,y\right)=J\Delta h\end{array}\},$$
(12)
$$f\left(x,y\right)=\left[{f}_{2}\left(x,y\right)-{f}_{1}\left(x,y\right)\right]=K\Delta h,$$