## Abstract

We describe a method of absolute distance measurement based on the lateral shearing interferometry of point-diffracted spherical waves. A unique feature is that the distance measurement is not confined only along a single line of the optical axis, but the target is allowed to take movement freely within a volumetric measurement space formed by the aperture angle of point-diffraction. Detailed measurement theory is explained along with experimental verification.

© 2006 Optical Society of America

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### Equations (8)

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(1)
$$\Delta {W}_{x}=W(x+S\u20442,y)-W(x-S\u20442,y)=\sum _{n=0}^{k-1}\sum _{m=0}^{n}{C}_{\mathrm{nm}}{x}^{m}{y}^{n-m}$$
(2)
$$\mathrm{where}\phantom{\rule{.2em}{0ex}}{C}_{\mathrm{nm}}=\sum _{j=1}^{\left(k-n+1\right)\u20442}2\left(\begin{array}{c}2j-1+m\\ 2j-1\end{array}\right){\left(\frac{S}{2}\right)}^{2j-1}{B}_{2j-1+n,2j-1+m}$$
(3)
$$\Delta {W}_{y}=W(x,y+S\u20442)-W(x,y-S\u20442)=\sum _{n=0}^{k-1}\sum _{m=0}^{n}{D}_{\mathrm{nm}}{x}^{m}{y}^{n-m}$$
(4)
$$\mathrm{where}\phantom{\rule{.2em}{0ex}}{D}_{\mathrm{nm}}=\sum _{j=1}^{\left(k-n+1\right)\u20442}2\left(\begin{array}{c}2j-1+n-m\\ 2j-1\end{array}\right){\left(\frac{S}{2}\right)}^{2j-1}{B}_{2j-1+n,m}$$
(5)
$$W(x,y)=\sqrt{{\left({x}_{c}-x\right)}^{2}+{\left({y}_{c}-y\right)}^{2}+{{z}_{c}}^{2}}+p$$
(6)
$$W(x,y)=R\sqrt{1+H}+p\approx R\left(1+H\u20442-{H}^{2}\u20448\right)+p$$
(7)
$$\mathrm{where}\phantom{\rule{.9em}{0ex}}H=\left(-2{x}_{c}x-2{y}_{c}y+{x}^{2}+{y}^{2}\right)\u2044{R}^{2}$$
(8)
$$R=1\u2044\left(4{A}_{5}+2\sqrt{{{A}_{4}}^{2}+{{A}_{6}}^{2}}\right)$$