## Abstract

A range sensing technique is demonstrated that finds the 3-D shape of diffusely reflecting objects. The technique works sequentially in depth direction and is based on structured illumination and focus sensing. A TV camera and analog electronics are used to find the locations in focus of each step of a focus series in TV real time. The depth resolution is not very high, however, the technique is simple, rapid, and well suited to get an overview of a scene in robot vision.

© 1988 Optical Society of America

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### Equations (10)

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(1)
$$D(s,\alpha )=\frac{\text{sin}[\alpha \xb7\mid s\mid \xb7(2-\mid s\mid )]}{2\xb7\alpha \xb7\mid s\mid},\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mid s\mid \le 2.$$
(2)
$$s:=\frac{\nu}{{\nu}_{c}},\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{\nu}_{c}=\frac{\text{sin}u}{\mathrm{\lambda}}.$$
(3)
$$\alpha :=\pi \xb7\frac{\delta z}{\delta {z}_{R}},\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\delta {z}_{R}=\frac{\mathrm{\lambda}}{{\text{sin}}^{2}u}.$$
(4)
$${D}_{n}({s}_{G},\alpha )=\frac{\mid D({s}_{G},\alpha )\mid}{\mid D({s}_{G},0)\mid}=\mid \frac{\text{sin}\sigma}{\sigma}\mid ;$$
(5)
$$\mathrm{\Delta}\alpha ({s}_{G};T=0)=\frac{\pi}{\mid {s}_{G}\mid \xb7(2-\mid {s}_{G}\mid )}.$$
(6)
$$\mathrm{\Delta}z({\nu}_{G};T=0)=\frac{1}{\mid {\nu}_{G}\mid \xb7(2\xb7\text{sin}u-\mathrm{\lambda}\xb7\mid {\nu}_{G}\mid )}.$$
(7)
$$\mathrm{\Delta}z({\nu}_{G};T=0)\approx \frac{1}{2\xb7\mid {\nu}_{G}\mid \xb7\text{sin}u}.$$
(8)
$$V(t)=R(t)\xb7[1+D(t)\xb7\text{cos}(2\xb7\pi \xb7t/{t}_{G})]+B,$$
(9)
$$\rho =1-T-\u220a/R(t).$$
(10)
$$z(x,y)=\sum _{i}{z}_{i}\xb7{d}_{i}/\sum _{i}{d}_{i},$$