## Abstract

We present a demonstration and analysis of an industrialized design of a spatially dispersive displacement sensor, which is composed of an AlGaInP gain chip in visible range, optical assembly, and a spectrum analyzer. The sensor utilizes the spatial dispersion of focus from the optical assembly and wavelength spectrum's deviation induced by the displacement of the target. As a result, the sensor delivers a quick and simple way of measuring displacement. By adapting the magnification and resolution of the optical assembly, a displacement sensor with a middle measurement range,
\sim 10\text{\hspace{0.17em} \mu m},
was obtained. However, we should note that
\text{25 \hspace{0.17em} nm} resolution is limited by the bandwidth and temperature fluctuation of the gain chip.

© 2007 Optical Society of America

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### Equations (88)

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(1)
\sim 10\text{\hspace{0.17em} \mu m}
(2)
\text{25 \hspace{0.17em} nm}
(3)
\text{660 \hspace{0.17em} nm}
(4)
\text{50 \hspace{0.17em} mW}
(5)
\text{150 \hspace{0.17em} mA}
(6)
25\text{\hspace{0.17em}}\xb0\text{C}
(8)
\sim 15\text{\hspace{0.17em} nm}
(12)
660\text{\hspace{0.17em} nm}
(15)
0.11\text{\hspace{0.17em} nm}
(16)
\text{0 .05 \hspace{0.17em}}\xb0\text{C}
(17)
\text{6 \hspace{0.17em} \mu m}
(18)
\text{0 .06 \hspace{0.17em} nm}
(21)
$$S\left(\lambda ,l\right)\propto G{\left(\lambda \right)}^{r\left(\lambda \mathrm{,}l\right)+1}R{\left(\lambda ,l\right)}^{r\left(\lambda \mathrm{,}l\right)}\text{,}$$
(22)
S\left(\lambda ,l\right)
(23)
R\left(\lambda ,l\right)
(24)
G\left(\lambda \right)
(25)
r\left(\lambda ,l\right)
(26)
S\left(\lambda ,l\right)
(27)
R\left(\lambda ,l\right)
(28)
G\left(\lambda \right)
(29)
{\lambda}_{\mathrm{max}}
(33)
R\left(\lambda ,l\right)
(34)
G\left(\lambda \right)
(35)
S\left(\lambda ,l\right)
(36)
{\lambda}_{\mathrm{max}}
(37)
{\lambda}_{\mathrm{max}}
(39)
-4\text{\hspace{0.17em} \mu m}
(40)
{\lambda}_{\text{max}}
(42)
+5\text{\hspace{0.17em}}\mu \text{m}
(43)
{\lambda}_{\mathrm{max}}
(44)
-4\text{\hspace{0.17em} \mu m}
(45)
{\lambda}_{\text{max}}
(46)
\sim 660\text{\hspace{0.17em} nm}
(48)
7\text{\hspace{0.17em} \mu m}
(49)
G\left(\lambda \right)
(50)
10\text{\hspace{0.17em} \mu m}
(51)
660\text{\hspace{0.17em} nm}
(52)
\text{1550 \hspace{0.17em} nm}
(53)
\text{25 \hspace{0.17em} nm}
(54)
\text{1550 \hspace{0.17em} nm}
(55)
G\left(\lambda \right)
(56)
G\left(\lambda \right)
(57)
G\left(\lambda ,T\right)
(58)
$$S\left(\lambda ,l,T\right)\propto G{\left(\lambda ,T\right)}^{r\left(\lambda \mathrm{,}l\right)+1}R{\left(\lambda ,l\right)}^{r\left(\lambda \mathrm{,}l\right)}.$$
(59)
G\left(\lambda ,T\right)
(60)
S\left(\lambda ,l,T\right)
(61)
G\left(\lambda ,T\right)
(62)
R\left(\lambda ,l\right)
(63)
G\left(\lambda ,T\right)
(64)
60\text{\hspace{0.17em} nm}
(65)
\text{15 \hspace{0.17em} nm}
(66)
G\left(\lambda ,T\right)
(67)
G\left(\lambda ,T\right)
(68)
R\left(\lambda ,l\right)
(69)
S\left(\lambda ,l\right)
(70)
G\left(\lambda ,T\right)
(71)
R\left(\lambda ,l\right)
(72)
S\left(\lambda ,l\right)
(73)
\sim 25\text{\hspace{0.17em} nm}
(74)
\text{660 \hspace{0.17em} nm}
(75)
\text{25 \hspace{0.17em} nm}
(76)
\text{10 \hspace{0.17em} \mu m}
(77)
R\left(\lambda ,l\right)
(84)
S\left(\lambda ,l\right)
(85)
S\left(\lambda ,l\right)
(86)
{\lambda}_{\mathrm{max}}
(88)
26\text{\hspace{0.17em} mm}\times \text{30 \hspace{0.17em} mm}\times \text{45 \hspace{0.17em} mm}