## Abstract

The acoustically modulated laser speckle contrast technique has been employed to quantify and classify 25 colors (made up by different percentages of the two base colors cyan and magenta) hidden behind a 5 mm thick opaque layer with 0.24% transmittance. The main components included two He-Ne lasers (543 and 633 nm), a consumer grade digital camera (Nikon 1 J1), focusing optics and a loudspeaker. The camera captured the laser speckle patterns with the sound on and off, respectively, from which the speckle contrast differences were calculated and used in a nearest neighbor classification algorithm. The classification accuracy was between 55% and 88% depending on the underlying reflectance of all the colors to be classified.

© 2013 OSA

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### Equations (19)

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(1)
$$\Delta C={C}_{off}-{C}_{on}=\frac{{\sigma}_{off}}{\u3008\overline{I}\u3009}-\frac{{\sigma}_{on}}{\u3008\overline{I}\u3009}$$
(2)
$$\u3008\overline{I}\u3009=\u3008{I}_{b}\u3009+\u3008{I}_{m}\u3009$$
(3)
$$\Delta C\approx \frac{\sqrt{{C}_{b}{}^{2}+2M}-{C}_{b}}{1+M}$$
(4)
$$D(color)=\sqrt{{\left[\Delta {C}_{633,uk}-\Delta {C}_{633,tn}(color)\right]}^{2}+{\left[\Delta {C}_{543,uk}-\Delta {C}_{543,tn}(color)\right]}^{2}}$$
(5)
$$IRD(\text{color})=\sqrt{{\left[{R}_{633}(\text{color})-{R}_{633}(\text{nearest}\text{color})\right]}^{2}+{\left[{R}_{543}(\text{color})-{R}_{543}(\text{nearest}\text{color})\right]}^{2}}$$
(6)
$${E}_{b}=\sqrt{{I}_{b}}\mathrm{exp}\left[i\left({\omega}_{0}t-{\phi}_{b}\right)\right]$$
(7)
$${E}_{m}=\sqrt{{I}_{m}}\mathrm{exp}\left[i\left({\omega}_{0}t-{\phi}_{m}+{\omega}_{a}t\right)\right]$$
(8)
$$\begin{array}{c}I=\left({E}_{b}+{E}_{m}\right){\left({E}_{b}+{E}_{m}\right)}^{*}\\ ={I}_{b}+{I}_{m}+2\sqrt{{I}_{b}{I}_{m}}\mathrm{cos}\left(\Delta \phi +{\omega}_{a}t\right)\end{array}$$
(9)
$$\begin{array}{c}\overline{I}={I}_{b}+{I}_{m}+2\sqrt{{I}_{b}{I}_{m}}\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int}}\mathrm{cos}({\omega}_{a}t+\Delta \phi )\text{d}t}\\ ={I}_{b}+{I}_{m}+2\sqrt{{I}_{b}{I}_{m}}\mathrm{sin}c\left(\frac{{\omega}_{a}T}{2}\right)\mathrm{cos}\left(\frac{{\omega}_{a}T}{2}+\Delta \phi \right)\end{array}$$
(10)
$$\u3008\overline{I}\u3009=\u3008{I}_{b}\u3009+\u3008{I}_{m}\u3009$$
(11)
$$\u3008{\overline{I}}^{2}\u3009=\u3008{I}_{b}^{2}\u3009+\u3008{I}_{m}^{2}\u3009+2\mathrm{sin}{c}^{2}\left(\frac{{\omega}_{a}T}{2}\right)\u3008{I}_{b}{I}_{m}\u3009+2\u3008{I}_{b}{I}_{m}\u3009$$
(12)
$${\u3008\overline{I}\u3009}^{2}={\u3008{I}_{b}\u3009}^{2}+{\u3008{I}_{m}\u3009}^{2}+2\u3008{I}_{b}{I}_{m}\u3009$$
(13)
$${\sigma}^{2}=\u3008{\overline{I}}^{2}\u3009-{\u3008\overline{I}\u3009}^{2}=\u3008{I}_{b}^{2}\u3009-{\u3008{I}_{b}\u3009}^{2}+\u3008{I}_{m}^{2}\u3009-{\u3008{I}_{m}\u3009}^{2}+2\mathrm{sin}{c}^{2}\left(\frac{{\omega}_{a}T}{2}\right)\u3008{I}_{b}{I}_{m}\u3009$$
(14)
$$C=\frac{\sigma}{\u3008\overline{I}\u3009}=\frac{\sqrt{\u3008{I}_{b}^{2}\u3009-{\u3008{I}_{b}\u3009}^{2}+\u3008{I}_{m}^{2}\u3009-{\u3008{I}_{m}\u3009}^{2}+2\mathrm{sin}{c}^{2}\left(\frac{{\omega}_{a}T}{2}\right)\u3008{I}_{b}{I}_{m}\u3009}}{\u3008{I}_{b}\u3009+\u3008{I}_{m}\u3009}$$
(15)
$${C}_{on}=\frac{{\sigma}_{on}}{\u3008\overline{I}\u3009}=\frac{\sqrt{\u3008{I}_{b}^{2}\u3009-{\u3008{I}_{b}\u3009}^{2}+\u3008{I}_{m}^{2}\u3009-{\u3008{I}_{m}\u3009}^{2}}}{\u3008{I}_{b}\u3009+\u3008{I}_{m}\u3009}$$
(16)
$${C}_{off}=\frac{{\sigma}_{off}}{\u3008\overline{I}\u3009}=\frac{\sqrt{\u3008{I}_{b}^{2}\u3009-{\u3008{I}_{b}\u3009}^{2}+\u3008{I}_{m}^{2}\u3009-{\u3008{I}_{m}\u3009}^{2}+2\u3008{I}_{b}{I}_{m}\u3009}}{\u3008{I}_{b}\u3009+\u3008{I}_{m}\u3009}$$
(17)
$$\Delta C={C}_{off}-{C}_{on}=\frac{\sqrt{{C}_{b}{}^{2}+{C}_{m}{}^{2}{M}^{2}+2M}}{1+M}-\frac{\sqrt{{C}_{b}{}^{2}+{C}_{m}{}^{2}{M}^{2}}}{1+M}$$
(18)
$${C}_{b}=\frac{\sqrt{\u3008{I}_{b}^{2}\u3009-{\u3008{I}_{b}\u3009}^{2}}}{\u3008{I}_{b}\u3009},{C}_{m}=\frac{\sqrt{\u3008{I}_{m}^{2}\u3009-{\u3008{I}_{m}\u3009}^{2}}}{\u3008{I}_{m}\u3009}\text{and}M=\frac{\u3008{I}_{m}\u3009}{\u3008{I}_{b}\u3009}.$$
(19)
$$\Delta C=\frac{\sqrt{{C}_{b}{}^{2}+2M}-{C}_{b}}{1+M}$$