## Abstract

Rapid calibration of liquid crystal variable retarder (LCVR) devices is critical for successful clinical implementation of a LC-based Mueller matrix imaging system being developed for noninvasisve skin cancer detection. For multispectral implementation of such a system, the effect of wavelength (λ), temperature (*T*), and voltage (*V*) on the retardance (δ) required to generate each desired polarization state needs to be clearly understood. Calibration involves quantifying this interdependence such that for a given set of system input variables
$\left(\lambda ,T\right)$, the appropriate voltage is applied across a LC cell to generate a particular retardance. This paper presents findings that elucidate the dependence of voltage, for a set retardance, on the aforementioned variables for a nematic LC cell:$\sim 253\text{\hspace{0.17em} mV}/\text{100 \hspace{0.17em} nm}$ λ-dependence and
$\sim 10\text{\hspace{0.17em}}\text{mV}/\xb0\text{C}$
*T*-dependence.
Additionally, an empirically derived model is presented that enables initial voltage calibration of retardance for any desired input wavelength within the calibration range of
$460\u2013905\text{\hspace{0.17em} nm}$.

© 2007 Optical Society of America

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### Equations (9)

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(1)
$$\frac{1}{2}\left(\begin{array}{c}1-{\mathrm{sin}}^{2}\left(\delta /2\right)+{\mathrm{cos}}^{2}\left(\delta /2\right)\\ 1-{\mathrm{sin}}^{2}\left(\delta /2\right)+{\mathrm{cos}}^{2}\left(\delta /2\right)\\ 0\\ 0\end{array}\right)=\frac{1}{2}\left(\begin{array}{cccc}1& 1& 0& 0\\ 1& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right).\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& -{\mathrm{sin}}^{2}\left(\delta /2\right)+{\mathrm{cos}}^{2}\left(\delta /2\right)& 0& -\mathrm{sin}\left(\delta \right)\\ 0& 0& 1& 0\\ 0& \mathrm{sin}\left(\delta \right)& 0& \mathrm{cos}\left(\delta \right)\end{array}\right)\cdot \left(\begin{array}{c}1\\ 1\\ 0\\ 0\end{array}\right),$$
(2)
$$\text{}\frac{1}{2}\left(\begin{array}{c}1+{\mathrm{sin}}^{2}\left(\delta /2\right)-{\mathrm{cos}}^{2}\left(\delta /2\right)\\ -1-{\mathrm{sin}}^{2}\left(\delta /2\right)+{\mathrm{cos}}^{2}\left(\delta /2\right)\\ 0\\ 0\end{array}\right)=\frac{1}{2}\left(\begin{array}{cccc}1& -1& 0& 0\\ -1& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right).\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& -{\mathrm{sin}}^{2}\left(\delta /2\right)+{\mathrm{cos}}^{2}\left(\delta /2\right)& 0& -\mathrm{sin}\left(\delta \right)\\ 0& 0& 1& 0\\ 0& \mathrm{sin}\left(\delta \right)& 0& \mathrm{cos}\left(\delta \right)\end{array}\right)\cdot \left(\begin{array}{c}1\\ 1\\ 0\\ 0\end{array}\right),$$
(3)
$${S}_{0\text{,}\parallel}={\mathrm{cos}}^{2}\left(\delta /2\right)\text{, \hspace{1em} \hspace{1em}}{S}_{0\text{,}\perp}={\mathrm{sin}}^{2}\left(\delta /2\right).$$
(4)
$$\delta \left(V,\lambda ,T\right)=\frac{2\pi l\Delta \eta \left(V,\lambda ,T\right)}{\lambda}.$$
(5)
$$\delta =\frac{2\pi l}{\lambda}\left(a{e}^{bV}+c\right).$$
(6)
$$\frac{\left|I-{I}_{\mathrm{min}}\right|}{{I}_{\mathrm{max}}-{I}_{\mathrm{min}}}={\mathrm{cos}}^{2}\left(\frac{\pi l}{\lambda}\left(a\cdot {e}^{b\cdot V}+c\right)\right).$$
(7)
$$MPE=\frac{{\displaystyle \sum \left|p-p\prime \right|}}{n}.$$
(8)
$$P\left(\lambda ,T\right)={\displaystyle \sum _{n=1}^{6}{C}_{n}}{\lambda}^{{p}_{n}}{T}^{{q}_{n}}\mathrm{.}$$
(9)
$$a\left(\lambda ,T\right)=\left(\u20131.38\mathrm{e}\u20137\right)\lambda T-\left(3.3434\mathrm{e}\u20134\right){T}^{2}+\left(0.017\right)T-1.488+\left(5.472\mathrm{e}\u20133\right)\lambda -\left(3.809\mathrm{e}\u20136\right){\lambda}^{2}.$$