## Abstract

Malus’s law, when used to calculate the attenuation ratio of the combination of two imperfect polarizers (two-CIP), will introduce an error, especially near the crossed-axis orientation. In this paper, first, the Jones matrix of the imperfect polarizer is deduced and an exact algorithm of the attenuation ratio of the two-CIP is proposed as well as its monotonic attenuation interval. Experimental results confirm that our deduced expression is more accurate than Malus’s law. Then based on this algorithm, an attenuation-ratio expression of the combination of three imperfect polarizers (three-CIP) is presented. In this three-CIP model, it is found that when the electric field amplitude ratio of the imperfect polarizer is *ϵ*, the attenuation ratio can change from 1 to ${\u03f5}^{4}$ monotonically in a general model when ${\mathrm{P}}_{1}$ and ${\mathrm{P}}_{3}$ are rotated and ${\mathrm{P}}_{2}$ is fixed, which is proved by experiment. Finally, it is deduced that the combination of *n* imperfect polarizers (*n*-CIP) can obtain a minimum attenuation ratio of ${\u03f5}^{2(n-1)}$, which indicates the number of imperfect polarizers needed to achieve the required attenuation ratio.

© 2010 Optical Society of America

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