Polarization Discrimination Imaging of objects hidden in turbid media: Detection of weak sinusoids through Stochastic Resonance

In Polarization Discrimination Imaging, the amplitude of a sinusoid from a rotating analyzer, representing residual polarized light and carrying information on the object, is detected with the help of a lock-in amplifier. When turbidity increases beyond a level, the lock-in amplifier fails to detect the weak sinusoidal component in the transmitted light. In this work we have employed the principle of Stochastic Resonance and used a 3-level quantizer to detect the amplitude of the sinusoids, which was not detectable with a lock-in amplifier. In using the three level quantizer we have employed three different approaches to extract the amplitude of the weak sinusoids: (a) using the probability of the quantized output to crossover a certain threshold in the quantizer (b) maximizing the likelihood function for the quantized detected intensity data and (c) arriving at an expression for the expected power in the detected output and comparing it with the experimentally measured power. We have proven these non-linear estimation methods by detecting the hidden object from experimental data from a polarization discrimination imaging system. When the turbidity increased to L/l = 5.05 (l is the transport mean-free-path and L is the thickness of the turbid medium) the data through analysis by the proposed methods revealed the presence of the object from the estimated amplitudes. This was not possible by using only the lock-in amplifier system.