When a low-power, monochromatic Gaussian beam is focused by a thin lens in air and the waist of the beam is in the plane of the lens, there is a shift of the focus position if the waist of the beam is much smaller than the size of the lens. The point of maximum intensity relative to the geometrical focal point shifts closer to the lens. We show that for ultra-intense light beams, when the Kerr effect is unavoidable, there is a nonlinear focal shift. The nonlinear focus position shifts closer to the lens for laser powers below the critical power. To avoid the nonlinear focal shift below the critical power, the correct combination of Gaussian beam waist and focal system has to be used in the experimental setup. It will be shown that as the Fresnel number N w associated with the Gaussian beam radius increases, the nonlinear focal shift first increases and then begins to decrease.

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Liquid crystal variable retarders (LCVRs) are often used in Stokes polarimeters as they allow the measurement of different polarization components by applying an electric field that manipulates the induced retardance. However, the optical retardance introduced by these devices is in general not homogenous across the aperture. Another problem with this type of devices is that the fast-axis orientation is not homogenous, and it changes with the applied voltage. For the optimization of polarimeters, in terms of the noise amplification from the intensity measurements to the polarimetric data, the condition number (CN) is often used, but the effects of LCVR spatial variations are not considered. This paper analyzes the impact of errors in LCVRs in a set of optimized Stokes polarimeters simulated by adding errors in the induced retardance and fast-axis orientation. Then, the CN is calculated to observe the effect of these errors on the optimization. We show how errors in the LCVRs lead to different impacts in the polarimetric measurements for different optimized polarimeters, depending on their experimental parameters. Furthermore, we present the propagation error theory to choose the best experimental parameters to reduce the nonideal effects in optimized polarimeters.

A spatially adaptive Mueller matrix imaging polarimeter is described, simulated, and demonstrated with preliminary experiments. The system uses a spatial light modulator (SLM) in the polarization state generator (PSG) to create spatial carriers that controlled by the pattern written to the SLM. The polarization state analyzer (PSA) is a commercial division of focal plane imaging polarimeter. The PSG/PSA pair form a 9-channeled partial Mueller matrix polarimeter that measures a 3 × 3 sub-matrix of the Mueller matrix. We demonstrate that adapting the PSG modulation to the spatial frequency structure of the scene can reduce channel crosstalk and improve reconstruction accuracy. Initial experiments are performed that demonstrate the SLM’s ability to produce sufficient modulation diversity to create the desired channel structure. Though there are several experimental challenges to obtain accurate Mueller matrix imagery, we demonstrate a system that adapts to the particular scene spatial frequency structure.

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