As an advanced imaging technique, the polarization imaging has attracted more and more interests and many applications have been developed in the fields, such as biomedical diagnostics, target identification and remote sensing due to its unique ability to detect the polarization information of objects. On the other hand, the grating with its periodic spatial structure has been used widely in various imaging systems including but not limited to holographic imaging, Talbot effect of self-imaging, and imaging spectrometer. Furthermore, a sinusoidal amplitude grating is of considerable interest in image analysis and optical system characterization. Although many techniques with applications of the gratings have been developed in the last decades, few investigations have been made to the sinusoidal amplitude grating in a polarization imaging system with arbitrary illumination condition of polarization and coherence. In this paper, the polarization imaging of a sinusoidal amplitude object illuminated with a partially polarized and partially coherent light is investigated. With the help of the unified theory of polarization and coherence, we have extended the use of sinusoidal trace analysis in the evaluation of optical system performance and presented theoretical analysis on the Stokes images of a sinusoidal amplitude grating.
In electronic engineering and control theory, a step response plays a fundamental role to evaluate the response of a system to its inputs change from zero to one in a very short time. From a practical standpoint, knowing how the system responds to a sudden input is important because large and fast deviations from the long term steady state may have extreme effects on the component itself and on other portions of the overall system dependent on this component. In addition, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.
The spatial resolution for polarization imaging system under illumination of any light source with arbitrary polarization and coherence has been investigated. Based on new factors referred to as the degree of polarization coherence, the resolution for polarization imaging has been studied as possible separations of two points in Stokes parameters with criteria charactering the accuracy of polarimetric images. Under the same illumination condition, these two closely spaced points resolvable for certain Stokes parameter will become unresolved for other Stokes parameters.