Polarization interference filters (PIF) has been widely used in many fields. A successful application is color filter used for color separation and recombination in developing new LCOS projection optical sub-systems. In this paper, several techniques are discussed in order to design PIF with any arbitrary output. We present genetic algorithm (GA) optimization method to specify the desired response at first, and then a new Jones Matrix formulation was introduced to determine the orientation angles of each retarder and analyzer, which are much different from conventional "Optical Network Synthesis." Moreover, the angle property using the extended 2 x 2 Jones Matrix is also analyzed. In particular, the designed Blue/Yellow filter is provided as an illustration.
By modifying the illumination of the ordinary microscope, the sectioned image of the object is then available at the image plane but with the unwanted ordinary image superimposed. After processing these composite images by decoding algorithm, the optically sectioned images substantially similar to those obtained by confocal microscope can finally be got. Here in this article, we derive the explicit formula of the image formation by using the mutual intensity theory and thus explain the sectioning ability and the decoding theory of this new sectioning microscope. We can conclude that this kind of selective-illumination microscope is actually a selective-illumination microscope.
The principal of this new analytical method is to analytically get the coefficients of exponentials, the sum of which approximates the desired rectangular spectrum function of PIF. An arbitrary desired rectangular spectrum could be approximated by a continuous function with ripples. This function can be written in polynomial mathematically, with many unknown coefficients and known special points, such as extremum points and the point of half transmission. A set of equations could be written for those special points, through the solving of which the unknown coefficients will be determined. The following procedures will be the same as the available synthesis procedures of birefringent networks. This method will greatly simplify the design procedure and give more freedom in control of the design spectrum output. An example is given for 5-piece-birefringent-crystal PIF.