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A vortex half-wave retarder (VHR) is a new type of polarizing element with a constant retardance across its clear aperture but its fast axis rotating continuously over the area of the optic. In polarization optics, the VHR-based polarization control method is very efficient to control the radial and azimuthal polarization states of light with a simple system configuration, ease of use, and high energy utilization efficiency. In optical manipulation, VHR can generate nondiffracting Bessel beams with an enlarged trapping region of optical tweezers. In the field of optical imaging, an imaging system with a vortex half-wave retarder has been reported to improve the resolution. Due to its many unique functions with novelty, vortex half-wave retarder has received a lot of interests in optical micro-operation, optical imaging, optical communication, optoelectronics, quantum information and remote sensing. In this paper, we study the performance evaluation for imaging with a 0-order vortex half-wave retarder by using a method referred to as Optical Transfer Matrix. After introduction of the Jones matrix for the vortex half-wave retarders as a general pupil matrix, we present the optical transfer matrix as the frequency transfer characteristics for the imaging system. As compared with a polarization imaging with a half-wave plate, the imaging system with a vortex half-wave retarder has a typical effect of apodizing by increasing a contrast for the high-frequency end.
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