Analysis of radially restored images for spherical single lens cellphone camera

A spherical single lens imaging system for cellphone camera is proposed in this research. The overall thickness from the front surface of the lens to the image sensor is approximately 4.5 mm, which is competitive compared to 6~7 mm of current cellphone camera modules that use compound lens system. One defect of this spherical single lens that deteriorates image quality is radially variant blur, which is produced by one of the optical aberrations called field curvature. We describe a novel method of blur restoration that employs polar image and polar Point Spread Function (PSF) converted from Cartesian image and Cartesian PSF. The blurred image was radially segmented into several regions, to which polar PSFs at different field angles were applied. Results of visual and quantitative evaluation indicate that number of segmented regions and weighted average of β / n$ ratios, i.e., ratio of bandwidth to the number Circulant Blocks (CBs) of the polar PSF Block-Toeplitz-with-Circulant-Blocks (BTCB) matrices affect the restored image quality and Mean Square Error (MSE). Evaluation results on restored images using different polar image resolutions revealed that high resolution obtains good pixel continuity, whereas low resolution results in radially expanding pixel vacancies.