In this talk we present a series of illustrative topics in Fourier Optics that are proving valuable in the design of EDOF
camera systems. They are at the level of final examination problems that have been made solvable by a student or
professoi having studied from one of Joseph W. Goodman's books---our tribute for his 75fr year. As time permits,
four illustrative topics are l) Electromagnetic waves and Fourier optics;2) The perfect lens; 3) Connection between
phase delay and radially varying focal length in an asphere and 4) tailored EDOF designs.
Optimization of a mobile imaging lens, which is for 5-megapixel, 1.4μm, CMOS image sensor, with multiple
configurations to reduce flare is presented. The most severe flare, which could cause artifacts such as "purple flare" in
images, is due to totally internal reflection (TIR) from optical surfaces in a mobile phone camera lens. We illustrate how
to optimize the lens for good performance and manufacturable tolerances to reduce flare due to TIR. The MTF,
distortion, relative illumination, lateral color, cumulative probability function for lens with tolerances and flare amount is
shown for the starting lens. An optimization method for lens design to reduce TIR flare is proposed and described. The
resulting optimized lens performance, tolerances and flare are compared with that of the starting lens.
The standard imaging lens for a high resolution sensor was modified to achieve the extended depth of field (EDoF) from
300 mm to infinity. In the module the raw sensor outputs are digitally processed to obtain high contrast images. The
overall module is considered as an integrated computational imaging system (ICIS). The simulation results for
illustrative designs with different amount of spherical aberrations are provided and compared. Based on the results of
simulations we introduced the limiting value of the PSF Strehl ratio as the integral threshold criteria to be used during
EDoF lens optimization. A four-element standard lens was modified within the design constraints to achieve the EDoF
performance. Two EDoF designs created with different design methods are presented. The imaging modules were
compared in terms of Strehl ratios, limiting resolution, modulation frequencies at 50% contrast, and SNR. The output
images were simulated for EDoF modules, passed through the image processing pipeline, and compared against the
images obtained with the standard lens module.
An accurate measurement of the point spread function (PSF) for the extended depth of field (EDoF) cell phone camera
with CMOS sensor is very important for image processing and image restoration. But due to the coarse sampling of the
PSF by CMOS sensor, the overall system including the imaging subsystem and sampling subsystem is a shift-variant
system with respect to the sample-scene phase parameter within sub-pixel range. In this paper, we present the sub-pixel
digital algorithm to estimate the overall camera PSF based on the measurement of a high resolution PSF of the imaging
lens. The sub-pixel digital algorithm averages the shifted high resolution PSFs of the lens over one active pixel area
with the assumption of uniform random distribution of point source location within one active pixel area. Then the
averaged high resolution PSF is down sampled onto Bayer plane to obtain the shift-invariant overall system PSF. We
applied this shift-invariant PSF for image restoration of blurred images captured with an extended depth of field camera.
The processed images are compared with originally captured images. Improvement of image quality is seen.
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