An Algorithm and Hardware Design for Fourier Slice Theorem Based Digital Refocusing
Date Issued
2011
Date
2011
Author(s)
Pan, Jia-Hong
Abstract
In general optimal camera systems, the sensor array of a camera is on a two-dimensional plane. When a 2D sensor array is used to capture 4D light field data in the world, the data we collect is the two dimensional projection of the four dimensional light filed data. As the result, the information we get is only part of the whole 4D data, other information is lost thus can’t be recorded.
In this thesis, an optical mask printed by the technique, Kodak LVT, is designed and placed in front of the sensors in a DSLR camera. In such case, the light intensities received by the two dimensional sensor array is the product of the light field data and the function of the mask. According to the convolution theorem, the data captured by camera sensors are the convolution of the light field data and the mask function in the frequency domain. If the function of the mask is a series of impulses in the frequency domain, the result of convolution is a series of copies of the light field data. By rearranging the frequency domain data, we reconstruct the information outside the projection plane of the 2D sensors, and recover all the 4D light field data in space. According to Fourier slice theorem, the operation of projection in the spatial domain is equivalent to taking a slice in the frequency domain. As the result, we can have images focused at different depths by taking different slices in the frequency domain. The approach is equivalent to having different lens settings in traditional camera systems.
Finally, for future real-time applications, we also design a hardware processor using the algorithm. The chip is implemented with TSMC 130 nm technology. The chip and core sizes are 17.58 mm2 and 12.53 mm2. Power consumption is 862.6 mW when the chip operates at 40 MHz.
Subjects
light field
Fourier slice theorem
digital refocusing
hardware design
Type
thesis
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