| In the thesis we describe a topic in the field of integrated computational imaging systems, where we seek to establish considerable improvement in extending the depth of field over the well-known classical limit established by Lord Rayleigh in the late 1870's. Theory, computer simulation and experiment are given for a new type of lens where the correlation among different segments of the aperture of the lens is broken. Three examples of these lenses are given. One is a lens partitioned into two parts by polarization. The second example is an all glass lens partitioned by optical path lengths. And the third is a combination of two logarithmic lenses, where the correlation between the lenses is broken by means of controlled optical path difference.;For a conventional lens partitioned by polarization or optical path length, we describe the partitioning methods from the view point of physical optics and random process theory. Through numerical and laboratory studies of the partitioned lens we find that the depth of field will be extended to be twice the Rayleigh limit. When combined with the Metric Parameter Maximum Entropy method for digital processing, the total extension in depth of field is three times for a two-step partition.;For the partitioned logarithmic lens, we design each of the logarithmic lenses to be responsible for a portion of the total depth of field. With this configuration, we are able to achieve highly invariant point spread functions over a wide range of object distances. The blurred images taken by this type of lens are processed by a modified total-variation based algorithm, where modification is made to handle the inexactness of the point spread function used for image deblurring. The depth of field for this integrated system is found to be 14 times the Rayleigh limit for an edge object and 20 times for a gray-scale object. |
