Abstract
Complex paraxial optical systems, consisting of multiple lenses and sections of free space propagation, can be described using the Linear Canonical Transform (LCT). Indeed it can be shown that many well know optical transforms such as the Optical Fourier Transform (OFT), Optical Fractional Fourier Transform (OFRT), the effect of a lens or Chirp Modulation Transform (CMT) are all subsets of the more general LCT. Using the ABCD Collins matrix formula it is possible to represent these integral transforms in a simpler form, which facilitates system analysis and design. Apertures are necessary in speckle based metrology systems to control the size of the speckle. We examine their effect on LCT systems and show using the "generalized Yamaguchi correlation factor" that a useful interpretation of the system's behavior, using the LCT, may still be obtained. Furthermore, we experimentally demonstrate our ability to determine simultaneous tilt and translation motion by capturing two, sequential, mixed doma in images with a single camera. We also show how localized deformations in an object may be measured using this system.
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