Spatial optical transforms with applications

Thesis (Ph. D.)--University of Rochester. College of Engineering and Applied Science. Institute of Optics, 1994.Two-dimensional transforms of objects under natural illumination are considered. An optoelectronic hybrid system is used to acquire the spatial transform. The optical portion of the system consists of a twin-imaging interferometer cascaded with a lens system that achromatizes the interference fringes. The interference fringes are detected by a CCD array, and postdetection processing is done by a digital computer. A generalized model for optical spatial transforms is introduced, which in its most general form consists of two independent imaging systems that share common object and exit-pupil planes. The spatial transform is detected in the exit-pupil plane. The radial shear and rotational shear interferometers are presented as examples. Two methods of improving the optical portion of the spatial-transform system are explored. The first is the use of a wavelength tunable laser as a diagnostic tool. With this tool a technique for constructing a beam-splitter cube that has extremely well-balanced paths is developed. The second approach to improving the optical system is the development of a design procedure for the lenses. A three-element design is presented that has length 320 mm and is capable of resolving over 10⁶ pixels with an operating spectral bandwidth of 100nm. In some spatial transforms presented, a tunable laser source and a moving diffuser are used to form a spatially incoherent narrow-band source. In order to verify the spatial coherence of these sources a technique for measuring spatial coherence is developed using the inverse relationship between the angular spread of light and the coherence length of the source. Coherence measurements using both white-light and laser sources are presented. A catalog of object-transform pairs is assembled and grouped into three series. In the first series, relationships between object features and transform features are explored including the inverse nature of the object and transform widths, the replication effect of gratings, and the edge-angle relationship. In the second series, features that are unique to the cosine and sine transforms are emphasized. Object position sensitivity and symmetry properties of the cosine and sine transforms are examined. The orientation ambiguity of the cosine transform is demonstrated along with a simple method of removing that ambiguity. In the third series the general cosinusoidal transform is demonstrated. The transform is shown to progress from cosine transform to Hartley transform to sine transform with the changing reference angle in the interferometer