Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann-Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image do...

Since its conception, holography has been put to a variety of uses including data storage, security, and interferometry. However, perhaps the most popular application of holography is using the technique to make three-dimensional images [1]. This paper describes an algorithm for computationally generating holograms along with methods to fabricate the hologram. Holography has since made a jump f...

Simultaneous spatial and temporal focusing pulses are created using parametric pulse shaping and characterized with scanning SEA TADPOLE. Multiple foci are created with optically-controlled longitudal and transverse spatial positions. The characterized foci are in agreement with the predictions of a Fourier optics model. The measurements reveal significant pulse front tilt resulting from the si...

The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,<), whose maximal compact subgroup is the Fourier group U(2) F ; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta...

Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation [J. Opt. Soc. Am. A 10, 2181 (1993)] provides a scaled output using a fixed lens. For obtaining a non-scaled...

An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. Alaboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains...

2014 The fiftieth anniversary of the publication of the first book on Fourier Optics, by P.-M. Duffieux, is recalled and the roles of the Fourier and many related transforms in image formation and image processing are recapitulated. Microsc. Microanal. Microstruct. 8 (1997) FEBRUARY 1997, PAGE 77

We consider optical systems composed of an arbitrary number of lenses and filters, separated by arbitrary distances, under the standard approximations of Fourier optics. We show that every such system is equivalent to (i) consecutive filtering operations in several fractional Fourier domains and (ii) consecutive filtering operations alternately in the space and the frequency domains.