The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making...

The requirements on and the performance of holographic Fourier transform lenses for a matched-filter optical processor are discussed. The holographic aberrations were analyzed using a ray-tracing computer program, and holographic lenses were fabricated and assembled into an optical processor. Analysis and experimental results show that holographic optics are capable of processing images of larg...

Spatial heterodyne spectroscopy (SHS) is a Fourier-transform spectroscopic technique that simultaneously records all path differences using a detector array. Compared to conventional Fourier-transform spectroscopy that measures interferogram samples sequentially in the time domain, SHS is insensitive to a changing scene; however, the effects caused by differences in the detector elements and/or...

We have developed digital 3D Fourier transform methods for comparing the 3D spatial frequency content and hence the axial and transverse resolution of confocal versus conventional microscope images. In particular, we have utilized these techniques to evaluate the performance of our recently-developed confocal transmission microscope for bright field and Nomarski DIC imaging. We have also found ...

Wave-front reconstruction with use of the Fourier transform has been validated through theory and simulation. This method provides a dramatic reduction in computational costs for large adaptive (AO) systems. Because such a reconstructor can be expressed as a matrix, it can be used as an alternative in a matrix-based AO control system. This was done with the Palomar Observatory AO system on the ...

The development of modeling algorithms for adaptive optics systems is important for evaluating both performance and design parameters prior to system construction. Two of the most critical subsystems to be modeled are the binary optic design and the adaptive control system. Since these two are intimately related, it is beneficial to model them simultaneously. Optic modeling techniques have some...

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the fast Fourier transform (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursiv...

Fourier transform digital holographic adaptive optics imaging system is described. The results from the simulation and experiment are reported that demonstrate the feasibility of this adaptive optics system. OCIS codes: 090.1995; 110.1080; 170.4470 Incorporation of the adaptive optics(AO) system into vision science has yielded retinal images with unprecedented resolution [1, 2]. The cone mosaic...