Over a dozen rainbows have been observed in a single water droplet. They appear as glare spots on the water droplet which take on coloration at the appropriate rainbow angles. The appearance of rainbows as colored glare spots in this situation is understood in terms of the caustics created in the vicinity of the droplet by the refracting light rays. The angular positions of the glare spots are ...

Although wave optics is the standard method of analyzing systems composed of a sequence of lenses separated by arbitrary distances, it is often easier and more intuitive to ascertain the function and properties of such systems by tracing a few rays through them. Determining the location, magnification or scale factor, and field curvature associated with images and Fourier transforms by tracing ...

In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics. More precisely, we show that if u and v are such that fractional Fourier transforms of order α have same modulus |Fαu| = |Fαv| for some set τ of α’s, then v is equal to u up to a constant phase fac...

Sampling theory for operators motivated by the operator identification problem in communications engineering has been developed during the last few years 1–4 . In 4 , Hong and Pfander gave an operator version of Kramer’s Lemma see 4, Theorem 25 . But they did not give any explicit kernel satisfying the hypotheses in 4, Theorem 25 other than the Fourier kernel. In this paper, we present that the...

The problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform is illposed since the Fourier phase information is lost. Therefore, prior information on the signal is needed in order to recover it. In this work we consider the case in which the prior information on the signal is that it is sparse, i.e., it consists of a small number of nonzero elements. ...

The fractional Fourier transform can be optically defined through a phase-space coordinate rotation of the Wigner distribution function associated with the input signal. This operation can be achieved by performing three successive shearing processes, which are reduced to a free-space Fresnel diffraction originated by a scaled version of the input object illuminated with a spherical wave. This ...

This paper discuss about FPGA implementation of radix-4 FFT algorithm, which is simulated ,synthesized, and downloaded on xcv1000 FPGA, which gives the operating speed of 52.3 MHz. Fourier transform play an important role in many digital signal processing applications including acoustics, optics, telecommunications, speech, signal and image processing. However, their wide use makes their comput...

As a generalization of the 2D Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics and signal and image processing. To reduce the digital implementation complexity of the 2D NsLCT, some previous works decomposed the 2D NsLCT into several low-complexity operations, including 2D FT, 2D chirp multiplication (2D...

Our aim in this paper is to obtain the best synthesis of a desired mutual intensity dis~but~on, by filtering in fractional Fourier domains. More specifically, we find the optimal fractional-domain filter that transforms a given (source) mutual intensity distribution into the desired one as closely as possible (in the minimum mean-square error sense). It is observed that, in some cases, closer a...