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...

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 ...

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 sampling theory is basic and crucial in engineering sciences. On the other hand, the linear canonical transform (LCT) is also of great power in optics, filter design, radar system analysis and pattern recognition, etc. The Fourier transform (FT), the fractional Fourier transform (FRFT), Fresnel transform (FRT) and scaling operations are considered as special cases of the LCT. In this paper,...

Spatial light modulators (SLMs) are key research tools in several contemporary applied optics domains. In this paper, we present the argument that an open platform for interacting with SLMs would dramatically increase their accessibility to researchers. We introduce HoloBlade, open-hardware implementation of SLM driver-stack, and provide a detailed exposition HoloBlade’s architecture, component...