Analog Fourier optical processing systems can perform important classes of signal processing operations in parallel, but suffer from limited accuracy. Digital-optical equivalents of such systems could be built that share many features of the analog systems while allowing greater accuracy. We show that the digital equivalent of any system consisting of an arbitrary number of lenses, niters, spat...

All-quantum signal processing techniques are at the core of successful advancement most information-based quantum technologies. This article develops coherent and comprehensive methodologies mathematical models to describe Fourier optical in full terms for any input state light. We begin this by introducing a spatially 2-D photon, associated with its wavefront expressible as creation operator. ...

The Special Affine Fourier Transformation or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Shift-invariant spaces also play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. Shannon’s sampling theorem, which is at the heart of modern d...

Based on the definition of the instantaneous frequency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fra...

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H€ansch TW, Picqué N. Frequency combs. In: Tr€ager F, editor. Handbook of lasers and optics. 2nd ed. Springer Berlin: Heidelberg; (2012). Ideguchi T et al. Adaptive real-time dual comb spectroscopy. arXiv:1201.4177 (2012). Jacquet, P., et al. Frequency comb Fourier transform spectroscopy with kHz optical resolution. In: Fourier transform spectroscopy. Washington, DC: Optical Society of America;...

The linear canonical transform (the LCT) is a useful tool for optical system analysis and signal processing. It is parameterized by a 2 2 matrix . Many operations, such as the Fourier transform (FT), fractional Fourier transform (FRFT), Fresnel transform, and scaling operations are all the special cases of the LCT. In this paper, we will discuss the eigenfunctions of the LCT. The eigenfunctions...