Related papers: Development of Multi-Fourier Transform interferome…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. it was shown how to build such…
The QUIJOTE Experiment was developed to study the polarization in the Cosmic Microwave Background (CMB) over the frequency range of 10-50 GHz. Its first instrument, the Multi Frequency Instrument (MFI), measures in the range 10-20 GHz which…
The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…
A new method, FM-FTS, combining Frequency Modulation heterodyne laser spectroscopy and Fourier Transform Spectroscopy is presented. It provides simultaneous sensitive measurement of absorption and dispersion profiles with broadband spectral…
Multispectral image pairs can provide the combined information, making object detection applications more reliable and robust in the open world. To fully exploit the different modalities, we present a simple yet effective cross-modality…
Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform, called steerable DFT…
An image-based technique for measuring the complex field in the pupil of an imaging system is presented. Two point source images, one with a small modification introduced in the pupil, are combined using a simple and non-iterative…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
The recent demonstration of a real-time direct imaging radio interferometry correlator represents a new capability in radio astronomy. However wide field imaging with this method is challenging since wide-field effects and array…
Despite the broadband nature of thermal light sources, optical spectroscopy over multiple spectral bands simultaneously remains challenging. Here, we demonstrate a practical Fourier transform infrared spectrometer (FTIR) that achieves…
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
Compact interferometers, called phasemeters, make it possible to operate over a large range while ensuring a high resolution. Such performance is required for the stabilization of large instruments dedicated to experimental physics such as…
We describe MIFS, a second generation integral-field spectrograph for the VLT, operating in the visible wavelength range. It combines a 1'x1' field of view with the improved spatial resolution provided by multi-conjugate adaptive optics and…
Millimetre-wave observations represent an important tool for Cosmology studies. The Line Intensity Mapping (LIM) technique has been proposed to map in three dimensions the specific intensity due to line (e.g. [CII], CO) emission, for…
Many media are divided into elementary units with irregular shape and size, as exemplified by domains in magnetic materials, bubbles in foams, or cells in biological tissues. Such media are essentially characterized by geometrical disorder…
Metal-dielectric layered stacks for imaging with sub-wavelength resolution are regarded as linear isoplanatic systems - a concept popular in Fourier Optics and in scalar diffraction theory. In this context, a layered flat lens is a…