Related papers: Initial Results from the USNO Dispersed Fourier Tr…
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…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
The new generation of radio interferometers is characterized by high sensitivity, wide fields of view and large fractional bandwidth. To synthesize the deepest images enabled by the high dynamic range of these instruments requires us to…
Chip-based optical frequency combs address the demand for compact, bright, coherent light sources of equidistant phase-locked lines. Traditionally, the Fourier Transform Spectroscopy (FTS) technique has been considered a suboptimal choice…
High-performance instruments at large ground-based telescopes have made integral field spectroscopy (IFS) a powerful tool for the study of extended objects such as galaxies, nebulae, or even larger survey fields on the sky. Here we discuss…
We present the architectural concept for the Far-Infrared Enhanced Survey Spectrometer (FIRESS) for the Probe Mission for far-IR Astrophysics (PRIMA). FIRESS spans the 24--235 micron range with four R ~ 100 slit-fed grating modules, each…
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…
We present here an overview of the Fourier Transform Scanning Tunneling spectroscopy technique (FT-STS). This technique allows one to probe the electronic properties of a two-dimensional system by analyzing the standing waves formed in the…
Neutron grating interferometry is an advanced method in neutron imaging that allows the simultaneous recording of the transmission, the differential phase and the dark-field image. Especially the latter has recently received high interest…
The on-chip broadband optical spectrometers which cover the entire tissue transparency window ({\lambda}=650-1050 nm) with high resolution are highly demanded for the miniaturized bio-sensing and bio-imaging applications. Here, we propose a…
Miniaturized spectrometers for Raman spectroscopy have the potential to open up a new chapter in sensing. Raman spectroscopy is essential for material characterization and biomedical diagnostics, however, its weak signal and the need for…
Recent advances in optical metasurfaces enable control of the wavefront, polarization and dispersion of optical waves beyond the capabilities of conventional diffractive optics. An optical design space that is poised to highly benefit from…
The optical elements comprised of sub-diffractive light scatterers, or metasurfaces, hold a promise to reduce the footprint and unfold new functionalities of optical devices. A particular interest is focused on metasurfaces for manipulation…
The fields of view of Extremely Large Telescopes will contain vast numbers of spatial sampling elements (spaxels) as their Adaptive Optics systems approach the diffraction limit over wide fields. Since this will exceed the detection…
Diffraction tomography (DT) has been widely explored in transmission-mode configurations, enabling high-resolution, label-free 3D imaging. However, industrial metrology applications, such as semiconductor inspection, typically involve…
Nonlinear interferometry with entangled photons allows for characterizing a sample without detecting the photons interacting with it. This method enables highly sensitive optical sensing in the wavelength regions where efficient detectors…
Several types of Wavefront Sensors (WFS) are nowadays available in the field of Adaptive Optics (AO). Generally speaking, their basic principle consists in measuring slopes or curvatures of Wavefront Errors (WFE) transmitted by a telescope,…
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 one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…