Related papers: Development of Multi-Fourier Transform interferome…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
We report a novel microscopy platform, termed Multi-Aperture Fourier ptychographic microscopy (MA-FPM), capable of realizing gigapixel complex field images with large data acquisition bandwidths - in gigapixels per second. MA-FPM is a…
Precision measurements of the Sunyaev-Zel'dovich effect in clusters of galaxies require excellent rejection of common-mode signals and wide frequency coverage. We describe an imaging, efficient, differential Fourier transform spectrometer…
Interferometric imaging is a well established method to image phase objects by mixing the image wavefront with a reference one on a CCD camera. It has also been applied to fast transient phenomena, mostly through the analysis of single…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
The Martin-Puplett interferometer (MPI) is a differential Fourier transform spectrometer (FTS), measuring the difference between spectral brightness at two input ports. This unique feature makes the MPI an optimal zero instrument, able to…
Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this…
Recent advancements in silicon photonics are enabling the development of chip-scale photonics devices for sensing and signal processing applications, among which on-chip spectrometers are of particular interest for precision wavelength…
Single-wavelength interferometry achieves high resolution for smooth surfaces but struggles with rough, industrially relevant ones due to limited unambiguous measuring range and speckle effects. Multi-wavelength interferometry addresses…
An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
The basic principle of astronomical interferometry is to derive the angular distribution of radiation in the sky from the Fourier transform of the electric field on the ground. What is so special about the Fourier transform? Nothing, it…
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…
Nonlinear interferometers allow for mid-infrared spectroscopy with near-infrared detection using correlated photons. Previous implementations have demonstrated a spectral resolution limited by spectrally selective detection. In our work, we…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
Fourier-transform infrared spectroscopy (FTIR) has matured into a versatile technique with relevance for environmental monitoring, pharmaceutical research, and food safety applications. However, compared to other spectroscopic methods, it…
Visible-infrared object detection has gained sufficient attention due to its detection performance in low light, fog, and rain conditions. However, visible and infrared modalities captured by different sensors exist the information…