By cross-correlating successive ultrasonic scans of the biological tissue that is excited by a transient source on the surface, recent experiments show that elastic wave displacement during the interval between the two scans can be measured everywhere in the tissue. Assuming that we know the displacement history, w(t, x), of a propagating shear wave everywhere, we identify the stiffness change ...

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributiona...

[1] The interpretation of radio occultation data in the lower troposphere is a complicated problem due to strong multipath effects. This problem can be solved on the basis of the wave optics. We analyze Microlab-1 radio occultation using two radio-holographic approaches: the radio-optics method, which employs the analysis of the local spatial spectra of the registered wave field, and the canoni...

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

The RATAN-600 antenna is a flexible multireflector system composed of reflectors of very large dimensions. An extended system, with improved performance in the millimetric range, includes a focal receiver array. Accurate electromagnetic analysis of such a system, and simulation of three-dimensional (3D) patterns, represents a substantial computational challenge. A fast Physical Optics method ba...

The accurate measurement of ultrashort pulses is necessary to optimize pulse compression for nonlinear optics and strong-field physics. Additionally, field-sensitive time-domain techniques enable measuring femtosecond and sub-femtosecond dynamics. In this paper, we introduce a single-shot measurement to characterize few-cycle fields. This polarization-sensitive timedomain measurement can retrie...