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The function is real-valued, positive-homogeneous of degree 1, and infinitely differentiable away from {=}. Also, we assume that does not have any critical points on the support of . Such a function, is usually called a phase function. In some contexts more general functions are considered and still referred to as phase functions.
The original paper by Gerchberg and Saxton considered image and diffraction pattern of a sample acquired in an electron microscope. It is often necessary to know only the phase distribution from one of the planes, since the phase distribution on the other plane can be obtained by performing a Fourier transform on the plane whose phase is known.
Code dates from 1968 available here: [11] 1983 BHCOAT Craig F. Bohren and Donald R. Huffman [1] Fortran: No specified but open source (public domain via [1]) "Mie solutions" (infinite series) to scattering, absorption and phase function of electromagnetic waves by a homogeneous concentring shells. 1997 BART [12] A. Quirantes [13] Fortran
Otherwise it is called unwrapped phase, which is a continuous function of argument t, assuming s a (t) is a continuous function of t. Unless otherwise indicated, the continuous form should be inferred. Instantaneous phase vs time. The function has two true discontinuities of 180° at times 21 and 59, indicative of amplitude zero-crossings.
or g — The particle phase function parameter, also called the asymmetry factor. θ {\displaystyle \theta } — The effective surface tilt, also called the macroscopic roughness angle. The Hapke parameters can be used to derive other albedo and scattering properties, such as the geometric albedo , the phase integral , and the Bond albedo .
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to functions given by integration against a rapidly-varying complex exponential. This method originates from the 19th century, and is due to George Gabriel Stokes and Lord Kelvin . [ 1 ]
A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).