Approximation of Fresnel Integrals with Applications to Diffraction Problems
نویسندگان
چکیده
منابع مشابه
Computation of Fresnel Integrals
This paper describes a method for spreadsheet computations of Fresnel integrals to six significant figures, based on successive improvements of known rational approximations which are accurate to only three figures. Outside the range of validity of the improved approximations, known series expansions are used to obtain the Fresnel integrals to six figures.
متن کاملComputation of Fresnel Integrals. II
This paper describes an improved method for computing Fresnel integrals with an error of less than 1 × 10(-9). The method is based on a known approximate formula for a different integral which is due to Boersma and referenced by Abramowitz and Stegun.
متن کاملFresnel coherent diffraction tomography.
Tomographic coherent imaging requires the reconstruction of a series of two-dimensional projections of the object. We show that using the solution for the image of one projection as the starting point for the reconstruction of the next projection offers a reliable and rapid approach to the image reconstruction. The method is demonstrated on simulated and experimental data. This technique also s...
متن کاملTime-domain Fresnel-to-Fraunhofer diffraction with photon echoes.
A photon echo experiment in Tm(3+):YAG is reported that shows, for the first time to the authors' knowledge, the time-domain equivalent of the transition from near- to far-field diffraction, including Talbot self-imaging effects. The experiment demonstrates the huge dispersion capability of photon echoes and opens the way to further exploration of space-time duality.
متن کاملOn the Fresnel Integrals and the Convolution
The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C + (x), C − (x), S + (x), and S − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x r + and x r are evaluated. The Fresnel cosine integral C(x) is defined by C(x) = 2 π x 0 cos ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2018
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2018/4031793