The Fresnel sine integral S(x), the Fresnel cosine integral C(x), and the associated functions S + (x), S − (x), C + (x), and C − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions with x r + , x r are evaluated. 1. Introduction. The Fresnel integrals occur in the diffraction theory...

This paper presented a theoretical and numerical investigation of the Compact Antenna Test Range (CATR) equipped with Super Hybrid Modulated Segmented Exponential Serrations (SHMSES). The investigation was based on diffraction theory and, more specifically, the Fresnel diffraction formulation. The CATR provides uniform illumination within the Fresnel region to test antenna. Application of serra...

A Fresnel zone plate lens can be constructed using a dye-doped liquid crystal filled cell and photo-induced alignment techniques. Light passing through a Fresnel zone patterned photo-mask causes the dye-doped liquid crystal to align in such a way to produce odd and even zones on the lens. Diffraction of incident light through the odd and even zones of the lens allows the light to constructively...

Scalar diffraction calculations, such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, x rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using fast Fourier transform (FFT); unfortunately, acceleration of the calculation of nonuniform sampled planes is limited due to the property of the FFT that im...

We investigated the diffractive focusing properties of ~111! GaAs linear Bragg–Fresnel lenses ~BFLs! developed for hard x-ray microscopy and microdiffraction of complex materials in confined geometries. We demonstrated that the use of GaAs yields significant processing advantages due to the reduced zone depth. Focal plane diffraction patterns of linear BFLs measured at the advanced photon sourc...