The significance of the similarity theorem for the fractional Fourier transform is discussed, and the properties of self-similar functions considered. The concept of the fractional Hankel transform is developed for use in the analysis of diffraction and imaging in symmetrical optical systems. The particular case of Fresnel diffraction from a circular aperture is discussed and the effects of the...

We report a simple, novel subdiffraction method, i.e. diffraction interference induced superfocusing in second-harmonic (SH) Talbot effect, to achieve focusing size of less than λSH/4 (or λpump/8) without involving evanescent waves or subwavelength apertures. By tailoring point spread functions with Fresnel diffraction interference, we observe periodic SH subdiffracted spots over a hundred of m...

A Fresnel lens with electrically-tunable diffraction efficiency while possessing high image quality is demonstrated using a phase-separated composite film (PSCOF). The light scattering-free PSCOF is obtained by anisotropic phase separation between liquid crystal and polymer. Such a lens can be operated below 12 volts and its switching time is reasonably fast (~10 ms). The maximum diffraction ef...

A conventional Fresnel zone plate (FZP) consists of concentric rings with an alternating binary transmission of zero and one. In an azimuthally structured Fresnel zone plate (aFZP), the light transmission of the transparent zones is modulated in the azimuthal direction, too. The resulting structure is of interest for extreme ultraviolet and x-ray imaging, in particular, because of its improved ...

The diffraction of ultrasound by a circular disk and an aperture of the same size have been investigated as a demonstration of Babinet‟s principle in the Fresnel regime. The amplitude and the phase of diffracted ultrasonic waves have been measured and a graphical treatment of the results is performed. The results verify Babinet‟s principle. It is also found that the wave without the diffracting...

Digital micro-holography technique, a combination of digital holography with microscopy, can be used to measure and analyse the micro-structure and status information of samples when the digital hologram registered is reconstructed numerically by some numerical methods based on the principle of scalar diffraction or coherent image. By summarizing the development of digital micro-holography, Fre...

We proposed an approach to construct a 2D Fresnel lenses by acoustic network. This lens iscomposed of an array of Helmholtz resonators. The resonance at individual resonators results ineffective focusing even the plate has subwavelength thickness. The FEM simulation resultspresented the ultrasonic wave propagation through the lenses together with the resultingdiffraction pat...

This paper proposed an edge detection scheme which is deduced from Fresnel diffraction. Analysis in this paper shows that Fresnel convolution kernel function performs well on edge enhancement when images are transformed into complex functions. Due to its mathematical complexity, the method is simplified into a linear convolution filter. The new edge detector is designed based on the simplified ...