Rojo-Velázquez, G.: Fractional Talbot field of finite gratings: compact analytical formulation. J. Opt. Soc. Am. A 18, 1252-1255
ABSTRACT We present a compact analytical formulation for the fractional Talbot effect at the paraxial domain of a finite grating. Our results show that laterally shifted distorted images of the grating basic cell form the Fresnel field at a fractional Talbot plane of the grating. Our formulas give the positions of those images and show that they are given by the convolution of the nondistorted cells (modulated by a quadratic phase factor) with the Fourier transform of the finite-grating pupil. (C) 2001 Optical Society of America.
- SourceAvailable from: Ming Jiang
[Show abstract] [Hide abstract]
- "The wave field can be expressed as a superposition of laterally shifted replicas of the exit wave field right after the grating . It is not possible to find reassembled images at every fractional Talbot distance Du,v. "
ABSTRACT: X-ray imaging is of paramount importance for clinical and preclinical imaging but it is fundamentally restricted by the attenuation-based contrast mechanism, which has remained essentially the same since Roentgen's discovery a century ago. Recently, based on the Talbot effect, groundbreaking work was reported using 1D gratings for X-ray phase-contrast imaging with a hospital-grade X-ray tube instead of a synchrotron or microfocused source. In this paper, we report an extension using 2D gratings that reduces the imaging time and increases the accuracy and robustness of phase retrieval compared to current grating-based phase-contrast techniques. Feasibility is demonstrated via numerical simulation.International Journal of Biomedical Imaging 02/2008; 2008:827152. DOI:10.1155/2008/827152
[Show abstract] [Hide abstract]
- "In the case of an ASF consisting of square pin-holes, the planes with a uniform intensity distribution lie at distances behind the ASF, where the N th fold compression of the singular window function occurs. According to the theory of TAIL design     and the used notation, the planes correspond to the distances l = "
ABSTRACT: The paper presents a new interpretation of the Talbot array illuminator (TAIL). According to our description the TAIL is equivalent to a sum of mutually shifted lenses modified by generalized pupil functions. The interpretation underlines the imaging abilities of TAILs and makes it possible to characterize an imaging process in a way based on the theory of the thin lens. The paper analyses the impulse response and the transfer functions corresponding to the image formation in spatially coherent and incoherent cases of illumination. Additionally we discuss the resolution of images created by the TAIL. The obtained theoretical results are verified experimentally.Journal of Optics A Pure and Applied Optics 05/2004; 6(6):651. DOI:10.1088/1464-4258/6/6/022 · 1.92 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: The performance of a low-resolution pixelated lens (PL) as a spot array generator is discussed. It is proved that if the lens is encoded onto a typical pixelated spatial light modulator, it will generate a large number of uniform foci only at non-paraxial focal planes. We show, numerically and experimentally, that in such non-paraxial conditions the PL generates a focal plane spot array with acceptable efficiency and uniformity. Moreover, it is shown that the quality of the focal plane spot array improves when the numerical aperture of the PL is increased.Optics Communications 12/2001; 199(5):345-353. DOI:10.1016/S0030-4018(01)01596-6 · 1.45 Impact Factor