Fresnel zone

About: Fresnel zone is a research topic. Over the lifetime, 2337 publications have been published within this topic receiving 37650 citations.

Simulation and experimental study of aspect ratio limitation in Fresnel zone plates for hard-x-ray optics.

Abstract: For acquiring high-contrast and high-brightness images in hard-x-ray optics, Fresnel zone plates with high aspect ratios (zone height/zone width) have been constantly pursued. However, knowledge of aspect ratio limits remains limited. This work explores the achievable aspect ratio limit in polymethyl methacrylate (PMMA) by electron-beam lithography (EBL) under 100 keV, and investigates the lithographic factors for this limitation. Both Monte Carlo simulation and EBL on thick PMMA are applied to investigate the profile evolution with exposure doses over 100 nm wide dense zones. A high-resolution scanning electron microscope at low acceleration mode for charging free is applied to characterize the resultant zone profiles. It was discovered for what we believe is the first time that the primary electron-beam spreading in PMMA and the proximity effect due to extra exposure from neighboring areas could be the major causes of limiting the aspect ratio. Using the optimized lithography condition, a 100 nm zone plate with aspect ratio of 15/1 was fabricated and its focusing property was characterized at the Shanghai Synchrotron Radiation Facility. The aspect ratio limit found in this work should be extremely useful for guiding further technical development in nanofabrication of high-quality Fresnel zone plates.

Fabrication of Fresnel zone plates with high aspect ratio by soft X-ray lithography

Abstract: High focusing efficiency Fresnel zone plates for hard X-ray imaging is fabricated by electron beam lithography, soft X-ray lithography, and gold electroplating techniques. Using the electron beam lithography, Fresnel zone plates which has an outermost zone width of 100 nm and thickness of 250 nm has been fabricated. Fresnel zone plates with outermost zone width of 150 nm and thickness of 660 nm has been fabricated by using soft X-ray lithography.

Particle-Size Measurement Using Forward-Scatter Holography*

Abstract: This study is an experimental and theoretical investigation of the application of forward-scatter Fresnel holography to water droplets. The theoretical holograms were constructed on a digital computer by determining the irradiance of the interference pattern formed by the light scattered from a droplet and a reference source, at discrete points on a hologram. The forward-scattered light is evaluated by assuming that the droplet is an opaque disk and utilizing the Rayleigh–Sommerfeld theory of diffraction. The reconstructed wave front is evaluated by performing the Fresnel transform on the hologram matrix. The corresponding experimental holograms were made with a helium–neon continuous-wave laser and using glass beads from 80 to 250 μm in diameter as models of the water droplets. The half-radiance width of the reconstructed wave-front radiance distribution is shown theoretically to increase linearly as the distance of the object from the hologram is decreased. Also, the half-radiance width increases logarithmically with hologram area. The theoretical and experimental radiance distributions in the plane of reconstruction were compared. Proper alignment of the hologram during reconstruction is necessary for the reconstruction of the original radiance distribution. Size can be measured by noting edge enhancement (radiance peak at the edge of the droplet) in the reconstructed image. A relationship between the diameter of the peak and the actual droplet diameter is determined for sphere diameters from 20 to 250 μm and object distances from 10 to 20 cm. Experimental accuracy to within 4% is achieved with this technique.

Coherence properties of a reflected optical wave in atmospheric turbulence

Abstract: The transverse spatial coherence radius is studied for both the monostatic and bistatic laser radar problems involving an optical wave propagating through atmospheric turbulence in the weak-fluctuation regime over a path of length L and then reflected in the reverse direction from a finite mirror with finite focal length FR. Formal expressions are developed for the wave structure function and the modulus of the complex degree of coherence in the general Gaussian-beam wave case, and tractable analytic results are derived for the special case of a diverging (or spherical) wave at the transmitter and observation points in the beam symmetrically located with respect to the beam centerline. By varying the focal length of the mirror, one minimizes the spatial coherence radius of a reflected spherical wave when the receiver is located near the plane defined by the radius of curvature of the mirror (i.e., L/FR ~ 2) and maximizes it when L/FR is approximately 6–7. Effects of inner scale, outer scale, and the high wave-number deviation from pure power-law behavior are taken into account in the assumed spectral models for refractive-index fluctuations. Analogous to line-of-sight propagation, the spatial coherence radius based on a modified spectrum is generally less than that based on the von Karman spectrum, particularly when the coherence radius is of the order of the inner scale of turbulence.

The Beynon Gabor zone plate: a new tool for de Broglie matter waves and hard X-rays? An off axis and focus intensity investigation

Abstract: Optical elements based on Fresnel zones are used in a range of applications, from X-ray telescopy to microscopy and recently also in the manipulation of de Broglie matter waves. In 1992 Beynon and co-workers presented a binary Gabor type zone plate (henceforth referred to as the Beynon Gabor zone plate). Because this zone plate has no higher order foci, it is in principle a very attractive candidate for focusing of de Broglie matter waves and in some cases X-rays. So far the Beynon Gabor zone plate investigations presented in the literature have concentrated on the intensity distribution along the optical axis and in the focal plane. Here we present a detailed numerical investigation of the Beynon Gabor zone plate, including an investigation of the off-optical axis, off focal plane intensity distribution for point source illumination. We show that at integer fractions of the focal length, the beam becomes nearly toroidal (doughnut-shaped). This offers potentially interesting new possibilities for de Broglie matter wave and X-ray optics, for example in STED-like applications. We further show that the increased intensity at the focal point predicted in the literature for a particular Beynon Gabor zone plate transmission function configuration is an artifact due to the lack of sampling nodes. We support our calculations with experimental measurements in the visible light range, using a Beynon Gabor zone plate fabricated with electron beam lithography.