Zonal diffraction efficiencies and imaging of micro-Fresnel lenses

Abstract

The dependence of the zonal e ciency of a transmission Fresnel lens on the number of quantization levels and on the polarization of the light, without and with an antire¯ection (AR) overcoating is investigated. The height of the grooves with a blaze structure is locally optimized for maximum e ciency. A decreasing structure height over the zonal radius from the centre to the outer zones improves the e ciency because of a better-adapted blaze. An additional increase in the e ciency can be obtained by increasing the AR coating thickness over the zonal radius from the centre outwards. Furthermore, the point spread functions (PSFs) for several quantization levels are compared for both polarization cases. While the AR overcoating has nearly no e ect on the shape of the x polarization PSF, the y polarization PSFs show di erences between both AR coating and no coating and is reduced with an increasing number of levels. Finally, the comparison between the measured e ciency of coated silicon Fresnel lenses and a calculation lead to acceptable results. All calculations are performed with the integral equation system method with parametrization of the grating pro®le, an exact electromagnetic grating di raction method for arbitrary pro®le shapes.

DOEs for color correction in broad band optical systems: validity and limits of efficiency approximations

“…This has been demonstrated at first for a micro-Fresnel lens. 28 Using an adopted approach for full optical systems we were able to analyze a hybrid diffractive-refractive microscope objective for mask inspection systems at 193 nm 29 and we investigated the focal properties of a sample diffractive blue laser disc pickup system. 29…”

Development of a Deep Silicon Phase Fresnel Lens Using Gray-Scale Lithography and Deep Reactive Ion Etching

“…Studies have been done regarding this improvement and a relation derived to predict the efficiency (η) of a multi-level diffractive lens, given the number (N) of steps used [12][13][14]:…”

Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction

“…Assuming a sufficiently large number of zones, a slowly varying zone width, and smoothly curved zones, LLGA allows for the calculation of complex diffraction amplitudes at local zone positions for each of the plane waves. A phase-correct superposition of all local amplitudes allows for the calculation of the point spread function or secondary quantities to qualifying an optical system (12,13,20), for example.…”

“…Fresnel-lenses, Bragg-Fresnel-lenses, cylindrical lens arrays, but also general (holographic as well as digital) beam-and wavefront shaping elements, summarized as Fresnel-zone plates (FZPs), nowadays have increasing applications in measurement and for the coupling of laser beams. At first, the LLGA was used in (11) for the description and optimisation of cylindrical lens arrays and in (12,13) for the analysis and synthesis of micro Fresnel-lenses, including the calculation of the polarisation dependent point spread functions in the focus. Depending on the numerical aperture (NA) of the FZPs, they often possess minimal zone widths in the range of the wavelength.…”