The optical analysis and design program RAYTRACE, which was developed at our institute, enables the simulation of micro-optical systems containing arrays of microlenses or other optical components. The most important features of the program are briefly described to show its broad application areas. A special simulation example showing the spot diagram and the intensity distribution in the focal plane of a simple Shack-Hartmann sensor with a diffractive microlens array for an incident aspherical wave is given. © 1998 Society of Photo-Optical Instrumentation Engi- neers. (S0091-3286(98)01906-0)

Simulation of micro-optical array systems with RAYTRACE

Equations for calculating the principal curvatures and principal directions of local wave fronts in an optical system that consists of diffractive curved or plane surfaces between isotropic and homogeneous media are presented. The equations for refractive and reflecting surfaces are obtained as special cases of the equations for diffractive surfaces. This method is a kind of generalized ray tracing and permits an easy determination of the position of the local focus or the position and direction of the local focal lines in the case of local astigmatism; it must be emphasized that elements and systems with spherical aberration or coma also have local astigmatism.

Local wave fronts at diffractive elements

Thick diffractive optical elements offer a promising way to achieve focusing or imaging at a resolution approaching 1 nm for X-ray wavelengths shorter than about 0.1 nm. Efficient focusing requires that these are fabricated with structures that vary in period and orientation so that rays obey Bragg's law over the entire lens aperture and give rise to constructive interference at the focus. Here the analysis method of ray-tracing of thick diffractive optical elements is applied to such lenses to optimise their designs and to investigate their operating and manufacturing tolerances. Expressions are provided of the fourth-order series expansions of the wavefront aberrations and transmissions of both axi-symmetric lenses and pairs of crossed lenses that each focuses in only one dimension like a cylindrical lens. We find that aplanatic zone-plate designs, whereby aberrations are corrected over a large field of view, can be achieved by axi-symmetric lenses but not the crossed lenses. We investigate the performance of 1 nm-resolution lenses with focal lengths of about 1 mm and show their fields of view are mainly limited by the acceptance angle of Bragg diffraction, and that aberrations can limit the performance of lenses with longer focal lengths. We apply the ray-tracing formalism for a tolerancing analysis of imperfect lenses and examine some strategies for the correction of their aberrations.

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A ray-trace analysis of x-ray multilayer Laue lenses for nanometer focusing

Besides refractive and reflective components, planar diffractive optical elements are promising for free space optical interconnects. The content of this chapter is focused on holographic optical elements (HOEs), which are diffractive elements fabricated by recording the interference pattern of an object and a reference wave in a photosensitive emulsion.

Diffractive components: holographic optical elements

Holographic optical lenses based on volume gratings commonly suffer from severe aberrations due to wavelength mismatch between recording (blue-sensitive material) and application (often employing diode lasers). Here, methods are described for the precompensation of the aberrations at the recording. Both, aberrations in the phase of the reconstructed wave from the desired wave (‘wave aberration’), as well as aberrations in intensity resulting from deviations from the Bragg condition during reconstruction (‘Bragg aberration’) need to be compensated for. The design method for generating the computer generated holograms is described which are used as precompensating elements in the recording step of the interferometrically produced holographic optical elements. The computer generated holograms are written on a laser pattern generator. Test results of our laser pattern generator are shown to demonstrate its capability for this process. The measurement of the aberrations at the design wavelength in the...

Wavelength Mismatch Correcting Elements for Volume Holograms Written on a Laser Pattern Generator

Equations for tracing rays through (aspheric) holographic optical elements (HOE) are reviewed, and, in addition, the diffraction efficiency of a thick HOE is taken into account. Expressions for calculating the phase functions of aspheric recording wave fronts of a thick HOE in the presence of a wavelength shift are given. A simple least squares fitting algorithm is used to compute analytic expressions of these phase functions. Finally, a method to calculate a focus of rays is described.

https://iopscience.iop.org/article/10.1088/0963-9659/1/2/005/pdf

N Lindlein

Papers

Practical notes on designing and analysing thick holographic optical elements