We have fabricated refractive optical elements in SU-8 resist using electron-beam lithography. Exposing an 8-μm-thick layer of SU-8 resist with a 30 kV electron beam, we demonstrate fabrication of an f/9 spherical lens, an f/2 spherical lens, and a prism with a 3° tilt. The elements all perform near the diffraction limit, with rms surface variations between 1/10 wave and 1/7 wave. The electron scattering from the thick resist is measured and shown to limit the technique to optical elements with relatively smooth surface figures.

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SU-8 resist is an epoxy resin dissolved with a photoinitiator in an organic solvent.The result is a negative resist originally developed for high aspect ratio MEMS applications. For some applications SU-8 has several advantages over the most commonly used e-beam resist, PMMA, which include a much higher sensitivity and increased chemical and mechanical robustness.We have used our Raith 150 electron beam lithography tool to investigate SU-8 in two different applications. First, we investigated the properties of a specially formulated SU-8 which can be spun as thin as -100 nm. This is much thinner than normal formulations but necessary for high-resolution lithography. We then exposed an array of single pixel lines with a pitch of 200 nm. At a dose of 30 pC/cm we obtained a line width of -60 nm.Second, using standard formulations of SU-8, we discovered that films as thick as 8 microns can be exposed with a 30 kV electron beam, the maximum of our system. Using the contrast curve as a calibration reference, we were able to make analog three-dimensional structures by spatially varying the dose as the feature is being written. With this technique we fabricated a 3 X 3 array of f/9 spherical lenses. Fred Williamson is with the Microtechnology Laboratory, University of Minnesota, Minneapolis, MN 55455 Eric Shields is with the

Trade studies used to design optical imaging systems frequently result in systems being undersampled. The resolution of such systems is limited by the finite size of the detector pixels rather than the cutoff spatial frequency of the optical system. Multiframe super-resolution techniques can be used to combine a number of spatially displaced images from such systems into a single, high-resolution image. Nonlinear optimization techniques have frequently been used to solve this problem. Such techniques define an objective function and use numerical optimization methods to obtain a solution. These numerical methods are often more efficient when derivatives of the objective function with respect to the variables can be calculated analytically rather than numerically. We demonstrate for the simple motion model of pure lateral translation that the derivatives of the objective function with respect to the image lateral shifts can be calculated analytically to speed optimization calculations.

Phase diversity algorithms allow a wavefront to be reconstructed from through-focus measurements of a point source or extended scene. These algorithms have traditionally been limited to systems that are Nyquist sampled. Many optical systems for remote sensing applications are designed to be undersampled, however. One approach to phase diversity with undersampled systems is to employ superresolution techniques to first create properly sampled scenes. This is demonstrated experimentally for a point object, but is applicable to extended scenes as well.