A differential equation design method for finite-conjugate, multi-mirror imaging systems

Soft-x-rays with wavelengths less than 200 nm are being used for many applications in astronomy, microscopy and lithography. The rapid development of the computer industry requires more advanced fabrication technologies for manufacturing higher-density silicon chips. Soft-X-ray projection lithography (SXPL) has been proposed to achieve tenth or sub-tenth of micron feature size. The specific requirements, such as near diffraction-limited performance, a large image field, and very low distortion for SXPL systems, are very difficult to achieve. Soft-x-ray imaging microscopy is developing as a technique to study the structure of macromolecules within living cells. It would be desirable to construct a reflective imaging microscope operating within the water window (23.3 to 43.6 A) to achieve a 100 A resolution for potential studies of the structures of DNA and RNA molecules. All-reflective, soft-x-ray imaging systems with near diffraction-limited performance with a modest numerical aperture (NA) over a large image field or with a large NA over a modest image field have confronted optical designers with new challenges.; In order to address the challenges of the new soft-x-ray applications, alternative optical design techniques are considered. Based on the conditions of aplanatism, a differential equation design method (DEDM) has been developed for design and optimization of finite-conjugate, multi-mirror imaging systems for soft-x-ray applications. The basic theory, numerical calculations, layout design, system optimization and surface fitting process for DEDM will be described. Applications of DEDM to several three- and four-mirror soft-x-ray projection lithography systems have demonstrated the ability of this design technique to improve the performance of the original systems. Also, a number of two-aspherical-mirror microscopes have been designed by using DEDM based on Schwarzschild configurations. Near diffraction-limited performances have been predicted for a numerical aperture of 0.4 while operating with soft-x-ray radiation with wavelength ranging from 40 A to 130 A.; These results of the application of DEDM to the design of soft-x-ray imaging systems indicate that DEDM is a very promising design and optimization technique for finite-conjugate, multi-mirror imaging systems. Particular strengths of DEDM have been identified by comparing the performance of optical systems designed by this method to that obtained via conventional optical design methods. Some future directions for extending DEDM will also be discussed.