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Short wavelength x-ray radiation microscopy is well suited for a number of material and life science studies. The x-ray microscope ͑XM1͒ at the Advanced Light Source Synchrotron in Berkeley, California uses two diffractive Fresnel zone plate lenses. The first is a large condenser lens, which collects soft x-ray radiation from a bending magnet, focuses it, and serves as a linear monochromator. The second is the objective zone plate lens, which magnifies the image of the specimen onto a high-efficiency charge coupled device detector. The objective lens determines the numerical aperture and ultimate resolution. New objective lens zone plates with a minimum linewidth of 25 nm and excellent linewidth control have been fabricated using Berkeley Lab's 100 keV Nanowriter electron beam lithography tool, a calixarene high-resolution negative resist, and gold electroplating. Although the condenser zone plate is less critical to the resolution of the instrument, its efficiency determines the flux on the sample and ultimately the exposure time. A new condenser zone plate was fabricated and has a 9 mm diameter, 44 000 zones, and a minimum zone width of 54 nm ͑optimally the condenser and objective should have the same zone width͒. It is also fabricated with the Nanowriter at 100 keV using poly͑methylmethacrylate͒ resist and nickel electroplating. The phase shift through the nickel absorber material enhances the diffraction efficiency over an amplitude only zone plate. To evaluate the microscope's performance transmission test patterns have been made and imaged. Lineout data show modulation for 30 nm lines and 60 ͑1:2͒ spaces to be almost 100%. These new diffractive optical elements represent a significant advancement in the field of high-resolution soft x-ray microscopy. Diffractive optical elements have been used to measure the wave front error of an extreme ultraviolet projection optical system. The reference wave is generated by the spherical wave generated by diffraction from a small freestanding pinhole.

Abstract-In this paper we continue the discussion of the causes for image deterioration in the Maximum Likelihood Estimator (MLE) method of tomographic image reconstruction that we initiated with the publication of a stopping rule for that iterative process. We introduce the concept of a feasible image, which is a result of a reconstruction that, if it were a radiation field, could have generated the initial projection data by the Poisson process that governs radioactive decay. From the premise that the result of a reconstruction should-be feasible, we examine the shape and characteristics of the region of feasibility in projection space. Although MLE reconstructions from computer simulated data pass through a feasibility region when started from a uniform intensity image field, as determined by our previously published stopping rule, attempts at using that rule to detect feasibility in reconstructions with real PET data failed-con;.sistently. We examine the reasons for that failure and design a more relaxed stopping rule that takes into account the fact that the prob-1 ability matrix defining a true tomographic instrument can only be known within some error margin. With the new rule, reconstructions from real data can be tested for feasibility. Results of the test and reconstructed images for the Hoffman brain phantom are shown.We conclude with a comparative examination of the current methods of dealing with MLE image deterioration and we endeavor to put the minds of current workers in the field at ease about having to stop MLE iterations when the images look acceptable.