Several groups have been developing x-ray microscopes for studies of biological and materials specimens at suboptical resolution. The X1A scanning transmission x-ray microscope at Brookhaven National Laboratory has achieved 55 nm Rayleigh resolution, and is limited by the 45 nm finest zone width of the zone plate used to focus the x rays. In principle, features as small as half the outermost zone width, or 23 nm, can be observed in the microscope, though with reduced contrast in the image. One approach to recover the object from the image is to deconvolve the image with the point spread function (PSF) of the optic system. Toward this end, the magnitude of the Fourier transform of the PSF, the modulation transfer function, has been experimentally determined and agrees reasonably well with the calculations using the known parameters of the microscope. To minimize artifacts in the deconvolved images, large signal to noise ratios are required in the original image, and high frequency filters can be used to reduce the noise at the expense of resolution. In this way we are able to recover the original contrast of high resolution features in our images.