A method of optical filtering in order to provide for enhancement of x-ray images whose quality has been degraded because of the use of extended x-ray sources (penumbra effect) is considered. This method employs spatial filtering techniques in a coherent optical system. A description of the penumbra effect follows from the mathematical description of imaging in incoherent optical systems. With the use of this model the degradation can be described in terms of the effect of the extended source on the frequency content of the resulting image. This leads to a precise definition of the ideal filter in terms of the spatial intensity distribution of the source and a general description of the filtering operations which will be required in all cases, independent of the exact source distribution. It is shown that the form of the ideal filter is such that the same optical system used in the filtering process is ideally suited for generating filters with, approximately, the required transmission characteristics. Experi mental results are presented.
John B. Minkoff, Sadek K. Hilal, William F. Konig, Moses Arm, and Louis B. Lambert, "Optical Filtering to Compensate for Degradation of Radiographic Images Produced by Extended Sources," Appl. Opt. 7, 633-641 (1968)