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This paper presents a straightforward analytical and numerical method for the design of a specific type of varied line‐space grating system. The mathematical development will assume plane or nearly plane spherical gratings that are illuminated by convergent light, which covers many interesting cases for synchrotron radiation. The gratings discussed will have straight grooves whose spacing varies across the principal plane of the grating. Focal relationships and formulas for the optimal grating‐pole‐to‐exit‐slit distance and grating radius previously presented by other authors will be derived with a symbolic algebra system. It is intended to provide the optical designer with the tools necessary to design such a system properly. Finally, some possible advantages and disadvantages for application to synchrotron radiation beamlines will be discussed.