A new method for focusing x rays and gamma rays is described that can focus monochromatic radiation from a point source or parallel beam down to a line image. If two focusing elements are used or if a single element bent in two directions is used, the radiation can be focused to a point image. Conversely, radiation from a point source can be converted into a parallel beam. The method makes use of bent diffraction crystals in which the intercrystalline‐plane spacing is varied as a function of position in the crystal. The Bragg angle for diffraction of monochromatic radiation will now vary as a function of position in the crystal, and this new degree of freedom can be used to obtain focusing of the diffracted beam. A number of ways to achieve this variation in crystal‐plane spacing is discussed, including the use of thermal gradients and the variation of the elemental composition of the crystal. The applications of this new focusing system to a gamma‐ray telescope and to the production of a real image of a strong x‐ray source are considered.

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