Geometrical aberrations in curved Bragg crystal spectrometers

Under some simplifying assumptions, the line profile of a reflection of a monochromatic line observed with a curved crystal spectrometer for an extended source and curved crystal geometry is derived. In particular, the effect of the finite dimensions of source and crystal is discussed for Johann and Johansson spectrometers. Analytical and numerical studies are provided. It is shown that some parameters produce line asymmetries and shifts of the reflected line's center of gravity. For single non-zero dimensions, analytical dependences for the shifts of the line's center of gravity are derived. From numerical calculations the change of the reflected amplitude and the peak width are obtained. (orig.)