Some methods of scanning in tandem two gratings of unequal angular dispersion

There are certain situations when more than one diffraction grating is used for dispersing light consisting of many wavelengths. One situation is that of a double monochromator using different gratings which have different angular dispersions. Another situation is when two gratings are used successively to obtain an inline dispersion arrangement for selecting one wavelength at a time from a laser source emitting many wavelengths. It is possible to couple two gratings so that both are set to track the same wavelength. There are certain mathematically exact properties of circles and triangles which can be applied to this situation, and these properties can be used to devise simple mechanical linkages which couple the axes of rotation of the tables on which the gratings have been mounted. The theory of the above considered situations is presented along with some schematic linkages which can be useful for coupling two or more gratings of unequal angular dispersion