Knowledge Bank

$Rowland1$ published an integral formula for the relative intensities to be expected in the diffraction orders of an echelette grating. On performing the integration, we obtain a formula (after correcting for two typographical errors) which differs from that obtained by Rowland in his third term. On the basis of this formula, conditions can be obtained so that a given wavelength can be in the blaze in a certain order. It will be shown that these conditions are not sufficient to determine the incident and diffracted rays uniquely, and further that a variety of blaze conditions exists. This leads to the possibility of several grating mountings which permit the operator to work in the blaze over a range of wavelengths. Two of these possibilities have previously been published by Greig and $Ferguson2$ and $Finkelstein3$.