Design of freeform holographic diffractive gratings for the Rowland circle mounting
Recently, thanks mainly to advances in diamond turning technology, it is possible to use optical elements with freeform surfaces, that can be described by the well-known power series equations. It is known that when the entrance slit of the spectral instrument is placed on a circle with a diameter equal to the radius of the diffraction grating, the spectral image formed by the rays passing in the meridional plane will be located on the same circle (Rowland circle). While applying the conditions to eliminate aberrations of the primary orders and using freeform surface parameters in Rowland circle layouts it is possible to obtain a very decent initial design. Numerical optimization with Zemax is done afterwards to obtain final result. 2 grating types are considered in this paper: a holographic type 1 grating, which means that the grating has equally spaced rectilinear grooves (classical grating) and a holographic type 2 - a grating recorded using sources also located on the Rowland circle. For the both grating types meridional coma is equal to zero for all values of the diffraction angles, and an additional parameter is used to compensate the first-order astigmatism. However, a more general version of holographic gratings of type 2 is possible, namely, the conditions satisfying the focusing on the meridional and sagittal sections are imposed on the distances to the recording sources, and an additional parameter is used to optimize the function, taking into account the total effect of the meridional and sagittal coma. In the present paper, both of these approaches and gratings, for which the recording parameters were outside the Rowland circle, are considered to give better results.