Modelling technique for far-infrared partially-coherent grating spectrometers

The optical modelling of far-infrared partially-coherent grating spectrometers has long been considered difficult, due to the multi-mode diffractive nature of the grating optics. However, for the next generation of far-infrared space missions the need for understanding the complex behaviour of these grating spectrometers has intensified. Conventional modelling techniques are difficult to apply because i) the field is partially coherent; ii) diffraction and focusing effects are crucially important; iii) diffraction integrals need to be sampled finely over large optical surfaces. We describe an effective approach based on propagating the correlation functions of the radiation field using the natural modes of the optical system. First, the transformation matrix of the system, T, is determined, which captures the natural modes of the optics. Next, the correlations functions are propagated through the optics using T. The result is a modal optics technique that captures all performance information, in terms of the spectral, spatial and coherence details, within a single framework. In the paper, we explain the foundations of the method and demonstrate its applicability based on a number of standard far-infrared optical systems. Our scheme is numerically powerful, and provides insights into the trade-offs needed to optimise performance. The analysis we will extended to partially coherent far-infrared grating spectrometers as a function of the incident spectral field compositions, scattering at the grating optics, and detector geometry to improve our understanding of such systems.