On the Instrument Profile of Slit Spectrographs

TL;DR

This paper presents a new analytical framework for understanding the instrument profile of slit spectrographs, incorporating diffraction and sampling effects to improve spectral resolution estimates.

Contribution

It introduces an operatorial approach to derive the line spread function, offering a more accurate approximation of spectral resolution under various illumination conditions.

Findings

Provides an analytic expression for the instrument profile.

Proposes an improved approximation for spectral resolution.

Enhances understanding of diffraction effects in spectrograph performance.

Abstract

We derive an analytic expression for the instrument profile of a slit spectrograph, also known as the line spread function. While this problem is not new, our treatment relies on the operatorial approach to the description of diffractive optical systems, which provides a general framework for the analysis of the performance of slit spectrographs under different illumination conditions. Based on our results, we propose an approximation to the spectral resolution of slit spectrographs, taking into account diffraction effects and sampling by the detector, which improves upon the often adopted approximation based on the root-sumsquare of the individual contributions from the slit, the grating, and the detector pixel.