Simulations of the Spectral Resolving Power of a Compact Space-Borne Immersion-Echelle Spectrometer Using Mid-Infrared Wave Tracing

TL;DR

This study uses wave-optics simulations to analyze how optical aberrations and slit configurations influence the spectral resolving power of a compact mid-infrared spectrometer with an immersion-echelle grating, relevant for space telescopes.

Contribution

It provides new insights into the effects of aberrations and slit presence on spectral resolution, challenging geometrical optics predictions and highlighting diffraction effects.

Findings

Spectral resolving power is largely unaffected by aberrations when a slit is used.

Diffraction from the slit enhances the resolving power, especially at longer wavelengths.

Aberrations impact can be estimated using the Strehl ratio in slit-less configurations.

Abstract

We performed wave-optics-based numerical simulations at mid-infrared wavelengths to investigate how the presence or absence of entrance slits and optical aberrations affect the spectral resolving power $R$ of a compact, high-spectral-resolving-power spectrometer containing an immersion-echelle grating. We tested three cases of telescope aberration (aberration-free, astigmatism and spherical aberration), assuming the aberration budget of the Space Infrared Telescope for Cosmology and Astrophysics (SPICA), which has a 20-$\mathrm{\mu m}$-wavelength diffraction limit. In cases with a slit, we found that the value of $R$ at around 10--20 $\mathrm{\mu m}$ is approximately independent of the assumed aberrations, which is significantly different from the prediction of geometrical optics. Our results also indicate that diffraction from the slit improves $R$ by enlarging the effective illuminated area on the grating window and that this improvement decreases at short wavelengths. For the slit-less cases, we found that the impact of aberrations on $R$ can be roughly estimated using the Strehl ratio.