Transmission curves of narrow-band filters in large-FoV and fast astronomical instruments

TL;DR

This paper investigates how small f-numbers, non-telecentricity, and large FoV affect the transmission curves of narrow-band filters in astronomical instruments, impacting photometric accuracy and instrument design.

Contribution

It provides a computational analysis of the combined effects on filter transmission curves, offering guidelines for filter design and instrument calibration.

Findings

Transmission curves can significantly differ from nominal shapes.

Blue-shift increases monotonically with distance from FoV center.

Photometric dispersion is introduced by filter shape distortions.

Abstract

Narrow-band filters are often used to constrain the chemical composition of astronomical objects through photometry. A challenge to derive accurate photometry is that narrow-band filters are based on interference of multiple reflections and refractions between thin layers of transparent dielectric material. When the light rays reach the surface of a filter not perpendicular to it, they cross the layers obliquely travelling a path longer than the thickness of the layers and different for each inclination. This results in a blue-shift of the central wavelength and a distortion of the transmission curve. Hence, particular care should be taken when narrow band filters are used in presence of small f-numbers and large non-telecentric angles, as frequent in the large field of view (FoV) instruments. Sometimes, the broadening and central wavelength shift of the transmission curve are considered and compensated in the design of filters for instruments with a small f-number. Here we consider the combined effect of small f-number, non-telecentricity and large FoV. Where single spectral lines are considered, a shift in central wavelength or a change in the shape of the transmission curve may introduce an instrumental dispersion in luminosity and in the linked color indices. We found that transmission curves of narrow band filters can be significantly different in shape than the nominal ones. The bottom limits for filters' effective FWHM for each f-number; the monotonic behavior of the blue-shift with distance from the center of FoV; the monotonic quality decrease of the transmission curves and the photometric dispersion introduced by the filters are computationally estimated. This work could represent a useful tool to evaluate the fitness of a particular filter at a particular facility.