A Fourier method for the determination of focus for telescopes with stars

TL;DR

This paper presents a Fourier-based method for accurately determining the optimal focus in telescopes by fitting a power function to images at various focus positions, demonstrating its effectiveness across different telescope types.

Contribution

Introduces a novel Fourier method for focus determination that overcomes limitations of existing techniques, validated on multiple telescope types including large RCCs.

Findings

Method is immune to common focus measurement issues.

Successfully tested on small and large telescopes.

Provides a reliable focus determination across different telescope designs.

Abstract

We introduce a Fourier method (Fm) for the determination of best focus for telescopes with stars. Our method fits a power function, that we will derive in this paper, to a set of images taken as a function of focuser position. The best focus position is where the power is maximum. Fm was first tested with small refractor and Schmidt-Cassegrain (SCT) telescopes. After the successful small telescope tests, we then tested Fm with a 2 m Ritchey-Chr\'etien-Coud\'e (RCC). Our tests show that Fm is immune to the problems inherent in the popular half-flux diameter method.