Finding perfect focus with V-Curve fitting based on a hyperbolic function

This article is about finding the best possible telescope focus by approximating a V-Curve with a hyperbolic function.

What is a V-Curve?

A V-Curve is the result of moving the focus of a telescope from an outside focus position into the focus and then further into the same direction out of focus again. This way a V-Curve comes into existence where the focus position is on the x-axis and the focus measure on the y-axis (right figure). Probably not surprising this curve is called V-Curve since it is similar to a V. There are different ways to measure the focus – for example the “Half-Flux Diameter” (HFD) and the “Full width at half maximum” (FWHM). In this case the I use the HFD measure.

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