Finally, after 6 weeks of intense effort by all involved, we have released our Quadratic Best Fit Focus routine. Ken is now evaluating it.
Those working on this project include @bulrichl, @mikaelA, @jmacon, and an early recruit Nicolàs de Hilster.
We have developed a system that allows us to compare our new routine with the current routine in SGP. I should be clear about what it does and does not do. It has nothing to do with star detection. It is the routine that evaluates the focus data comprising the set of Focuser Positions vs average HFR for each image to decide what the new best focus position should be.
To demonstrate the improvement our routine provides we have plotted graphs of Temperature versus Focuser Position, comparing what SGP produces versus our new Quadratic routine. To visually observe how the routine is operating, we have produced graphs of all 3233 focus runs that our log contributors have provided. An example:

This example illustrates one of the kinds of focus curves that SGP has difficulty with. The quadratic curve models this curve nicely. The red X shows a data point that the routine decided was bad data and ignored. The purple down arrow centered on the quadratic curve is the best focus determined by the quadratic routine.
The following charts display the results of a single night of taking continuous auto focus runs with my Televue NP127is refractor, a total of 154 focus runs. The first graph plots the SGP focus positions vs Temperature, the second plots the Quadratic Routine focus position vs Temperature. Quadratic clearly produces superior results.
The routine has evolved through many iterations over the past 6 weeks and has been thoroughly tested on a wide range of hardware, focus settings, observing conditions, and focus curve quality.
