Plots of focus point versus temperature for L, R, G, B, Ha, C2, CO, CN filters on a Takahashi TOA130 using an Optec Gemini focuser. Y axis is focus position (in steps); X axis is temperature (in centigrade).

The linear best fit equations (least squares method) for each filter will be used to calculate an overall "steps per degree" rate of focus change and to calculate offsets for each filter from a selected reference filter.

The measurements were obtained via the Sequence Generator Pro (SGP) auto focus routine. Care must be taken to reject solutions using the "weighted average" method and only accept "best fit" solutions as the values between these two methods do not correlate. The SGP focus analysis method has many flaws and could be vastly improved - in particular its seemingly arbitrary propensity to flit between solution methods - meantime care needs to be taken to note which method was used.

The L, R, G, B, Ha filters are Astrodon parfocal 3mm thickness filters

The C2 (513nm) , CO (427nm) , CN (387nm) filters are Semrock narrow band 2mm thickness filters. The Semrock filters are not anti reflection coated, so reflection halos around bright stars may cause problems. Picking a field avoiding overly bright stars is preferable (M44 and M39 are good candidate fields) .

Selected individual plots of focus point versus temperature for specific filters with added focus uncertainly error bars derived from the measured half flux radius (HFR) values are shown below to indicate the uncertainty of the focus/temp slope over the range of temperatures sampled under the measured seeing conditions.

Nights with high humidity tended to increase the spread of measured focus positions for a given temperature. Low humidity leads to better reproducible results . These measurements were taken over a 2 month period (late March to early May 2019) corresponding to the start of the Andalusian rainy season to its decline into warmer and drier weather from May onwards.

The focus uncertainty in focuser steps (Seeing limited focus zone - SLFZ) is calculated from:

SLFZ = 2 x (HFR x FR) / SD

Were HFR is half flux radius in micrometers (measured by SGP in fractions of pixels, then converted using sensor pixel size - 5.4um), FR is focal ratio (F/5.5) and SD is focuser step distance (0.11 um).

The SLFZ measured in focuser steps is derived from the length of travel through the true focus point where the star image is theoretically smaller than the measured HFR. The 2 x term accounts for the distance before and after the focus point from the two positions where the radius of the light cone is equal to the HFR value.

The plots below also show that the narrower the bandwidth of the filter the better the results with respect to line fitting (R-squared value)

1. Lum filter details: Y axis is focus position (in steps); X axis is temperature (in centigrade). R-squared = 0.9665







2. Red filter details: Y axis is focus position (in steps); X axis is temperature (in centigrade). R-squared = 0.9835







3. C2 filter details (513nm): Y axis is focus position (in steps); X axis is temperature (in centigrade). R-squared = 0.9924







[h1]Results[/h1]







The filter focus data was combined to find the best fit focus shift slope after solving the individual filter best fit equations for the middle 9 degrees centigrade data point. Then the filters focus point offsets from the R filter where calculated. The individual filters focus point versus temperature data sets where then each adjusted using the calculated offsets and an overall best fit equation generated.

[h2]Focus Offsets[/h2]

L -589

R 0

G -1171

B -998

Ha -581

C2 -7102

CO -5087

CN -1213

[h2]Best fit equation[/h2]

F = 640.85 x T + 75482 - where F is focus point in steps and T is temperature in degrees centigrade

[h2]Focus shift[/h2]

641 steps per degree centigrade