I have an optical corrector that needs to be adjusted to a certain position between a camera and a telescope, the manufacturer provides a table with a few x and y parameters of the telescope that determine that position of the corrector but my telescope parameters are beyond this table, so I would like to know if there is a formula that could determine this, which I'm pretty sure there is. The table goes like this.
\begin{array}{|c|c|c|c|c|c|c|c|} \hline F-ratio / Mirror Diameter & 200 & 250 & 300 & 400 & 500 & 800 \\ \hline 3 & 54,64 & 56,13 & 57,04 & 58,07 & 59,25\\ \hline 3,3 & & 56,61 & 57,48 & 58,46 & &\\ \hline 3,5 & & 56,9 & 57,73 & 58,66 & 59,14 &\\ \hline 3,8 & 56,09 & 57,29 & 58,05 & 58,9 & 59,34 & 59,89\\ \hline 4,5 & & 57,91 & 58,5 & 59,17 & 59,52\\ \hline 5 & & 58,16 & 58,64 & 59,19 &\\ \hline 6 & 57,95 & 58,32 & 58,64 & 59 & 59,19 &\\ \hline \end{array}
But the telescope it's going to be installed has an F-ratio of 4 and a Mirror Diameter of 910mm
Thanks for any help.
The mirror is of parabolic profile? I suppose F ratio is Focal length to Mirror diameter ratio.
An interpolation by curve fitting for an assumed function may be sufficiently accurate.
The first column should be:
$$ F/D\, Ratio ; D= Mirror Dia $$
$F/D=4$ ratio can be interpolated between $(3.8-4.5).$ Required mirror dia lies outside the given table domain. At this $F/D$ value, the profile is almost a circle near to a shallow spherical mirror. Calculate Focal length by multiplying $F/D$ with $D$ value.
Plot corrector position as a function of $F,D.$ One example could be
$$ c= a F^2+ b D^2 $$ where $(a,b)$ can be found by least square curve fitting from the given data range.