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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.

Christos Oscar Kambiselis
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    Another consideration: the $f$-number is within their range but the telescope diameter isn't. Will whatever formula they've used be valid outside that range, or is it an approximation that starts to go awry outside the range of the table? That would be a question for the manufacturer. – timtfj Dec 18 '18 at 19:17
  • #Christos Better to pose the question in optics/physics sites. – Narasimham Dec 18 '18 at 19:54
  • @timtfj I believe the diameter stops at 800mm because there aren't many companies that built such large mirrors, their website only states that the f-ratio can't be under 3 but doesn't limit the mirror diameter or the focal length. – Christos Oscar Kambiselis Dec 19 '18 at 21:42
  • @ChristosOscarKambiselis I wondered i if that was it. Also whether the one $800$ mm entry was there for a specific telescope that they make or know of. – timtfj Dec 19 '18 at 22:17

1 Answers1

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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.

Narasimham
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    The telescope is a folded Newtonian style, which means it has a concave main mirror, a flat secondary, and a diagonal mirror the two later of course have no other job than to direct the light to the desired focusing point and make the telescope structure shorter in length, and should not make any difference to the equation. – Christos Oscar Kambiselis Dec 19 '18 at 22:00