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How to calculate secondary obstruction

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I'm trying to calculate my 130P-DS's true focal ratio.

It's labelled as F5 but I'm trying to calculate how much of the secondary mirror is blocking the primary.

The secondary's minor axis is believed to be 47mm. I presume this means the diameter of circle when tilted at 45°?

The primary's diameter is 130mm.

Do I find the area of each circle then divide one into the other?

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I don't see much point in doing that - calculating "effective" F/ratio.

F/ratio is only important for beam characteristics (angle at which light comes in) - and that won't change with central obstruction - it will still be F/5 beam.

What you might want to calculate is effective aperture - or what is equivalent clear aperture of 130mm reflector.

You'll need to take into account secondary obstruction - but also reflectivity of mirrors, which is probably going to contribute more to light loss than central obstruction.

Secondary is most often quoted by its minor axis - so that is diameter of profile presented to incident light.

Here is calculation assuming 94% reflectivity (this is a bit harder figure to find and it is often given as peak reflectivity - but it changes over visible spectrum and is maybe better represented by 93% for regular and 97% for enhanced coatings).

clear_aperture = sqrt((130^2  - 47^2) * 0.93 * 0.93) = ~112.7mm of clear aperture.

Do be careful - above 112.7mm does not mean that 130PDS is equivalent to 112.7mm refractor in terms of gathering power. Refractors also have loss of light in their optical elements and reflection on air/glass surfaces.

Say that you loose something like 0.5% per air glass surface and you have triplet scope - it would then need to be 114.4mm aperture scope in order to have 112.7mm clear aperture.

I'd say that 130PDS is equivalent to 115mm refractor, and in fact - this refractor would be good replacement for 130PDS:


As with x0.8 FF/FR it has ~640mm of FL and same equivalent clear aperture.


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I agree with Vlad, the focal ratio, or at least the important characteristics influenced by focal ratio is/are unaffected by the secondary dimensions. Can you tell us what you are trying to work out from this?

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On 03/06/2022 at 13:38, vlaiv said:

What you might want to calculate is effective aperture - or what is equivalent clear aperture of 130mm reflector.

This would seem to make the most sense - presumably to allow comparisons of light gathering ability between different sized ’scopes. AstroBlender has a recent video on this topic FYI. 


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