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Min. distance to artificial star ?

26 replies to this topic

#26 AndresEsteban

AndresEsteban

Ranger 4

• Posts: 339
• Joined: 28 Nov 2013
• Loc: Rio de Janeiro, Brazil

Posted 18 September 2020 - 08:41 PM

Taking the formulas been given by Joe1950 and translating to metrics (we need USA to go into metrics for god sake!)

We'll have:

L = distance in meters from the artificial star to the telescope objective

D = Objective diameter in millimeters

f = focal ratio, adimensional

n = induced error fraction denominator in the "lambda/n" induced error, Thus, Lambda /4 => n= 4; lambda/8 => n=8.

L [m] = n . (D [mm] / f ) ^2  / 302.4

Example:

D = 17.5 inches = 444.5 mm
f = 4.5

n = 8 (mean induced error of lambda/8)

so:

L [m] = 8 . ( 444.5 / 4,5)^2 /302.4 = 8 x 9757.05  / 320.4 =  2058.12 m or 846.86 ft

Clear skies for us all!
Andy

Edited by AndresEsteban, 18 September 2020 - 08:48 PM.

#27 BGRE

BGRE

Gemini

• Posts: 3,005
• Joined: 21 Mar 2016
• Loc: New Zealand

Posted 19 September 2020 - 05:00 AM

Can one use geometric analysis to figure this out?

I am thinking the following ...

1. you want to illuminate the entrance pupil (full aperture) with perfect plane-wave illumination.

2. consider the artificial star is a point source, projection the light as a spherical wavefront.

3. as the distance from the pojnt source increases, the spherical wavefront approaches a plane wave.

4. knowing the aperture of your scope, you can calculate the error of a spherical wavefront from a true plane wave ... at the edge of the aperture ... in terms of wavefronts .. as a function of distance from the source.

5.  apply some criteria for this .... .... < 1/8 wave of green

Not that way as it grossly overestimates the distance required.

Raytracing is the most reliable method since there's a lot of misinformation out there including the 20 times the focal length rule.

There are 2 conditions that should be met

1) the angular diameter of the artificial star should be less than half the angular diameter of the Airy disk (i.e. < 1.22*lambda/D).

2) The distance should be such that the additional wavefront error at the best focus is sufficiently small (i.e. less than the desired wavefront error when imaging a star at infinity).

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