How to Figure Required Telescope Diameter?

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SUMMARY

The discussion focuses on calculating the required diameter of a telescope's primary mirror to resolve objects of specific angular diameters. The user initially attempted to utilize the Nyquist-Shannon sampling theorem and photon wavelength but encountered inaccuracies in their results. The conversation highlights the need to reverse the Dawes' limit formula, which is essential for determining the mirror size based on diffraction principles. Understanding the relationship between Airy discs and point spread functions is crucial for accurate calculations.

PREREQUISITES
  • Understanding of the Dawes' limit formula
  • Familiarity with Airy discs and point spread functions
  • Knowledge of diffraction principles in optics
  • Basic programming skills for implementing calculations
NEXT STEPS
  • Research the mathematical derivation of the Dawes' limit formula
  • Study the effects of diffraction on telescope performance
  • Learn about the Rayleigh criterion and its applications in optics
  • Explore programming techniques for simulating optical systems
USEFUL FOR

Astronomy enthusiasts, optical engineers, and anyone involved in telescope design and performance optimization will benefit from this discussion.

willgtl
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A awhile ago I wrote a program to calculate various things like maximum resolving power of a given telescope's primary mirror, angular diameter of an object of a given size from a given distance and mirror diameter required to see an object of a given angular diameter.

However, I seem to have completely failed on the last part. I just now looked back at that program and got results of tens of kilometers when I know my result should've been mere dozens of meters. Looking at the code, I appear to have involved the Nyquist-Shannon sampling theorem and photon wavelength, with no recollection as to why.

I have a feeling I'm completely off-base. Could someone enlighten me on how to essentially reverse the Dawes' limit formula, and find the mirror size required for a given angular diameter? Thanks!
 
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From wiki:

"A calculation using Airy discs as point spread function shows that at Dawes' limit there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip."

Does this help? No sampling required, but it is based on diffraction.
 

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