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# The Airy Disk (groundwork)

Started by EdZ, 05/02/2003 11:16AM
Forum Member

Join Date: Jul 2002

Location: Cumberland RI, US

Posts: 151

The Airy Disk
!!!!!EDITED 5-3-03!!!!!

This discussion progressed substantially elsewhere. The primary outcome that I will note here is numerous published works have incorrect explanations of these various criteria, Dawes Limit, Rayleigh Limit and Airy disk. I edited out any information from incorrect sources. If you have a desire to know more about this topic, contact me and I will forward the extent of the discussions pertaining to this. Thank you. edz

Dawes Limit = 4.56/D inches = 116/Dmm. D.L. is the first point at which a double star is elongated enough to suspect the presence of two stars.

As aperture increases, the diffraction disk gets smaller and hence the greater the resolving power. Dawes limit is not used to measure an achievable black space between two point sources.

Rayleigh Limit = 5.35/D inches = 136/Dmm.

Resolving power is dependant on wavelength of the light observed and the diameter of the objective.

Beiser: the angular width of the RADIUS of the diffraction (Airy) disk central point is represented as: A = 1.22 h / D, where
A in radians = 1.22 x h(lambda) / D (aperture of scope in meters)
Lambda is the wavelength of light = used avg of 500um or 500 nanometers = 500 x 10^-9 meters.
Visible light is between 420um and 600um. Some sources use 550um for this calculation.

For a 150mm scope, then A = 1.22 x 500 x 10^-9 meters / 0.15meters = 0.000004 radians
Converting radians to arcsec, then 0.000004 x 360/2pi x 60 x 60 = 0.83 arcsec.

Based on Rayleigh limit criteria, 5.35/D inches or 136/Dmm(some sources use 5.45/D or 140/D:
Resolution for telescopes of D: 4” = 1.33arcseconds, 5” = 1.09 arc”, 6” = 0.89arc”, 7” = 0.76arc”, 8” = 0.67arc”, 9” = 0.59arc”, 10” = 0.54arc”. To confirm the ability of your telescope to achieve these results, it would be necessary to observe and record various results for doubles near and beyond the projected limits for your scope.

edz
Forum Member

Join Date: Jul 2002

Location: Cumberland RI, US

Posts: 151

NOW COMES THE QUESTION:
!!!!!!!EDITED 5-3-03!!!!!

In my research of the Airy disk formula, I noted numerous well-regarded astronomy references and several websites that have published astronomy related formulae referring to a shortened form of the formula for calculating the Airy disk radius. That shortened form in all cases was given as A = 1.22/D where it is stated that A = arcsec and D = scope diameter in meters.

This has been proven to be innaccurate. The correct formula is theta = 1.22 lambda/D. This formula does provide results for the radius of the Airy disk in radians that must be converted to arcseconds. The results are nearly equivalent to the results one would get using Rayleigh criteria as 5.45/D.

Numerous reference books and websites, some by noted authors, have explanations for Dawes Limit, Rayleigh Limit and how these relate to Airy disk. Many of these references are incorrect.

An excellent source is http://www.licha.de/AstroWeb/articles_fullsize.php3?iHowTo=16

Neither Dawes nor Rayleigh indicates a condition where two stars are completely separated. Rayleigh indicates somewhat greater separation than Dawes. Neither is equivalent to the diameter of the Airy disk.

The distance between the centers of two point sources that appear completely separated needs to be at least twice the value determined by the wavelength formula. This would be approximately equal to twice the value determined by the Rayleigh Limit formula 5.45/D.

If you need further information
You may contact me at ezazaz@juno.com
Thank you,
Ed Zarenski
Cumberland, RI

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