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
!!!!!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
