When a star is observed with a telescope, the light is diffracted or spread apart into an Airy disk. The resolution limit is defined as the minimum angular separation between two stars that can still be perceived as separate by an observer. The angular diameter of the Airy disk is determined by the aperture of the instrument.
Rayleigh's resolution limit is reached when the two stars are separated by the theoretical radius of the first dark interval around the Airy disk, which is larger than the disk's apparent radius, so that a distinct dark gap appears between the two disks. Most astronomers say they can still distinguish the two stars when they are closer than Rayleigh's resolution limit. Sparrow's Resolution Limit is reached when the combined light from two overlapping and equally bright Airy disks is constant along a line between the central peak brightness of the two Airy disks. However, at the Sparrow resolution limit the two Airy disks will appear to be just touching at their edges, which according to Sparrow is due to a brightness contrast response of the eye. The same reasoning applies to the resolution of two wavelengths in a spectroscope, where lines of emission or absorption will have a diffraction induced width analogous to the diameter of an Airy disk.
Sparrow's resolution limit is nearly equivalent to the theoretical diffraction limit of resolution, the wavelength of light divided by the aperture diameter, and about 20% smaller than the Rayleigh limit. For example, in a 200 mm (eight-inch) telescope, Rayleigh's resolution limit is 0.69 arc seconds, Sparrow's resolution limit is 0.54 arc seconds.
Dawes' limitedit
Sparrow's resolution limit was derived in 1916 from photographic experiments with simulated spectroscopic lines and is most commonly applied in spectroscopy, microscopy and photography. The Dawes resolution limit is more often used in visual double star astronomy.
Sparrow criterionedit
The Sparrow criterion expresses the resolution limit in term of the joint intensity curve when observing two very closely separated wavelengths of equal intensity. They are considered resolved when the intensity at the midpoint between the peaks shows a minimum.
Referencesedit
^Sparrow, C. M. (1916). "On Spectroscopic Resolving Power". The Astrophysical Journal. 44: 76. doi:10.1086/142271. ISSN 0004-637X.
Eugene Hecht, 2002, "Optics"
Rainer Heintzmann & Gabriella Ficz, 2006, "Breaking the resolution limit in light microscopy", Briefings in Functional genomics, Vol. 5, pp 289–301.
Ariel Lipson, Stephen G. Lipson, Henry Lipson, 2010, "Optical Physics"
January 01, 1970
sparrow, resolution, limit, estimate, angular, resolution, limit, optical, instrument, diffraction, pattern, matching, contents, rayleigh, criterion, dawes, limit, sparrow, criterion, referencesrayleigh, criterion, editwhen, star, observed, with, telescope, li. Sparrow s resolution limit is an estimate of the angular resolution limit of an optical instrument 1 Diffraction pattern matching Sparrow s resolution limit Contents 1 Rayleigh criterion 2 Dawes limit 3 Sparrow criterion 4 ReferencesRayleigh criterion editWhen a star is observed with a telescope the light is diffracted or spread apart into an Airy disk The resolution limit is defined as the minimum angular separation between two stars that can still be perceived as separate by an observer The angular diameter of the Airy disk is determined by the aperture of the instrument Rayleigh s resolution limit is reached when the two stars are separated by the theoretical radius of the first dark interval around the Airy disk which is larger than the disk s apparent radius so that a distinct dark gap appears between the two disks Most astronomers say they can still distinguish the two stars when they are closer than Rayleigh s resolution limit Sparrow s Resolution Limit is reached when the combined light from two overlapping and equally bright Airy disks is constant along a line between the central peak brightness of the two Airy disks However at the Sparrow resolution limit the two Airy disks will appear to be just touching at their edges which according to Sparrow is due to a brightness contrast response of the eye The same reasoning applies to the resolution of two wavelengths in a spectroscope where lines of emission or absorption will have a diffraction induced width analogous to the diameter of an Airy disk Sparrow s resolution limit is nearly equivalent to the theoretical diffraction limit of resolution the wavelength of light divided by the aperture diameter and about 20 smaller than the Rayleigh limit For example in a 200 mm eight inch telescope Rayleigh s resolution limit is 0 69 arc seconds Sparrow s resolution limit is 0 54 arc seconds Dawes limit editSparrow s resolution limit was derived in 1916 from photographic experiments with simulated spectroscopic lines and is most commonly applied in spectroscopy microscopy and photography The Dawes resolution limit is more often used in visual double star astronomy Sparrow criterion editThe Sparrow criterion expresses the resolution limit in term of the joint intensity curve when observing two very closely separated wavelengths of equal intensity They are considered resolved when the intensity at the midpoint between the peaks shows a minimum References edit Sparrow C M 1916 On Spectroscopic Resolving Power The Astrophysical Journal 44 76 doi 10 1086 142271 ISSN 0004 637X Eugene Hecht 2002 Optics Rainer Heintzmann amp Gabriella Ficz 2006 Breaking the resolution limit in light microscopy Briefings in Functional genomics Vol 5 pp 289 301 Ariel Lipson Stephen G Lipson Henry Lipson 2010 Optical Physics Retrieved from https en wikipedia org w index php title Sparrow 27s resolution limit amp oldid 1170345499, wikipedia, wiki, book, books, library,
