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The factor of 2 is also often omitted, giving yet another definition and causing the function maximum to be 0.5:
480:
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365:) is a sombrero function. Thus a sombrero function also appears in the intensity profile of far-field
422:
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167:{\displaystyle \operatorname {somb} (\rho )={\frac {2J_{1}(\pi \rho )}{\pi \rho }}.}
49:
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449:
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41:
252:{\displaystyle \operatorname {somb} (\rho )={\frac {2J_{1}(\rho )}{\rho }}.}
320:{\displaystyle \operatorname {somb} (\rho )={\frac {J_{1}(\rho )}{\rho }}.}
420:
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factor is omitted, giving the following alternative definition:
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William R. Hendee, Peter Neil Temple Wells (1997-06-27).
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44:, and is so-called because it is shaped like a
358:{\displaystyle \operatorname {circ} (\rho )}
48:hat. This function is frequently used in
369:through a circular aperture, known as an
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441:
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424:The perception of visual information
13:
14:
492:
454:MathWorld--A Wolfram Web Resource
54:Bessel function of the first kind
393:Theory of Remote Image Formation
390:Richard E. Blahut (2004-11-18).
52:. It can be defined through the
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333:of the 2D circle function (
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398:Cambridge University Press
427:. Springer. p. 204.
176:The normalization factor
36:) is the 2-dimensional
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76:{\displaystyle J_{1}}
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20:Sombrero function 3D
448:Weisstein, Eric W.
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28:(sometimes called
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481:Signal processing
434:978-0-387-94910-9
331:Fourier transform
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26:sombrero function
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50:image processing
38:polar coordinate
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450:"Jinc Function"
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30:besinc function
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400:. p. 82.
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40:analog of the
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42:sinc function
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34:jinc function
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457:. Retrieved
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33:
29:
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367:diffraction
182:somb(0) = 1
377:References
371:Airy disk
350:ρ
344:
310:ρ
303:ρ
278:ρ
272:
242:ρ
235:ρ
207:ρ
201:
156:ρ
153:π
145:ρ
142:π
114:ρ
108:
475:Category
83:) where
46:sombrero
431:
404:
180:makes
459:1 Jan
461:2019
429:ISBN
402:ISBN
341:circ
329:The
269:somb
198:somb
105:somb
32:or
477::
452:.
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373:.
97:.
92:+
88:=
24:A
463:.
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347:(
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300:(
295:1
291:J
284:=
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275:(
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232:(
227:1
223:J
219:2
213:=
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204:(
187:π
178:2
162:.
148:)
139:(
134:1
130:J
126:2
120:=
117:)
111:(
94:y
90:x
86:ρ
69:1
65:J
56:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
