Talk:Airy disk

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Photoreceptor spacing

"The smallest f-number for the human eye is about 2.1. The resulting resolution is about 1 micro meter. This happens to be about the distance between optically sensitive cells, photoreceptors, in the human eye."

I dispute this, foveal cones are typically 1.5μm in diameter with a 0.5μm gap between each, thus giving the array a 2μm spacing. However this may not be the case for the entire retina so I will leave the article until someone more knowledgeable can confirm this —The preceding unsigned comment was added by 131.251.0.55 (talk) 22:29, 6 May 2007 (UTC).[reply]

I'm no eye expert, but it would make sense to have a 2µm spacing, as in visible light, directly applying the equation just before this statement, the airy disk is about 1µm, that's true, but for 400nm. The airy disk would then vary between 1µm and 1.8µm in the visible spectrum (taken here between 400 and 700nm). Then again, we would have to take into account the repartition of the three different cones... Palleas 14:37, 15 May 2007 (UTC)[reply]

The peak cone density of the human fovea is about 170,000 per square millimeter, which translates into a spacing of approximately 2.5 µm spacing, depending on how they are packed (reference included in the article). The section on the eye also neglected spherical aberration, which is the real limit on resolution at larger apertures. Visual acuity is a complicated subject that cannot be addressed accurately with these back-of-the-envelope calculations. See the article on the eye. This section of the article probably needs further cleanup.

--Drphysics (talk) 09:29, 20 September 2008 (UTC)[reply]

Spherical Aberration Image

Might this be better placed in the article on lens aberrations? neffk (talk) 15:12, 22 April 2008 (UTC)[reply]

Maybe request Airy beams

as per http://www.physorg.com/news140438326.html. Emesee (talk) 09:39, 13 September 2008 (UTC)[reply]

An Airy beam has little relation to Airy disks. It is more closely related to a Bessel beam. Airy beams could be included in a more general discussion of 'non-diffractive' light or unconventional solutions to Maxwell's equations along with Bessel beams and knotted light. See Light Beam with a Curve. --Drphysics (talk) 16:26, 20 September 2008 (UTC)[reply]

Page problems

The page has has problem generating formulas for the past couple of days. I'm just editing this page ni the hope that a change will alert someone to the need for service. Thanks!
65.202.227.47 (talk) 13:50, 1 October 2008 (UTC)mjd[reply]

Diffraction rings look too bright

Hi, I was wondering whether the right computation has been done to render the density plot at the top right corner of the article: the outer rings seem far too bright compared to the central peak. In other words, the rings should vanish much faster IMO. The right formula is to be of the (J₁(r)/r)² form, and the image showed here is more likely to represent something of the J₀(r)² form. PS: I've also made this statement on the page dedicated to the image. Cheers, MatP (talk) 16:26, 5 November 2008 (UTC)[reply]

It's some sort of logarithmic scale. The colours do match to the given legend, and it is noted to haved a "scaled" colour function - if you read the source code you can see exactly how it works. I was planning to update the image anyway, with a linear and logarithmic version.Inductiveload (talk) 08:43, 19 March 2009 (UTC)[reply]

lack of definition

The symbol d used in this page is not defined and must be guessed —Preceding unsigned comment added by 88.163.195.44 (talk) 08:13, 14 February 2010 (UTC)[reply]

Early in section 1 it includes:"where θ is in radians and λ is the wavelength of the light and d is the diameter of the aperture." Is that not sufficient?

Interferometrist (talk) 13:24, 24 April 2010 (UTC)[reply]

Math error: rms size of comparable gaussian beam

The section "Approximation using a Gaussian profile" is relevant for the exact reason stated: that the rms of the Airy function itself is infinite (but just in the mathematical sense). However I believe the math is wrong, because the rms of the gaussian IN TWO DIMENSIONS is not w but (according to a quick calculation) sqrt(2) w. I will change that but first need to find a verification in the public domain to reference. Tell me if you disagree.... Interferometrist (talk) 14:03, 24 April 2010 (UTC)[reply]

That sounds good. By the way, "RMS spot size" is a poorly defined term (and the wikilink to RMS is no help); a "spot size" is not an ensemble. ("RMS" means "root mean square". This is the (square) root of the mean of the squared value of what?) Geoffrey.landis (talk) 15:49, 21 January 2011 (UTC)[reply]

coherent vs. in-coherent

the article does not state weather the diffraction pattern is for coherent or incoherent illumination. also, it is not stated weather the maximum intensity calculation is for coherent or incoherent illumination.

the Airy disc pattern for the coherent case is just const*J(x)/x. without squaring the expression. i cant find the right intensity statement —Preceding unsigned comment added by 62.0.44.101 (talk) 07:07, 11 May 2010 (UTC)[reply]

Mathematical details mistake

There seems to be a mistake in the mathematical details section. Taking the derivative of P{\theta), \frac{dP}{dz}=2 \frac{J_1(z)^2}{z}. So somebody should change that. —Preceding unsigned comment added by 147.52.186.60 (talk) 15:13, 5 October 2010 (UTC)[reply]

Image useful?

The bottom image http://en.wikipedia.org/wiki/File:Spherical-aberration-slice.jpg is a very nice image, but since it mostly seems to be about showing the effects of spherical aberration, which is not discussed in the article, it could be questioned why it is included. I would suggest incorporating the middle image of this figure (the non-aberrated image, which does show the Airy pattern) in the article, and deleting the top and bottom. Geoffrey.landis (talk) 15:31, 21 January 2011 (UTC)[reply]

Definition of 'x' in section 'Approximation ...'

The symbol 'x' in the section on the Gaussian profile approximation can not be the same as the x introduced in the section 'mathematical details'. The x in the gaussian approximation section must have the physical dimension of length, while the x in the section on the mathematical details is dimensionless. I would guess from the figure caption in the gaussian approximation section that 'x' should be replaced by the off-axis coordinate 'q' defined earlier, but not entirely sure... --JocK (talk) 02:59, 10 October 2011 (UTC)[reply]