Posted by
James Pawley on
URL: http://confocal-microscopy-list.275.s1.nabble.com/Out-of-Office-autoreply-courtesy-tp6917499p6934665.html
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Hi All,
The Rayleigh criterion described by Guy implies that exactly centered
between the two peaks (of equal brightness!) the intensity will drop
to 75% of that at the peaks (often referred to as 25% contrast). This
value seems to have been chosen because it was felt that the eye
could not reliably detect a smaller "darkening" and more to the
point, the maths were easier.
Enter electronic image capture and display, where by fiddling the
contrast and brightness one can "enhance" even a slight dip in
intensity enough to make it visible to the eye, leading to the
Sparrow Criterion, where the 0.51 comes from.
The point is that these neither of these criteria are really very
practically useful for a number of reasons:
1) Electronic images must be quantized in space and intensity. If you
use Nyquist and put 2 or 3 pixels between the peaks, then the
"darkest" one will be a lot brighter than 75% because the math
function describing the sum of the two Airy Disks shows only a very
narrow dip to 75% and this will be averaged with "the sides of the
canyon," if you see what I mean. So, depending on exactly how the
point object lines up on the sampling grid, at Rayleigh spacing, the
inter-peak contrast is closer to 10% than 25%.
2) Rayleigh wasn't worried about photons. We are, because of Poisson
Statistics. To see, say, 10% contrast with one-sigma reliability
requires at least 100 photons to be counted from the dimmest pixel.
In fluorescence imaging, this is only likely to occur on fixed
specimens.
3) Rayleigh was interested in bright objects on a black background.
This fits well with fluorescence microscopy but not so well with any
kind of brightfield because in the latter case the "background"
(average intensity) has considerable Poisson Noise superimposed upon
it and this can "create" apparent features out of random statistical
fluctuations. So you may need to collect many more photons to
discriminate real features reliably in brightfield. Black backgrounds
do not have this problem
4) All this nice math falls apart when the two point objects are not
of equal brightness. And they seldom are. Ditto, if there is
significant background.
But getting back to the original question: If "one Airy unit" is the
radius of the Airy disk to the first zero, and as it turns out, this
is very nearly equal to the full-width-at-half-maximum of the central
peak, should we use One Airy as the default pinhole setting or 2 Airy
which would include the whole peak? And how does this decision affect
the signal levels detected from features that are larger than points?
JP
***************************************************************************
Prof. James B. Pawley, Ph.
608-238-3953
21. N. Prospect Ave. Madison, WI 53726 USA
[hidden email]
3D Microscopy of Living Cells Course, June 10-22, 2012, UBC, Vancouver Canada
Info:
http://www.3dcourse.ubc.ca/ Applications accepted after 11/15/12
"If it ain't diffraction, it must be statistics." Anon.
>Guy (and list), in a couple of super-resolution talks I've attended
>they were using 0.51 instead of 0.61 for the constant. Do you know
>the rationale behind this?
>Thanks, Brian
>
>Brian Armstrong PhD
>Light Microscopy Core
>Beckman Research Institute
>1450 East Duarte Rd
>Duarte, CA 91010
>626-256-4673 x62872
>
http://www.cityofhope.org/SharedResources/LightMicroscopy/LightMicroHome.htm>
>
>-----Original Message-----
>From: Confocal Microscopy List
>[mailto:
[hidden email]] On Behalf Of Guy Cox
>Sent: Wednesday, October 26, 2011 2:46 AM
>To:
[hidden email]
>Subject: Airy Units - was: RE: "Out of Office autoreply" courtesy
>
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>
>You are right, it has been totally drowned out!
>
>The Airy unit is defined by the size of the Airy disk, that is the size
>of the disk representing the image of a point object. Airy was an
>astronomer and thus derived it by reference to stars (which, though
>huge, are so far away that they appear as point objects). John Strutt,
>Lord Rayleigh, proposed a general resolution criterion that two objects
>can be considered resolved if the maximum of one Airy disk lies on the
>first minimum of the other. This criterion, the radius of the central
>disk (ignoring surrounding haloes) is given by r = 0.61 lambda /
>NA, where lambda is the wavelength of the light being used.
>
> Guy
>
>
>Optical Imaging Techniques in Cell Biology
>by Guy Cox CRC Press / Taylor & Francis
>
http://www.guycox.com/optical.htm>______________________________________________
>Associate Professor Guy Cox, MA, DPhil(Oxon)
>Australian Centre for Microscopy & Microanalysis,
>Madsen Building F09, University of Sydney, NSW 2006
>
>Phone +61 2 9351 3176 Fax +61 2 9351 7682
> Mobile 0413 281 861
>______________________________________________
>
http://www.guycox.net>
>
>
>-----Original Message-----
>From: Confocal Microscopy List [mailto:
[hidden email]]
>On Behalf Of Peter G. Werner
>Sent: Sunday, 23 October 2011 4:55 AM
>To:
[hidden email]
>Subject: Re: "Out of Office autoreply" courtesy
>
>*****
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>
>And I hate to point this out, but the question I originally asked
>(concerning the definition of Airy Units) has been drowned out by all
>the
>commentary about the "Out of Office autoreply" that my initial email
>generated.
>
>If nobody has an answer to the question, no worries, but I'd hate to see
>the
>topic get lost under the weight of discussion of listserv function.
>
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***************************************************************************
Prof. James B. Pawley, Ph.
608-238-3953
21. N. Prospect Ave. Madison, WI 53726 USA
[hidden email]
3D Microscopy of Living Cells Course, June 10-22, 2012, UBC, Vancouver Canada
Info:
http://www.3dcourse.ubc.ca/ Applications accepted after 11/15/12
"If it ain't diffraction, it must be statistics." Anon.