As I said, I was sticking to the two 'classic' 19th century formulae, from Abbe and Rayleigh. Rayleigh's formula is for incoherent imaging and fluorescence imaging is incoherent, to all intents and purposes. But the criterion is arbitrary - if you use full-width half maximum you will get a (slightly) different result.
Abbe's formula assumes coherence but widefield imaging is not truly coherent. So Michael is quite right. The question is discussed in Born & Wolf if anyone wants to go there (I don't!). But the fact remains that the resolution one can obtain in practice, with the best corrected optics, closely matches what Abbe's formula predicts. For the biologist, going further is pointless.
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)
Electron Microscope Unit, Madsen Building F09,
University of Sydney, NSW 2006
______________________________________________
Phone +61 2 9351 3176 Fax +61 2 9351 7682
Mobile 0413 281 861
______________________________________________
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-----Original Message-----
From: Confocal Microscopy List [mailto:[log in to unmask]] On Behalf Of MODEL, MICHAEL
Sent: Saturday, 21 February 2009 12:47 AM
To: [log in to unmask]
Subject: Re: Resolution for fluorescence, brightfield and luminescence
The formula for resolution in bright field is not exact. The problem was solved by Hopkins and Barham, Proc Phys Soc B, 63, 737-744, 1950. The effect of condenser on resolution is also shown on the Olympus site, http://www.olympusfluoview.com/java/resolution3d/index.html
Mike
-----Original Message-----
From: Confocal Microscopy List [mailto:[log in to unmask]] On Behalf Of Guy Cox
Sent: Thursday, February 19, 2009 7:49 PM
To: [log in to unmask]
Subject: Re: Resolution for fluorescence, brightfield and luminescence
In widefield fluorescence the emission wavelength is the only one that matters. Using the Rayleigh criterion the resolution (r) will therefore be r = 0.61 x wavelength / NA - though as Julio says this is a somewhat arbitrary criterion.
In confocal both wavelengths count, and if the pinhole is infinitely small the Rayleigh resolution r becomes r / sqrt2, so is somewhat better, though most microscopists work with a pinhole size equal to the Airy disk, which will not give any resolution improvement. However the contribution of the shorter excitation wavelength still means you do slightly better than in widefield (for a simple calculation just assume a wavelength midway between Ex & Em).
In multiphoton fluorescence only the excitation wavelength counts, but the resolution becomes r / sqrt2 without the need for any pinhole - this helps to counteract the loss from the longer wavelength.
For more details see Guy Cox & Colin Sheppard, 2004. Practical limits of resolution in confocal and non-linear microscopy. Microscopy Research & Technique, 63, 18-22
In transmitted light microscopy resolution is determined by diffraction at the sample (which cannot occur in fluorescence) and this is the famous relation given by Abbe:
r = wavelength / 2xNA.
This assumes that the condenser NA equals or exceeds the objective NA, and so long as this is the case condenser NA doesn't come into it. With a very small condenser NA (parallel illumination) the resolution is worse: r = wavelength / NA. Anything in between will give you resolution in between these extremes. Thus while condenser NA does affect the result it has much less effect than objective NA.
Unlike Rayleigh, Abbe is a 'hard' criterion - it describes the limiting case which a lens can possibly resolve, since rays from smaller detail will not enter the objective.
I hope this helps,
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) Electron Microscope Unit, 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 <http://www.guycox.net/>
________________________________
From: Confocal Microscopy List [mailto:[log in to unmask]] On Behalf Of Julio Vazquez
Sent: Friday, 20 February 2009 4:23 AM
To: [log in to unmask]
Subject: Re: Resolution for fluorescence, brightfield and luminescence
Hi Monique,
I won't attempt to give you a definite answer on this, but point you to some literature on the topic:
http://micro.magnet.fsu.edu/primer/anatomy/numaperture.html
http://www.olympusfluoview.com/theory/resolutionintro.html
http://zeiss-campus.magnet.fsu.edu/referencelibrary/pdfs/ZeissConfocalPrinciples.pdf
plus a couple of points:
for fluorescence, I believe the relevant wavelength generally used in the formula would be the average of the peak excitation and peak emission values, although I'm sure the real value would be a more complex one (if your emission as a tail in the longer wavelengths, these will spread your PSF, thus reducing resolution)
The second point that I would stress (and some will probably disagree with this) is that the definition of the minimum resolvable distance is a somewhat arbitrary one. Namely, if you are imaging two diffraction limited spots of similar intensity, their images will be two PSFs, and the minimum resolvable distance will be the distance between the center of the two PSFs so that when you do an intensity profile you see a dip in contrast that you deem is sufficient for you to know with a certain degree of certainty that you have two spots (about 75% of max peak values). Obviously, this depends also on the contrast and noise in your image, and also depends on the fact that you have a priori knowledge that you are looking at two diffraction limited spots. In a real situation, you don't necessarily know that, and therefore you criteria for "certainty" may be a bit different...
Julio.
--
Julio Vazquez, PhD
Director of Scientific Imaging
Fred Hutchinson Cancer Research Center
1100 Fairview Ave. N., mailstop DE-512
Seattle, WA 98109-1024
Tel: Office: 206-667-1215/ Lab: 206-667-4205
FAX: 206-667-6845
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http://www.fhcrc.org/science/shared_resources/imaging/
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On Feb 19, 2009, at 8:10 AM, Vasseur Monique wrote:
Dear all,
My question is:
On the same microscope, same objective, same immersion medium and same
sample, is there a difference in resolution depending of the microscopy
method I am using (fluorescence, luminescence or brightfield) since the
lightpath is not the same?
Is it correct to consider the following?
For brightfield: r = (1.22 * illumination wavelenght)/(NA objective +
NA condenser)
For fluorescence and confocal: r = (0.61 * excitation (?) wavelenght) /
NA objective
For luminescence: r = (0.61 * emission (?) wavelenght) / NA objective
Thanks in advance,
monique
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