Search the CONFOCAL archive at
http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal

Hi Julio,
 
I was trying to avoid a re-initiation of the disussion about sampling on this list short time ago, however, if you use the Nyquist calculator kindly provided by SVI on their wiki (no commercial interest) 
http://support.svi.nl/wiki/NyquistCalculator, you come up with very different (smaller) numbers for the sampling compared to the 'optimal' numbers of Zeiss. The 'optimal' is suited to avoid 'gaps' between samples, but is undersampling according to Nyquist. 
I wish it wasnt, bacause as you mention, sampling at Nyquist rate really can take very long, so you have to trade signal and rely on deco to deal with very noisy input pictures (which fortunately it does). But missing the oportunity to make use of the knowledge about the bandwidth of your aquisition device -and to filter the signal accordingly- really sounds to me like be a bad idea.
And if you doubt you need the high frequencies because you suspect there is not enough contrast, why not using a lower NA lens instead?
 
Cheers, jens

________________________________

Von: Confocal Microscopy List im Auftrag von Julio Vazquez
Gesendet: Mi 23.05.2007 20:25
An: [log in to unmask]
Betreff: Re: resolution when pixel size is limiting


Search the CONFOCAL archive at http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal 

Hi Jens,  

Please correct me if what I say below is inaccurate. My understanding is that Zeiss calculates the lateral resolution as 0.51 lambda(ex)/NA for pinholes set at 1 Airy unit or higher, and 0.37 lambda (average)/NA for pinhole settings much smaller than 1 Airy unit, with a grey zone in between.  Under those conditions, their "Optimal" image size setting results in pixel dimensions that are half the resolution given by their formula. This value does not depend on the pinhole setting.

They also calculate the axial full-width at half-max  by a complex formula:

FWHM(axial) = Square root of [(0.88* lambda(em)/(n - sqrt(n^2 -NA^2)^2 + (sqrt(2)* n* Pinhole/NA)^2]

I believe their recommended "optimal" z section thickness is half this number. This value depends on the pinhole setting.


All the formulas are detailed in the Zeiss publication: Confocal Laser Scanning Microscope Principles. The formula for the Axial FWMH is formula 4 on page 11.  I would argue that for most purposes, Zeiss'  "Optimal" settings fall somewhere close to Nyquist, and are probably a good start point for setting up one's image and stack parameters. Other systems (DeltaVision for widefield, or our old Leica confocal) recommend significantly smaller z steps. In any event, the Zeiss paper highlights the complexities of calculating "resolution" on a confocal system.

As a commentary, I agree the Zeiss "optimal" settings are not strictly "Nyquist", but I would also argue (and here I am venturing well beyond my comfort zone) that "Nyquist" was developed originally for other purposes than microscopy, and there is a fair degree of arbitrariness to it. Basically, if you sample a theoretical periodic signal, the more you sample, the closer you will get to representing the actual signal. The value of 2.4, in my somewhat simplistic understanding, is just a compromise where you get a fair representation of the sampled signal, while minimizing resources (data storage space, processing time, etc...), but at 2.4 samples per cycle, you only get a crude representation of the original signal (although you do preserve the frequency, which you wouldn't if you sampled at 2x or less).  On the other hand, in microscopy, a number of factors impose a limit beyond which sampling will start producing more losses and no substantial gains, and I would be hard pressed to come with an "optimal" theoretical value.  In practice, it will depend on the sample and the type of information the user needs to record...

--
Julio Vazquez
Fred Hutchinson Cancer Research Center
Seattle, WA 98109-1024

[log in to unmask]
http://www.fhcrc.org <http://www.fhcrc.org/> /



On May 22, 2007, at 11:46 PM, Rietdorf, Jens wrote:


	Search the CONFOCAL archive at http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal 
	Julio,
	 
	just a minor comment; hitting the 'optimal' on the Zeiss LSM does not produce Nyquist in either xy or z direction.

	regards, jens