Posted by
Daniel James White on
Mar 18, 2011; 9:07am
URL: http://imagej.273.s1.nabble.com/Re-JACoP-optics-and-sampling-basics-tp3685364.html
Dear Gauri and Leoncio,
On Mar 18, 2011, at 5:00 AM, IMAGEJ automatic digest system wrote:
>
> Date: Wed, 16 Mar 2011 23:11:30 -0500
> From: "Vergara, Leoncio A." <
[hidden email]>
> Subject: Re: JACoP
>
> If I understood your question, this is very basic knowledge.
>
> xy calibration is asking for the dimension of the pixels in your images. Usually pixels are square.
Thats not quite true.... pixels usually lie on a square grid (or could also be some other regular or non regular pattern)
but this does not make them intrinsically "square"
Pixels in a digital image are "point" samples, existing at some definite spatial place.
(Pixels on a CCD camera chip ARE little squares.. but that is something totally different
single point scanning confocals have scanning mirrors and a "point" detection - no CCD camera involved there)
The "shape" of a pixel is defined by the point spread function (PSF) of the optics, not by the distribution of the points on the detection grid.
See the famous and illuminating note by Alvy Ray Smith:
A Pixel Is Not A Little Square, A Pixel Is Not A Little Square, A Pixel Is Not A Little Square! (And a Voxel is Not a Little Cube). Microsoft Technical Memo 6, 1995
http://www.alvyray.com/memos/6_pixel.pdf> Your confocal software should be able to tell you the pixel size. Pixel size depends on the magnification but is mainly determined by the scanning pattern, number of pixels in x and y and zoom factor.
>
> z calibraton is basically the z-step you used when capturing a z-series (aka z-stack) in your confocal. If you are only capturing single planes, you can probably ignore that dimension.
>
> the x, y and z dimensions determine the size of the voxels in volumetric datasets.
Nearly... these are the distances "between" the point samples in xyz space.
Not the imaginary and non existent length of the edge of the square that a pixel is not.
The "size" or "shape" of the pixel or voxel is defined by the point spread function.
If the spatial sampling is set up correctly on a confocal to get all the spatial info that the lens can resolve,
then there should be is overlapping information in adjacent voxels,
according to the famous
Nyquist-Shannon sampling theorem.
http://en.wikipedia.org/wiki/Nyquist-Shannon(especially see fig 5 and fig 6 of that wiki page to get the point. )
This is all basic stuff that you need to know in order to operate a confocal properly.
In essence, pixel separation should be no less than 2.3x smaller then the optical resolution - as defined by the Rayleigh Criterion and Abbe's famous equation.
which described that the resolution is proportional to the wavelength of light and strongly dependent on the numerical aperture of the lens (the second number written on it)
On a single point scanning confocal the Numerical Aperture of the lens (NA) is by far more important than the magnification (Mag only sets the max field of view).
NA defines the "resolution" of the lens - it sets the spatial frequency upper limit... the smallest separation of features that can make it through the lens to the detector.
Not the smallest thing you CAN see... you can see single molecules if they scatter or emit light...
here we are talking about the distance between 2 features/objects,
where they can be resolved as 2 distinct features.
Magnification is cheap and easy - Numerical aperture is hard and expensive.
cheers
Dan
Dr. Daniel James White BSc. (Hons.) PhD
Senior Microscopist / Image Visualisation, Processing and Analysis
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Max Planck Institute of Molecular Cell Biology and Genetics
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