Re: JACoP - optics and sampling basics

[Daniel James White]

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
Light Microscopy and Image Processing Facilities
Max Planck Institute of Molecular Cell Biology and Genetics
Pfotenhauerstrasse 108
01307 DRESDEN
Germany

[phone] (German Mobile)
[phone] (Work phone at MPI-CBG)
[phone] (Fax MPI-CBG LMF)

http://www.bioimagexd.net  BioImageXD
http://pacific.mpi-cbg.de                Fiji -  is just ImageJ (Batteries Included)
http://www.chalkie.org.uk                Dan's Homepages
https://ifn.mpi-cbg.de  Dresden Imaging Facility Network
dan (at) chalkie.org.uk
( white (at) mpi-cbg.de )

[Vergara, Leoncio A.]

Thanks for the detailed clarification, I am well aware, I have been doing Confocal microscopy for more years than I can confess and I have even been teaching concepts similar to what you describe in our microscopy course to graduate students for the last 5 years or so... maybe not as well as you describe... I was trying to provide a simplified answer to (what I thought) was a simple question. In most image analysis programs pixels and voxels are handled as little squares and little rectangular prisms.... in 3D reconstruction programs for geometrical calibration purposes, the z dimension of the voxel is the z-step, not the optical section thickness...

Leoncio A. Vergara MD
Assistant Director
Center for Biomedical Engineering
Assistant Professor
Microbiology and Immunology
University of Texas Medical Branch
409-750-2153 (cell)

-----Original Message-----
From: Daniel James White [mailto:[hidden email]]
Sent: Friday, March 18, 2011 4:07 AM
To: ImageJ Interest Group
Cc: Vergara, Leoncio A.; Gauri Akolkar - Kulkarni
Subject: Re: JACoP - optics and sampling basics

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
Light Microscopy and Image Processing Facilities
Max Planck Institute of Molecular Cell Biology and Genetics
Pfotenhauerstrasse 108
01307 DRESDEN
Germany

[phone] (German Mobile)
[phone] (Work phone at MPI-CBG)
[phone] (Fax MPI-CBG LMF)

http://www.bioimagexd.net  BioImageXD
http://pacific.mpi-cbg.de                Fiji -  is just ImageJ (Batteries Included)
http://www.chalkie.org.uk                Dan's Homepages
https://ifn.mpi-cbg.de  Dresden Imaging Facility Network
dan (at) chalkie.org.uk
( white (at) mpi-cbg.de )