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>An interesting point was made here by Jim Pawley:
>
>>I agree that sampling a bit higher than Nyquist never hurts,
>>especially if you deconvolve (as you always should), but I think
>>that it is a mistake to think that one can "separate" out the noise
>>by decon. I think that noise is pretty fundamental.
>
>I had always heard that if you're doing confocal microscopy, at
>least point-scanning confocal with a pinhole size of 1AU or smaller,
>that deconvolution was superfluous, because you shouldn't be getting
>out of focus light. So what is gained by deconvolution when one is
>sampling voxel by voxel?
>
>Peter G. Werner
>Merritt College Microscopy Program
Hi Peter,
This is indeed "widely assumed". However, it is beside the point. The
process of decon is applied to 3D, fluorescence microscopy data sets
for (at least) two major different reasons:
1) It removes much of the effect of out-of-focus light (if there is
any) and therefore produces a major improvement in the visibility of
structures in widefield data. For confocal data, the resolution
improvement is much less significant.
2) It effectively smooths the data out so that anything smaller than
the PSF is removed from the processed result. This is good for two
reasons:
a) The process effectively averages the intensity data of the 64-125
voxels needed to sample the central peak of the PSF, improving the
S/N by a factor of between 8 and 11.
b) It also meets the Nyquist Reconstruction Condition:
If you have 2.5 pixels between the central peak and the first zero,
you have 5 pixels across the diameter of the first-zero ring and
(about) 25 pixels will be needed to sample this blob in 2D and
(about) 125 voxels in 3D. 125 measurements just to measure the
brightness and location of one point. (The "about" has to do with how
may counts one must register in a pixel for it to be considered part
of the PSF, a PSF that will in general not be so conveniently aligned
to the pixel grid. 100 might be a good guess for a 3D PSF.)
But it is possible to "know" (measure?) the PSF independently, and
the PSF imposes constraints on the relative brightness of these 125
points. Decon is the best process of imposing this constraint onto
the measured data (For confocal, the 3D Gaussian mentioned earlier is
a good approximation to the PSF. Although it is imprecise (it has a
longer tail), if the Gaussian Laser beam doesn't considerably
overfill the objective aperture, the spot will in fact be more like a
Gaussian than an Airy disk. More to the point, the data are usually
so Poisson-Noisy, that it won't make a great difference, and it is a
lot easier to do.).
The decon process may seem to reduce image contrast (by
averaging-down the bright noise peaks) but one can compensate for
this by changing the display look-up table (contrast control) and
when you do this, you will find that the processed confocal data is
far less noisy than was the raw data. It is also free from
"impossible" features that were really only Poisson Noise excursions
usually one-pixel wide (which is about 4 smaller than the width of
the PSF, the smallest feature that the optical system can pass
legitimately.). Indeed, one should never make statements regarding
the exact shape of small structures (near the resolution limit)
recorded in confocal microscopes until the data have been
deconvolved. Nyquist would not approve.
Best
JP
--
***************************************************************************
Prof. James B. Pawley, Ph.
608-238-3953
21. N. Prospect Ave. Madison, WI 53726 USA
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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.
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