Jim Pawley wrote:
 
>if we assume that the imaging process is "Linear and
>Shift-invariant" (conditions for deconvolution as per Peter Shaw:
>Conditions met in fluorescent imaging, widefield or confocal), in the TOTAL
>absence of noise (statistical or otherwise), using infinitely small pixels
>(you can never get around Nyquist) and given PERFECT knowledge of the
>point-spread function, ANY set of 3D image data can be deconvolved (using a
>perfect computer!) into one, and only one object-function i.e. the
>processed image could have only one solution and hence the "spatial
>resolution" would be infinitely high.
 
>There are, of course, "infinitely many" snags: leaving aside bleaching,
>collecting the image would take an infinite time, ditto for recording the
>PSF etc. etc.
 
>How does this work?  Well, the "shift-invariant" part of the condition says
>that any image is just made up of point objects, each of which will be
>blurred in the same way (Tim Holmes' Blind Deconvolution/Minimum Entropy
>Method doesn't assume that you know the PSF but still assumes that there is
>one.).
 
 
The problem is that shoft-invariance does not, in fact, hold!
 
A simple reductio ad absurdum:
 
Consider a specimen consisting of a fluorescent plane extending across
the entire field of view of the microscope.  A widefield microscope
will not (assuming perfection in everything, as above, of course) see
any change in intensity wherever it is focussed; it cannot obtain
any information about the location of the object.  If there are two
such planes it cannot tell them apart.  The same applies to a solid
object - for example a piece of the uranyl glass that Jim uses, or
the sign-makers' fluorescent plastic that is my cheapskate alternative.
 
A confocal microscope, on the other hand, *can* distinguish our single
or double fluorescent planes, and will identify them *almost* as well
as it would points.
 
Resolution (especially depth resolution) depends in any microscope
on what type of object you are imaging.  However this dependence will
be different in deconvolved wide-field images vs confocal images,
so ultimately any resolution comparison must depend on defined
objects (usually points) and cannot be extrapolated to other types
of object.
 
                        Guy Cox