GUY COX WRITES:
>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.
 
The intention of my remarks was not to restart the Confocal/Widefield-
deconvolution debate but merely to point out that the term "spatial
resolution" is not really very well defined in the latter case and can be
arbitrarily high (small?) if the the S/N ratio is "good enough". (ditto
deconvolution applied to confocal data)
 
It is also true that, in real microscopes, the "shift-invariance condition"
does not hold.  At the very least, the PSF function changes with distance
off the optical axis, and usually also with depth into the specimen. (You
can compensate spherical aberration only in homogeneous media.  Cells that
are prepared in such a way that they still produce contrast in DIC or
phase-contrast do not qualify.)  In real measurements, these PSF errors may
place a practical limit on the "resolution" obtainable even before S/N
does.  In this case, the resolution obtained is more a measure of the
specimen preparation method than of the capabilities of the imaging
technique. This is less true of the Blind Deconvolution approach but even
here, some of the assumptions that must be placed on the shape of the PSF
in order not to require an "infinite amount" of computer time, may not be
justified (i.e. that even if the PSF is initially unknown, it is at least
constant, or alternatively one may assume that the way it varies within
each planar image is known and this may not be true etc.)
 
In general, I agree with the comment about the differences that
characterize the abilities of the two techniques to distinguish single or
double horizontal planar features.(Remembering the role of S/N, the
contrast is even more one-sided if one considers a planar NON-fluorescent
feature in a sea of fluorescence!)  However, the story does get a bit
tricky in terms of defining the "perfect" WF microscope in this case:
Actual WF users often employ very small settings of their field apertures
to illuminate only the area of immediate interest at the level of the focus
plane.  This makes the WF microscope "semi-confocal" in its operation
because now the intensity of the exciting illumination striking a planar
feature (within the field of view) DOES drop off as one focuses away from
this plane.
 
I also agree that any comparison of the two techniques can only be done
usefully if the geometry, staining contrast and anti-fade properties of the
specimen are carefully defined: something that it is very hard to do.
 
                   ***************NEW ADDRESS**************
Prof. James B Pawley,                                        Ph.  608-263-3147
Room 1235, Engineering Research Building,         NEW NEW NEW FAX 608-265-5315
1500 Johnson Dr. Madison, Wisconsin, 53706.
[log in to unmask]