Re: How many pixels?

On Wed, 19 Apr 2006 17:08:17 GMT, "NoSpam" <NoSpam@xxxxxxxxxxx> wrote:

Hi,

There have been a few postings recently which made me think about the
maximum
useful number of pixels in a microphotograph. I will present some numbers
and my
conclusion is that about 2 to 4 Megapixels in a digital camera will do
justice to
the capabilities of any light microscope.

It is possible that I have overlooked something and that my conclusions are
incorrect.
Please let me know what you think.

The smallest separation observable with a light microscope is given by
wavelength di-
vided by the product of 2 times the NA. For a wavelength of 0.5 microns and
a NA of
about 1.0 the minimum resolvable distance would therefore be 0.25 microns.
Objectives
with a NA of about 1.0 magnify about 100 times.A resolution element of 0.25
microns
in the object plane will therefore appear with a 25 micron linear size at
the exit pupil
of the objective. A typical value for the diameter of this pupil is 20mm or
about
20 000 microns.There will therefore be 20,000microns/25microns or 800
resolution
alements along a given diameter in this pupil. If we square this number we
get the
approximate number of resolved pixels in the exit pupil as 0.64 Megapixels.
These are
all the resolved picture elements which a camera has to record. Further
magnification
or reduction in size of the exit pupil will not change this fundamental
requirement for
taking a picture at 100x linear magnification with a NA of 1.0.

If instead of a 100x objective with a NA of 1.0 we use a 10x objective with
a NA
of 0.25, then the linear size of a resolved object element in the exit pupil
decreases
by a factor of [(100/10)x(0.25/1.0)] or by 2.5. The total number of pixel in
the exit
pupil will then be 2.5x2.5=6.25 as large as the above number of 0.64
Megapixels
and about 4 Megapixels will be required.

If these consideration reflect reality then cameras with more than 4
Megapixels
will not be needed for microphotography. For high magnification half that
number
may be all that is needed.

I am interested in your comments.

G.R.


What about final magnification at the camera sensor? I.e., if the
oculars are 10X and the objective is 100X, the final mag is 1,000X.
This assumes that the camera is parfocal with the oculars (which can
be done).



Gary Gaugler, Ph.D.
Microtechnics, Inc.
Granite Bay, CA 95746
916.791.8191
gary@microtechnics dot com
.

Relevant Pages

  • Re: How many pixels?
    ... approximate number of resolved pixels in the exit pupil as 0.64 Megapixels. ... taking a picture at 100x linear magnification with a NA of 1.0. ... If these consideration reflect reality then cameras with more than 4 ...
    (sci.techniques.microscopy)
  • How many pixels?
    ... about 1.0 the minimum resolvable distance would therefore be 0.25 microns. ... approximate number of resolved pixels in the exit pupil as 0.64 Megapixels. ... taking a picture at 100x linear magnification with a NA of 1.0. ...
    (sci.techniques.microscopy)
  • Re: How many pixels?
    ... useful number of pixels in a microphotograph. ... approximate number of resolved pixels in the exit pupil as 0.64 ... taking a picture at 100x linear magnification with a NA of 1.0. ... match the size of the resolution elements formed in that pupil to the ...
    (sci.techniques.microscopy)
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