Re: How many pixels?

See my comments in-line.

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.

In English: It is called photomicrography, not microphotography, which is the generation of very small images.

....

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.

More or less. d = 0.61*Lambda/NA = 0.31um if the condenser's NA is at least 1.0 and using your example above.

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.

Yes. D = d * magnification of objective = 31um.

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.

Yes. FOV / D = 645 lines along its diameter for the above example.

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.

No. The active pixel size must be half of the smallest seperation of your lines (Nyquist theorem). Otherwise you under-sample your image. In this example, you need an active pixel size of 31/2um = 15.5um. And to resolve 675 lines you need 1350 pixels along one dimension => 1,822,500 pixels (WITHOUT BAYER FILTER or in green light) to capture the entire image information. Otherwise you need to multiply this by the square root of 2.

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.

You can repeat this easily for other microscope objectives. Try an APO lens that offers an NA of 0.16 or 0.20 at a magnification of 4x and you need way more pixels.

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.

Yes for Achromats and a FOV of 18 to 20mm. But the answer is not correct in general. 4 MPixels is not enough to cover all when a low-power APO lens is used. Especially not when a Bayer filter is used to record a color image. BTW, most newer plan lenses are corrected for 25mm FOV or higher.

Gregor

.

Relevant Pages

  • Re: Dark adaptation on exit pupil size
    ... >has on exit pupil size. ... >of average exit pupil size with age, but have not run across anything ... >that discuss the increase in exit pupil size with dark adaptation. ... factor of several thousand over the photopic eye. ...
    (sci.astro.amateur)
  • Re: eyepiece limits
    ... > However, Al says, "Large secondaries also limit your visual performance ... > the secondary when the exit pupil exceeds the size of the pupil of the ... so you don't want to use an eyepiece yielding too large ... > an exit pupil for that reason. ...
    (sci.astro.amateur)
  • Re: Dark adaption and pupil size - an experiment (longish)
    ... >>once your eye's pupil exceeds the exit pupil of the telescope, ... >>easier to center the eye on the exit pupil. ...
    (sci.astro.amateur)
  • Re: Dark adaption and pupil size - an experiment (longish)
    ... >once your eye's pupil exceeds the exit pupil of the telescope, ... >easier to center the eye on the exit pupil. ... telescope is larger than the eye's pupil, ...
    (sci.astro.amateur)
  • Re: eyepiece limits
    ... essentually "maxed-out" your brightness if you go beyond the pupil size of the ... However, Al says, "Large secondaries ... "visiblity" of the dark spot of the secondary when the exit pupil exceeds the ... large an exit pupil for that reason. ...
    (sci.astro.amateur)