Pixel Array Size Needed to Replace Photomicrographs on Film
||Ted Clarke, Scientific Photographer and Instrument Maker
Some of you may have read previous articles by me
in “Microscopy Today” and know that I am a strong proponent of digital
imaging for photomicrographs and photomacrographs. I require that the
digital images match the resolution and field size of traditional film
images, with the 4X5 Polaroid film most commonly used in metallurgical
laboratories where I worked before early retirement. My development of
an affordable universal student microscope for home microscopy resulted
in a need for color digital images that would meet my requirements at
a reasonable cost. This need was met by recording on 35 mm film with subsequent
scanning of selected film images to a Kodak Master Photo CD. More recently
I purchased a CanoScan FS2710 film scanner for digitizing my family’s
collection of slides and negatives for saving on CD’s. This article will
review how I arrived at my requirements and how well they were met by
digital cameras and by film scanning.
The definition of the spatial resolution of the microscope
begins with the diffraction pattern image of two nearly adjacent point
sources of light formed through a circular aperture. The point sources
are separated in object space so that the first minimum of one pattern
coincides with the central maximum of the other diffraction pattern.
This is the Rayleigh criterion of resolution. The image of these two point
sources is the sum of the two pattern intensities as shown in Figure
Recording a straight line series of overlapping Airy discs at the
Rayleigh limit with a CCD would require at least two pixels per Airy disk
with the pixels centered on the central maximum and first minimum corresponding
to a pixel size of one fourth the Airy disc diameter. The delta Y separation
in the image can be related back to the separation of the point sources
in object space through the application of Abbe’s sine condition for a
lens free of spherical aberration; this is the objective lens resolution
given in Figure 2.
click image to enlarge (125K)
Diffraction pattern image of two closely spaced point sources of
light just resolved.
click image to enlarge (105K)
Equation for resolution with sample calculation.
The recording of photomicrographs requires consideration
of the field size limitations of the microscope. The compound microscope
optics produce an intermediate image which was conventionally enlarged
for viewing with a 10X eyepiece and projected with 10X enlargement for
recording on 4X5 film or with 2.5X enlargement for recording on 35mm film.
Until recently the intermediate field size was limited to about 18mm.
Modern research microscopes may now have an intermediate field size as
large as 26mm in diameter as shown in Figure 3. The
size of the rectangle in the intermediate image enlarged to form the photomicrograph
is important in determining the physical size of the CCD array and relay
lens magnification for digital recording. The intermediate field size
traditionally recorded on 4X5 film is an 8.9X11.4mm rectangle as shown
in Figure 3. Recording a 17.8X17.8mm square format image
from the 26mm intermediate image diameter would make good use of the modern
optics when necessary.
FINAL PRINT RESOLUTION
Resolution of the final photomicrograph is rarely
mentioned in quantitative terms. The viewing and recording optics of
the light microscope have been consistant with Abbe’s definition of usefull
magnification, which is related to the resolving ability of normal vision
when the photomicrograph is viewed from 250mm. Images from the lower
power objectives generally meet an Abbe magnification criterion of 500X
the NA of the objective. An Abbe criterion of 1000X the NA is commonly
used with the highest power objectives so that the finest detail resolvable
by the objective can be easily seen when higher NA is not available.
Images from the lower power objectives place more demand on the resolution
of the film or CCD, as indicated in the analysis given in Figure
4. Assuming a traditional 10X enlargement of the intermediate
image to achieve photomicrograph resolution of between 6 and 3 line pairs
per mm, the intermediate image resolution ranges between a corresponding
60 and 30 line pairs per mm.
click image to enlarge (138K)
Intermediate image field size comparison of modern with older microscope
technology and the rectangular field portion traditionally recorded
on 4X5 film.
click image to enlarge (155K)
Derivation of photographic print resolution from Abbe’s criterion.
PIXEL ARRAY SIZE REQUIREMENT
A minimum pixel array size that is needed to achieve
6 line pairs per mm resolution in the image area of a 4X5 Polaroid film
print is derived in Figure 5. The calculation agrees
well with the now widespread use of 1280X1024 through 1600X1200 pixel
CCD cameras for scientific imaging. The calculation assumes that the
three-color values for each pixel are not interpolated as with consumer
product cameras having a color mosaic filter pattern over the pixels,
which reduces spatial resolution by at least 30%. Non-interpolated pixel
values can be obtained by many approaches. The most common non-interpolated
color capture is by sequential capture of red, green and blue images using
a color filter wheel or tunable liquid crystal filter. Film scanners and
some color digital cameras record the image by scanning the optical image
with a red, green and blue filtered trilinear array.
Estimate of minimum pixel array size to match the resolution of
a Polaroid 4X5 film print recorded with an Abbe magnification of
500 times the NA of the objective.