At the roots of the
electronic comunnications industry is Claude Shannon's ideas
on information theory. His classic equation defining the
transmission capacity C of a data channel is,
C = W log2(SNR+1)
C the data capacity is usually measured
in bits per second. The photographic equivalent is image
detail. This includes both the actual numbers of pixels
you see in an image and their quality or tonality. A color
image has more information than a B&W image and as such
requires more capacity to capture and display.
W is the bandwidth of the channel
in hertz. This corresponds closely to the optical 50% MTF
frequency f50. The higher the MTF 50, the higher the perceived
image sharpness. Lenses, electronic image sensors, film
and even printers have their own MTF
SNR is the signal-to-noise ratio
. Film grain is the film equivalent of electronic noise.
SNR is difficult to measure in the world of film photography.
Kodak uses a system it calls print grain index to measure
grain. The SNR of a photo depends on the overall range of
luminosity in an area of the photo and the size and luminosity
range of the grain in that area. SNR is highest, in contrasty
detailed areas, like those seen in the B&W MTF currve
you see on the left. It is lowest, and hence noise/grain
is most visible, in smooth areas like the cloudless blue
skies of a desert landscape image.
of scanned images by R.N.Clarke has shown that if MTF
was the only factor effecting image quality it would take
about 12 megapixels for a digital camera to equal 35mm photos
shot with a fine grain modern film. However noise/grain
effects the overall quality and plays an important role.
These relationships led my friend Norman
Koren to make the following conjecture which I call
IQ = W log2(SNR+1)
Perceived image quality, IQ is proportional to total information capacity, which is
a function of both W, which
is the image visual capacity in one dimension (sharpness)
and noise (grain).
W = MTF 50
* sensor size
the product of MTF 50 and image sensor size. MTF 50 is measured
in line pairs/mm and the sensor or film size is measured
in mm. If the image is recorded on film, the film size replaces
the size of the sensor. MTF 50 can
be calculated for the camera system by using a combination
of lens data, sensor or film data, and a computer based
mathematical model. SNR depends
on the luminosity range of the pixels in the image,usually
256:1 for 8 bits per color RGB pixels and the noise/grain
as measured in the image.
The image quality of digital cameras will equal 35mm with
fewer pixels than predicted by MTF alone because digital
cameras with large sensors--all the pro-level SLR's-- have
much less noise.
Skies in digital camera images are virtually grainless.
That makes a big difference in perceived quality. Many photographers
will perceive images from the current generation of high-end
6 megapixel cameras-- the Canon EOS D60 and the Nikon D100--
to be equal to 35mm. We are there now! On the other hand
digital cameras with very small sensors --the point and
shoot variety-- have significant noise, even if they have
the same number of pixels.