[Leica] PIXEL PITCH SIZE

[jean.louchet at gmail.com (Jean Louchet)]

George,

You are right to point out the fact that on most serious cameras the pixel
size is somewhere between 5 and 10 microns. There is a physical explanation
to this.

ZVisible light wavelength is spread between (roughly) 0.4 and 0.7 microns.
Lenses do have both geometrical optical aberrations and diffraction that
limit their resolution.


Again in very rough terms, geometrical aberrations are greater at large
apertures, inversely proportional to the inverse of the f-number. Technology
may help reduce them (better glass with higher refractive indexes and less
dispersion, more complex designs, aspheric elements etc.) to a certain
extent - we all know Leica are very good at this.
On the other hand, diffraction can't be avoided, it is a physical law.
Parallel light coming through a hole (here, the diaphragm) in a "perfect"
lens will draw on the film or sensor, not a single point as we woulod like
it, but a "diffraction pattern" that looks a bit like the circles when one
drops a stone into a lake. The main spot, the central diffraction pattern
has a diameter equal to 1.22*f*lambda/d where f is the focal length, lambda
the wavelength and d the diaphragm diameter. As the f-number "n" equals f/d,
the diffraction diameter is 1.22*n*lambda.

As lambda is not a single value but is spread between 0.4 and 0.7 microns,
the diffraction pattern is really ugly with colour fringes on its sides and
the effects of diffraction are still visible and annoying inside a circle
with diameter approx. 2*n*lambda. As lambda is around 0.5 microns, this
means the diffraction pattern diameter will be about 2 microns at f:2l;  4
microns at f:4,  etc.

As the actual blur pattern is the addition of the effects of diffraction to
those of geometrical aberrations, and as it is very expensive to correct
geometrical aberrations,in most lenses the blur diameter is a convex
(parabola-like) curve with its minimum (= best sharpness) a couple of
f-stops above full aperture- the good old Nikon 1.4/50 had its optimum at
the centre of the image, at about f:5.6. Top lenses like the recent Leica
ones have their optimum very close to full aperture (and this is at a
cost!). All in all, one can safely say that the best blur circle diameter of
a given lens, measured in microns/micrometers, is equal to about twice its
maximum aperture.

This is why with a top-of-the-range lens with aperture 2.8 it is wise to
choose a pixel size around 6 microns. Quid erat demonstrandum :-)

By the way, some P&S cameras are sold as 12 Megapix. Their sensors are often
about 4.5 x 6 mm large . This means the pixel size is 1.5 microns, which is
totally ridiculous - even worse since most of them use high-factor zooms
that go with even more aberrations and low maximum aperture. Actually there
can't be more than 0.7 MPix useful in these cameras! All the rest is just
redundent data.

On the other hand, a pocket camera like the D-lux 4 uses a lens with a very
small zoom factor (hence low aberrations) , a high max aperture (hence low
diffraction) and ... I don't remember its sensor size but here advertising
10 MPix looks like it makes sense.

If I had to draw a conclusion, it is that what matters most of all is the
sensor size. Megapixels don't mean anything if the sensor is too small.

Jean