In article , Fernando Gonzalez Gentile <fgnzalez@xxxxxxxxxxxxxxx> writes
on 23/07/2003 20:58, Thomas Heide Clausen at omlist@xxxxxxx wrote:
Uhmm...I came across this site myself:
http://studweb.studserv.uni-stuttgart.de/studweb/users/mas/mas12462/OM/
MTF/mtf
-overview.html
Hi Thomas,
Could you bring a simple explanation about what is this modulation transfer
function? Just to understand the concept involved and the graphs...
The Modulation Transfer Function (MTF) of an optical system is a measure
of its ability to reproduce information of different resolutions. It is
a bit like the frequency response of an audio system, such as a
microphone or recording tape, the only difference is that instead of
audio frequencies it plots the response of "spatial frequencies".
Spatial frequencies are just sinusoidal intensity profiled patterns of
light and dark extending along a single axis, extending off to infinity
(or at least to the field coverage of the lens) in the orthogonal axis.
If there are 10 sine cycles through white and black every millimetre
then that corresponds to a spatial frequency of 10cy/mm. These look
just like bar patterns on a resolution chart, but they are sinusoidal
intensity rather than square wave intensity. The square intensity
profile introduces higher harmonic spatial frequencies.
Obviously viewing distance of these patterns is important so, to avoid
confusion, the horizontal axis of the MTF chart is usually scaled as
cycles per unit of distance at the focal plane or as cycles per unit
angle, such as degree or milliradian, in object space or normalised to
cycles per picture width. The vertical axis is just the contrast which
that particular spatial frequency is reproduced by the optical system,
normalised to unity at 0cy/unit so that overall transmission is not
included.
There is a well defined MTF limit for any optical system, the
diffraction limit of the system, and no practical optical system can
exceed this. This curve not only has an upper limit of contrast for
each spatial frequency, but a limiting spatial frequency which cannot be
exceeded. How close you can get to the diffraction limit is the
difference between a good lens and a bad one. Only two factors
influence the diffraction limited MTF - the wavelength of the light used
in the measurement and the aperture of the optical system. Hence you
can often see several different MTFs for a single lens - even a perfect
one, covering MTF at different f/#s and light wavelengths. For a
practical lens, the usual curves show the MTF at different points in the
field and with the sine patterns aligned radially or tangentially to the
optic aperture.
If you are interested in comparing practical MTF curves with perfection
then the following formula will produce the diffraction limit curve for
any lens with a circularly symmetric aperture:
MTF = (2T - sin(2T))/pi
T = acos(W.f.s) when w.f.s <= 1 and 0 when W.f.s > 1
where:
f = f/# of the optical system
W = wavelength of the light (in mm)
s = spatial frequency in cy/mm at the focal plane
T is in radians
You should end up with a curve which is almost triangular in shape, with
the MTF decreasing as spatial frequency increases and then flattening
out slightly as the MTF falls to a few percent, before cutting off
completely.
You can see from this that a lens which is f/11 cannot resolve any
spatial frequencies which are greater than 170cy/mm in green light,
which is one reason why you won't find f/11 on many digital cameras
which have 3um pixels - 170cy/mm is just under 6um per cycle, and you
need two pixels to reproduce a cycle. So those mega pixel cameras which
do offer an f/11 option either have large pixels (as in the professional
and expensive ones) or the picture you get at f/11 actually contains no
more information than one from a nominally lower resolution camera, or
they are using a special aperture technique. Similar things apply on
film of course, which ultimately limits the performance that can be
obtained from 35mm film and why few 35mm lenses go beyond a normal
aperture of f/16-22 - that's pretty much the resolution limit of film.
There are techniques to overcome this both with film and digital lenses,
such as central spots etc., but they simulate higher f/#s with a large
aperture rather than the actual aperture corresponding to the focal
length. Usually an ND filter gives better results, because the central
sot gives unusual bokeh, just like a mirror lens, at normal apertures.
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers
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