> > That is what MTFs (Modulation Transfer Function) are for. The MTF for
> > optical systems can be either computed (see Canon's EF Lens Work) or
> > measured.
>
> Yes I know this, it is what I was referring to without calling it MTF -
> and my point was that Nyquist renders MTF incalculable for pixel-based
> *systems*. It is also difficult to measure sensibly, as the position and
> orientation of a conventional MTF target relative to the pixel locations
> affects the amount of aliasing and consequent artefacts.
>
I'm not sure exactly what you mean about the Nyquist limit making the MTF
incalculable or why you emphasize systems. One can still measure the MTF
for an optical system, even above the Nyquist limit. A straight foreword
method for measuring MTF uses a sinusoidal pattern in front of the system
and measures its response out the back. If you want to measure the MTF
above the Nyquist frequency the only complication is that the output signal
is alaised to a lower frequency.
You are correct that the phasing of the sinusoid relative to the pixels
affects the response of the system. That is why modern MTF targets are
slightly tilted. For example, the test target for
ISO 16067-2
Photography - Electronic scanners for photographic images -
Spatial resolution measurements: Part 2 Film scanners
looks like:
<<ISO 16067.jpg>>
The wedge shaped resolution targets are specifically designed for visual
estimates of resolution. The tilted edges are used for measuring MTF. As
stated in the introduction to the draft:
"The edge SFR measurement method described in this standard uses a computer
algorithm to analyze
digital image data from the film scanner. Pixel values near slanted vertical
and horizontal edges are
used to compute the SFR values. The use of a slanted edge allows the edge
gradient to be measured
at many phases relative to the image sensor photoelements, so that the SFR
can be determined at
spatial frequencies higher than the Nyquist limit. This technique is
mathematically equivalent to a
moving knife edge measurement."
>
> About all you can determine easily is the theoretical MTF
> possible at the CCD, according to the Nyquist limit, which tells you about
>
> as much about scanner system performance as an MTF test of film does about
>
> a camera/film system. We can't rip the lens out of these things and test
> them separately either.
>
Again, I am not sure what you mean by this. When we place a test slide in a
scanner and measure the scanner's MTF we are measuring the MTF for the
entire system - optics, CCD, and electronics. Knowledge of the CCD's MTF
provides us with an upper bound for what the MTF can be.
>
> There are special resolution targets available for empirical determination
>
> of pixel-based MTF - eg for targets made for
> scientific use - but I am not aware of any which are suitable for 35mm or
> other filmscanners. Sinepatterns would doubtless make one for a few
> thousand $$, but that is somewhat beyond my means;)
>
Most of the patterns Sinepatterns makes are available off the shelf in 2
inch squares and are suitable for testing 35 mm film scanners. But the
costs start around US$700. I have taken their idea for a composite pattern
and made my own pattern that can be used to measure the MTF of systems at
frequencies from 0.5 lpm up to 220 lpm. Unfortunately the slide belongs to
work. :-( However, the same digital pattern can be printed out and used
for testing cameras - I have not done this yet but plan to some day.
