Resolution limit of image sensor

Charles Schuler wrote:
"Marc Wossner" wrote in message
ups.com...
Hi NG,

Can someone please explain to me if there is a connection between the
Nyquist sampling theorem and the resolution limit of a digital image
sensor? I mean, does it imply something like a lowest mark as far as
pixel spacing is concerned? - I´m quite new to digital photography and
keep reading about this stuff but must admit that it´s by far too
theoretical for me!

As the image detail approaches one-half the spatial sampling frequency,
aliasing starts to become a problem. Aliasing means that artifacts show up
that were not in the scene but were caused by too low of a spatial sampling
frequency or too much image detail. The fix is a blur filter (or anti-alias
filter) mounted on top of the sensor.

Which in-turn reduces potential resolution of the sensor by 30-40% or
more, depending on its "strength." This can be seen with various
cameras now.
Which is why a camera (if one existed) that shot three images through a
monochromatic CCD through red, green and blue filters would have far
greater image resolution.

Don Stauffer in Minnesota wrote:

There was much work done on this in the thirties by early TV engineers,
since in the vertical direction image tube TV and kinescopes are
"sampled" systems. Much of the work was done' experimentally, and the
guru was an engineer by the name of Ray Kell. The resulting widely
used value, now called the Kell factor, was around 0.7. That is, for a
system with N samples in a given direction (either vertical or
horizontal) one can resolve about 0.7N lines.

When we got our hands on our first CCD chip at work in the late '70s, I
did an analysis (numerical, sort of Monte Carlo) and found a value
very close to that for mosaic arrays. While it did depend a bit on
fill factor, the dependence wasn't strong. I still use 70% as a good
expectation.

Now wait a minute Don, you got me a little bit confused.
As the Kell factor can´t be the prime limiting one, because it implies
a higher resolution than Nyquist allows, does it apply on the already
Nyquist limited resolution?
I mean, Nyquist says the theoretical max resolution is half the
sampling frequency (in lines or pixels). And this value is than again
limited by the Kell factor so that the max useful resolution is about
70% of the theoretical max. - Is that right?
Now Rich states that the AA filter reduces potential resolution of the
sensor by 30-40%. Those values fit so amazingly good in the above
scheme that I wonder if the reduction is really due to the AA filter.

Mark Wossner

Marc Wossner wrote:
Don Stauffer in Minnesota wrote:

There was much work done on this in the thirties by early TV engineers,
since in the vertical direction image tube TV and kinescopes are
"sampled" systems. Much of the work was done' experimentally, and the
guru was an engineer by the name of Ray Kell. The resulting widely
used value, now called the Kell factor, was around 0.7. That is, for a
system with N samples in a given direction (either vertical or
horizontal) one can resolve about 0.7N lines.

When we got our hands on our first CCD chip at work in the late '70s, I
did an analysis (numerical, sort of Monte Carlo) and found a value
very close to that for mosaic arrays. While it did depend a bit on
fill factor, the dependence wasn't strong. I still use 70% as a good
expectation.

Now wait a minute Don, you got me a little bit confused.
As the Kell factor can´t be the prime limiting one, because it implies
a higher resolution than Nyquist allows, does it apply on the already
Nyquist limited resolution?
I mean, Nyquist says the theoretical max resolution is half the
sampling frequency (in lines or pixels). And this value is than again
limited by the Kell factor so that the max useful resolution is about
70% of the theoretical max. - Is that right?
Now Rich states that the AA filter reduces potential resolution of the
sensor by 30-40%. Those values fit so amazingly good in the above
scheme that I wonder if the reduction is really due to the AA filter.

Mark Wossner

Ah, but remember, there are two LINES per line pair or per cycle. So
the Kell factor is 40 per cent in terms of cycles or line PAIRS.

So if we have a 1000 line array, say 1000 vertical rows by whatever
columns, that says ON AVERAGE (sampled data) we can resolve about 700
lines, or 350 line pairs or cycles.

Marc Wossner wrote:
Don Stauffer in Minnesota wrote:

There was much work done on this in the thirties by early TV engineers,
since in the vertical direction image tube TV and kinescopes are
"sampled" systems. Much of the work was done' experimentally, and the
guru was an engineer by the name of Ray Kell. The resulting widely
used value, now called the Kell factor, was around 0.7. That is, for a
system with N samples in a given direction (either vertical or
horizontal) one can resolve about 0.7N lines.

When we got our hands on our first CCD chip at work in the late '70s, I
did an analysis (numerical, sort of Monte Carlo) and found a value
very close to that for mosaic arrays. While it did depend a bit on
fill factor, the dependence wasn't strong. I still use 70% as a good
expectation.

Now wait a minute Don, you got me a little bit confused.
As the Kell factor can´t be the prime limiting one, because it implies
a higher resolution than Nyquist allows, does it apply on the already
Nyquist limited resolution?
I mean, Nyquist says the theoretical max resolution is half the
sampling frequency (in lines or pixels). And this value is than again
limited by the Kell factor so that the max useful resolution is about
70% of the theoretical max. - Is that right?
Now Rich states that the AA filter reduces potential resolution of the
sensor by 30-40%. Those values fit so amazingly good in the above
scheme that I wonder if the reduction is really due to the AA filter.

Mark Wossner

If you look at the images from Leica's M8 (no low-pass filter) and
compare them to another camera with the same pixel count, you'll see
what I mean. Sharpest raw images I've ever seen, except for perhaps
Canon's 1DsMkII.
Of course, you pay for this with moire popping up every so often. The
Leica uses no AA filter, Sony's entry level 10 megapixel DSLR uses a
weak one and less noise reduction and it resolves better than the other
10 megs out there and even 12 megs.
http://www.dpreview.com/reviews/sonydslra100/page29.asp

"Marc Wossner" writes:
Just to check my understanding: If I have a sensor with 3034 horizontal
pixels and a spacing of 7,8 µm it can resolve:

max frequency = scan frequency/2

= 1517 lines in this direction
= structures wich are not closer than 3,9 µm to each other

Is that correct?

Partly, though you have to be careful about terminology.

With 3034 pixels per row in the sensor, its theoretical maximum
resolution is 1517 "line pairs" per image width. Using line pairs (or
sine wave cycles, which are similar) in this way is pretty much
universal in the world of film cameras and lenses. But the video world
tends to measure resolution in "lines", counting black and white
separately, instead of line pairs. So your maximum resolution could
also be 3034 "lines", as long as you are clear that this is not cycles
or line pairs.

On the other hand, to resolve two structures as distinct, they generally
need to be spaced at least 2 pixels apart, so they can be separated by
one pixel of a different colour. So you shouldn't count on resolving
things closer than about 15 um with this sensor. (There are special
cases when the things you are looking at can be closer than that - e.g.
when you're trying to resolve stars which are point sources).

Dave

"Rich" writes:

As the image detail approaches one-half the spatial sampling frequency,
aliasing starts to become a problem. Aliasing means that artifacts show up
that were not in the scene but were caused by too low of a spatial sampling
frequency or too much image detail. The fix is a blur filter (or anti-alias
filter) mounted on top of the sensor.

Which in-turn reduces potential resolution of the sensor by 30-40% or
more, depending on its "strength." This can be seen with various
cameras now.
Which is why a camera (if one existed) that shot three images through a
monochromatic CCD through red, green and blue filters would have far
greater image resolution.

No. A monochrome camera, or a colour camera that uses 3 successive
exposures through a filter, or one that uses 3 sensors and a
beamsplitter, will still suffer from aliasing artifacts. All of these
camera designs still need an anti-aliasing filter to avoid aliasing.

These designs are not vulnerable to misinterpreting fine detail
(incorrectly) as colour, so leaving out the anti-aliasing filter is not
so visibly awful as doing this with a Bayer-sensor camera. But you will
still get moire effects and incorrect detail due to aliasing.

Dave

I´m sorry Don, but there seems to be a serious misunderstanding on my
side as far as the resolution limits by Nyquist and by the Kell factor
are concerned. Is my proposed scheme correct or am I missing something
interely?

Marc Wossner


Marc Wossner wrote:
Don Stauffer in Minnesota wrote:

There was much work done on this in the thirties by early TV engineers,
since in the vertical direction image tube TV and kinescopes are
"sampled" systems. Much of the work was done' experimentally, and the
guru was an engineer by the name of Ray Kell. The resulting widely
used value, now called the Kell factor, was around 0.7. That is, for a
system with N samples in a given direction (either vertical or
horizontal) one can resolve about 0.7N lines.

When we got our hands on our first CCD chip at work in the late '70s, I
did an analysis (numerical, sort of Monte Carlo) and found a value
very close to that for mosaic arrays. While it did depend a bit on
fill factor, the dependence wasn't strong. I still use 70% as a good
expectation.

Now wait a minute Don, you got me a little bit confused.
As the Kell factor can´t be the prime limiting one, because it implies
a higher resolution than Nyquist allows, does it apply on the already
Nyquist limited resolution?
I mean, Nyquist says the theoretical max resolution is half the
sampling frequency (in lines or pixels). And this value is than again
limited by the Kell factor so that the max useful resolution is about
70% of the theoretical max. - Is that right?
Now Rich states that the AA filter reduces potential resolution of the
sensor by 30-40%. Those values fit so amazingly good in the above
scheme that I wonder if the reduction is really due to the AA filter.

Mark Wossner

Ah, but remember, there are two LINES per line pair or per cycle. So
the Kell factor is 40 per cent in terms of cycles or line PAIRS.

So if we have a 1000 line array, say 1000 vertical rows by whatever
columns, that says ON AVERAGE (sampled data) we can resolve about 700
lines, or 350 line pairs or cycles.

I´m sorry, I just found what I overlooked: Nyquist is about line
pairs, Kell is about lines. That´s what you tried to tell me Don, but
I was temporarily blind!

Marc Wossner

Far enough with theory up to this point. Here´s a practical question.
dpreview states on
http://www.dpreview.com/reviews/cano...kii/page23.asp that the
Canon EOS-1D Mark II (3504x2336 pixel) resolves 1850 lines per height
horizontal and 1650 lines per height vertical. According to the Kell
factor it should resolve about 70% and the vertical value corresponds
to that. But the horizontal value is just 53% of the max. Where comes
this difference from?

Marc Wossner

Marc Wossner wrote:

Far enough with theory up to this point. Here´s a practical question.
dpreview states on
http://www.dpreview.com/reviews/cano...kii/page23.asp that the
Canon EOS-1D Mark II (3504x2336 pixel) resolves 1850 lines per height
horizontal and 1650 lines per height vertical. According to the Kell
factor it should resolve about 70% and the vertical value corresponds
to that. But the horizontal value is just 53% of the max. Where comes
this difference from?

I have to correct myself again because I just read that the Kell factor
applies in the vertical direction. But why doesn´t it apply
horizontaly as well?

Marc Wossner