FAQ - Perhaps there are real professionals here today rather than uppity technicians?

I'm not sure your assessment is totally applicable in all cases.

If we limit the domain to digital cameras for a certain limited range
of desired purpose then I do agree. But the range of applications is
rather wide and some areas do have more demanding requirements. Also,
cameras are not only used to take snapshots - my original field of
research was in medical imaging where it is quite important to make
sure you see the correct fine detail and not some artefact. I have some
nice photo examples that show where a surgeon could be led to excise
healthy tissue due to imaging artefacts.

CMOS image sensors are insensitive: so noise (hence light-gathering
power) is a real problem.

CCD sensors are used in astronomy where light-gathering power is also
important.

Also, the frequency response may be flat for certain applications - but
for instance can result in changes of shading ortexture for very fine
textures - which is OK for some photographers but not, for example, if
you make your living by taking faithfully accurate photos for fashion
design or hairdressing.

But I'm interested what leads you to assert that noise and light
gathering power are unimportant?

Chris

chris_bore@yahoo.co.uk wrote:
> 
> I'm not sure your assessment is totally applicable in all cases.

I wasn't making an assessment I was offering a counterexample to your
assessment. What I was  deriding was the notion that you can speak of
the "signal" as if it exists at some point in physical reality that you
can isolate and point to. And presumably if such a point exists then
that point is where the Dirac pulse in the sampling process exists. And
thus we might reason that if we can't find and isolate that very point
we must then start tampering with the Dirac pulse to come up with a more
"non-dirac" model for sampling. That's nonsense - you will never find
and isolate that point (in some cases that's just more obvious). The
Dirac pulse simply represents the notion that the reconstructed signal
passes through the sample points (the response is always flat). 

-jim  

> 
> If we limit the domain to digital cameras for a certain limited range
> of desired purpose then I do agree. But the range of applications is
> rather wide and some areas do have more demanding requirements. Also,
> cameras are not only used to take snapshots - my original field of
> research was in medical imaging where it is quite important to make
> sure you see the correct fine detail and not some artefact. I have some
> nice photo examples that show where a surgeon could be led to excise
> healthy tissue due to imaging artefacts.
> 
> CMOS image sensors are insensitive: so noise (hence light-gathering
> power) is a real problem.
> 
> CCD sensors are used in astronomy where light-gathering power is also
> important.
> 
> Also, the frequency response may be flat for certain applications - but
> for instance can result in changes of shading ortexture for very fine
> textures - which is OK for some photographers but not, for example, if
> you make your living by taking faithfully accurate photos for fashion
> design or hairdressing.
> 
> But I'm interested what leads you to assert that noise and light
> gathering power are unimportant?
> 
> Chris

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OK, but I wasn't meaning to suggest a 'non-Dirac' model for sampling.
Just to state that the signal is convolved with the sampling function -
and so its frequency content is modulated by the FT of the sampling
function. And that this is important in many cases where the actual
process of sampling cannot even approximate to a measurement that is
fast by comparison with the way the signal is changing at that time.

Chris

chris_bore@yahoo.co.uk wrote:
> 
> OK, but I wasn't meaning to suggest a 'non-Dirac' model for sampling.

OK, I thought you were meaning to suggest something else. I interpreted
your original response "we tend to work with the easy math rather than
always using the hard stuff" incorrectly. That implied to me that the
existing model was simply a convenience. Add to that, the original
poster you were responding to made a reference to a "sampling function"
which is the familiar one used as the standard model for sampling and
asked the question "Where do these Diracian impulses come from?". So it
did appear to me you were meaning to suggest something else.

> Just to state that the signal is convolved with the sampling function -
> and so its frequency content is modulated by the FT of the sampling
> function. And that this is important in many cases where the actual
> process of sampling cannot even approximate to a measurement that is
> fast by comparison with the way the signal is changing at that time.

That's a bit cryptic and fuzzy.  I'm guessing what your saying is that
the signal you're measuring is not bandlimited and the use of a sensor
with some width has the effect of mitigating some of the artifacts
caused by the lack of a bandlimited signal (i.e. a narrow sensor would
have even more artifacts). Now, normally in DSP this is referred to as
an anti-alias filter. Ideally, what your calling a "sampling function"
should have a cross-section shaped like a sinc function. This idealized
sensor would be numerous pixels wide (overlapping sensors) and would
have its peak at the center of the current pixel with nulls at the
center of all neighboring pixels and it would have side lobes that have
their peaks between the neighbors and fall off in amplitude by 1/d as
you move d distance away from the center. If your "sampling function"
looked like that, you would see significant improvement in the removal
of those higher frequencies that are beyond the measuring capability of
your chosen sample spacing.

-jim

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(someone, previously snipped, wrote)

>>The primary problem with an image sensor is the signal
>>being measured is not bandlimited. If the signal were in fact properly
>>bandlimited then one could simply derive the signal magnitude at the
>>exact center of each sensor in the array. In order to do that one must
>>assume that each sensor is sized and located with perfect exactness.
>>That is, of course, another real limitation to realizing the perfect
>>sampling that the theory predicts. The width of the sensor is not.

Optical systems are band limited by the size of the lens.  Whether or 
not that limit is appropriate for the sample size in use is a different 
question.

Photographers stop down the lens for increased depth of field, but it is 
well known that it also decreases the sharpness due to diffraction 
effects.

For scanning electron beam video cameras the beam size acts somewhat as 
a filter on the sampled signal in addition to any filtering by the 
optical system.  As the beam tends not to have a sharp profile it isn't 
a bad filter.

Semiconductor sensors do tend to have a sharp edge.  The finite size 
needed for sufficient light collection offers some filtering.

Most video signals have a relatively small amount of high frequency 
content which is an important part of video compression systems.
As I understand it, TV news people are instructed not to wear clothes 
with thin stripes, one of the most obvious sources of aliasing in video 
signals.

-- glen