Re: Any thoughts /news on Foveon sensors?

Edmund <nomail@xxxxxxxxxxx> writes:

>> It's almost the same. In digital audio, the independent variable is
>> time, the sampling rate is in samples/second, and the Nyquist limit is
>> the point at which the signal frequency is half the sample frequency.
>> In other words, you need more than two samples per cycle to resolve
>> a signal without aliasing.

>At least exactly 2 samples per cycle in fact.

You can't sample at *exactly* the Nyquist frequency and expect correct
results. You can get a signal that seems to have anywhere between zero
and the correct amplitude, depending on the phase difference between the
signal and the sample clock. That's why the sampling theorem says "less
than Nyquist" rather than "less than or equal to".

>> In imaging, the independent variable is space, and the signal is 2D
>> instead of 1D. So the sample rate is in samples per mm or samples per
>> inch, and the Nyquist limit is the point at which the signal frequency
>> is half the sample frequency. In other words, the wavelength is twice
>> the pixel spacing at the Nyquist limit, or you need more than two pixels
>> per cycle to resolve a signal without aliasing.

>Thank for explaining, can I find more info on this on the Internet?

Probably; try a Google search. But you're likely to get a more thorough
explanation from any image processing textbook.

>I like to know what kind of errors are made without these anti-aliasing.
>In audio e.g. the SACD they just sample very high and don't use anti
>aliasing anymore.

Oh yes they do - the difference is that the critical AA filter is now
digital, not analog.

In the old days, audio sampling was actually done at 44.1 kHz, giving a
Nyquist frequency of 22.05 kHz. To get a 20 kHz audio bandwidth, you
needed an analog AA filter that was flat to 20 kHz, then down something
like 100 dB at 22.05 kHz. This required an expensive multi-stage analog
filter that had to be tuned for correct response.

Now suppose you have better A/D and can sample at 8X the final frequency
(8X oversampling), at 352.8 kHz. The Nyquist frequency for this step is
176.4 kHz. You still need an analog anti-aliasing filter, but now the
filter needs to be flat to 20 kHz and 100 dB down at 176 kHz - a much
easier set of requirements. Then, once you have your data stream at
352.8 kHz, you pass this through a *digital* filter that is flat to 20
kHz but down 100 dB at 22 kHz. This digital filter takes a lot of
multiplies, but that's cheap today and the filter is more accurate and
stable than the analog one and requires no tuning. Then you just throw
away 7 out of every 8 samples to get the final sample rate of 44.1 kHz.
But the process used *two* anti-aliasing filters, one analog and one
digital. This is usually not practical in imaging, because smaller
sensors spaced closer together have manufacturing, noise, and
sensitivity problems.

(The above is somewhat simplified. In practice, the digital lowpass
filter and the every-8th-sample steps are always combined into one,
which reduces the number of multiplies by a factor of 8. Also, the
analog filter only needs to be 100 dB down by about 330 kHz, since
input frequencies between 176 and 330 kHz will be aliased to new
frequencies that are still above 22 kHz, and they will be removed by the
digital low-pass filter. It's only frequencies in the range 333-373 kHz
that will alias down into the audio band.)

>That popped to my mind too, to use a prism for this purpose.
>But that is already done, OK.

High-quality video cameras are usually made this way (as well as a few
not-so-high-quality ones). But the prism blocks get large and expensive
as the physical size of the sensors scale up if you get more pixels by
larger sensors, and the prism/sensor alignment precision needed
increases if you get more pixels by decreasing the pixel pitch. Either
way, they're expensive to scale up to still camera resolution standards.

In addition, prisms mean that a substantial length of the light path
between lens and sensor is in glass, not air. This causes spherical
aberration in the image if the lens is designed for an air path. TV
zoom lenses intended for 3-chip cameras are designed with the prism as
part of the lens design to compensate for this, and a fixed-lens "ZLR"
digital camera could do that too. But SLR still camera lenses are all
designed for air paths between rear element and image plane.

Dave
.

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