Re: Noise levels as a function of pixel size

In article <doht14$2lde$1@xxxxxxxxxxxxxxxxxx>, Ilya Zakharevich <nospam-abuse@xxxxxxxxx> writes
[A complimentary Cc of this posting was NOT [per weedlist] sent to
Kennedy McEwen
<rkm@xxxxxxxxxxxxxxxxxxxx>], who wrote in article <J1FYSwBtAxqDFw0W@xxxxxxxxxxxxxxxxxxxx>: 
>> >Nope.  The maximal f-number of the lens is irrelevant.  What is
>> >important is the actual f-number used for the shot.  So with 16x
>> >scaling f/45 becomes f/2.8.


>> The maximal f-number is highly relevant, since that is what determines
>> both the exposure control and the optical resolution limits.

>Do not know what you mean by "exposure control". 

Control of exposure, in this case control by aperture, as in a shutter
priority metered system.


Kennedy, I was discussing the situation when one particular shot made
with a larger sensor produces the same result as one taken with a
smaller sensor.  Apparently, you are discussing something else;
actually, I do not know what.  I can't continue until I understand
what is the context of your statements...

Since we don't make digital cameras for one particular shot, let alone develop entire technologies for it, what you claim to be discussing is quite a pointless subject. For what it is worth, I was discussing where the technology can go, what is achievable with it and what the tradeoffs between the relevant formats you have proposed actually are - for all shots, not just one!


>The optical
>resolution limit has nothing to do with f-number of the fully open
>lens.


It certainly has, since the maximum theoretical fully open lens is
f/0.5, whilst the practical limit is around f/0.7.  That doesn't leave
much engineering room if the maximum diffraction limited aperture is
around f/1, even if the range does go well into the diffraction limit
zone to f/2.8.


As I said, maximum NA of a diffraction-limited in-the-air lens I know
is 0.93.

That would have to be pretty high humidity air, since the maximum theoretical NA of any lens is 1/n, where n is the refractive index.

 So I have no idea what you are speaking about (even if under
f/0.5 you mean NA=1...).

The correct formula for f/# is 1/(2xNA), so certainly f/0.5 corresponds to the maximum numerical aperture. However, quite often you will see NA quoted as 1/(2.f/#) where, rather the photographic approximation for f/# is used, resulting in highly over-optimistic values for f/# less than 1 and NA greater than 0.5. I suspect that your figure above is such an example, since it is very unusual to see NA specified in air with such a high refractive index. Alternatively, you are using the wrong figure (again!) and the NA is quoted in a medium of significant refractive index, eg. microscope oil.

>I'm not discussing f/45 lenses. I'm discussing *shots*. 

As I am.  The difference is that I am recognising that f/45 is
sub-optimal on 4x5" due to


Somebody counted (one of Davids?), and 50% of published 4x5in images
are made at f/45; this is why I discuss this number.

Published images do NOT represent the limits of the 4x5" medium - not by a long way. Unaided visibility limits correspond to around 250ppi at the nominal close viewing distance of 10" - and that is for a good, young eye! Even if you assume an A4 book page, rather than a typical publication size of 10x8", that requires less than 750ppi on the original 4x5" film, which is nowhere near its resolution capabilities. In short, the benefit of 4x5" film for such publication is NOT the resolution of the medium, but its improved SNR over a smaller format. Hence the use of a high f/# optic, which is well into diffraction limited region compared to the medium at the focal plane (film) is quite acceptable for the final application. It is NOT, however, an acceptable baseline for the extrapolations that you have made and which have resulted in a pixel size which no physical lens could ever resolve.

Since no lens can match the pixel sizes you propose, the only benefits they can provide are, just as in the example you have used as your baseline, improved SNR through averaging. With a sampled sensor, this can be achieved much more efficiently by physical averaging at the focal plane through the use of larger pixels.

To be blunt, your assumptions about the baseline you have chosen are seriously flawed and whilst there are errors in your extrapolation they are insignificant compared to the conclusion that you have reached.

AFAIK, 4x5in-format lenses max the resolution about f/16.

The aperture at which the ideal lens resolution equals the resolution of the film is INDEPENDENT of the focal plane format. For most colour films this is rarely above f/5.6, although practical lens limitations from other aberrations can increase the optimum point up to f/11. The resolution achievable at f/16 is well below the resolution capability of film.

>??? Who talks about single aperture? 

You effectively are, by requesting a pixel pitch which is so small that
it can only be resolved by an ideal lens which has an f/# only
marginally greater than the theoretical limit of f/0.5.

Please do not put words in my mouth.

I am not putting words into your mouth. When you ask for a pixel which can only be utilised at one practical aperture then you are talking about single aperture applications, whether you understand what you are saying or not! 

I'm taking about a lens which gives a close-to-diffraction limit
performance at f/2.8.

Which is significantly larger than the pixel size you are proposing to place at the focal plane. If the lens cannot resolve individual pixels, or even close to it, then the simpler solution is to use larger, better SNR, pixels. The ONLY justification for a smaller pixel is the resolution it provides, which can only be achieved with faster lenses which are still diffraction limited (or close to).

Nowhere did I say anything about single
aperture.

Your pixel size implied that any smaller aperture than the theoretical maximum would reduce the effective resolution of the sensor. Since this was already well below the resolution limits of the pixel, anything more than that single aperture would be pointless.

[And I have no idea what "resolving a pitch" would mean;

I find it incredible that you argue on this subject when you have no idea that the lens has to be capable of resolving the pixel pitch to make any case whatsoever for small pixels. If the lens can't resolve the pixel pitch then the pixel size can be increased without any loss in resolution but a gain in SNR. Added to which, it is technologically easier to make larger pixels.

That is a win-win situation, as opposed to your lose-lose argument.

maybe you live a world where the camera is more expensive than its
lenses, so you want to use only the settings which would extract the
maximal resolution from the camera?]

I live in a world where the performance of the lens can, and often does, exceed the capability of the sensor - that is WHY the sensors have to be fitted with anti-aliasing filters. Why would anyone buy a sensor which no lens could ever achieve its full capability?
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)
.

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