Re: Nikon D40 vs D40x ISO newbie question

On 2007-04-30 07:19:17 -0700, "Roger N. Clark (change username to rnclark)" <username@xxxxxxxxx> said:

C J Campbell wrote:
http://www.clarkvision.com/imagedetail/digital.sensor.performance.summary

It appears that your charts are an argument that more photons reduces picture quality and that there is nothing you can do about it. Yet here you claim that better micro lenses can correct the problem.

Argh. I meant more pixels, not more photons. I really hate typing as a means of communication.

The number of collected photons is a fundamental limit to picture
quality. Dynamic range can be no greater than the number of collected
photons, and noise is set by Poisson statistics. That is independent
of the efficiency of collection. You can never do better than
Poisson statistics. Thus, in any light collection system, the system's
dynamic range and noise is set by the number of photons you actually collect.
Other noise sources in the electronics only add to the noise, so noise
due to the random arrival times of photons is the best one can do.
This is a fundamental physics limit, and in general is called photon noise,
or photon noise limited.

So, either the limit on sensor size has been reached as you said, or it can be increased further with better micro lenses or other engineering solutions, which you also said. It seems to me to be a contradiction, so please understand if a simple tax accountant seems confused.

Let me try and explain and please ask further questions if what I say
is not clear to you (or anyone else reading).

So we've established photon noise is a fundamental limit. The noise in
a light signal is the square root of the number of photons collected.
So if you collect 90,000 photons, the noise is 300, thus the
signal-to-noise ratio = 90,000/300 = 300. The dynamic range is
90,000. Let's say we have no other noise sources in our sensor or
electronics, so we say the system is photon noise limited and
has reached a fundamental limit. A fundamental limit is not
an absolute best that can be done limit.

But that does not mean it can't be improved. Let's say the sensor
converts 1/3 of the photons that are incident on the pixel, and
let's say the dead space on the sensor is about 20% (the lines
between pixels and support electronics on the pixel that are
not sensitive to light). We say the Quantum Efficiency (QE)
is 33% and the active area, or fill factor, of each pixel is
80%.

So we can do a couple of things: we can improve the QE or
the fill factor. Micro lenses collect light from a larger
area and focus it down to smaller spot. Manufacturing 8 to
10 million tiny lenses is not easy and manufacturing processes
to do that have been improved over the years. That is what
Canon announced with the 1D mark III: they shrunk the pixel size
and improved the micro lenses to keep the total light collected
the same.

An analogy is collecting rain drops in buckets in your yard
during a rain storm. Lets say you place 100 buckets on a 10x10
grid spaced every foot. The buckets are 0.5 foot in diameter.
Let's say the rain fall is constant all day. Let's also say
the rain drops arrive at random intervals and are modeled
by Poisson statistics (probably a good assumption in reality).
Say we collect for one hour.
The amount of rain in each bucket is not the same. The noise
we get in measuring the amount of water in each bucket is
the square root of the number of rain drops in the bucket.
Our data regarding measuring the amount of water is
"rain drop noise limited."

Now let's replace the 0.5 foot diameter buckets with buckets
measuring 0.75 foot in diameter but still spaced every foot.
That increases our collection efficiency from 20% to 44%.
We collect more water in the same interval, and our measured
result will be a little more precise because we collected
more rain drops. We can maximize out efficiency by designing
square buckets that are 1-foot in outside dimension increasing
our collection efficiency to almost 100% (the width of the buckets
limits us a little).

Another way we could improve efficiency with our 0.5-foot diameter
buckets is to put funnels over each bucket. Say the funnel was
1-foot square at the top. We've increased efficiency to near 100% without
changing the bucket.

If we want to collect even more photons, we must use larger buckets
(or buckets + funnels) spaced at larger intervals. For example we
could use square buckets 2-feet on a side and double the area our
buckets cover. We would collect 4-times the number of rain drops
as our 1-foot square buckets. All the system have been Poisson
noise limited.

Our buckets have been 100% efficient (assuming nice metal or plastic
buckets). Lets say we make the buckets out of some absorbing
material, so we lose some water. The water lost to absorption
is not counted when we measure the depth of water in the
bucket. The noise we measure from bucket to bucket is the
square root of the number of drops making up the water in the
bucket. We are still Poisson statistics limited, and we still
say we are "rain drop noise limited."

So we can have photon detectors that are not perfect and which could
be improved, but the noise we see from the system is photon noise limited
and improving other electronics will not improve the noise we see
in our images. We say the system is photon noise limited.

Dos this help?

Roger

Some. However, I did not make the leap where the noise we get in measuring the amount of water in each bucket is the square root of the number of rain drops in the bucket. I did not see the justification for that conclusion.

As I understand it, noise in digital photography is of two types: fixed pattern and random. Fixed pattern noise is caused by imperfections in the sensor. All cameras exhibit some fixed pattern noise and it differs from camera to camera as well as from model to model. It is easily screened out by the camera software. The random noise is caused by several things, including heat buildup, electron transfer between sensors, electromagnetic interference, etc. The less light there is and the longer the exposure time the more you are likely to be recording something other than light. This does not seem to me to be dependent on sensor size. Making the pixels larger seems to also make the sensor more likely to pick up stray non-light signals as well as light. The signal to noise ratio would remain constant, would it not? Placing the pixels closer together would make them more likely to interfere with one another, but I don't see how larger pixels helps that -- in fact, it might aggravate the problem.

Anything that would make a pixel more likely to catch photons would make it more likely to catch other particles as well. This seems to me to be fundamentally a filtering problem rather than a pixel size problem. I can see how micro-lenses boost the signal to noise ratio; but this is a filtering problem.

For a given size of sensor, however, more pixels should catch more light, not less. Consider placing stacks of coins in a chest. You can put a lot more coins in the chest if they are smaller because the space between the stacks is less.

On a sensor, the performance of individual pixels might be less with smaller and more closely spaced pixels, but the overall performance of the sensor should remain the same or increase, should it not? You lose fewer photons to the spaces between the photo-sites, so overall your image quality and signal to noise ratio for the entire sensor should be improved.

Taking your rain bucket example, if I fill up an area of 40x30 feet with ten gallon buckets as closely packed as I can put them, I will catch less rain than if I fill up the same area with quart buckets as closely packed as I can put them. Each quart bucket will catch less rain than a ten gallon bucket, but the total amount of water collected by all the buckets will increase. The only limit that I can see would be if each bucket was smaller than a raindrop and therefore could not collect any rain at all. However, photons are very tiny and we are not anywhere near making a photo-site that is so small that a photon cannot enter it.
--
Waddling Eagle
World Famous Flight Instructor

.

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