Re: Kinda Miss TG...

On Nov 10, 6:01 pm, Richard Jernigan <rnjerni...@xxxxxxxxx> wrote:
On Nov 11, 1:45 am, "Richard Yates" <rich...@xxxxxxxxxxxxxxx> wrote:





dsi1 wrote:
On Nov 9, 5:09 pm, Richard Jernigan <rnjerni...@xxxxxxxxx> wrote:
On Nov 10, 3:39 pm, Richard Jernigan <rnjerni...@xxxxxxxxx> wrote:

On Nov 7, 9:48 am, dsi1 <d...@xxxxxxxxxxxxx> wrote:

There's no way to physically represent in the real world,
multiplying or dividing by a number less than 1. Our brains have a
tough time correlating that action to anything in our world so
you're just gonna have to have faith in this. Sorry to have to
give you that news... :-)

!!!?????

The local diesel power plant here on this tiny island runs at about
. 46 efficiency. That means that a little less than half the energy
that would be available from complete oxidation of the diesel fuel
comes out of the plant as electricity. Am I not allowed to multiply
the potential fuel energy by .46 in the real world? Does the power
plant exist only on the astral plane, not the real world?

I can't drive my bicycle through its concrete walls. It emits a loud
noise and a certain amount of black smoke. When it was first built,
a wiring error caused power to be dropped to the whole island, a
very noticeable effect when we earn our living by running four
gigantic radars. I always thought the power plant was real, but now
that I find it doesn't exist, why are we hiring people to operate
and maintain it? And what does it do with all that diesel?

Oh, by the way, .46 is less than one, in case you are puzzled by my
question.

Yesterday, in the process of understanding my digital camera, I
divided by Planck's constant (among other calculations) to find the
number of photons incident on the sensor at the exposure setting ISO
400. Planck's constant is 6.626068 × 10^-34 m^2 kg / s. Written out
as a decimal, it would have 33 zeros between the decimal point and
the 6. A number somewhat less than one. Yet I blithely divided by
it when calculating the number of photons hitting a pixel in my
Nikon D300 when I set the ISO speed to 400. Am I not in the real
world? Is the Nikon supernatural technology?

RNJ

For a lunchtime snack, I sliced the remaining piece from a block of
cheese into four pieces. Before I got out the knife, the cheese was
about 2 3/4 inches thick. When I got done, the four pieces were each
about 11/16 inch thick, (1/4) x (2 3/4). Unfortunately, I did the
calculation in my head. The cheese immediately vanished from the real
world, and I had to get along with just milk and crackers.

RNJ

Rest assured that I can multiply numbers too, even fractions! My point
was that we can't really understand the concept of multiplying by
fractions. If you're a person with a normal mind, you're not
multiplying by a number less than one - you're multiplying the whole
number numerator and the whole number denominator separately, then
placing the products in the appropriate location or you're doing
repeated whole number divisions or some other process. I'm pretty sure
that you're not truly multiplying by a fraction. Heck, you could be,
and if you say you are, I will not to argue your abilities in this
matter.

My post was merely to explain why multiplying by a fraction is a tough
concept to get a handle on. The reality is that we multiply fractions
in a practical, utilitarian sense, we just cannot do this directly,
nor can we understand how it really works - mostly we have faith that
it does.

I agree with the general point of your post, although I think it was
overstated and hence Richard's response(s). The case is clearer with
dividing by fractions than with multiplying by them. I know that I always
think of that as multiplying by the inversion of the fraction. I would be
interested to read of any concrete examples that Richard can think of where
dividing by a fraction is the natural way to think about a concrete
operation. (I also am waiting to hear how many photons turned out to be
hitting that sensor!) RY

Several hundred.

I didn't go into the details of the illuminance curve implicit in the
definition of ISO film speed, I just wanted the order of magnitude.
Dividing by Planck's constant results in numbers that are beyond
astronomical, but you also divide by the frequency of green light, a
big number, and you multiply by the microscopic area of the individual
photodiode, all processes which dsi1 seems to say have no basis in
reality.

I was interested for two reasons. One of the regular posters on the
Nikonians forum regularly says that the number of photons hitting an
individual photodiode is small enough for "shot noise" to be a
significant factor in the dynamic range of the sensor.

Shot noise can be heard in high gain vacuum tube circuits because
electrons don't arrive at tube collector at a constant rate. They
arrive at a constant average rate, but the rate varies with time. Part
of the variability with time can be heard as a hissing noise in highly
amplified circuits. It's "shot noise" by analogy to pouring lead shot
onto a drumhead. The rate at which the shot hits one part of the
drumhead may be the same as every other, averaged over a second or
two, but within a hundredth of a second different amounts of shot will
have hit one spot relative to another.

The same happens with sensors in modern digital cameras. The photons
arrive like rain. Over thirty or forty exposures of a few hundredths
of a second, the average number of photons collected by a pixel will
be the same tomorrow as today, but individual exposures will vary,
because it doesn't rain photons at exactly the same rate everywhere
all the time. This is what makes photos taken in low light or at high
shutter speeds look noisy. Averaged over a number of pixels, the
number of photons collected will be the same from one photo to the
next, but within an individual photo, it will have rained a little
harder on some pixels that on others, making things look speckly.

The approximate number of photons per pixel I calculated means that
modern cameras operate in the domain where shot noise is significant.

The other claim is that modern cameras operate near the maximum
theoretical efficiency of the current technology. That is they come
close to contributing an electron of sensor charge for every photon
that strikes the pixel. This is indeed the case, with quantum
efficiencies greater than 90% being routine. With thermal noise being
on the order of a few electrons per pixel per exposure, this is very
good performance indeed. Shot noise dominates thermal noise in
reasonbly short exposures.

This doesn't hold for long exposures. The other night I was out taking
photos of the lights of a village across the lagoon, overtopped by
moonlit clouds. A minute at ISO 1600. Still pretty speckly, even after
the camera spent 40 seconds or so collecting a thermal noise sample to
subtract out.

But back to the point. All this was done in half an hour or so, mainly
spent in looking up photometric definitions. I drew one very simple
figure on the back of an envelope. The rest was done by using a
spread*** to multiply and divide by both sub-sub-sub-microscopic*
and astronomically large quantities, almost without stopping to think
about it.

RNJ

*Remember, Planck's constant is a number with 33 zeros to the right of
the decimal point before you get to the first non-zero digit. The
average radius of a hydrogen atom in its ground state (5.29x10^-11
meter) is a number with only ten zeros before you get to the first
nonzero digit.- Hide quoted text -

- Show quoted text -

Richard,
when you multiply an integer by itself it gets bigger, but when you
multiply a (+) fraction by itself it gets smaller. Doesn't that seem
weird?
.