Magnitude from photon counts

SNIP

If you expose long enough, you will get a white image. This time can be
greatly extended by taking multiple images and adding them together
outside the camera. Doing this it is possible to get arbitrarily deep
pixel wells. People have made images with exposures of tens of hours
this way, starting and stopping to avoid daylight.

By "pixel wells" do you mean accuracy of determination of brightness?

I don't see how this works. Surely the noise is proportional to the length
of exposure, so it adds across multiple exposures linearly? Why must this
occur outside the camera, aren't you just adding the pixel count in the
camera anyway? Is there any requirement that the exposures be separated in
time to reduce the correlation of some noise source?

Chris L Peterson writes:

You'll have to define "best photometry". CCDs offer higher quantum
efficiency, which means they detect more signal, and theoretically,
more signal means better photometry. However, there are other
sources of noise that tend to create a floor below which CCD
photometry has difficulty getting.

Which noise sources? CCDs suffer two systematic sources: thermal noise
and readout noise.

Is that all you can think of? What about the noise caused by
someone using a broad filter and flattening a red dark sky field
with a blue twilight sky flat? There are all kinds of systematic
effects.

PMTs also have thermal noise, and the large cathode
makes the noise level higher. To get good results, PMTs have to be
cooled, which is much more difficult and expensive than cooling CCDs.

I've seen simple thermoelectic coolers that can make a C31034A
operate at a dark current of a few counts per second. All the
professional-grade CCDs I've used are cooled with liquid nitrogen.

PMTs themselves don't have readout noise, although there is an
equivalent noise from the readout electronics. That noise with PMTs is
quite a bit less than with CCDs (a fraction of an electron, compared
with several electrons). For integration times longer than a few
seconds, CCDs will beat PMTs for S/N.

Not necessarily.

Considerable effort has been
expended by some people to move that floor lower, with some success,
but I am personally not aware of any proof that CCDs are always
better than PMTs, even for long exposures.

"Always" is a strong word. But in most cases CCDs yield better results.

Let's put it this way: compare the CCD photometry of Pluto-Charon
mutual events with the PMT photometry of Pluto-Charon mutual events.
Same size telescope. Which is better? The PMT photometry.

There are several advantages. They are much easier to calibrate than
PMTs,

Surely you jest; who ever took bias and flat calibrations with a
PMT? Who has to worry whether the overscan is a simple constant
or a function of line number with a PMT? Who has to worry about
a two-dimensional bias structure with a PMT?

and allow for multiple sources in the same exposure- that is,
differential photometry. You can't do that with a PMT, so you either
have to compare reference stars at different times, which introduces a
lot of error, or use several PMTs in a fiber-fed configuration, which
has the problem that the different sensors have different responses that
are hard to calibrate.

Don't try to argue that CCDs allow you to do some things that a PMT
cannot do, because that was never the issue. The issue is "best
photometry", and that can involve single sources. If you want to
get away from that issue, then I can start talking about how
inefficient it is in terms of data collection and storage to take
megabytes worth of data to obtain a single number.

Chris L Peterson writes:

Stupendous Man wrote:

One of the big problems with CCDs is that they are composed of a
number of pixels, which act in some ways as individual detectors.
It is very difficult to calibrate the relative response of each pixel
at levels much below 1 percent. It is especially difficult to ensure
that measurements of stars on one section of a CCD (say, the
upper-left corner) suffer from no systematic error relative to
those of stars in another section (say, the bottom-center edge)
at the sub-percent level.

That is not the case. In fact, it is precisely the fact that CCDs are
composed of many pixels that helps make them so good for photometry.

On the contrary, the very fact that a PMT design images the primary
mirror on the cathode means that the light is spread out over a
large area of the detector, which makes it much less sensitive to
signal variations caused by mistracking of the telescope. When the
instrument is rigidly bolted to the telescope, the spot on the
cathode is fixed and does not move. With a CCD, taking multiple
exposures to get, for example, a lightcurve, means that you won't
necessarily have the object on the same pixels each time. Indeed,
it is often advisable to dither the telescope to purposely prevent
the object from falling on the same pixels. You are therefore at
the mercy of the quality of the flat field. Suppose the filter
acquires a new dust speck after the flats were taken? Sometimes
there isn't enough twilight to get a decent set of flats through
all the various filters, and dome flats can be a problem due to
the difficulty of getting truly uniform illumination.

With careful calibration (that is, bias, flat, and dark frames) the
relative response of CCD pixels is normalized to better than 11 bits
across the entire device (quite a bit better with some pro setups). That
is a few hundredths of a percent, good enough to make millimagnitude
measurements.

And how did you determine that the flat didn't change at the few
hundredths of a percent level during the night?

For bright, isolated stars, photomultiplier tubes looking
at one star at a time typically provide better relative photometry
from the ground than CCDs.

Not usually.

Then explain why the best Pluto-Charon mutual event photometry
was produced by a PMT.

For precise photometry, you need reference objects.

True for both PMTs and CCDs.

With a CCD, you usually have those in the same field.

Oh, you may have another object, but it won't necessarily be a
reference object. Yes, you can do differential photometry, but
you'll still need a proper standard star to get calibrated
photometry.

With PMTs, you need to do
much more complex calibration, which adds a lot of error.

In both cases, standard stars need to be observed elsewhere in the
sky. The calibration is equally complex.

PMTs are
mostly used for dim, fast changing sources where you are less interested
in absolute magnitude than you are in the relative magnitude over a
short period.

I used a PMT when I was most interested in getting millimagnitude
photometry.

Of course, amateur use of PMTs for precision photometry is almost
unheard of, due to the difficulty and expense of cooling the tube. Solid
state coolers aren't practical, so these are instruments that operate in
dewars of LN.

As if CCDs don't operate in dewars of LN?

Martin Brown writes:

Chris L Peterson writes:

Steve Taylor wrote:

One could use a photon counting PM tube and counting electronics though
and read photon flux directly. Probably less noise too.

Unless you need to get counts over very short intervals, CCDs have lower
noise and higher QE than PM tubes. As long as you can integrate long
enough to beat the readout noise (about 10 electrons) a CCD provides the
best photometry. PMTs are mainly used for recording rapidly changing
events, where you need to watch the photon record from second to second.

You'll have to define "best photometry". CCDs offer higher quantum
efficiency, which means they detect more signal, and theoretically,
more signal means better photometry. However, there are other
sources of noise that tend to create a floor below which CCD
photometry has difficulty getting. Considerable effort has been
expended by some people to move that floor lower, with some success,
but I am personally not aware of any proof that CCDs are always
better than PMTs, even for long exposures.

CCDs are surely better for imaging these days though?

The issue was photometry, not imaging.

On Thu, 27 Jan 2005 15:17:57 GMT, wrote:

Which noise sources? CCDs suffer two systematic sources: thermal noise
and readout noise.

Is that all you can think of? What about the noise caused by
someone using a broad filter and flattening a red dark sky field
with a blue twilight sky flat? There are all kinds of systematic
effects.

That isn't noise. That is instrumental error. Instrumental error can be
corrected for; noise can't.


I've seen simple thermoelectic coolers that can make a C31034A
operate at a dark current of a few counts per second.

Which is considerably worse than the noise of a CCD.

All the
professional-grade CCDs I've used are cooled with liquid nitrogen.

As I pointed out.


Let's put it this way: compare the CCD photometry of Pluto-Charon
mutual events with the PMT photometry of Pluto-Charon mutual events.
Same size telescope. Which is better? The PMT photometry.

Well, this is exactly the sort of case I've repeatedly pointed out where
a PMT photometer still is best- a rapidly occurring event where absolute
magnitude isn't the primary goal.

There are several advantages. They are much easier to calibrate than
PMTs,

Surely you jest; who ever took bias and flat calibrations with a
PMT? Who has to worry whether the overscan is a simple constant
or a function of line number with a PMT? Who has to worry about
a two-dimensional bias structure with a PMT?

When I used to use PMTs, I used calibration steps exactly analogous to
bias and dark frames. The two dimensional structure of the photocathode
was measured by scanning because the surface did not have a uniform
response.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Thu, 27 Jan 2005 15:29:43 GMT, wrote:

On the contrary, the very fact that a PMT design images the primary
mirror on the cathode means that the light is spread out over a
large area of the detector, which makes it much less sensitive to
signal variations caused by mistracking of the telescope. When the
instrument is rigidly bolted to the telescope, the spot on the
cathode is fixed and does not move. With a CCD, taking multiple
exposures to get, for example, a lightcurve, means that you won't
necessarily have the object on the same pixels each time. Indeed,
it is often advisable to dither the telescope to purposely prevent
the object from falling on the same pixels. You are therefore at
the mercy of the quality of the flat field. Suppose the filter
acquires a new dust speck after the flats were taken? Sometimes
there isn't enough twilight to get a decent set of flats through
all the various filters, and dome flats can be a problem due to
the difficulty of getting truly uniform illumination.

You are supposing a lot of problems that are routinely and trivially
dealt with.

Your experience with photometry is obviously quite different from my
own. There is a reason that PMTs are used for only a small fraction of
photometry measurements. That is because in most cases CCD measurements
yield higher quality data, particularly where absolute magnitude is at
issue. They have a much better signal to noise ratio, and they can be
characterized and calibrated much better. They are much more stable with
time. If you are monitoring some sort of occultation, or a dim fast
rotator, a PMT photometer may be the best solution. But for most work,
the CCD is the tool of choice.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Fri, 28 Jan 2005 02:00:32 +1100, "Peter Webb"
wrote:

If you expose long enough, you will get a white image. This time can be
greatly extended by taking multiple images and adding them together
outside the camera. Doing this it is possible to get arbitrarily deep
pixel wells. People have made images with exposures of tens of hours
this way, starting and stopping to avoid daylight.

By "pixel wells" do you mean accuracy of determination of brightness?

Each pixel can only store a finite number of electrons before it
saturates and data is lost. If your goal is the accurate determination
of brightness, you need to count the electrons in each pixel well and
clear the chip before this happens. For photometry, it is the well depth
that determines the maximum exposure length. If a longer exposure is
needed (for example, you have a dim target and a bright reference in the
same field) you can take multiple exposures and add the data frames.


I don't see how this works. Surely the noise is proportional to the length
of exposure, so it adds across multiple exposures linearly?

No, noise does not accumulate linearly (readout noise is different,
since it adds a fixed level every time an image is read). The primary
noise sources accumulate as the square root of the exposure time. In
other words, the signal grows faster than the noise. A longer exposure
yields a better S/N.

Why must this
occur outside the camera, aren't you just adding the pixel count in the
camera anyway? Is there any requirement that the exposures be separated in
time to reduce the correlation of some noise source?

By definition noise is uncorrelated. A long exposure can be made as a
single shot, or if saturation is a problem, multiple shots added
together. Except for the readout noise contribution, the two scenarios
produce identical results, both theoretically and in actual practice.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Wed, 26 Jan 2005 06:32:21 -0800, Bill C wrote:

Even worse, if you left it exposed for days and
days, then it might record down to 30th, 40th or 50th magnitudes... and
you get to Olbers' Paradox of the whole image being a white brightness
like the surface of the Sun!

Doubtless it would eventually go white, but from random noise, nothing to
do with Olber's Paradox, which, as the name implies, is a paradox (ie it
doesn't happen the way it seems it should)

Chris L Peterson writes:

Which noise sources? CCDs suffer two systematic sources: thermal noise
and readout noise.

Is that all you can think of? What about the noise caused by
someone using a broad filter and flattening a red dark sky field
with a blue twilight sky flat? There are all kinds of systematic
effects.

That isn't noise. That is instrumental error. Instrumental error can be
corrected for; noise can't.

Anything that contributes to the error is a form of noise.

I've seen simple thermoelectic coolers that can make a C31034A
operate at a dark current of a few counts per second.

Which is considerably worse than the noise of a CCD.

Depends on the temperature of the CCD.

All the
professional-grade CCDs I've used are cooled with liquid nitrogen.

As I pointed out.

What you pointed out is that it is more difficult and expensive
to cool PMTs than CCDs, and a thermoelectric cooler that you can
plug into a handy electrical outlet is hardly more difficult or
more expensive than a dewar repeatedly filled with liquid
nitrogen.

Let's put it this way: compare the CCD photometry of Pluto-Charon
mutual events with the PMT photometry of Pluto-Charon mutual events.
Same size telescope. Which is better? The PMT photometry.

Well, this is exactly the sort of case I've repeatedly pointed out where
a PMT photometer still is best- a rapidly occurring event where absolute
magnitude isn't the primary goal.

They were *not* rapidly occurring events. What you said was that
CCDs beat PMTs for integration times longer than a few seconds.
The typical integration time for Pluto-Charon mutual event photomety
was a minute.

There are several advantages. They are much easier to calibrate than
PMTs,

Surely you jest; who ever took bias and flat calibrations with a
PMT? Who has to worry whether the overscan is a simple constant
or a function of line number with a PMT? Who has to worry about
a two-dimensional bias structure with a PMT?

When I used to use PMTs, I used calibration steps exactly analogous to
bias and dark frames. The two dimensional structure of the photocathode
was measured by scanning because the surface did not have a uniform
response.

Your photometer wasn't designed properly if you had to worry about the
two-dimensional structure of the cathode. The primary mirror is
supposed to be imaged on the cathode, not the focal plane.

Chris L Peterson writes:

On the contrary, the very fact that a PMT design images the primary
mirror on the cathode means that the light is spread out over a
large area of the detector, which makes it much less sensitive to
signal variations caused by mistracking of the telescope. When the
instrument is rigidly bolted to the telescope, the spot on the
cathode is fixed and does not move. With a CCD, taking multiple
exposures to get, for example, a lightcurve, means that you won't
necessarily have the object on the same pixels each time. Indeed,
it is often advisable to dither the telescope to purposely prevent
the object from falling on the same pixels. You are therefore at
the mercy of the quality of the flat field. Suppose the filter
acquires a new dust speck after the flats were taken? Sometimes
there isn't enough twilight to get a decent set of flats through
all the various filters, and dome flats can be a problem due to
the difficulty of getting truly uniform illumination.

You are supposing a lot of problems that are routinely and trivially
dealt with.

Not as trivial as you think.

Your experience with photometry is obviously quite different from my
own.

Twenty six years worth of photometry. Far easier to get millimagnitude
results using a PMT.

There is a reason that PMTs are used for only a small fraction of
photometry measurements. That is because in most cases CCD measurements
yield higher quality data,

On faint objects, which happens to be what most people are measuring
these days.

particularly where absolute magnitude is at issue.

Apparent magnitude.

They have a much better signal to noise ratio,

You're repeating yourself. As I noted previously, there are noise
sources that create a floor that is difficult to get below.

and they can be characterized and calibrated much better.

I disagree.

They are much more stable with time.

On the contrary, what matters is the entire system, not just the
detector itself. When a new speck of dust falls on the filter or
the dewar window, you've just created another artifact in the flat
field. Even though the senstivity of the detector itself could be
rock steady, the effective sensitivity has changed in the sense
that it affects the image.

If you are monitoring some sort of occultation, or a dim fast
rotator, a PMT photometer may be the best solution. But for most work,
the CCD is the tool of choice.

Depends entirely on the nature of the work.