CCD sensitivity and resolution

How does one figure out the arc second resolution potential for a CCD chip?
Is there a way to know what magnitude limit a CCD imager has?

On Fri, 25 Jan 2008 20:49:27 GMT, "TMA" wrote:

How does one figure out the arc second resolution potential for a CCD chip?
Is there a way to know what magnitude limit a CCD imager has?

Calculate the resolution A (in arcsec per pixel) as

A = 206265 * d / F

where d is the size of the pixel, and F is the focal length of the
telescope, both in the same units.

Calculating the magnitude limit is quite complex. It depends primarily
on the QE (as a function of wavelength) of the sensor, the exposure
time, and on the aperture of the telescope. You also need to consider
the various noise sources: readout, dark current, sky, and the
statistical noise on the signal itself. Some of the noise sources are
themselves dependent on the exposure time and the focal ratio of the
telescope.

_________________________________________________

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

Chris L Peterson wrote:
On Fri, 25 Jan 2008 20:49:27 GMT, "TMA" wrote:

How does one figure out the arc second resolution potential for a CCD chip?
Is there a way to know what magnitude limit a CCD imager has?

Calculate the resolution A (in arcsec per pixel) as

A = 206265 * d / F

where d is the size of the pixel, and F is the focal length of the
telescope, both in the same units.

Calculating the magnitude limit is quite complex. It depends primarily
on the QE (as a function of wavelength) of the sensor, the exposure
time, and on the aperture of the telescope. You also need to consider
the various noise sources: readout, dark current, sky, and the
statistical noise on the signal itself. Some of the noise sources are
themselves dependent on the exposure time and the focal ratio of the
telescope.

Chris is quite right on both counts. I'd like to add a little bit to
his discussion about magnitude limit.

The bottom line is that you want the signal in the brightest pixel of
the star image to be at least 2 or 3 times the noise. (Higher if you
want to do decent astrometry.) The amount of signal you get depends on
the QE, the exposure time, the aperture, *and on the seeing*. If the
seeing is excellent, or if your pixels subtend a lot of sky, most of the
starlight will fall in one pixel -- ideal for detection, not so good for
precision astrometry. As the pixel size shrinks, or as the seeing gets
worse, the same number of photons will now be spread over more pixels,
and that lessens the peak signal and hurts detection.

The other half of it is noise. Shot noise (because light comes in
discrete photons) goes as the sqrt of the number of electrons (NOT the
sqrt of the data number!). The same calculation also applies to other
sources of electrons -- stray light, dark current, skyglow. There's
also read noise in the on-chip amplifier, which is generally independent
of the signal level. There are other noise sources too, but read noise
and shot noise are the two biggies. Add them in quadrature (square root
of the sum of their squares) to get the total.

If your camera has a lot of read noise but a very dark background, all
you have to do is to get the signal 2 or 3 times as much as the read
noise and you're OK. Doubling the exposure would get you stars 50%
fainter. But if shot noise is the bigger concern -- as is usually the
case -- you must quadruple the exposure to gain a factor of 2 in
sensitivity. The signal goes up by a factor of 4 but the noise by a
factor of 2.

Hope this helps.

-- Bill Owen

On Fri, 25 Jan 2008 20:49:27 GMT, "TMA" wrote:

How does one figure out the arc second resolution potential for a CCD chip?
Is there a way to know what magnitude limit a CCD imager has?

The resolution of the CCD chip in arc seconds would be 206,265 times
the pixel pitch divided by the focal length of the telescope. Use the
same units for pixel pitch and focal length.

The limiting magnitude of the CCD chip depends on the aperture of the
telescope, the length of the exposure, conditions at your site, etc.
To learn what the limting magnitude is you would have make images and
see what you get.

Bud

Chris L Peterson:
Calculate the resolution A (in arcsec per pixel) as

A = 206265 * d / F

where d is the size of the pixel, and F is the focal length of the
telescope, both in the same units.

Calculating the magnitude limit is quite complex. It depends primarily
on the QE (as a function of wavelength) of the sensor, the exposure
time, and on the aperture of the telescope. You also need to consider
the various noise sources: readout, dark current, sky, and the
statistical noise on the signal itself. Some of the noise sources are
themselves dependent on the exposure time and the focal ratio of the
telescope.

Damned near impossible. Add air/light pollution to the imponderables.
I think that it would be a lot less trouble to measure the magnitude
limit over a number of exposures under ideal skies. If (and I recognize
that's a big if) Hubble GSC 2.2 is accurate, I have captured mag 21
stars with my Tak 180mm f2.8 astrograph and SBIG STL-11000 from my
suburban location.

There is a mag 19 star (according to GSC 2.2) in the images that I
captured with the a 76mm 'scope and Canon 20D DSLR in a four-minute
exposure and posted at
http://www.davidillig.com/ast-73p_s-w060429.shtml.

Davoud

--
usenet *at* davidillig dawt com

On Fri, 25 Jan 2008 23:12:26 GMT, Davoud wrote:

Damned near impossible. Add air/light pollution to the imponderables.

I wouldn't go that far. I have a fairly simple flux calculator in a
spreadsheet that does a pretty accurate job of estimating limiting
magnitude for a given sensor, exposure time, sky background, aperture,
and desired S/N. But...

I think that it would be a lot less trouble to measure the magnitude
limit over a number of exposures under ideal skies.

.... you're right, it's easy to measure, and you're going to get the most
realistic idea of your camera's performance that way.

If (and I recognize
that's a big if) Hubble GSC 2.2 is accurate, I have captured mag 21
stars with my Tak 180mm f2.8 astrograph and SBIG STL-11000 from my
suburban location.

That sounds about right. Do you recall what kind of exposure time was
required?

_________________________________________________

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

Is the pixel pitch just the width of a pixel?

The resolution of the CCD chip in arc seconds would be 206,265 times
the pixel pitch divided by the focal length of the telescope. Use the
same units for pixel pitch and focal length.

The limiting magnitude of the CCD chip depends on the aperture of the
telescope, the length of the exposure, conditions at your site, etc.
To learn what the limting magnitude is you would have make images and
see what you get.

Bud

On Sat, 26 Jan 2008 00:21:47 GMT, "TMA" wrote:

Is the pixel pitch just the width of a pixel?

It depends on the sensor. Some have dead space between the pixels, so
the active area isn't as wide as the spacing between them. A lot of
newer sensors use little lens arrays over the top to try and get the
sensitive area larger.

In any case, when calculating resolution, the pitch is the distance
between adjacent pixels, which isn't necessarily the actual pixel width.
Also, some sensors have different pitches horizontally and vertically,
and therefore different resolutions. If so, you can calculate them
separately.

_________________________________________________

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

Davoud:
If (and I recognize
that's a big if) Hubble GSC 2.2 is accurate, I have captured mag 21
stars with my Tak 180mm f2.8 astrograph and SBIG STL-11000 from my
suburban location.

Chris L Peterson:
That sounds about right. Do you recall what kind of exposure time was
required?

About three minutes.

The magnitudes (21--or less) are correct, but I made a misstatement. I
see that GSC 2.2 has a magnitude limit of 19.5. Sure enough, using
XEPhem with field stars set to mag 30, the dimmest stars displayed are
in the mag 19 range. I have stacks of FITS images that show stars
dimmer than shown in XEPhem, though they don't always show up in my
reduced images because I try to process for aesthetics.

Davoud

--
usenet *at* davidillig dawt com

On Sat, 26 Jan 2008 16:45:30 GMT, Davoud wrote:

About three minutes.

The magnitudes (21--or less) are correct, but I made a misstatement. I
see that GSC 2.2 has a magnitude limit of 19.5. Sure enough, using
XEPhem with field stars set to mag 30, the dimmest stars displayed are
in the mag 19 range.

Yes, mag 19 sounds reasonable for three minute exposures. I've got
images showing stars around mag 21, but with exposure times more in the
hour range (and with less sky background).

I have stacks of FITS images that show stars
dimmer than shown in XEPhem, though they don't always show up in my
reduced images because I try to process for aesthetics.

Makes sense. The dimmest stars are going to be right up against the
noise floor, and when you process for aesthetics, you usually pull up
your black level to hide that noise. It's a fun exercise to see just how
deep you can get- something you can try if you ever get a long enough
stretch of good conditions that you can "waste" some time on
non-aesthetic imaging g. From your comments over the last couple of
years (since you got some top-notch equipment on line, naturally) it
sounds like your good imaging opportunities have been depressingly rare.

_________________________________________________

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