Author: Tom Droege Date: 960107 Revision: #0 960107 Key Words: instrumentation, CCD
It is encouraging that most things are working as designed. Once the wires were in the right place, there were no "funny" problems except for the "false" port pulses. This has been given a "tech" fix - a capacitor across the output. Later we will design the problem out. Once up and running I have been able to just go down in the basement, throw some switches, and it just works. A very good sign.
A larger than expected full scale signal from the CCD chip lead to suspicion that the Kodak supplied scale factor of 10uv per electron may be significantly different from the actual scale factor. Since of order 2 volts full scale output signal has been observed, this implies a full well capacity of 200,000 electrons. This is well above the 85,000 electrons specified in the data sheet. If this is true, then a scale factor change in the electronics is appropriate to make use of the additional dynamic range.
It is proposed that if there are n electrons in the well and many measurements are made, then the RMS value of the measurement should be the SQRT of the number of electrons. If k in e-/ADU (ADU = ADC bit value) is the scale factor converting ADU to electrons then:
SQRT(k*Pixel ADU Mean Value) = k*RMS Pixel Value
and k = ADU Mean Value/(RMS Pixel Value)^2
To test this, the camera was set to look at the day time sky through a pin hole and a stack of white paper. The paper stack was adjusted to give a value near full scale. There are several problems. The pin hole tends to provide a good focus at any distance, so there is a tendency to see the grain of the paper and thus increase the RMS value of the measurement. The light value is also not constant, even though the sky is clear. There was a steady decrease in light during the measurement. To overcome this, shorter and shorter sample strings were taken until the difference was small.
The value of k derived from the amplifier gains and the Kodak 10uv per electron is 1.35 electron per ADU. The value obtained from this experiment was 1.41 electron per ADU. If anything, the measured number is low, since the RMS value is very sensitive to changing conditions during the measurement during the experiment.
It is therefore concluded that the Kodak value is roughly correct, and the larger range observed indicates a larger well capacity. This is good news for dynamic range, but bad news for noise level. The 1.41 scale factor and the measured dark value of 15 RMS ADU means the noise level is 21 electrons RMS.
We found a nice star to study in a run with a slightly better focus than the F1P4A.FOC.
The star is at RA 9h45m47.9sec, Decl. -1 deg 54' 49" and is listed in Sky Catalog 2000.0 as a V 7.9 magnitude. Since we are taking data with the V filter, this looked like a nice star for calibration. We note that even looking over a small field, we could find many stars that should have been in Sky Catalog 2000.0 and were not, and some that were there that we could not see. Hmmm!
The subject star peak is 18,100 ADU above the sky background. The sky background is 21500 counts above the dark value. From this we can conclude:
ADU Counts Magnitude 26,000,000 0 260,000 5 2600 10 26 15 .26 20
Note that this is conservative, because it uses the peak value rather than adding up the pixels around a peak. This is probably indicative of "finding" a faint star. For a bright star we can add up the local pixels, but for a faint star it may take a lot of computing time to dig it out of the noise.
We note for this run the sky background was greater than this magnitude 7.9 star at magnitude 7.7. This is mag 13.4 per square arc second. Where did I hear that sky background was numbers like mag 20 per square arc second? We were looking looking within 30 degrees or so of the full moon for this run. I suppose that this has something to do with it.
Converting the sky ADU counts to electrons, taking the square root, and then back to ADU gives a noise level of 123 counts. This is mag 5.4 below the mag 7.9 star and would indicate a one sigma limit of 13.3 due to the sky background. This seems to be in pretty good agreement with the estimate of mag 12 by Michael Richmond looking at somewhat inferior data.
Looking at a clear area near the measured star, a sigma of 114 ADU counts was computed. Computing as in the earlier calculation, this gives a k of 1.65 electrons/ADU and a noise of 25 electrons.
Using 1000 photons per sq cm per nanometer for mag 0, the 100 nanometer width of the V filter, 20 sq cm of lens, the 469 second integration time, and a mean qe in the pass band of .3 we get 281,000,000 electrons for a mag 0 star. The above table indicates that we see a peak value for mag 0 of 36,000,000 or about right for the integral when we add up everything.
There is still lots to do to make the data better. Looking at the pixels from a star, a diagonal to the south and later time is noted. There are two adjustments to be made. One is a rotation of the CCD to cause a star to track down a line of pixels. At this time, a 4 pixel error is accumulate in both time and rotation. Time is easy, since it is just a matter of time and an adjustment of the VCO. Angle is another matter, and the present unit was not put together too well and sticks when adjustments are made. Better adjustment is not too likely with this particular unit. The next one will contain a teflon pad and improved parts.
Indications are that we will reach the design goal of mag 15 when we get some dark sky. This with the V filter in place. The filter costs about mag 2 so the mag 17 estimate is not far off. There is still a lot to gain by a better focus and alignment.