Pixelation error

[RJN]

I have been playing with Polaris data trying to get a reasonable light curve and this has led me back into an investigation of a well-known type of systematic error that affects the type of photometry that is automatically computed and recorded.

It is easy to note that the C1-B values for Polaris (Alpha UMi) jump around well in excess of sqrt(N) statistical error. What causes this? I think it is "pixelation error" where the point spread function (PSF) for Polaris moves slightly across the CCD camera array as the Earth rotates. Now C1 measures the highest pixel count in the neighborhood of Polaris. As the Earth turns, the peak of the PSF for Polaris moves and the true peak moves even inside the highest pixel. So even if every pixel were completely uniform in sensitivity, the shift of the PSF peak would cause C1 to jump around. So I decided to test for this.

I went into the CI archive for Polaris for 040910 and 040909 and used 180s data only. C1-B varied well outside the statistical error. I then plotted C1-B for both days aligned at the SAME SIDEREAL TIME. Therefore, if the camera is stable, the PSF should peak in exactly the same places in the pixels, and C1-B should show similar variability over each night. Here is the plot I found:


Now it appears that the two data sets do indeed track each other and that the difference between the two data sets is close to just statistical errors. C1 is the most extreme but I see the same with C9, I think. Gotta go. More later.

- RJN

[tilvi]

I have been playing with Polaris data trying to get a reasonable light curve and this has led me back into an investigation of a well-known type of systematic error that affects the type of photometry that is automatically computed and recorded.

It is easy to note that the C1-B values for Polaris (Alpha UMi) jump around well in excess of sqrt(N) statistical error. What causes this? I think it is "pixelation error" where the point spread function (PSF) for Polaris moves slightly across the CCD camera array as the Earth rotates. Now C1 measures the highest pixel count in the neighborhood of Polaris. As the Earth turns, the peak of the PSF for Polaris moves and the true peak moves even inside the highest pixel. So even if every pixel were completely uniform in sensitivity, the shift of the PSF peak would cause C1 to jump around. So I decided to test for this.

I went into the CI archive for Polaris for 040910 and 040909 and used 180s data only. C1-B varied well outside the statistical error. I then plotted C1-B for both days aligned at the SAME SIDEREAL TIME. Therefore, if the camera is stable, the PSF should peak in exactly the same places in the pixels, and C1-B should show similar variability over each night. Here is the plot I found:

Now it appears that the two data sets do indeed track each other and that the difference between the two data sets is close to just statistical errors. C1 is the most extreme but I see the same with C9, I think. Gotta go. More later.

- RJN

Yes. It does follow the same trend over the nights, atleast for polaris. But, whether its PSF behaviour or pixel sensitivity, we need to get rid of it. I had posted the follwing plot earlier, counts vs Zenith angle, for polaris and it does shows the same trend over different nights. And since the angular change for polaris is very small (< 1degree), PSF should be expected to behave uniformly. I think we should try one of the method suggested by Dr Noah, to get the pixel sensitivity gradient across the CONCAM. And the latter method of making a uniiform white illumination seems to be physible.

[RJN]

Tilvi,

Yes, your plot shows the same thing! Very good. I have been thinking about whether this is caused by pixel sensitivity or "top count pixelization". I think I have new data that can show that the later is more important. CI recently had a frame where a cloud covered Polaris. The (FITS, JPG) address of this frame is:
http://nightskylive.net/ci/ci040906/ci0 ... 4046p.fits
http://nightskylive.net/ci/ci040906/ci0 ... 34046p.jpg
See also the photometry file for Polaris that whole UT day:
http://nightskylive.net/ci/ci040906/HD8890.html

The cloud that covered Polaris appeared to have a slowly varying surface brightness over the pixels that Polaris is stuck inhabiting. The pixel counts were: C(567,796)=608, C(567,797)=569, C(567,798)=589, C(567,799)=568 and C(568,799)=615. These are consistent with completely constant C value of about 590 over these four pixels, as the sqrt(N) statistical error (one sigma) is about 24.

Alternatively, one could take the pixel counts at face value to compute relative sensitivity. Then, the relative sensitivity between the high pixel (615) and low pixel (568) is about 1.083, an 8.3 percent effect. Now C1 varies for Polaris 6607 and 5505, a relative difference of 20 percent. So although statistical fluctuations are possible, it appears unlikely that pixel sensitivity can explain the effect.

After review, another key point comes into play: that the 6607 and 5505 pixel values recorded for the top/bottom C1 count for Polaris discussed above BOTH COME FROM THE SAME PIXEL. The C1 pixel is precisely pixel (567,799) for both the high and low measurement. So unless this pixel has a highly variable sensitivity over 30 minutes, the pixel sensitivity effect is smaller than the "top count pixelization" effect where amount of light falling into the top C1 pixel changes as the PSF center moves across the pixel.

Still, I agree that pixel sensitivity is important and flat fielding should be built in to the photometry as best as possible.

- RJN

[tilvi]

Tilvi,

After review, another key point comes into play: that the 6607 and 5505 pixel values recorded for the top/bottom C1 count for Polaris discussed above BOTH COME FROM THE SAME PIXEL. The C1 pixel is precisely pixel (567,799) for both the high and low measurement. So unless this pixel has a highly variable sensitivity over 30 minutes, the pixel sensitivity effect is smaller than the "top count pixelization" effect where amount of light falling into the top C1 pixel changes as the PSF center moves across the pixel.

Still, I agree that pixel sensitivity is important and flat fielding should be built in to the photometry as best as possible.

- RJN

Yes. I agree that since the counts varies for the same pixel over a short time, we should not expect that it has such varying sensitivty.
But for me it looks like that the fits files you have taken contains lots of droplets. So it might have affected the counts.

I took data for Polaris on another clear night and the pixel counts vary by less than 2 sigmas for the same pixel over a time of more than one hour.
http://nightskylive.net/ci/ci040817/HD8890.html

Fits files:
http://nightskylive.net/ci/ci040817/ci0 ... 4803p.fits

http://nightskylive.net/ci/ci040817/ci0 ... 5507p.fits

Here are the values for pixel (567,798) from UT 22:48 to 23:55.
C1-B: 7806-8627
C5-B: 5210 -5369
C9-B: 3591 -3676
C16-B: 2273-2300