1. Scientific Detector Workshop, Taormina Sicily, June 2005 -1- Raw H2RG Image  Two Hawaii2RG images provided by Gert Finger is the starting point of this analysis of the nosie variance in the images, normally use for the “Photon Transfer Curve” means of relating variance to Poisson statistics to system gain. The second image appears virtually identical.

2. Scientific Detector Workshop, Taormina Sicily, June 2005 -2- Difference H2RG image  The difference of these two images still shows structure, but much of it has disappeared. Note the vertical stripes which will appear prominently in the power spectrum.

3. Scientific Detector Workshop, Taormina Sicily, June 2005 -3- Central 1024 Difference  Choosing the central 1024x1024 pixels in preparation for Fourier transforming the difference.  Again, note not only the wide-spaced vertial stripes, but the closely spaced stripes.

4. Scientific Detector Workshop, Taormina Sicily, June 2005 -4- Power Spectrum  The power spectrum of the difference shows noise which has obvious power features: Horizontal line = vertical stripes Spots = closely spaced vertical stripes Central spot = various large-scale features remaining in difference

5. Scientific Detector Workshop, Taormina Sicily, June 2005 -5- Binned Power Spectrum  Binning the power spectrum 8x8 and increasing the stretch makes non-uniformity in the power spectrum more obvious.  The power at the Nyquist frequency (corners) is significantly smaller than the asymptote as k -> 0.  The Poisson variance from the photons impinging on the detector has been suppressed by convolution with some sort of pixel-to-pixel correlation. The best estimate of the pre- convolution is the k->0 asymptote.  There is also significant non- circular uniformity apparent, indicating that the convolution is worse in the horizontal direction than the vertical direction.

6. Scientific Detector Workshop, Taormina Sicily, June 2005 -6- Masked for Averaging  To make a quantitative estimate of the error in variance estimation, mask out the features which are obviously caused by large scale detector characteristics rather than pixel-to- pixel correlations.

7. Scientific Detector Workshop, Taormina Sicily, June 2005 -7- Azimuthal Average  Despite the fact that the power spectrum is not accurately circular, take an azimuthal average so that we can examine the power spectrum as a function of |k|.

8. Scientific Detector Workshop, Taormina Sicily, June 2005 -8- Power Spectrum as a function of k  Take a cut through the azimuthal average to show the variance as a function of wavenumber.  The big peak at k~0 is large-scale structure which is caused by detector non-uniformities.  K=63 is the Nyquist frequency and the direct pixel-to-pixel correlation.  The big challenge is to understand what variance comes from pixel-to-pixel variations and what comes from large scale structure. We have used differencing to suppress the latter, but it is not perfect.

9. Scientific Detector Workshop, Taormina Sicily, June 2005 -9- Ln Power Spectrum and k 2 Fit  As a naïve starting point, imagine that the pixel-to-pixel correlation has a Gaussian form. If so we can fit the natural log of the power with a parabola.  This has a reasonable match to high k, but obviously does not explain low k large- scale features.

10. Scientific Detector Workshop, Taormina Sicily, June 2005 -10- Ln Power Spectrum and k4 Fit

11. Scientific Detector Workshop, Taormina Sicily, June 2005 -11- Ln Power Spectrum and k 4 Fit  A more likely pixel-to-pixel correlation arises from mutual capacitance, which might vary as r -3. I don’t recall the 2-D Fourier tranform of this, but a Lorenzian FT’s to an exponential, so we might expect that ln power should go linearly with k. Fitting a quartic polynomial demonstrates another division of power between pixel-to- pixel variance and large scale detector structure.  Quantitatively, the difference between Nyquist and k=0 is an offset in logarithm of 0.20, which means that a gain determined by “variance over signal” will be underestimated by a factor of 1.22.