Background photo courtesy of NOAO. Taken with LBNL p-channel CCD with extended red sensitivity.

1. Pixel Area Variation in CCDs and Implications for Precision Photometry Roger Smith & Gustavo Rahmer (Caltech) Pixels change size ; centers may be displaced. % % Guider 0.26% 36 NIR Detectors 3 bandpasses Spectrograph slit 560mm diameter 36 CCDs, 6 bandpasses QE QE Actual X X 1 pixel 1 pixel Signal Signal actual Nominal X ideal QE X 1 pixel Signal X HOW FLAT FIELDING CAN HURT YOU We present a technique for determining what fraction of CCD flat field variations is due to repartitioning of charge between pixels as opposed to the QE variation normally assumed. While the fully depleted p-channel CCDs developed at LBNL for SNAP compare favorably to conventional n-channel CCDs , we find that variation in pixel size accounts for significantly more Pixel Response Non-Uniformity (PRNU) than QEin both cases,and thus the application of flat fields at full spatial resolution will do more harm to photometric precision than good, except in areas where abnormally large sensitivity drop outs occur. ` Sensitivity variation Conventional wisdom Pixel boundary offsets Alternative possibility Some mixture of both Reality Origin of boundary offsets What causes granularity in flats? • If we average lots of bright flat fields, the shot noise drops below the intrinsic pixel to pixel variation. • This variation has been widely assumed to be due to sensitivity. • It is usually removed by dividing by a flat field in which the lower spatial frequencies have been suppressed, since low spatial frequencies are presumed to be due to illumination effects. …but is this correct ? Sample test. Pixel boundaries are defined by the peak of the barrier potentials. These are defined by implants between columns and by electrode voltages between lines. Cumulative errors (scale, alignment) in the lithography are very small, but any implant or electrode can be offset slightly. An electrode or mask can be etched to a different width or can have local edge roughness, and of course there can be impurities or crystal defects which distort electric fields. So, although the average pitch is well controlled there can be some randomness in boundary positions. Pixel Response Non-Uniformity is typically <1% rms. The error in boundary position need only be ~100nm to produce this. When pixel boundaries are relocated, incident flux is allocated differently between pixels but total signal is conserved. There is no error from aperture photometry. Profile fitting may be affected by the shift in centers. PRNU SMOOTHING RATES Average of all Average of 10 Single E2V Averaging along lines (average of columns) reduces the standard deviation as 1/√N indicating that pixel values are uncorrelated along lines. The observed 1/N smoothing rate along columns provides strong evidence for pixel size variations:boundary relocation within the smoothing box has no effect on integrated charge, while errors at the outer boundaries are divided by N. Line plots Dust spots Stitching % PRNU is the flat field divided by a 9x9 boxcar-smoothed version of itself. This removes mid-frequency sensitivity ripples as well as any illumination gradient. This image is actually the reciprocal of PRNU: boxcar divided by flat instead of flat divided by boxcar, so white = less sensitive. Given that the PRNU is small the standard deviation is unaffected. Column plots Expanded scale Single Average of 10 Average of all SNAP The smoothing curves are qualitatively similar to E2V’s but the SNAP CCD has less random pixel size variation and more periodic line & column structure. To suppress periodic structure, the average of all rows is subtracted from each row, and the average of all columns is subtracted from each column. This only reduces the standard deviation from 0.45% to 0.40%. The suppression of the floor demonstrates that it is indeed due to the periodic line and column width structure. Slopes are now closer to theory. Stddev/mean = 3960/858,810= 0.46% After div by 9x9 boxcar, stddev = 0.45% Line plots Comparison with other p-channel CCDs for the Dark Energy Camera shows that periodic patterns depend on CCD orientation on the wafer. Presumably patterns are rastering errors in the mask writer. Column plots FIT TO POWER SPECTRUM Adding small amount of white noise gives an excellent fit Simulation fits PRNU at high frequencies 2D FFT (0,0) at center; log intensity, but linear frequency scale Low zone at center and broad weak rings in both 2D FFTs are due to division by 9x9 boxcar to make PRNU image. Brightening of upper and lower areas is due to random pixel boundary displacements along columns. Bright axes indicate slight width variations of entire rows and columns. Raw flat field Simulation E2V The amplitude of the pixel size power spectrum (green) is predicted from the standard deviation of the PRNU image. The only fitting required is to determine the relatively small white noise component. Surprising Discovery ! The power spectrum of pixel area variations is independent of the distribution chosen for boundary offsets. Same, after suppressing periodic line/col structure Adding some white noise gives an excellent fit Simulation fits PRNU at high frequencies 2D FFT Same scale as the FFT for the e2V CCD. Generally darker since overall PRNU is lower. Flatter since pixel height variation is smaller relative to random QE variations. Brighter axes are consistent with row & column patterns observed. There is little evidence of pixel width variation along rows for either CCD. SNAP SNAP CCDs exhibit qualitatively similar behavior to E2V’s. Although overall PRNU is less and the white noise floor (presumed to be random QE variation) is greater, it is still the case that Standard deviation for shot noise < QE variation < Pixel size variation. These CCDs are 250um thick fully depleted p-channel devices on high resistivity Silicon with 10.5um pixels, whereas the e2v CCDs are conventional thin n-channel devices with 30um pixels. They are made at different foundries with different processes, so the fact that they exhibit such similar behavior suggests that the effects seen will be found in all CCDs. SPIE Astronomical Telescopes and Instrumentation, Marseille, 2008-06-23, 6pm. Poster 7021-87 Background photo courtesy of NOAO. Taken with LBNL p-channel CCD with extended red sensitivity.