1. NIRISS NRM bad pixel tolerance analysis David Lafrenière 2012 February 21

2. Simulation description Master PSF OTE phase maps RevV NRM mask G7S6SC Polychromatic, using F430M filter profile Created with oversampling of 11x11 compared to NIRISS pixels Soummer, Pueyo, Sivaramakrishnan, Vanderbei OpEx 2007, same as WebbPSF algo) Pointing Telescope pointing error for acquisition and dithers: 15 mas RMS Telescope pointing jitter while guiding: 5 mas RMS Simulated at 0.01 pixel precision using oversampled PSFs

3. Simulation description Detector Pixel flat field error: 0.1% Non-uniform intra-pixel sensitivity 1 at pixel center, decreasing to a mean of 0.8 at pixel corner (with RMS of 0.05) Gaussian shape 21 e- read noise per CDS Mean dark current of 0.012 e-/sec Inter-pixel capacitive coupling included Bad pixels included (see later for details)

4. Simulation description Observation L’=7.5 mag star 256x256 subarray (t frame =0.66 s) Read mode, TFIRAPID, N frame =1, N group =14 Peak pixel kept at <70000 e- in last read 9 dithers on a 3x3 grid with 4” step Assumed that the central 7x7 pixel box at each dither position was free of bad pixels 121 integrations at each dither position 3 hour clock-time total on target plus a similar sequence on a calibrator 12 min exposure on each of target and calibrator

5. Bad pixels Varied fraction of bad pixels from 0% to 5% Randomly distributed, assumed that 5/6 th of bad pixels are grouped in a “cross pattern” while 1/6 th are individual pixels Bad pixels assumed completely unusable Bad pixel fraction 1%Bad pixel fraction 5% 128x128 subarray

6. Bad pixels overlaid on PSF A single exposure, on a log display scale Bad pixel fraction 1%Bad pixel fraction 5%

7. Analysis 1.Mask bad pixels. Using integer shifts only, center all PSFs such that their brightest pixel is aligned 2.Average all images together to obtain a “clean” PSF image 3.For each image, shift the “clean” PSF image by fraction of pixel to align it precisely with the image, then substitute bad pixels for the corresponding values from the shifted “clean” image. 4.Apply a fractional shift to all images to precisely register them to a common center. 5.Average all images to obtain a new, and better, “clean” PSF. 6.Repeat 3 & 4 using the new “clean” PSF image to substitute bad pixels. 7.Apply the usual procedure to extract the CP and SqV from each image, then average them.

8. Results – detection limits Limiting contrast (in difference of magnitude) as a function of angular separation 0.06”0.08”0.10”0.20”0.30”0.40” 0% 7.758.268.548.898.938.98 0.5% 7.668.178.458.768.738.79 1% 7.668.168.438.728.678.75 2% 7.427.928.198.498.428.49 3% 7.127.637.928.248.188.24 4% 6.937.457.748.088.028.08 5% 6.667.207.507.867.817.85

9. Results – detection limits Magnitude loss in contrast compared with 0% bad pixels 0.06”0.08”0.10”0.20”0.30”0.40” 0% 0.00 0.5% -0.09 -0.13-0.20-0.19 1% -0.09-0.10-0.11-0.17-0.26-0.23 2% -0.33-0.34-0.35-0.40-0.51-0.49 3% -0.63 -0.62-0.65-0.75-0.74 4% -0.82-0.81-0.80-0.81-0.91-0.90 5% -1.09-1.06-1.04-1.03-1.12-1.13

10. Results – detection limits Factor of loss in contrast compared with 0% bad pixels 0.06”0.08”0.10”0.20”0.30”0.40” 0% 1.00 0.5% 1.09 1.131.201.19 1% 1.091.101.111.171.271.24 2% 1.361.371.381.451.601.57 3% 1.79 1.771.822.001.98 4% 2.132.112.092.112.312.29 5% 2.732.652.612.582.812.83

11. Conclusion Relatively good tolerance to bad pixels using dithers To limit the loss in contrast at any separation to less than 0.5 mag compared with 0% bad pixels, the bad pixel fraction should be less than 3%