Summary of SPIE ATI contrib :

1. Summary of SPIE ATI contrib: A framework for modeling the detailed optical response of thick, multiple segment, large format sensors for precision astronomy applications (paper 9150—41) Andrew RasmussenSLAC National Accelerator Laboratory LSST Camera Instrument Scientist + P. Antilogus, P. Astier, C. Claver, P. Doherty, G. Dubois-Felsmann, K. Gilmore, S. Kahn, I. Kotov, R. Lupton, P. O’Connor, A. Nomerotski, S. Ritz, C. Stubbs & sensor testing teams LPHNE/IN2P3/CNRS UPMC, NOAO, Harvard, Brookhaven, Princeton, UCSC SPIE 2014Astronomical Telescopes & Instrumentation

2. Who needs a pixel partition model? • LSST sensors are • large format (16Mpix) back-illuminated • Highly segmented (16x 1Mpix segments) • Aspect ratio 10 (100μm thick, with 10μm pitch) • Scope • Reasons to build an optical response model • What tools are practical? • How can the model be tuned? • How will results be used?

3. Issues relating to the recording fidelity of imaging sensors • Photon transfer curves (PTC) • Greater information content than system gain. Poisson interpretation of PTC makes “gain” a poorly defined quantity and can systematically over-predict sensor QE curves if this gain is used. • Brighter-fatter effect • Correlation between recorded PSF size and integrated source flux • Anisotropic charge sharing • Evidence drawn from a generalization of PTCs that pixel response itself responds to flat field statistical fluctuations • Tree rings • Flat field distortions due to fossil impurity nonuniformities in ingot • Astrometric shifts • Fixed pattern, neighboring pixel response anti-correlation • Pixel area variation constraints from PRNU pixel sum statistics and/or power spectral density of these statistics

4. Issues relating to the recording fidelity of imaging sensors (2) • Device fixed pattern features - these reveal placement of the sensor format on top of the wafer • Tearing* - transient bimodal contour features in flat field response that span multiple amplifiers • Bamboo(竹林)* - periodic distortions in flat field response • Spot projector data - confirmation of pixel size variation hypothesis for some of the preceding effects • Backside bias voltage dependence – smoking gun for bent field lines as origin of pixel size variation * These are not expected issues with delivered science sensors – but aid in our understanding of drift mechanisms

5. Distortion effects seen in flat field illumination: fixed pattern Fringing (expected to not be an issue on LSST - F/1.2) Tree rings (~30 pixel period), approx. parallel to fringes Water marks on AR coating? Projections of dust particles?

6. Distortion effects seen in flat field illumination: fixed pattern (2) *Spot projector has been used to verify that flat field response distortions are not QE distortions (e.g., P.Doherty, SPIE ATI 2014) edge rolloff* 9 10 11 12 13 14 15 16 midline charge redistribution* 8 7 6 5 4 3 2 1

7. Launching position: (x,y,z)=(9.31,8.71,100)um BSS=-48,-58,-68,-78V Drift calculation examples Depth (distance from gates) Serial address (x) Parallel address (y) 2um 8um [01] [11] y y 2um 2um x x [00] [10] 8um 8um @ (-5,-5)um @ (-5,-5)um

8. Cross-cuts in the periodic electrostatic barrier (perturbative) field Depth (distance from gates) Depth (distance from gates) Serial address (x) Parallel address (y)

9. Backdrop field validation - 55Fe X-rays Simulated data (for specific backdrop field) data (ASCA) grade specific pulseheight distributions X-ray charge cluster pulseheight e.g., Prigozhin et al. 1998

10. Backdrop field validation - 55Fe X-rays (2) σ=0.5pix σ=0.15pix Expected probability distributions in sum ratio p4/p9 for sample sigma values Response matrix p(p4/p9|σ) p4/p9 distributions for various backside bias voltages

11. Backdrop field validation - 55Fe X-rays (3) Predictions using Jacoboni [1977] velocity saturation model (surface conversions) σ (p96) [pixels] No velocity saturation (approx) backside bias voltage [V]

12. Backdrop field validation (4) Tree ring distortion feature amplitude depends on backside bias: Tree ring feature extraction 1% 1% 1%

13. Backdrop field validation (5) Functional derivative Impurity gradient Drift coefficient function is drawn from the drift calculation

14. Include perturbative terms & periodic potentials Heavy use of method of images to impose translational invariance at equipotential boundary conditions Barrier terms (channel stops & barrier clocks) Channel occupancy terms (collected conversions) Typical scale units for dipole moments:

15. Bamboo flat field distortion (rel) pixel parallel address Detail of “bamboo” flat field distortion showing 41 pixel step-and-repeat period Backside bias voltage dependence of bimodal fixed pattern flat field distortion Flat field distortion (rel.) Astrometric shift (pixels)

16. Relative barrier strengths (channel stops vs. barrier clocks) Antilogus et al. 2014: Pixel correlations vary By factor of 3 (A01 vs. A10) Channel stop barrier strength is tuned to reproduce the factor of 3 between pixel area distortion response to collected charge in (0,0) (A01vs A10)

17. Results & comparisons to data: midline midline feature modeled as a isolated channel stop implant extending across sensor’s width cf. a (black:data; red:drift calculation) Flat field distortion (rel.) Astrometric shift (pixels)

18. Results & comparisons to data: edge rolloff cf. b (black:data; red:drift calculation) Flat field distortion (rel.) nb: no guard drain bias included in calc. Edge rolloff modeled as a truncation in the channel stop array of implants Astrometric shift (pixels)

19. Pixel distortion Greens function(induced by collected charge dipole moment) 1p0 8p0 2p0 16p0 (4p0) 4p0 Detailed mean-variance curves, autocorrelation matrices and point-source distortion may be computed (also for adjacent BSS, barrier clock and wavelength/SED)

20. Summary & outlook • Modeling framework will assist in estimation of instrumental imaging systematics that will be present in on-sky data for future dark energy experiments • Framework is based on first principles (electrostatics) and constrained by measurements that favor specific coordinates in parameter space • Wavelength & SED dependence of pixel response is available parasitically – computed as part of the drift calculation. • Quantitative matches to fixed pattern flat field distortion features suggest: • significant fractions of focal plane pixels may be retained & analyzed (vs. trimmed & discarded). If trimmed, expect 1.25-3% loss in coverage per 10 pixel band. • use of ancillary pixel data (area, position, shape transfer, σ(x,y,z) will facilitate analysis • Drift calculation results will be encoded into an efficient pixel partition library for use with image simulators (e.g. phosim) to improve fidelity and determinism of instrument systematics • Impacts on science by unmitigated systematics are unknown – engaging the LSST Dark Energy Science Collaboration for assistance in approaching these questions • DECam is already in operation and is affected by pixel systematics. We plan to: • Adapt framework parameters to perform drift calculations for DECam • Validate drift model using similar methods to what was outlined above • A testbed for astronomical data analysis using ancillary pixel data may be exercised with DECamdata.

21. Systematic effects to focused images consistent with autocorrelation features Ellipticity kernel S2E1 Brighter/Fatter Source input parameters: aspect ratio = 1.05:1.0 FWHM = 3.0 pix centroid = (0.25,0.25) Orientation = 30° parallel φ E1 component E2 component serial Black: no covariance Red: covariance model parameterized by the drift coefficients: Orientation (delivered) Ellipticity(delivered)

22. backup

23. Backup • Mean-variance • Autocorrelation matrices • Ellipticity & brighter/fatter

24. Autocorrelation maps from simulated flat fields(two drift coefficients, all distance effects applied < 0.5 pixels)

25. Comparison of PSFs with FWHM different by a factor of sqrt(2): FWHMinput=3*sqrt(2) pix FWHMinput=3 pix 0.2pix 0.2pix ΔFWHMRSS S2E1 0.06 pix2 0.06 pix2 Conversions in central pixel

27. Backup • Drift calcs details • Tearing onset • Tree ring astrometric & flat field distortion

28. Example drift calculation:edge rolloff effects NB: no guard ring.. σ(x,z) moment = 20ξ0 & 40ξ0 flat field response (pix) astrometric shift (pix) Δx(x,z) NB: specific predictions for diffusion-position coupling! σmax(x) φ (x,z)

29. Quantitative agreements between drift model & flat field distortions: “tearing” onset features Black: data; Red: calculation “dark border” (occurs between adjacent amplifier segments) ξ=+5ξ0 ξ=+1ξ0 ξ=-5ξ0 ξ=-1ξ0 “bright finger” (occurs in column pairs straddling isolated, hole-saturated channel stops)

30. Example of a drift coefficient calculation – for tree ring flat field-, astrometric- and pixel shape distortions Drift coefficient curves specific to backside bias setting Scaling parameter determination by fitting observable quantities Pixel-level and PSF-level distortions arising from a periodic function in underlying “hidden variable” Predicted wavelength dependence of PSF-level distortions (excl. pixel-level)

31. Backup • Backdrop field math & total field expressions

32. “backdrop” drift field strength

33. Lo-stretch (left) & hi-stretch (right) flat fields