Signal Processing Algorithm Description & Evaluation with - PowerPoint PPT Presentation

Signal Processing Algorithm Description & Evaluation with Simulation Brooke Russell Yale University DUNE APA Consortium Meeting October 2 nd 2017

Outline • Last meeting • Hanyu summarized single phase LArTPC signal formation and a full TPC simulation • Today I’ll describe • a technique to extract the ionization electron signal • a quantitative evaluation of this method using the simulation • limitations to this work and ongoing work to address these shortcomings 10/2/2017 Russell 2

Illustration of topology dependent signal & intra- and inter-wire dependence of field response Motivates 2D deconvolution with careful ROI selection 10/2/2017 Russell 3

1D Deconvolution • Deconvolution has been used in ICARUS and ArgoNeuT ∞ 𝑆(𝑢, 𝑢 ′ ) ∙ 𝑇 𝑢 𝑒𝑢 • 𝑁 𝑢 ′ = ׬ −∞ • Original signal 𝑇 𝑢 • Measured signal 𝑁 𝑢 ′ • Response function 𝑆(𝑢, 𝑢 ′ ) 𝑁(𝜕) 𝑁 𝜕 • 𝑇 𝜕 = 𝑆(𝜕) ⟹ 𝑇 𝜕 = 𝑆 𝜕 ∙ 𝐺(𝜕) • Filter function 𝐺(𝜕) needed to suppress high frequency noise • Deconvolve relative to the time dimension (1D) 10/2/2017 Russell 4

1D Deconvolution Technique Tension with Signal Formation Picture • Fie ield ld response • Shockley-Ramo Theorem 𝑗 = −𝑟𝐹 𝑥 ∙ Ԧ 𝑤 𝑟 𝑓𝑜𝑒 − 𝑊 𝑡𝑢𝑏𝑠𝑢 ) න 𝑗 𝑒𝑢 = 𝑟 𝑛 ∙ (𝑊 𝑛 𝑛 • Can infer: • Shape and normalization • Time duration of induced current • Induction range The weighting field extends beyond a single wire region 10/2/2017 Russell 5

2D Deconvolution • Deconvolve with respect to time and wire dimensions ∞ … + 𝑆 1 𝑢 0 − 𝑢 ∙ 𝑇 𝑗−1 𝑢 + 𝑆 0 𝑢 0 − 𝑢 ∙ 𝑇 𝑗 𝑢 + 𝑆 1 𝑢 0 − 𝑢 ∙ 𝑇 𝑗+1 𝑢 + ⋯ 𝑒𝑢 • 𝑁 𝑗 𝑢 ′ = ׬ −∞ • 𝑁 𝑗 (𝑢′) - measured signal from wire i, • 𝑇 𝑗 (𝑢) - signal within the boundaries of wire i , where ± a half pitch defines the wire boundaries • 𝑆 𝑜 (𝑢 0 − 𝑢) - average response of wire i , where 𝑜 =∥ 𝑗 ∥ • Fourier transform in matrix notation, 𝑁 1 𝜕 𝑆 0 𝜕 𝑆 1 𝜕 ⋯ 𝑆 𝑜−2 𝜕 𝑆 𝑜−1 𝜕 𝑇 1 𝜕 𝑁 2 𝜕 𝑇 2 𝜕 𝑆 1 𝜕 𝑆 0 𝜕 ⋯ 𝑆 𝑜−3 𝜕 𝑆 𝑜−2 𝜕 ⋮ = ⋮ ⋮ ⋱ ⋮ ⋮ ∙ ⋮ 𝑁 𝑜−1 𝜕 𝑆 𝑜−2 𝜕 𝑆 𝑜−3 𝜕 ⋯ 𝑆 0 𝜕 𝑆 1 𝜕 𝑇 𝑜−1 𝜕 𝑁 𝑜 𝜕 𝑆 𝑜−1 𝜕 𝑆 𝑜−2 𝜕 ⋯ 𝑆 1 𝜕 𝑆 0 𝜕 𝑇 𝑜 𝜕 • Now, by inverting 𝑆 and applying software filters for the wire and time dimensions, respectively, we’ve taken into account the induction range inherent to LArTPCs to extract charge 10/2/2017 Russell 6

2D Deconvolution • Deconvolution amplifies low-frequency noise for induction wire planes 𝑇 𝜕 = 𝑁(𝜕) 𝑆(𝜕) ⋅ 𝐺(𝜕) • Low frequency software filters are used to find induction plane signals in the deconvolved waveform • Tight low-frequency filter for short signals • Loose low-frequency-filter for prolonged signals 10/2/2017 Russell 7

ROI Refinement 10/2/2017 Russell 8

Algorithm Description 10/2/2017 Russell 9

Qualitative Performance • 1D deconvolution • Signal smearing • Less efficiency for reconstructing charge for tracks at large angle with respect to wire plane • 2D • Better recovers the true signal • More efficient recovery of charge for difficult topologies 10/2/2017 Russell 10

Performance Point Charge Percentage of total charge recovered Relative positive charge in percentage (+ charge, - charge) per wire Deconvolution results of a point charge of 10k electrons simulated 1m from wires planes • Time smearing : about 2.7 ticks and 2.3 ticks for induction and collection planes, respectively • Wire smearing : due to long range of induction, more pronounced on U plane • Charge bias : mismatch in field response (in signal formation and deconvolution) is mitigated by diffusion 10/2/2017 Russell 11

Noise Induced Charge Resolution Bin-to-bin correlations on induction planes Noise-like on collection plane 10/2/2017 Russell 12

Noise Induced Charge Resolution Total l Charge Resolution Wit ithin in th the Enti tire Center Bin in Char arge Resolu lution ROI Win indow Cor orrespondin ing to o Di Different ROI win indows 10/2/2017 Russell 13

Line Charge Bias, Resolution & Inefficiency Cha Charge Bi Bias Significant in induction planes at large 𝜄 𝑦𝑨 , a ramification of bipolar cancelation Cha Charge Res esolu lutio ion Dominated by noise induced charge fluctuation, especially problematic from noise in induction plane magnified by bipolar response in deconvolution Ine Ineffic iciency Ratio of reconstructed charge to true charge 10/2/2017 Russell 14

Signal Processing Results on Data Point Sources Line Source Fairly good charge matching across all three wire planes 10/2/2017 Russell 15

Signal Processing Results on Data • Average waveform from tracks of restricted angular range • Inter-plane charge matching 10/2/2017 Russell 16

Limitations ROI Finding • Failure to find ROI for large 𝜄 𝑦𝑨 tracks is a common source of inefficiency in current signal processing • Improving this is a current area of investigation 10/2/2017 Russell 17

Limitations 2D Field Resposes • We presently use Garfield to calculate 2D Field responses • Have residual limitations for modeling a 3D effect • Computing limitations make a direct 3D calculation difficult; this is an area of active development • Data-MC response comparison 2D Garfield simulation scheme illustration indicates there is room for further improvement 10/2/2017 Russell 18

Summary • Presented a method for ionization electron charge extraction in single phase LArTPCs • Evaluated the signal processing technique with a new full TPC simulation • Provided explanation of current technique limitations and areas of future development 10/2/2017 Russell 19

Backup Slides 10/2/2017 Russell 20

TPC Simulation 𝑋𝑏𝑤𝑓𝑔𝑝𝑠𝑛 = 𝐸𝑓𝑞𝑝𝑡𝑗𝑢𝑗𝑝𝑜 ⊗ 𝐸𝑠𝑗𝑔𝑢𝑗𝑜𝑕 ⊗ 𝐸𝑣𝑑𝑢𝑗𝑜𝑕 + 𝑂𝑝𝑗𝑡𝑓 ⨀𝐸𝑗𝑕𝑗𝑢𝑗𝑨𝑏𝑢𝑗𝑝𝑜 Charge deposition input: Geant4 or WCT tool or manual • Ionization • Recombination • Electron attachment • Diffusion • Statistical fluctuation • Field response • Electronics response Inherent electronics • 2 MHz sampling noise model • 2V max • 12 bit ADC 10/2/2017 Russell 21

Signal Formation • Field response • Electronics response • Event topolo logy True charge in one wire region Intra-wire field response Reconstructed charge (using average dependence response) in one wire region Inter-wire field response Reconstructed charge from center and dependence neighboring wire regions 10/2/2017 Russell 22

Signal Formation 𝜄 𝑧 = 90 ° with 𝜄 𝑦𝑨 varying • Field response • Electronics response • Event topolo logy • Results in topology- dependent signals 𝜄 𝑦𝑨 = 0 ° with 𝜄 𝑧 varying 10/2/2017 Russell 23