Status of TPC Signal Simulation & Processing Jyoti Joshi Brookhaven National Laboratory LBL/Sim/Reco Meeting, 11/07/2016
Outline * Signal Processing Method * LArTPC Noise Experience * Signal Processing Challenges 2
Introduc>on: Signal Processing Sense Wires U V Y V wire plane waveforms Liquid Argon TPC Charged Particles Cathode Plane Incoming Neutrino Edrift t Y wire plane waveforms * TPC signal consists of >me and charge informa>on from induc>on and collec>on planes • Same amount of charge seen by all wire planes * The goal of signal processing is to extract both >me and charge informa>on reliably 3
TPC Signal Size • E"field:( – Electron(dri/(velocity( – Recombina6on(factor( • Electron(life6me( – Dri/(distance( ! (dri/(6me( ! (signal(size( • Track(angle( – Time(structure(of(signal( • Minimum(ionizing(vs.(heavy(ionizing( – Recombina6on(etc.( • Diffusion 4
Field and Electronic Response Field and Electronic Response Field Response Func>on Electronics Shaping Func>on * Using 2D garfield simula2on with 3mm * Cold electronics: wire pitch • Four shaping 2me - 0.5, 1, 2, 3 us * Charge vs. Time averaged for a single • Four gain seHngs - 4.7, 7.8, 14, 25 mV/fC electron * Further stretched signal for U and V considering 3D wires 5
Deconvolu>on Deconvolu>on Deconvolu)on* Time*domain* M( ) t R t ( t ) S t ( ) dt = ∫ − ⋅ ⋅ 0 0 t Fourier*transforma)on* M ω ( ) R( ) S( ) = ω ⋅ ω Frequency*domain* The goal of the M( ) ω S( ) F ω ( ) deconvolu>on ω = ⋅ R( ) ω process is to extract charge and >me informa>on from An);Fourier** S(t) transforma)on** the TPC signals 1* Back*to*)me*domain* 6 DPF, 2015 Jyo> Joshi 6
Deconvolu>on Filter Perfect Signal Adding Integer ADC Add Random Noise Add Filter 7 DPF, 2015 Jyo> Joshi 7
Noise Sources in Detector Electronics Noise (ENC) * Dominant noise sources are from the circuits and components directly connected to input node • i 2n arises in the sensor, e.g, from the leakage current; i 2nF may arise in the feedback circuit • i 2diel a thermal fluctua2ons in dielectrics • e 2n associated with the gain mechanism in the input transistor (known as “series noise”) Digi>za>on Noise * Digi2za2on noise is due to the signal digi2zed using 12-bit ADC. * Digi2za2on noise is usually made smaller than the electronics noise. 8
Excess Noise Sources * Noise associated with first transistor of the cold ASIC - Unavoidable - Expected ENC ~500 electrons at LAr temp (for 150 pF) - Depends on shaping 2me, wire length and TPC geometry * Noise from warm shaping amplifier & ADC - Negligible as compared to first transistor * Noise from other circuits in readout chain - Low frequency coherent noise from voltage regulator * Noise from wire bias power supplies - Negligible * Noise from cathode HV - Anode sensi2vity due to ripple from HV * ASIC satura2on due to wire mo2on - Charge generated due to wire mo2on in E.field 9
Noise Performance in MicroBooNE PSNR: Peak Signal to Noise RMS MicroBooNE- NOTE-1016-PUB.pdf ENC acer noise filtering is around 400 electrons for 85% of channels * ~ 10% Non-func2onal channels * Measured efficiency requiring two wire planes with real loca2on of dead * channels is about 97.3% 10
MicroBooNE- NOTE-1016-PUB.pdf * Socware noise filter is applied which improves peak-signal-to-noise ra2o by a factor of 2 11
Impact of Coherent Noise Filtering on Signal * Distor2on of Signal due to regulator noise removal specially when par2cle traveling parallel to the wire plane i.e, when signal is also coherent across many wires * Effect Signal Protec2on decreases with signal size closer to coherent noise U-Plane V-Plane Y-Plane MicroBooNE- NOTE-1016-PUB.pdf Worst Case Scenario 12
Impact of Non-Func>onal Channels Volume efficiency of a detector with can be es2mated as: where, p is efficiency for a single plane & n is number of planes Efficiency, if there are less number of planes: X. Qian But requiring less number of planes implies increase in ambigui2es (i.e, fake hits) And number of fake hits can be es2mated as: 13
Poten2al hits vs. real hits for 1% and 5% dead region See difference b/w solid & dashed lines X. Qian Hence the reconstruc2on becomes very challenging! 14
Signal Processing Challenge: Dynamic Induced Charge * The field response model shown before neglected the induced charge contribu2ons from the adjacent wires * The induced current on each wire can be derived by Shockley-Ramo therorem: Garfield Simula2ons 1.7 deg track from ver2cal The electron dric lines (orange color) are superimposed on the weigh2ng field contours * Induc2on signal strongly depends on local charge distribu2on * Due to this induced signal on adjacent wire, the digi2zed signal on wires is more complicated and strongly depends on track angle. 15 DPF, 2015 Jyo> Joshi 15
MicroBooNE- NOTE-1017-PUB.pdf 16
Deconvolu>on Scheme with DIC * Including effects of induced charge from adjacent wires : ( ) ⋅ M i ( t 0 ) = R 0 ( t − t 0 ) ⋅ S i ( t ) + R 1 (t − t 0 ) ⋅ S i + 1 ( t ) + ... dt ∫ t M i ( ω ) = R 0 ( ω ) ⋅ S i ( ω ) + R 1 ( ω ) ⋅ S i + 1 ( ω ) + ... * With induced signals, the signal is linear sum of direct signal and induced signal, can be represented in a matrix form: M ( ) R ( ) R ( ) ... R ( ) R ( ) S ( ) ω ω ω ω ω ω # $ # $ # $ 1 0 1 n 1 n 1 − % & % & % & M ( ) R ( ) R ( ) ... R ( ) R ( ) S ( ) ω ω ω ω ω ω % 2 & % 1 0 n 2 n 1 & % 2 & − − ... ... ... ... ... ... ... % & % & % & = ⋅ % & % & % & M ( ) R ( ) R ( ) ... R ( ) R ( ) S ( ) ω ω ω ω ω ω % & % & % & n 1 n 1 n 2 0 1 n 1 − − − − % & % & % & M ( ) R ( ) R ( ) ... R ( ) R ( ) S ( ) ω ω ω ω ω ω ( ) ( ) ( ) n n n 1 1 0 n − * Inversion of matrix `R’ can be done with deconvolu2on through 2D Fast Fourier Transforms (FFT) 17 DPF, 2015 Jyo> Joshi 17
Challenges in Signal Processing: 2D Deconvolu>on MicroBooNE- Exercised Two-dimensional deconvolu>on technique to NOTE-1017-PUB.pdf extract number of ionized electronics from wire planes Raw signal is very small: Track traveling perpendicular to wire plane 18
Challenge with Induc>on Plane Low Frequency filter in deconvolu2on step, can remove the long signal. Understanding of response func2on and Region of Interest (ROI) selec2on is very important 19
Current Implementa>on in dunetpc code * Noise model used is simple white gaussian noise * There is also another noise model (acer noise filtering) based on coherent noise removal which has exponen2al feature in low frequency from 35ton data * Field response func2on used is the average one, currently no contribu2on from induced charge from adjacent wires and hence 1D-deconvolu2on * More code structure improvements (David Adams) 20
Summary * Many Challenges in TPC Signal Simula2on and Processing * Noise model from data (acer noise filtering) already exists * Work is ongoing on 3D field response calcula2ons (Bres & Leon) * New improvements in simula2on code structure (David Adams) * More realis2c Signal Simula2on code with data-drive noise model and detailed response func2on development in Wire-Cell framework (Xiaoyue) 21
BACK-UP 22
Fast Fourier Transformation (FFT) & AutoCorrelation * FFT is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. Fourier analysis converts a function from time domain to the frequency domain by factorizing the matrix into a product of mostly zero factors. FFT computes the same result in O( N log N ) operations which DFT computes in O( N 2 ) * Autocorrelation is the cross-correlation of a signal with itself. Basically, it is the representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals. Relation b/w FFT & AutoCorrelation According to Weiner-Khintchine theorem , the autocorrelation function of a random process is the Fourier transform of its power spectrum. 23
Gain and Shaping >me • Choice of gain doesn’t impact on the S/N ra2o, higher gain can be sensi2ve to ADC overflow • Longer Shaping 2me has smaller noise (higher S/N ra2o), but slightly worse two peak separa2on Simulated Double Track Waveform : Bo Yu 24
Raw and Convoluted Signal Raw Signal - MIP Convoluted Signal 25
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