Definition FPN S Ampling - Stanford University
Lecture Notes 7Fixed Pattern Noise Definition Sources of FPN Analysis of FPN in PPS and APS Total Noise Model Correlated Double SamplingEE 392B: Fixed Pattern Noise7-1
Fixed Pattern Noise (FPN) FPN (also called nonuniformity) is the spatial variation in pixel outputvalues under uniform illumination due to device and interconnectparameter variations (mismatches) across the sensor It is fixed for a given sensor, but varies from sensor to sensor, so if vo isthe nominal pixel output value (at unifrom illumination), and the outputpixel values (excluding temporal noise) from the sensor are vij for1 i n and 1 j m, then the fixed pattern noise is the set of values voij voij vo FPN consists of offset and gain components – increases with illumination,but causes more degradation in image quality at low illumination FPN for CCD image sensors appears random CMOS (PPS and APS) sensors have higher FPN than CCDs and sufferfrom column FPN, which appears as “stripes” in the image and can resultin significant image quality degradationEE 392B: Fixed Pattern Noise7-2
FPN ImagesFor CCD sensorEE 392B: Fixed Pattern NoiseFor CMOS sensor7-3
Sources of FPN CCD image sensors only suffer from pixel FPN due to spatial variation inphotodetector device parameters and dark current – neither the CCDs northe output amplifier (which is shared by all pixels) cause FPN (additionalnonuniformity can result if more than one output amplifier is used,however) In CMOS image sensors pixel transistors cause additional pixel FPN andcolumn amplifiers cause column FPN. As a result FPN is in general higherthan in CCDsEE 392B: Fixed Pattern Noise7-4
Main sources of FPN in PPS:idcADvT , ColCfvoopvREF vos Pixel FPN is mainly due to the variation in the photodetectorparameters (e.g., area AD ) and dark current Column FPN is due to the variation in the column amplifierop, feedback capacitor value, resetparameters, e.g., offset voltage vostransistor threshold voltage and overlap capacitance value ColEE 392B: Fixed Pattern Noise7-5
In APSvDDvDDvT R , ColRvT F ,idcWFLFADCDvoibias In addition to variation in the photodetector parameters and darkcurrent, pixel FPN is caused also by variations in transistorparameters Column FPN is mainly due to variation ibiasEE 392B: Fixed Pattern Noise7-6
PPS and APS FPN APS suffers from higher pixel FPN than PPS but PPS generally suffersfrom higher column FPNPPSEE 392B: Fixed Pattern NoiseAPS7-7
Quantifying FPN FPN is quantified by the standard deviation of the spatial variation inpixel outputs under uniform illumination (not including temporal noise). Itis typically reported as a % of voltage swing (or well capacity) FPN standard deviation values of 0.1% to 4% of well capacityhave been reported Experimentally, FPN is measured as follows: Set a constant uniform illumination level (including no illumination) Take many images For each pixel compute the average output value (to average outtemporal noise) Estimate the standard deviation of the average pixel values Repeat the procedure for several uniform illumination levelsEE 392B: Fixed Pattern Noise7-8
Analysis of FPN Suppose we are given the standard deviation of each parameter thatcasues FPN, we now show how to compute its contribution to the totalFPN Assume the parameter values to be random variables Z1,Z2, . . ., Zkexpressed asZi zi Zi,where zi is the mean of Zi (i.e., nominal value of the device parameter)and Zi is the variation of Zi from its mean, and has zero mean andstandard deviation σZi Assuming sufficiently small device parameter variations, we canapproximate the pixel output voltage (for a given illumination) as afunction of the device parameters using the Taylor series expansion, ask! vo ""Vo(Z1, Z2, . . . , Zk ) vo(z1, z2, . . . zk ) · Zi" zz,z,.zi 1 2ki 1EE 392B: Fixed Pattern Noise7-9
where vo(z1, z2, . . . zk ) is the nominal output voltage and vo/ zi is thesensitivity of vo w.r.t. the ith parameter (evaluated at the nominalparameter values) So the variation in Vo can be represented by the random variablek! vo ""· Zi Vo " zz,z,.zi 1 2ki 1 To quantify FPN, we find the standard deviation of the output voltage,σVo , i.e., the standard deviation of the r.v. Vo Assuming that the Zis are uncorrelated (may not be a good assumptionin general), we can write# k &'2 ! vo ""σVo %· σZ2 i" zi z1,z2,.zki 1EE 392B: Fixed Pattern Noise7-10
Column and Pixel FPN For a CMOS (PPS or APS) image sensor, let the column deviceparameters be Z1 , Z2, . . ., Zl and the rest be the pixel device parameters,we can define the column variation asl! vo ""Y · Zi" zz,z,.zi 1 2ki 1and the pixel variation ask! vo ""· ZiX " zi z1 ,z2,.zki l 1 We quantify column FPN by σY and pixel FPN by σX (vary withillumination) Since (by assumption) X and Y are uncorrelated2σV2o σY2 σXEE 392B: Fixed Pattern Noise7-11
Offset and Gain FPN The pixel output voltage vo and FPN σVo vary with illumination The nominal output voltage from a pixel can be expressed in terms of thephotocurrent density asvo hjph voswhere h is the pixel gain in V·cm2/A (not to be confused with sensorconversion gain g) and vos is the pixel offset (which includes the dark signalopas well as the offset voltages due to the amplifiers used, e.g., vosfor PPS) Assuming all photodetectors have the same QE, and thus under uniformillumination, they have the same photocurrent density, we can now writethe pixel output voltage variation as))( k( k""! h "! vos " Vo Zi jph Zi"" zi z1,z2,.zk zi z1 ,z2,.zki 1i 1 H jph VosEE 392B: Fixed Pattern Noise7-12
We quantify offset FPN by σVos and gain FPN by σH · jph Offest FPN is reported as % of well capacity Gain FPN is referred to as Pixel Response Nonuniformity (PRNU) and isreported as % of gain factor variation, i.e., 100σH /h Note that H and Vos are not necessarily uncorrelated, since somedevice parameters can affect both offset and gainEE 392B: Fixed Pattern Noise7-13
Analysis of FPN in PPS The figure shows the device parameters consideredidcADvT , ColCfvoopvREF vosopAD is the photodiode area, idc is its dark current, vosis the opamp offsetvoltage, Col is the overlap capacitance, and vT is the threshold voltageEE 392B: Fixed Pattern Noise7-14
The output voltage in steady state is given by1opvo (Q Col vT ) · vREF vos,Cfwhere Col vT is the “feedthrough” charge (when the reset transistor isturned off), and the charge Q accumulated on the photodiode capacitanceQ (jphAD idc)tint The following table lists the absolute values of the parameter senitivities voand effect on FPN ziParameter Sensitivity Effect on FPNtintADpixel/gainC · lumn/offsetvTColEE 392B: Fixed Pattern Noiseidc tint Col vTCf2 ADCt2int · et7-15
Offset FPNσVos#))2 &(( &'2'2 &'2 tt CvivCintdcintolTTolσC f %σidc σv2op σC σvosCfCf2Cf olCf T Gain FPNσH · jph Pixel FPN#)2 &'2 ( tAD tintint jph %σAD σC fCfCf2σX *&jphtintσADCf'2 &tintσiCf dc'2 Column FPN#(())2 & '2 &'2 it Cv AjtvCdc intol TD ph intTolσY %σv2op σ σvσCCfosCf2Cf olCf T2 Note that the FPN variance σV2o σX σY2 can be written as the sum ofthree terms, a term that is independent of the signal, a term thatincreases linearly with the signal, and a term that increases quadraticallywith the signalEE 392B: Fixed Pattern Noise7-16
Example Assume the following device parameter means, standard deviations, andthat tint 30msParameter MeanσSensitivityAD50µm2 0.4%AD 15 103jphV/µm2idc5fA2%idc1.5mV/fAopvos0V2mV1Cf20fF 0.2%C f 11.6 1011V/F37500jphV/fFvT R0.8V 0.2%v T R0.02Col0.4fF 0.4%C ol0.04V/fFEE 392B: Fixed Pattern Noise7-17
Offset FPNParameter Contribution to σVosidc0.15 mVopvos2 mVCf0.0464 mVvT R0.032 mVCol0.064 mVandσVos 2mV,op valuewhich is basically equal to the opamp offset σvos Gain FPN at jph 2.64 10 6A/cm2 (high illumination)Parameter Contribution to σH · jphAD7.92 mVCf3.96 mVandσH · jph 8.85mVEE 392B: Fixed Pattern Noise7-18
The following figure plots total FPN σVo , pixel FPN σX , and column FPNσY , assuming monochromatic illumination F0 photons/cm2.s at quantumefficiency QE 0.3109Pixel FPNColumn FPNTotal FPN87FPN (mV)65432101210EE 392B: Fixed Pattern Noise13102illumination Fo (photon/cm s)14107-19
Analysis of FPN in APSvDDvDDvT R , ColRidcADCDvT F ,WFLFvoibias In steady state and assuming soft reset, the output voltage is given by)( Q2LF vT F ibias ,vo vDD vT R CDknWFwhere the charge accumulted on the photodiode is given byQ (AD jph idc)tint ColRvDDThe ColRvDD term is the “feedthrough” charge (when the reset transistoris turned off)EE 392B: Fixed Pattern Noise7-20
Example Consider the following parameter means and standard deviationsparameter meanσeffect on FPNidc5fA2%idcpixel/offsetAD50µm2 0.4%ADpixel/gainCD20fF 0.4%C D pixel/offset,gainvT R1.1V 0.2%v T Rpixel/offsetColR0.4fF 0.4%C olRpixel/pffsetvT F0.9V 0.2%v T µA1%ibiascolumn/offset You will compute the FPN component values in the homeworkEE 392B: Fixed Pattern Noise7-21
Image Sensor Total Noise Model Combining temporal noise and FPN, we can express the total inputreferred noise charge asQn Qshot Qreset Qreadout Qfpn,where Qshot is the r.v. representing the noise charge due to photodetectorphoto and dark current shot noise and is Gaussian with zero meanand variance 1q (iph idc)tint electrons2 Qreset is the r.v. representing the reset noise and is basicallyindependent of the signal Qreadout is the r.v. representing the readout circuit noise (possiblyincluding quantization) and is basically independent of the signalEE 392B: Fixed Pattern Noise7-22
Qfpn is the r.v. representing FPN (in electrons), and can berepresented either as a sum of pixel and column components1Qfpn (X Y )gwhere g is the sensor conversion gain in V/electron,or offset and gain components1Qfpn ( Hjph Vos)gThus it has one component that is independent of signal and onethat grows with the signal The noise components are assumed independent Thus the total average noise power is the sum of three components: One that does not depend on the signal (due to reset and readoutnoise and offset FPN) One that increases linearly with the signal (iph or jph) (due to shotnoise and gain FPN) One that increases quadratically with the signal (due to gain FPN)EE 392B: Fixed Pattern Noise7-23
Noise as Function of Photocurrent 3Average Noise power (V 2 )10 410 510 610 710 1610 1510 14 131010 1210 1110iph (A)EE 392B: Fixed Pattern Noise7-24
Correlated Double Sampling (CDS) CDS is a multiple sampling technique commonly used in image sensors toreduce FPN, and reset and 1/f noise You sample the output twice; once right after reset and a second timewith the signal present. The output signal is the difference between thetwo samples CDS only reduces offset FPN (does not reduce gain FPN) CDS does not cancel offset FPN due to dark current variation In CCDs, PPS, photogate and pinned diode APS, CDS cancels resetnoise. In photodiode APS it increases itEE 392B: Fixed Pattern Noise7-25
CDS in PPSWordResetSSSRCoSCoRResetSRWord, SSEE 392B: Fixed Pattern Noise7-26
Cancellsop, vT , and Col FPN due to vos Temporal noise due to reset (terms Vo22 and Vo32 in our analysis) Readout noise due to op-amp 1/f noise Does not cancel Offset FPN due to idc variation. This is called Dark SignalNon-uniformity (DSNU) Gain FPN (or PRNU) Other temporal noise components Adds Opamp noise due to reset read (Vo42 term) KTCnoise due to SS and SR transistorsEE 392B: Fixed Pattern Noise7-27
To summarize, the total noise charge for the two samples are given by:Qn1 Qreset Qread1 Qfpn1Qn2 Qshot Qreset Qreadout2 Qfpn2Note that Qfpn1 is simply an offset FPN whereas Qfpn2 is the sum of offsetand gain FPN (PRNU). However, Qfpn1 does not include the offset FPNdue to dark current variation (DSNU), whereas the offset part of Qfpn1includes itThe difference between the two samples is thus:Qn2 Qn1 Qshot (Qreadout2 Qreadout1) Qprnu QdsnuEE 392B: Fixed Pattern Noise7-28
PPS FPN With and Without CDS The following figure plots PPS FPN with and without CDS (assumingopthat vos, vT , and Col are eliminated)109CDSw/o CDS87FPN (mV)65432101210EE 392B: Fixed Pattern Noise1310illumination Fo (photon/cm2 s)14107-29
PPS Offset FPN With and Without CDS10102020303040405050606010203040without CDSEE 392B: Fixed Pattern Noise5060102030405060with CDS7-30
CDS in 3T APSResetSSWordSRCoSCoRWordSSResetSREE 392B: Fixed Pattern Noise7-31
Cancells All offset FPN terms involving vT R, vT F , ColR,WFLF ,and ibias Does not cancel DSNU Reset noise PRNU Readout noise AddskT(reset noise component during reset readout Reset noise 2CDindependent of that during signal readout) Readout noise during reset readout kTCdue to SS and SR transistorsEE 392B: Fixed Pattern Noise7-32
To summarize, the total noise charge for the two samples are given by:Qn1 Qshot Qreset1 Qreadout1 Qfpn1Qn2 Qreset2 Qreadout2 Qfpn2The difference is:Qn1 Qn2 Qshot (Qreset1 Qreset2) (Qread1 Qread2) Qprnu Qdsnu An important advantage of photogate and pinned diode APS is that resetnoise is eliminated using CDS instead of doubledEE 392B: Fixed Pattern Noise7-33
i dc 5fA 2%i dc pixel/offset A D 50µm 2 0. 4%A D pixel/gain C D 20fF 0. 4%C D pixel/offset,gain v TR 1.1V 0. 2%v TR pixel/offset C R 0.4fF 0. 4%C R pixel/pffset v TF 0.9V 0. 2%v TF pixel/offset W F L F 4 2 0. 2% W F L F pixel/offset i s 1. 88µA 1%i s column/offset k e 7-21
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layer. Unlike them, our proposed Recursive Feature Pyramid goes through the bottom-up backbone repeatedly to enrich the representation power of FPN. Additionally, we incorpo-rate the Atrous Spatial Pyramid Pooling (ASPP) [14,15] into FPN to enrich features, similar to the mini-DeepLab design in Seamless [59]. Recursive Convolutional Network.
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