CMOS Image Sensor Design_h20_5_noise_sources.pdf
- 1. INF5350 – CMOS image sensor design Lecture 5 – Noise and modelling S/N 15-September-2020
- 2. Agenda • Check project status • Takeaways from previous lecture&exercises • Noise and S/N in CMOS image sensors 14.09.2020 IN5350 2
- 3. Project schedule Task/milestone Start Finish Chose topic/scope 1-Sep 8-Sep Create project plan (tasks, milestones, schedule) 8-Sep 15-Sep MS1 – project plan approved by Johannes 15-Sep 22-Sep Study literature on the topic (include summary in report) 22-Sep 29-Sep Design implementation&simulation 29-Sep 13-Oct Write up prelim report (inc references, design, results) 13-Oct 20-Oct MS2 – submit preliminary report to Johannes 20-Oct 20-Oct Design/simulation (fine tuning) 20-Oct 27-Oct Write up final report (incl references, design, results) 27-Oct 3-Nov MS3 – Presentation and discussion 3-Nov 3-Nov MS4 – submit final report to Johannes 10-Nov 10-Nov Exam 18-Nov ✅ 14.09.2020 IN5350 3 ✅
- 4. NOISE SOURCES IN IMAGE SENSORS
- 5. Two noise categories 14.09.2020 5 1. Temporal noise 2. Fixed pattern noise Temporal noise: random disturbance which changes every time a capture is taken Fixed pattern noise: fixed pattern superimposed on the image. Same pattern in each frame, but pattern varies randomly from sensor to sensor (which is why it is termed noise)
- 6. Temporal noise example 14/09/2020 IN5350 6 Temporal noise changes randomly with time (ie for every capture) Example pixel row profile: Column position Pixel value
- 7. Photon shot noise • Temporal noise that changes randomly from pixel to pixel and capture to capture (even if light level is constant) • Follows Poisson’s probability distribution: • p(x) = probability of x incidents (e.g. x photons detected in a pixel during Tint), • e = natural logarithm base (~2.72), • µ = mean value, i.e. statistical average of x, ie ∑𝑥𝑥 𝑥𝑥 � 𝑝𝑝(𝑥𝑥) 𝑝𝑝 𝑥𝑥 = 𝜇𝜇𝑥𝑥𝑒𝑒−𝜇𝜇 𝑥𝑥! 14.09.2020 IN5350 7 µ = mean value
- 8. Convenient Properties of Poisson process Signal/Noise of ideal photon detector (𝝁𝝁/𝝈𝝈): 𝑺𝑺𝑺𝑺𝑺𝑺 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝑥𝑥) 𝑉𝑉𝑉𝑉𝑉𝑉(𝑥𝑥) = 𝜇𝜇 𝜇𝜇 = 𝝁𝝁 𝑽𝑽𝑽𝑽𝑽𝑽 𝒙𝒙 = 𝜎𝜎𝑥𝑥 2 = � 𝑥𝑥=0 ∞ 𝑥𝑥 − 𝜇𝜇 2𝑝𝑝(𝑥𝑥) = 𝝁𝝁 Ex: if a pixel detects an average of 100photons, then S/N=10 (20dB) 14.09.2020 IN5350 8 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝑥𝑥) = � 𝑥𝑥=0 ∞ 𝑥𝑥 � 𝑝𝑝(𝑥𝑥) = 𝝁𝝁
- 9. 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0 2 4 6 8 10 12 14 16 18 20 Poisson distribution plots at various mean values (µ) µ=1 µ=2 µ=10 Number of incidences (e.g. photons or electrons) Probability of occurrance (no unit) 14.09.2020 IN5350 9
- 10. Photon shot noise examples Ref: Wikipedia µ=0e- µ=1e- µ=2e- µ=4e- µ=10e- µ=30e- µ=100e- µ=1000e- µ=10000e- 14.09.2020 IN5350 10
- 11. Fixed pattern noise (FPN) • FPN (also called nonuniformity) is the time invariant spatial variation in pixel output values under uniform illumination (incl total darkness) due to device and parameter variations (mismatches) across the sensor • Fixed for one sensor, but the nonuniformity pattern changes randomly from sensor to sensor. Hence, the ‘noise’ term. • E.g. vertical or horizontal stripes, white pixels, black pixels, shading, … IN5350 14.09.2020 11
- 12. FPN compensation • FPN in pixels can be compensated digitally • For instance, dark FPN (ie FPN under zero illumination) can be removed by subtracting a dark image from regular captures – But FPN compensation too costly in commercial products. Instead, sensor must be designed for FPN to be invisible to human eye => 10x below temporal noise Original picture Dark image After compensation A B A - B IN5350 14.09.2020 12
- 13. Dark current = both temporal noise and fixed noise (FPN) • Thermally generated electrons (or holes) in the pixel. Adds to the photo-generated signal charge and thus creates a pedestal offset. • Problem is that dark current is a random process (Poissonian, just like photons). Hence, it appears as noise in the picture or video at high temperatures and/or long integration times. • Mean value accross the array (Ndark) is a constant value and not defined as noise, since not random. In fact, it can be measured and subtracted from the pixel values (Black. • Standard deviation (σdark) is temporal noise IN5350 14.09.2020 13
- 14. Thermal noise • Thermal agitations of electrons within a resistance (fundamental in all circuits) Random variation for every capture Example row profile in darkness: IN5350 14.09.2020 14
- 16. Introduction • Signal/noise ratio (S/N or SNR) is an essential quality performance parameter of any sensor • SNR quantifies how precise, accurate, reliable, trustworthy, .. the sensor output value is • Modelling SNR is important when making design desicions such as pixel size, circuit topology, ADC resolution, etc. • This section covers SNR modelling, incl correlated double sampling, and the impact of FPN 14.09.2020 IN5350 16
- 17. Outline • Define signal and noise for CMOS image sensors • Create model of S (from photons to bits) • Create model of N (shot noise, RN, ADC..) • Create model of CDS sampling process • Discuss how FPN influences SNR 14.09.2020 IN5350 17
- 18. Signal-to-noise ratio (SNR) 14.09.2020 18 Input signal (a.u.) Output signal (a.u.) Sensor Input signal Output signal&noise σ=rms noise=std.dev. µ 𝑆𝑆𝑆𝑆𝑆𝑆 ≝ 𝜇𝜇 𝜎𝜎 S/N in dB: 20log( 𝜇𝜇 𝜎𝜎 ) µ=mean sig IN5350
- 19. Model of signal chain (multiple blocks) 14.09.2020 IN5350 19 G1, σ1 G2, σ2 G3, σ3 Sin/ σin Sout/σout 𝑆𝑆𝑜𝑜𝑜𝑜𝑜𝑜/𝜎𝜎𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑆𝑆𝑖𝑖𝑖𝑖𝐺𝐺1𝐺𝐺2𝐺𝐺3 𝜎𝜎𝑖𝑖𝑖𝑖 2 𝐺𝐺1 2 𝐺𝐺2 2 𝐺𝐺3 2 + 𝜎𝜎1 2 𝐺𝐺2 2 𝐺𝐺3 2 + 𝜎𝜎2 2 𝐺𝐺3 2 + 𝜎𝜎3 2 S: signal Gi: gain of module i σi: rms noise added by ith module (uncorrelated with the others) NB! Noise sources added together. However, only in power (V2) domain, not in voltage domain due to the noise voltage (and/or noise current) being random with zero mean value.
- 20. Pixel+ADC model 14.09.2020 IN5350 20 CGfd, σkTC Gsf, σsf Gadc, σadc Sin/ σin Sout/σout 𝑆𝑆𝑜𝑜𝑜𝑜𝑜𝑜/𝜎𝜎𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑆𝑆𝑒𝑒−𝐶𝐶𝐺𝐺𝑓𝑓𝑓𝑓𝐺𝐺𝑠𝑠𝑠𝑠𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎 𝑆𝑆𝑒𝑒−𝐶𝐶𝐶𝐶𝑓𝑓𝑓𝑓 2 𝐺𝐺𝑠𝑠𝑠𝑠 2 𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎 2 + 𝜎𝜎𝑘𝑘𝑘𝑘𝑘𝑘 2 𝐺𝐺𝑠𝑠𝑠𝑠 2 𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎 2 + 𝜎𝜎𝑠𝑠𝑠𝑠 2 𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎 2 + 𝜎𝜎𝑎𝑎𝑎𝑎𝑎𝑎 2 Floating diffusion Source follower A/D converter Se-: number of photo-electrons generated by photodiode Sout: ADC output signal (DN or LSBs) σkTC, σsf: rms noise voltage from FD and SF, respectively (V rms) σadc: rms noise from ADC after gain (LSB rms) Gadc: ADC conversion gain, (2^Nbits-1)/Vref_adc (LSB/V) CGfd: floating diffusion conversion gain (V/e-) Eliminated with CDS Readnoise, RN Photon shot noise
- 21. Calculating rms noise value (σ) from noise spectrum, N(f) • Integrate N(f) across all frequencies to get σ • N(f): noise spectrum (V2/Hz) • σ: rms noise voltage (V) 14.09.2020 IN5350 21 df f Nout out ∫ ∞ = 0 ) ( σ
- 22. Frequency domain representation 14.09.2020 IN5350 22 H(f) N(f) Sin(f) Nin(f) Sin(f): input signal spectrum (V2/Hz) H(f): transfer function of any linear time-invariant system, e.g. pixel, amplifier, filter, ADC, CDS, .. N(f): noise spectrum of additive noise source inside H(f), e.g. Johnson noise or 1/f-noise from resistors or transistors (V2/Hz) Sout(f) Nout(f) 2 ) ( ) ( ) ( f H f S f S in out ⋅ = ) ( ) ( ) ( ) ( 2 f N f H f N f N in out + ⋅ =
- 23. Signal chain in frequency domain 14.09.2020 IN5350 23 H1(f) N1(f) Sin(f) Nin(f) H(f): transfer function of any linear time-invariant system, e.g. pixel, amplifier, filter, ADC, CDS, .. N1(f), N2(f), N3(f): noise spectrum of noise sources (V2/Hz) H2(f) N2(f) H3(f) N3(f) Sout(f) Nout(f) 2 3 2 1 ) ( ) ( ) ( ) ( ) ( f H f H f H f S f S in out ⋅ = ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 3 2 3 2 2 3 2 1 2 3 2 1 f N f H f N f H f H f N f H f H f H f N f N in out + ⋅ + ⋅ + ⋅ =
- 24. CIS signal chain from photons to bits CIP CCM 14.09.2020 IN5350 24 𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴
- 25. Pixel light flux for a given scene illumination obj D f F = Esc=scene irradiation (W/m/m2) ρsc=scene reflectivity (no unit) F=lense F-nummer (=f/Dobj) Dobj= lens aperture (m) f = lens focal length (m) Ad=detector area (m2) λ=light wavelength (m) Ed=detector irradiation (W/m/m2) 14.09.2020 IN5350 25 2 4 ) ( ) ( ) ( F E E sc sc d λ ρ λ λ =
- 26. Calculation of pixel value after ADC ref adc N PGA sf pix pix sc sc ADCout V G G CG d T A QE F hc E S bits _ 0 int 2 1 2 ) ( ) ( 4 1 / ) ( − ⋅ = ∫ ∞ λ λ λ ρ λ λ SADCout=output value (DN aka LSBs) Esc(λ)=spectral irradiation (W/m/m2) ρsc(λ)=scene reflectivity (no unit) Tint=camera exposure time (s) F=lense F-nummer (=f/Dobj) h=Plancks constant (6.6x10-34 J s) c=speed of light (3x108 m/s) Apix=detector area (m2) λ=light spectral wavelength (m) 14.09.2020 IN5350 26 CGpix=conversion gain (V/e-) Gsf=source follower gain (no unit) Nbits=ADC resolution (no unit) Vadc_ref=ADC saturation level (V)
- 27. Temporal noise sources • Photon shot noise =>µ=Se-, σ=sqrt(Nph) – Nph: mean value of photons • Dark current noise =>µ=Ndc, σ=sqrt(Ndc) – Ndc: mean value of dark current electrons • Read noise =>µ=0, σ=RN (V rms) – RN: temporal noise in darkness from pixel+ADC 14.09.2020 IN5350 27 2 2 2 / / CG G N S S SNR sf RN dc e e ADCout σ + + = − − 2 2 2 2 2 2 2 RN G G CG N G G CG S adc sf pix dc adc sf pix e ADCout + + = − σ adc sf pix e ADCout G G CG S S − =
- 28. Read noise sources • Temporal noise at zero illumination • Read noise =>µ=0, σ=RN – RN: rms noise floor in dark from pixel+ADC – Pixel source follower noise sources • White noise • 1/f noise – ADC noise • White noise • 1/f noise • Quantization noise =>µ=0, σ=1LSB/sqrt(12) 14.09.2020 IN5350 28
- 29. Example of 4T pixel output signal with noise 14/09/2020 IN5350 29 kT/C noise Reset level (Vrst) White noise and 1/f noise, Npix(f) Signal level (Vsig) Vpix(t) t RST TX
- 30. White noise and 1/f noise in transistors 14.09.2020 IN5350 30 N(f) N(f)=k N(f)=1/f N(f)=1/f2