CMOS Image Sensor Design_h20_5_noise_sources.pdf

CMOS Image Sensor Design_h20_5_noise_sources

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
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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 (increferences, 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 (inclreferences, 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
✅
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✅

4. NOISE SOURCES IN IMAGE
SENSORS

5. Two noise categories
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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
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Temporal noise changes randomly
with time (iefor 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 T
int),
•e = natural logarithm base (~2.72),
•µ = mean value, i.e. statistical average of x, ie∑
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????????????????????????=
????????????
????????????
????????????
−????????????
????????????!
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µ = mean value

8. Convenient Properties of Poisson process
Signal/Noise of ideal photon detector (????????????/????????????):
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????????????????????????????????????????????????(????????????)
????????????????????????????????????(????????????)
=
????????????
????????????
=????????????
????????????????????????????????????????????????=????????????
????????????
2=
�
????????????=0
∞
????????????−????????????
2
????????????(????????????)=????????????
Ex: if a pixel detects an average of 100photons, then S/N=10 (20dB)
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????????????????????????????????????????????????(????????????)=�
????????????=0
∞
????????????�????????????(????????????)=????????????

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)
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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-
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11. Fixed pattern noise (FPN)
•FPN (also called nonuniformity) is the time
invariantspatial 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, …
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12. FPN compensation
•FPN in pixels can be compensated digitally
•For instance, dark FPN (ieFPN 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
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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 (N
dark) 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 (σ
dark) is temporal noise
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14. Thermal noise
•Thermal agitations of electrons within a resistance
(fundamental in all circuits)
Random variation for every
capture
Example row profile in darkness:
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15. SIGNAL/NOISE MODEL

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 sectioncovers SNR modelling, incl correlated
double sampling, and the impact of FPN
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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
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18. Signal-to-noise ratio (SNR)
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Input signal (a.u.)
Output signal (a.u.)
Sensor Input signal Output signal&noise
σ=rmsnoise=std.dev.
µ
????????????????????????????????????≝
????????????
????????????
S/N in dB: 20log(
????????????
????????????
)
µ=meansig
IN5350

19. Model of signal chain (multiple blocks)
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G
1,
σ
1
G
2,
σ
2
G
3,
σ
3
S
in/σ
in S
out/σ
out
????????????
????????????????????????????????????/????????????
????????????????????????????????????=
????????????
????????????????????????????????????
1????????????
2????????????
3
????????????
????????????????????????
2
????????????
1
2
????????????
2
2
????????????
3
2
+????????????
1
2
????????????
2
2
????????????
3
2
+????????????
2
2
????????????
3
2
+????????????
3
2
S: signal
G
i: gain of module i
σ
i: rmsnoise added by i
th
module (uncorrelated with the others)
NB! Noise sources added together. However, only in power (V
2
) domain,
not in voltage domain due to the noise voltage (and/or noise current)
being random with zero mean value.

20. Pixel+ADCmodel
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CG
fd,
σ
kTC
G
sf,
σ
sf
G
adc,
σ
adc
S
in/σ
in S
out/σ
out
????????????
????????????????????????????????????/????????????
????????????????????????????????????=
????????????
????????????−????????????????????????
????????????????????????????????????
????????????????????????????????????
????????????????????????????????????
????????????
????????????−????????????????????????
????????????????????????
2
????????????
????????????????????????
2
????????????
????????????????????????????????????
2
+????????????
????????????????????????????????????
2
????????????
????????????????????????
2
????????????
????????????????????????????????????
2
+????????????
????????????????????????
2
????????????
????????????????????????????????????
2
+????????????
????????????????????????????????????
2
Floating
diffusion
Source
follower
A/D
converter
S
e-: number of photo-electrons generated by photodiode
S
out: ADC output signal (DN or LSBs)
σ
kTC, σ
sf: rmsnoise voltage from FD and SF, respectively (V rms)
σ
adc: rmsnoise from ADC after gain (LSB rms)
G
adc: ADC conversion gain, (2^Nbits-1)/Vref_adc(LSB/V)
CG
fd: floating diffusion conversion gain (V/e-)
Eliminated with
CDS
Readnoise, RNPhoton shot noise

21. Calculating rmsnoise value (σ) from noise
spectrum, N(f)
•Integrate N(f) across all frequencies to get σ
•N(f): noise spectrum (V
2
/Hz)
•σ: rms noise voltage (V)
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dffN
outout∫
∞
=
0
)(σ

22. Frequency domain representation
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H(f)
N(f)
S
in(f)
N
in(f)
S
in(f): input signal spectrum (V
2
/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 (V
2
/Hz)
S
out(f)
N
out(f)
2
)()()( fHfSfS
inout
⋅=
)()()()(
2
fNfHfNfN
inout +⋅=

23. Signal chain in frequency domain
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H
1(f)
N
1(f)
S
in(f)
N
in(f)
H(f): transfer function of any linear time- invariant system, e.g. pixel,
amplifier, filter, ADC, CDS, ..
N
1(f), N
2(f), N
3(f): noise spectrum of noise sources (V
2
/Hz)
H
2(f)
N
2(f)
H
3(f)
N
3(f)
S
out(f)
N
out(f)
2
321
)()()()()( fHfHfHfSfS
inout⋅=
)()()()()()()()()()()(
3
2
32
2
321
2
321fNfHfNfHfHfNfHfHfHfNfN
inout +⋅+⋅+⋅=

24. CIS signal chain from photons to bits
CIP
CCM
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????????????
????????????????????????????????????????????????????????????????????????

25. Pixel light flux for a given scene illumination
obj
D
f
F=
E
sc=scene irradiation (W/m/m
2
)
ρ
sc=scene reflectivity (no unit)
F=lense F-nummer (=f/D
obj)
D
obj= lens aperture (m)
f = lens focal length (m)
A
d=detector area (m
2
)
λ=light wavelength (m)
E
d=detector irradiation (W/m/m
2
)
14.09.2020 IN5350 25
2
4
)()(
)(
F
E
E
scsc
d
λρλ
λ
=

26. Calculation of pixel value after ADC
refadc
N
PGAsfpixpixsc
sc
ADCout
V
GGCGdTAQE
Fhc
E
S
bits
_0
int2
12
)()(
4
1
/
)( −
⋅





=
∫
∞
λλλρ
λ
λ
S
ADCout=output value (DN aka LSBs)
E
sc(λ)=spectral irradiation (W/m/m
2
)
ρ
sc(λ)=scene reflectivity (no unit)
T
int=camera exposure time (s)
F=lense F-nummer (=f/D
obj)
h=Plancks constant (6.6x10
-34
J s)
c=speed of light (3x10
8
m/s)
A
pix=detector area (m
2
)
λ=light spectral wavelength (m)
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CG
pix=conversion gain (V/e- )
G
sf=source follower gain (no unit)
N
bits=ADC resolution (no unit)
V
adc_ref=ADC saturation level (V)

27. Temporal noise sources
•Photon shot noise =>µ=S
e-, σ=sqrt(N
ph)
–N
ph: mean value of photons
•Dark current noise =>µ=N
dc, σ=sqrt(N
dc)
–N
dc: mean value of dark current electrons
•Read noise =>µ=0, σ=RN (V rms)
–RN: temporal noise in darkness from pixel+ADC
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222
// CGGNS
S
SNR
sfRNdce
e
ADCout
σ++
=
−
−
2222222
RNGGCGNGGCGS
adcsfpixdcadcsfpixeADCout
++=
−
σ
adcsfpixeADCout GGCGSS
−=

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)
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29. Example of 4T pixel output signal with
noise
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kT/C noise
Reset level (Vrst)
White noise and 1/f noise, N
pix(f)
Signal level (Vsig)
V
pix(t)
t
RST
TX

30. White noise and 1/f noise in transistors
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N(f)
N(f)=k
N(f)=1/f
N(f)=1/f
2