Sub electron noise readout for scientific CCDs Research Techniques Seminar September 14, 2010 Gustavo Cancelo

Sub electron noise readout for scientific CCDs

Research Techniques SeminarSeptember 14, 2010

Gustavo Cancelo

• CCD low noise readout:– Juan Estrada.– Ken Treptow.– Gullermo Fernandez Moroni.– Gustavo Cancelo.– Tom Diehl.– Kevin Kuk.– Ted Zmuda.

• DES collaboration:

Outline:• Brief introduction to CCDs.• Applications.• Low noise readout.• Future work.• CCD full well issue.• Outreach.

Charge Coupled Devices (CCD)LBNL CCDs used for DES DECam: High resistivity, 250µ thick

Most scientific CCDs: Low resistivity, thinned down to 20µ to increase depletion.n-channel: better charge mobility but higher dark current.

High QE in near infrared. Z>11g of mass, good for direct DM search.p-channel, better than n-channel for space telescopes

Charge Coupled Devices (CCD)

• Photon Transfer Curve:– Full well– Readout gain– Pixel and dark current non

uniformity– more...

Photon Transfer Curve (PTC)Potential well

The location and size of the well’s maximum potential is a function of the pixel layout, Si process, doping concentrations and externally applied voltages.

Outline:• Brief CCD introduction.• Applications.• Low noise readout.• Future work.• Full well issue.• Outreach.

Hexapod

Optical Lenses

CCDReadout Filters

Shutter

Mechanical Interface of DECam Project to the Blanco

Dark Energy Camera (DECam)

Blanco 4m TelescopeCerro Tololo, Chile

New wide field imager for the Blanco telescope (largest focal plane in the southern hemisphere) Largest CCD project at FNAL. DECam is being built at FNAL including CCD packaging, full characterization, readout electronics. CCD facilities at SiDet and 5+ years of experience positions FNAL as a leader for this task.

Focal plane with 74 CCDs (~600 Mpix).All the scientific detectors in hand, packaged and characterized at FNAL.

DECam has allowed us to build at FNAL a powerful CCD labclosely monitoring production of dies for more than 2 years, giving quick feedback on performance

developed CCD package for focal plane that meets scientific requirements

produced/tested 240+ CCDs like an efficient factory

the experience building silicon trackers transferred nicely to this project. The work in this talk has been possible thanks to this CCD lab.

designed and buildreadout electronicsfor a large focal plane

Galaxy Cluster counting(collaboration with SPT, see next slides)

20,000 clusters to z=1 with M>2x1014Msun

Spatial clustering of galaxies (BAO)300 million galaxies to z ~ 1Weak lensing300 million galaxies with shape measurements over 5000 sq degSupernovae type Ia (secondary survey)~1100 SNe Ia, to z = 1

Survey AreaOverlap with South PoleTelescope Survey (4000 sq deg)

Overlap with SDSS Stripe 82for calibration (200 sq deg)

Connector region(800 sq deg)

Dark Energy Survey optimized to measure the equation of

state parameter w for Dark Energy. Relation between pressure and

density.

error ellipseDES expects factor of 5 improvement over current experiments

DES upgrade DECam estimates redshift from the colors of the objects. FNAL scientists are now planning a spectrograph to complement DES data. The CCD work in astrophysics at FNAL is NOT over.

4 DES filterscolors change as galaxy moves in z

X000fibers

several spectrographs

multi object spectrographusing many DECam parts

Beyond DES --- LSST

next big survey, to be built in the mountain next to DECam. Huge CCD camera (3.2 Gpix) with a more demanding electronic performance (faster readout and lower noise!)

It makes a lot of sense for FNAL to get involved in this. In this talk I will show you that we are now meeting the LSST readout requirements. In a few weeks we will be testing a detector with almost the correct format for LSST. The CCD work in astrophysics at FNAL is NOT over.

slide by P. O’Connor (BNL)

Another CCD application: DAMIC

limited by exposure mass(need bigger detector)

Limited by detection threshold. Most experiments can not lower threshold because of the electronic readout noise in their detectors. Room for CCDs!

SUSY models

from Petriello & Zurek 0806.3989

Ideal, threshold set below 1e- (i.e. noise below 0.2e-)

14

σ = 2e

Two features:CCDs are readout serially (2 outputs for 8 million pixels). When readout slow, these detectors have a noise below 2e- (RMS). This means an RMS noise of 7.2 eV in ionization energy!

The devices are “massive”,1 gram per CCD. Which means you could easily build ~10 g detector. DECam would is a 70 g detector.

• 7.2 eV noise low threshold (~0.036 keVee)• 250 μm thick reasonable mass (a few grams detector)

DECAM CCDs are good for low threshold DM search

One good reason to look for low mass dark matter : The DAMA/LIBRA result

Bernabei et al, 2008

~8 σ detection of annual modulation consistent with the phase and period expected for a low mass dark matter particle (~7 GeV) consistent with recent COGENT results.

muons, electrons and diffusion limited hits.

nuclear recoils will produce diffusion limited hits

Particle detection with CCDs

1 gram of Si

CCD copper dewar inside lead shield.

DAMAw/o chan

DAMAw chan.

DAMIC

thanks to our low noisewe have the best result in the worldand we are reaching the DAMA region

COGE

NT

CRESST

The low noise readout system would allow to set a lower threshold for this search.Number of recoils increase al low energies.

Neutrino coherent scattering:

SM cross section is relatively large, the challenges are detector sensitivity and background control.

• SM and new physics.• Help understand how to study

supernovae neutrinos.• Monitoring of nuclear reactors.

we are here ~100 cpd/keV/kg @ 100eV

recoil energy (keV)

even

t rat

e ( c

pd/k

eV/k

g)

lower noise in this case means that we can see the recoils with over a larger background

Expected rate for nuclear recoils ~30m from the center of a 3GW reactor. (From the Texono collaboration)

• CCD threshold <100 eV (goal ~10 to 15eV)

noise reduction

Neutron Imager : more CCD R&D at FNAL

this is done all the time with CCD, but we want to skip the scintillator to improve resolution.

• Neutron imaging is complementary of x-ray imaging, sometimes the only option– Cargo scanning.– Nuclear technology.– Archeology, paleontology.– Materials research.

~1mm resolution

Neutron Imager : more CCD R&D at FNALmotivated by exchange with neutron physicists during ICFA school

this is done all the time with CCD, but we want to skip the scintillator to improve resolution.

borated CCD

readout

our spatial resolution will bethe position of the position resolution of measuring alphas in the CCDs pixels.

alphas in CCDs using 241Am

thanks to the plasma effect the alphas are clearly identifiable in our the CCDs, and we can measure their full energy. The lower energy photons coming from the source can be easily separated.This is interesting for other reasons, there is not much experience with alphas in CCDs and they allow for a good measurement of the space charge effects in silicon.

so we are now setting a first test with a borated plate over the CCD. If things look good we will try to deposit Boron on the surface of the detector (or maybe the detector package). Working closely with neutron physicist on this project.


CCD architecture

• CCDs have one or more arrays of small pixels.– DES CCD have 8Mpixels of 15 x 15 microns.

• Pixels are readout serially through one or more video amplifiers.– Pixel charge shifts vertically into an horizontal register and then the horizontal register

is readout serially.• Most CCD noise comes from the video and external readout.

– When cold at ~-100˚C, the dark current is negligible.– Charge transfer efficiency is better than 99.99% (i.e. 1 ppm charge diffusion).

CCD arrayCCD transfer function

CCD readout noise

CCD gain defined in digital units per e- (ADU/e-)

Output video circuit

CCD Images

FITS image:Each pixel is a n-bit digital representation of the pixel charge.

T TPedestal Pixel

Fragment of video output

Correlated Double Sampling (CDS)

for an integration window T

Where sigi(t) is the i-th image pixel and pedi(t) is the pedestal.

CDS can be done in the analog (continuous) or digital (sampled) domain.

T

iii dttpedtsigT

cds0

)()(1

CCD video output

Reset feed through noiseReset pulses (different height)

One pedestal and one pixel valueSumming well clock feed trough buried in noise.

Reset pulses are ~ 50,000 e-

1/f + WGN

Low frequency correlation

CCD noise

• CCD noise measured by the LBNL designers using a test board.– 1/f noise up to 50 KHz.– WGN at higher frequencies.

• VREF and VDD power supply noise is critical.• Pulsed signals: RESET and summing well noise change the baselines.

1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+061.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

Single transistor

20C 5/2 0C 5/2

-20C 5/2 -40C 5/2

-60C 5/2 -80C 5/2

-100C 5/2 -120C 5/2

-140C

Frequency [Hz]In

pu

t-re

ferr

ed n

ois

e [V

/(H

z).5

]

CCD noise and CCD readout noise

• CCD noise– Dark current is negligible at cryogenic temperatures.– Mainly shot noise from signal (Poisson).

• CCD readout noise:– 1/f noise.– Thermal (shot) noise (WGN), limited by high bandwidth amplifiers and

external LPF.

• CCD readout system noise sources– Power supplies.– Readout amplifier chain.– Analog to digital converter.– EMI.

Correlated Double Sampling (CDS)

4

3

2

1

)()(1

)()(1

0

t

t

t

t

iii

T

iii dttxdttxT

cdsdttpedtsigT

cds

For the white and Gaussian noise w ~ N(0,σ²), the CDS is the optimum estimator.

It actually grows for longer T because the 1/f noise grows exponentially as f->0.

Twcds0

2but

Integration intervals: t4-t3 = t2-t1 = T

Video fragment: Npix pixels and Npix pedestals long.

Pedestal i Pixel i

Pedestal i+1 Pixel i+1

s(n) pedestals and pixels

n(n) correlated noise

w(n) white Gaussian noise

x(n) = s(n) + n(n) + w(n)

Tncds0

2

CCD noise measured with the Monsoon system

• 3.5e- at 10μs.• Below 2e- for T > 40μs.• The noise increases for

long pixel observations T > 70 us.

• Meets comfortably DeCam specs of 10e- at 4μs

σ = 3.5e

This is good, but how can we do better?

CCD video noise spectrum

• System noise 5 to 10 times higher than CCD noise.

• Resonances indicate EMI induced noise.

• Too much low frequency content.

CCD device noise:• WGN of 10µV over (10Hz-100KHz),

equivalent to 4e-/sample RMS.

CCD system noise: 20 to 30 e-/sample RMS.

1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05 Single transistor

20C 5/20C 5/2-20C 5/2-40C 5/2-60C 5/2-80C 5/2-100C 5/2

Frequency [Hz]

Inp

ut-

refe

rred

no

ise

[V/(

Hz)

.5]


• More resonances at 60 and 120 Hz induced by AC power.

120Hz resonances

• EMI:• Conductive noise.• E and M coupled noise.

• We can’t change the interference source, but we can move the sensitive system.

Correlated double sampling (CDS)• Advantages:

– Generates a single data point per pixel.– Pedestal subtraction.– The CDS filtering is implemented by a simple analog circuit.

• Disadvantage:– One sample/pixel eliminates the possibility of signal processing.

Alternative method• Sample the video output.

– N samples of the pedestal and the pixel value every T.– Digital Signal Process the data using digital filters and estimators.

• Advantage:– Lower noise.

• Disadvantage:– More computing resources.

24 bit Σ-Δ ADC based readout system

Gain: 35 ADUs/e-

Single sample rms: 1.5e-

Output sample rate: 2.5samples/µs.ADC noise spectrum is flat (WGN)

1e- at 1µs

0.3e- at 10µs

FFT of 50Ω terminated input

CDS of 50Ω terminated input

Digital signal processing & estimation

CDS transfer function

The CDS filters very low frequency noise close to DC.Minimum noise rejection at f~0.4/TPix.Nulls at f=k/TPix, where k=1,2,3,…Better filtering for higher frequencies.Transfer function maximums follow a |sin(x)/x| decay.

Noise power spectrum noisecds STS2)(

Snoise is the WGN (band limited by analog filters) 1/f noise in BW 0 – 10 KHz .

Tpix is a “free” parameter

noiseS

f

Tpix

Video without noise

Correlated noise

f .TPix

?

Cumulative CDS transfer function

Let’s assume that most of the noise is band limited WGN

noiseS

f

dfTKdfSTdfSBWBWBW ff

noise

f

cds 22)()(

Noise power

If the input power noise is flat and band limited. 90% of the CDS noise is due to low frequency noise (0< fnoise < 1/TPix).If we add 1/f noise 90% of the noise is within 0< fnoise < α/TPix, α<1.

Eliminating low frequency noise beyond what CDS can do is interesting:We use estimation.

WGN only

WGN + 1/f

Cumulative CDS transfer function

WGN only

WGN + 1/f Can we estimate low frequency content and subtract it from the CDS noise?How many low frequency modes do we need to estimate?

Example:Tpix = 10 to 12µs.Data sample: 20 pixels + 20 pedestals long data sets.Estimation of 20 to 30 modes.The first 3 or 4 modes may not be needed.For longer integration times we need mode modes.

Estimator• χ2 estimator, because it does not assume a particular noise model:

– Inversion of a large matrix.– Only one time and can be done off-line.– Numeric problems if matrix is too large and rectangular.

– Linear model is not orthogonal. Estimation errors are correlated.– Study covariance matrix

• Goal:– Implement the estimator and the digital CDS in an FPGA.– FPGAs have a couple hundred multipliers working in parallel at > 100 MHz.

signal model:

2*Npix steps with N total samples, Ns samples per step

Pedestal i Pixel iPedestal i+1 Pixel i+1

s(n) pedestals and pixels

n(n) correlated noise

w(n) white Gaussian noise

pixN

iii nUsns

2

1

)()(

)()()()( nwnnnsnx

Where Ui(n) is a step (Heaviside) function centered at pixel or pedestal i.

Estimation of correlated noiseThe idea is that if we know the amplitude and phases of p terms of the correlated noise we can subtract them.Of course we also need to know the pedestal and pixel values si for all i=1…2Npix.Number of parameters to be estimated: p+2Npix.

Linear estimation model: xHHHnwHnx TT 1)(ˆ)()(

where θ is a (p+2Npix)x1 vector

H non orthogonal because the step functions are non orthogonal to the Fourier basis.

noiseT CHHC

1 If w~N(0,σ2) is WGN

ICnoise2 1

2

HH

C T

For H orthogonal this is equal to I

N

C 22

In our case H is not orthogonal, so some estimation errors are larger than others.

We can eliminate the pedestal and pixel values si from the estimation problem.

)()()( nxnxny where <x(n)> is the average signal+noise value in each pixel (step function)

x(n) y(n)

Less parameters need to be estimated.H is better behaved.The CDS of low frequency noise is subtracted from the total CDS of signal+noise.

New linear model: yHHHnwHny TT 1)(ˆ)()( where θ is a px1 vector

Digital CDS using the 24 bit ADC

Monsoon: analog CDS

The digital CDS using the 24 bit ADC x3 lower in noise at 12µs.

σ = 3.5e

24 bit ADC: Digital CDS

σ = 1.1e

Estimation results

30% improvement35% improvement

0.77e-0.87e-

No

ise

in e

lect

ron

s

No

ise

in e

lect

ron

s

Can we still do better?What are the limitations of the estimator?

Estimator limitations

noiseS

• We have observed noise minimums at 10 to 12 µs.

• Estimation example:– 20 pixels (and 20 pedestals).– 2.5Msamples/s.– 10µs/pix.– Total samples: 1000.

• CDS has low gain for the first 5 modes. We may not need them.– We can locate 1/f noise corner

frequency at low CDS gain.– The 1/f noise corner ~10KHz. – In our example the first mode is at

2.5KHz.– 1/f occupies 4 to 5 modes.

The estimation error is improved if we lower the WGN noise power and/or if we add more samples N.

12 HHC T

N

kHH T

1

Lowering the WGN

• Most of the WGN comes from power supplies that power the CCD output video (i.e. CCD internal or external amplifiers) and the ADC (i.e. quantization noise).– We showed ADC = 1e- at 1µs, 0.3e- at 10µs, goes with 1/sqrt(N)– Currently, power supply noise is too high and can be improved.– Grounding and shielding noise. Can also be improved.

• Lowering the WGN is the first priority because it also improves the parameter estimation.

• WGN reduction of 50% is possible.• This is a 0.3e- noise reduction at 10µs.

Estimation errors

• Longer observation times may not be the solution:– Increasing the number of

samples improves our estimation by 1/sqrt(N).

– The 1/f noise moves closer to the maximum of the CDS transfer function. 1/f grows exponentially.

– We need to estimate mode low frequency modes.

– We need to handle a larger H matrix. Larger numerical errors.

• Increasing the sampling rate would be the way to go but we are already using a state of the art ADC.

noiseS

Covariance of H

• Estimation errors are much larger for the first few modes (not shown in the plot) .• For the modes 5 to 15 the errors are between 4.5 and 2 times larger.• Lower frequency signals have larger estimation errors.

12

HH

C T

Our H is not orthogonal, how bad conditioned is this matrix

compared to an orthogonal matrix?

For an orthogonal matrix the estimation errors are uncorrelated and inversely proportional to the sqrt of the number of samples N.

IN

C 22

12

HH

N TSo, we look at

CDS weights the errors.Large errors in the first few modes go down significantly.

Estimation resultsN

ois

e in

ele

ctro

ns

35% improvement

Lowest mode not estimated

Estimating more modes

• Increasing the pixel readout time (e.g. 30µs) – The covariance function

coefficients (HTH)-1 of the estimation errors do not increase but we have more parameters to estimate.

– The problem is the 1/f noise.

noiseS

Noisy video

20 pedestals + pixels

• The green, blue and red symbols are the estimation parameters for 3 time consecutive data sets. Each data set is 20 pixels long (i.e. 20 pedestals and 20 pixels).

– We estimate Fourier coefficients, so we can calculate the amplitude and phase.– The estimated amplitudes of low freq. modes are consistent for modes 5 and above.

• The estimation of lower modes (i.e. 1 to 5) are not because they have a large error.– The estimated phases , of course, are different and need to be accounted for.– It means that the statistics on our estimation can be improved by the previous estimations, at

least for some time. There are several estimators that do that, such as sequential χ2, ARMA, Wiener, Kalman, etc.

Green, red and blue are time consecutive data sets.

Parameter estimation time consistency

Do we understand what we see?

• At ~12µs we see minimum noise of 1 e- before the estimator and 0.77 e- after applying the estimator.– The ADC noise for 12µs is 0.3 e-.– The rms power supply noise is 700 ADUs (i.e. 20 e-). This gives us 0.7 e-

at 12µs.• If we use the flat spectrum noise approximation. The estimation

errors are almost uncorrelated and can be added in quadrature using:

P

pptot coeff

P 1

21 where pp

CDSTcoeff HHp

1

coeffp= red circles

For 12µs we obtain a σtot = 0.7 e-

The expected total error is 0.62 e-.We measure 0.77 e-. The difference is that for the calculations we are using the flat spectrum approximation (i.e. no 1/f, no EMI noise).


Hardware implementations

• We have used a 24 bit ADC integrated to the DES Monsoon system. – The Monsoon system still drives all CCD voltages and clocks.– We lowered the noise to 1.1 e- at 12µs using CDS and to 0.77 e- using

estimation.– We understand the remaining noises and know how to lower them.

• Future work:– Implement the digital CDS and the estimator in an FPGA of the existing

system to prove that we can read 8Mpixel images with sub electron noise levels.

– Design a multichannel board using the 24 bit ADC for DAMIC and CCD R&D (i.e. fast readout for LLST R&D and DECam upgrade R&D).

• This board can be produced in few months.• It will include quiet power supplies for the CCD video outputs.• Still requires the Monsoon for CCD clocks and other power supplies.

Future work

• Start the conceptual design of a new lower readout noise system that addresses all noise problems including EMI.– This design requires manpower for software and framework.– Most likely has to be project driven.

• Ambitious noise goals:– 3 electrons/sample.– This will give us a monotonic 1/sqrt(N) decay up to ~12µs (0.55 e-)

with CDS only.– Further improvement using the estimator.

Interesting for LSST

• LSST noise requirements: 5e- at 2µs readouts.

We are here: 3e- at 2µs

Future work

• LBNL 12 video channel CCD (LSST candidate).– CCD arrives in 2 to 3 weeks. Testing starts immediately.– Readout cables are being built.– Use 12 channel DES readout card for most characterization.– Use the current 1 channel low noise readout to validate noise

requirement at 2us/pixel.


Degradation not gradual

A lower full well smears images

• At nominal vertical clock voltages the images look smeared.

• The full well partially recovered if the vertical clocks were set to higher voltages.

• Hypothesis:• Fowler Nordheim electron tunneling effect into

the SiO or NiO creates a permanent electric field that opposes to the externally applied field.

• Tunneling requires higher than usual voltages. • Work plan:

• Try to reproduce the lower full well problem using a good CCD.

• Apply high enough voltages to create tunneling.• If the full well reduction is observed, try to

recover with higher Vclock voltages.• If the full well reduction is observed, try to

invert the tunneling applying high voltage with the opposite polarity.

• Daniele Bortolotti’s summer work

• We have been able to repeat the full well problem in the lab and we half validated the hypothesis.

• We were not able to revert the tunneled charge.

• I think we applied to high of a negative voltage and damage the CCD in a way that we do not fully understand.

• We have a good plan on how to continue these studies.

Cosmic rays before applying HVReadout: Vclocks at nominal +5.5 volts

Cosmic rays, after applying 60volts to VclocksReadout: Vclocks at nominal +5.5 volts

Cosmic ray, after applying 60volts to VclocksReadout: Vclocks at nominal +8.5 volts

Photon Transfer Curves

• Red: before applying high voltage (good CCD, readout with nominal Vclk=+5.5v)• Blue: full well reduction after +60v to Vclk (all other CCD inputs grounded).• Black: full well recovery increasing Vclk at readout to +8.5v.


Outreach: XI ICFA on instrumentation in EPP

• CCD cooled at ~-20˚C using a chiller. Ni gas to avoid condensation.– ~ 50 enthusiastic students in groups of 5 to 7.– Hands on CCD lab with image and data analysis, noise measurements,

PTC, and more.

THANK YOU !

Spare slides


• System noise 5 to 10 times higher than CCD noise.

• Resonances indicate E or M induced noise.

• Too much low frequency content.

The noise should look like this.One 1/f corner frequency at 200Hz. Another at 10KHz.This amounts to 10µV over (10Hz-100KHz), or 4e-/sample RMS.

But it looks like this: 20 to 30 e-/sample RMS.

1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05Single transistor

20C 5/20C 5/2-20C 5/2-40C 5/2-60C 5/2-80C 5/2

Frequency [Hz]

Inp

ut-

refe

rre

d n

ois

e [

V/(

Hz

).5

]

0.3e- at 12µs

The ADC noise is 0.3e- where are the other 0.8e- coming from?• CCD output amplifier:

– Power supply noise, specially low frequency noise (WGN and 1/f).– Thermal noise (WGN)

• Analog readout circuit:– JFET and preamp thermal noise (WGN).– Power supply noise (WGN and 1/f).– EMI: Grounding and shielding (spectrum).

Minimizing WGN is very important

1.1e- at 12µs

Full well issue

• Daniele Bortolotti’s summer student work

Fowler Nordheim tunneling

REF: [1] Frohman-Bentchkowsky, The Metal-Nitride-Oxide-Silicon (MNOS) Transistor Characteristics and Applications, Proceedings IEEE, Aug. 1970.[2] S. Holland et al., Electrical breakdown in Thin gate and Tunneling Oxides, IEEE Journal of Solid-State Circuits, Feb. 1985.

LSST CCD and readout

• CCD and readout are critical components.• Not clear to me why they want to have the readout electronics in the cold and vacuum.

– More expensive, difficult to service.– Noise requirements can be achieved with electronics outside.

Future work

• Build a multi channel readout card including:– 24-bit ADC per channel.– Ultra quiet power supply for CCD output stage.– FPGA for digital signal processing.– Improves EMI sensitivity.– Sub electron noise.

• Quick turnaround design: ~3 months.• All other CCD required signals are provided by existing systems such

as Monsoon or Leach.• Applications:

– Multi CCD for DAMIC.– 12 channel LBNL CCD.– General CCD R&D.

Estimation results15 modes – 1 step estimation 15 modes – 2 step estimation

Samples, 2.5samples/μs Samples, 2.5samples/μs

No

ise

in e

lect

ron

s

No

ise

in e

lect

ron

s

30% improvement 35% improvement

Can we still do better?What are the limitations of the estimator?

0.87e- 0.77e-

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Sub electron noise readout for scientific CCDs Research Techniques Seminar September 14, 2010 Gustavo Cancelo