bridging correction the camera gap including · by the physics of photon statistics ... - excess...
TRANSCRIPT
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Keith Bennett, Ph.D., Stephanie Fullerton, Ph.D., Eiji Toda, Hiroyuki Kawai, Teruo Takahashi
ADAPTED FROM PRESENTATION GIVEN AT METHODS AND APPLICATIONS OF FLUORESCENCE,GENOA, ITALY
SEPTEMBER 10, 2013
System Division
BRIDGINGTHEGAP
Impact and Correction of Camera Noise for Computational Microscopy including Precision Localization Nanoscopy
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Cameras are NOT perfect!
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Why is a camera manufacturer
proclaimingthat
cameras are not perfect?
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Because NO camera is perfect&
Because understanding why matters to your science
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WHAT IS THE GAP?
The GAP {Perfect Camera
Actual Camera
The difference between the performance of an actual camera and a theoretically perfect camera
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THE AMOUNT OF THE GAP DEPENDS ON:
{{ {
{
1. Sensor technology
CCDEMCCDsCMOS
2. Camera specifications
3. Input photon level
Quantum EfficiencyCamera Noise
Read noiseExcess NoisePhoto‐response non‐uniformity (PRNU)
Ultra low lightLow Light
IntermediateHigh
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UNDERSTANDINGWHY THERE IS A GAP ENABLES:
• Appropriate camera selection
• Optimized camera usage
• Optimized experimental design
• More reliable data analysis
BetterResults
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THE REAL CAMERAS
CCD
• Well established technology• All electron to digital conversion done in one chain
• Limited speed• Moderate read noise• Very low dark current• High QE• Best pixel response uniformity
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THE REAL CAMERASEMCCD
• Back‐thinned for increased QE• High voltage gain register on sensor to achieve on‐chip amplification
• All electron to digital conversion through one chain(either for EM or no EM)
• Read noise is low due to gain• Stochastic EM amplification adds excess noise and long tail
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THE REAL CAMERASCMOS
• Newest technology• Every pixel and column has own amplifier
• Very low mean rms read noise• Pixel dependent read noise • Fastest speeds and largest field of view
• FPGA processing achieves excellent response uniformity (low PRNU)
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SEEING THEPREDICTED
GAP
Single Pixel Noise & SNR
Fixed Pattern Noise &Image SNR
(from specs)
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THE PERFECT CAMERA
Every photon is converted into one electron
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Signal (Photons)
Perfect Camera Signal to Noise Ratio
In a perfect camera, the SNR of a single pixel is limited only by the physics of photon statistics… i.e. shot noise.
100% QE
0 e‐read noise
0% fixed pattern noise
Every electron is digitized exactly as expected every time
Every pixel and amplifier perform identically and predictably
{{{
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EFFECT OF QE ON THE GAP
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Signal (Photons)
Signal to Noise Ratio (SNR)
Perfect
QE 70%
QE 50%
A reduction in QE reduces SNR at all light levels
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RELATIVE SNR (rSNR) PLOTS CLEARLY SHOW THE GAP
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Perfect
QE 70%
QE 50% rSNR shows differences among cameras over full range of signal level
All SNR graphs in this talk will be presented as rSNR{ }
rSNR is the SNR for a camera plotted relative to the perfect camera
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THE SIMPLE SIGNAL TO NOISE RATIO (SNR)
QE: Quantum EfficiencyS: Input Signal Photon Number (photon/pixel)F: Noise Factor (= 1 for CCD/sCMOS and √2 for EM‐CCD)Nr: Readout NoiseM: EM Gain (=1 for CCD / CMOS)Ib: Background
“Changing the Game”
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QE: Quantum Efficiency, P: Input Signal Photon Number, M: EM Gain Fn: Noise Factor (assumes dark current and read noise are negligible)
PQE
PQEPQESNR
PQE
FPQE
PQEMFPQEMSNR
eff
n
2n
22
QEFQEQE
neff
EMCCDS: EXCESS NOISE IS THE REASON FOR THE GAP
SNR for CCD / CMOS SNR for EM‐CCD
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THE REAL CAMERAS
CCD EMCCD CMOS
Sensor Type Charged Coupled DeviceInterline
Electron Multiplying CCDBack‐thinned
Complimentary Metal Oxide Sensor
Camera Name ORCA‐R2 ImagEM x2 ORCA Flash4.0 V2
Pixel Number 1024 x 1344 512 x 512 2048 x 2048
Pixel Size 6.45 µm x 6.45 µm 16 µm x 16 µm 6.5 µm x 6.5 µm
QE ( @650 nm) 58 % 90 % 72 %
Frame Rate 18 fps / 8 fps 70 fps 100 fps / 30 fps
Relative read noise (Nr/M), single‐frame rms 10 e‐ / 6 e‐ < 0.2 e‐ (M = 200) 1.9 e‐ / 1.3 e‐Noise Factor (Fn) 1 √2@ M>10 1
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R (r
SNR
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Signal (Photon, no background)
Perfect sCMOS Flash4.0 (100 fps)ORCA-R2 (CCD)ImagEM X2 (EMCCD)sCMOS Flash4.0 (30 fps)ImagEM X2 (BT CCD mode)
MIND THE GAP: PREDICTED PIXEL rSNR PERFORMANCE FOR THE MOSTCOMMON CAMERAS
= 650 nm
A camera with the highest SNR at the lowest light level may not be the best at higher light levels
1.
The SNR of an EMCCD above 1 electron/pixel is comparable to a camera with QEeff =QE/2 due to excess noise from EM gain.
1.{ 2. {
2.
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BEYOND THE SWEET SPOT: THE GAP EXPANDS AT HIGH LIGHT IF PRNU IS NOT CORRECTED
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Model:• QE: 70%• Noise Factor (Fn): 1• Read Noise 3
photons rms• PRNU (s): 1%
• PRNU reduces SNR at high light
• Cannot be subtracted from image
• “Raw” PRNU varies by sensor
• Can be corrected in camera to varying degrees
ImageSNR{
All SNR curves will be rSNR @ =650 nm
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MEASURINGTHE
REAL GAPAn in‐depth look at noise in CCD, EMCCD and CMOS cameras
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Coun
t
Dark reading (ph)
ORCA‐R2 INTERLINE CCD: PREDICTABLE AND ROBUST
‐ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91.0
10 100 1,000 10,000signal (photon)
Mean intensity: 17,300 e-: 130.5e-
PRNU: not measurable
PRNU is insignificant{1. Bright Image: shot noise limited
Read Noise(Nr/QE)
Shot Noise & QE
{2.Read noise histogram has single Gaussian distribution
=650 nm
58% QE Limit
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EMCCD: SOME SURPRISING RESULTS
Thickness variations from back-thinning process causes spectrally-dependent PRNU
• Cannot be removed during manufacturing
• Must be calibrated by users for their specific spectrum.
• Individual pixel map required for correction
550 nm 850 nm
Mean: 30157s: 369.5 (1.2%)
Mean: 30508s: 432 (1.4%)
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Photons
Calculated Single Frame rSNR
eQE: 95% (gain off)Nr/eQE = 8.4 photonsPRNU: 1.4%
The Gap for EMCCD in CCD mode becomes very wide due to PRNU
{1.
{2.
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COMPLEX BEHAVIOR: A CLOSER LOOK AT EMCCD SNR WITH HIGHAND LOW GAIN
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Input photon number (photon)
Series1Series2Gain = 5
Gain = 400
Complex Behavior
- Excess noise (eQE)- PRNU- Saturation- High read noise
(34 e- @ M=5, 70 fps)- Gain hard to measure
Satu
ratio
n
90% QE Limit
Excess Noise
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EMCCD GAIN CAUSES UNEVEN PROBABILITY DISTRIBUTIONS
In simulated probability distribution functions for EMCCD, the output at high gain is not Poisson due to the electron multiplication process!
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ability [a
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Photon equivalent
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ability [a
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Photon equivalent
Long tailLong tail
2 Photon Average InputGain = 200
10 Photon Average InputGain = 200
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ORCA‐FLASH4.0 V2 (SCMOS): A VERY COMFORTABLE SWEET SPOT
0.00.10.20.30.40.50.60.70.80.91.0
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rSNR
Signal (Photons @650 nm)
Shot Noise & QE
The “Sweet Spot”
70% QE Limit
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NOT ALL CAMERAS ARE CREATED EQUAL: FLASH4.0 SWEET SPOT BROUGHT TOYOU BY HAMAMATSU CAMERA ENGINEERS
Signal amplified and digitized in column‐parallel ADC.FPGA provides offset and gain correction to the raw digitized signal.
PRNU: ~2%
{ Raw Data Bright Image
{Corrected Data Bright Image
PRNU: ~0.5%
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Rms read noise matches single frame rSNR.
Does not fit a Gaussian distribution, i.e. is not completely modeled by a single “read noise.”
SCMOS: PIXEL‐DEPENDENT READ NOISE
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ber o
f pixels
Temporal read noise (e‐, rms)
(30 s/ row)
0.85 e‐Median
1.51 e‐ rms
Single Frame Read Noise (measured)
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photon equivalent @ 650 nm
Single Frame Dark Histogram
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BRIDGINGTHE GAP
Using knowledge of camera noise to get highest camera performance provides improved Precision Localization Results
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WHAT ISMOST
IMPORTANT?accuracy
resolution
frame ratesample contrast
background
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TWO PHASES OF PRECISION LOCALIZATION MICROSCOPY
1. Collect Image Data
Prepare Sample Minimize BackgroundOptimize Optical SystemConsider Camera Induced Noise
2. Reconstruct Superresolution Image
Calibrate Camera Implement Noise CorrectionsApply Statistical Algorithms
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Adapted from: J. Chao et al (Ober Lab), Nat. Meth10, 2013) doi:10.1038/nmeth.2396
STANDARD PRACTICE IS NOT THE BEST PRACTICE: USING EMCCD WITH GAINYIELDS LEAST ACCURATE RESULTS
http://www.wardoberlab.com/
CCD QE: 100%, read noise = 1.8 ph, no background; No fixed pattern noise.
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COMPENSATING READ NOISE VARIATION
Courtesy Prof. Joerg Bewersdorf, Yale University
Incorporating pixel‐specific read noise into the Maximum Likelihood Probability Model eliminates and narrows the asymmetric distribution of localized molecules caused by higher read noise pixels.Courtesy F. Huang, Bewersdorf Lab
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SELECTING AND USING CAMERAS: CASE STUDIES
{{
{
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{ResultsAccurate measurement of the distance between two fluorophores of different colors. distance ~0.77 nm using a dichroic beamsplitter to direct each color of light to separate halves of the CCD camera.
{DetailsSpeed: 5 – 50 s / measurementLight: ~4,000 – 10,000 ph/ mol/frame
~105 ph / mol before bleaching
Imaging: Simultaneous 2 colorCamera: Back‐thinned EM‐CCD, gain off
Nature (2010)| doi:10.1038/nature09163
{CameraCorrection
Measured PRNU maps for each color. Improved localization relative accuracy by ~2– 4 nm.
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Localization Microscopy with Minimal Bleaching. Plasma membrane dynamics for > 60 s (594 frames). 40% better localization precision than “conventional” EMCCD localization
Courtesy of J. Chao et al (Ober Lab) Adapted from Nat Meth (2013) doi:10.1038/nmeth.2396
Speed: ~60s / reconstructed imageLight: ~100 photons /molecule frame
Mag: 630XCamera: EM‐CCD, Gain ~1000
1 m
Implemented detailed statistical EM noise model into maximum likelihood reconstruction probability model.
1 m{Results
{CameraCorrection
{Details
Cholera toxin B subunit scale bar: 1 m
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{Results32 reconstructed frames / sec (6.6 x 6.6 m2) field of view; fixed and living cells showed cellular dynamics not visible in reconstructions using longer data collection times.
{Details Speed: 0.03 s/ reconstructed imageLight: ~3,000 photons /mol/ frame
Mag: 60X, Camera: sCMOS, 3200 fps
Courtesy of F. Huang,(Bewersdorf Lab)
{CameraCorrection
Implemented pixel‐specific read noise into probability model for MLEM.
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Courtesy of F. Huang. Bewersdorf Lab, Yale Adapted from F. Huang et al., Nature Methods 10(7): 653‐658 (2013)
Localization Precision “conventional” EMCCD vs. sCMOS
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MINIMIZING THE GAP: MATCHING THE CAMERA TO YOURNEEDS
Speed / Field of View
Light R
equired
Faster (or more pixels)
Higher AccuracyBetter ResolutionLower Sample Contrast
EMCCD (Gain ON)UAIM
(BT)‐CCD
EMCCD (Gain‐On)
“Conventional” Localization
Scientific CMOS“Conventional” Localization
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HAVE YOU DONE A GAP ANALYSIS?
{
{
{
1. How much light do I have?
The relative performance of CCD, back‐thinned CCD, EMCCD and sCMOS cameras is light‐level dependent.
2. Do I know my camera’s strengths and weaknesses?
3. What is the goal of my experiment?
No camera is perfect; proper use is required for the best results and to avoid errors
The most appropriate choice of camera depends upon the specific super resolution / localization experiment
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Acknowledgements
Prof. Zhen‐li Huang, Huanzhong University of Science and TechnologyF. Long et al, OPTICS EXPRESS 17741 (2012)
Prof. Joerg Bewersdorf, Yale UniversityF. Huang et al., Nature Methods 10(7): 653‐658 (2013)
Prof. Raimund Ober, Texas Southwestern UniversityJ. Chao et al, Nat Meth (2013) doi:10.1038/nmeth.2396
HamamatsuHiroyuki Kawai: camera measurementsTeruo Takahashi: simulationsStephanie Fullerton: presentation preparation
Keith [email protected]
See a movie of 32 fps dynamics in the supplementary materials of the article by Huang et al.