system. The noise can be numerically specifiedas the standard deviation � of the distributiondescribing the probabilistic behavior of thesystem. The errors due to noise cannot be elim-inated; they can only be reduced. A familiartechnique for reducing noise is data averag-ing. For imaging applications, the noise ateach pixel can theoretically be reduced by thesquare root of the number of measurementsaveraged together. While this is fairly true forshot noise and CCD read noise, there can besignificant deviations from this for CMOS readnoise averaging [3].Sensors such as CCDs and scientific CMOS

have numerous sources of noise. The majorsources of noise are dark noise �d , readoutnoise �r , and shot noise �n , which is the noiseinherent to the light signal itself. There areother minor sources of noise which are verysmall relative to these noise sources and aretherefore negligible for the purposes of thisarticle. The noise sources discussed in Table 1

(below) are generally considered to be inde-pendent of each other. This assumption sim-plifies the calculation to arrive at the totalnoise based on their individual contributions.Equation 1 describes how the total noise can be calculated from the individual contributions:

�2=�d

2+ �r

2+ �n

2+ ..... (1)

S H O T N O I S EPhoton shot noise is the fluctuation in theimage photons themselves. Due to the proba-bilistic nature of the individual photons thatcomprise the light flux hitting the detector,the intensity of light follows a Poisson distrib-ution, even with a perfectly stable light source.The width of this distribution is characterizedby the standard deviation, which is equal tothe square root of the average number of pho-tons and scales as such with intensity. Of thethree noise sources listed in Table 1, only shotnoise increases with the signal incident on thesensor. Therefore, when the light levels aresufficiently high, shot noise outweighs the

B I O G R A P H YJames Joubert has over10 years of experience inthe microscopic imagingof biomolecular systems.He has a BS in chemistryfrom Louisiana Tech Uni-versity and is currentlycompleting his PhD in bioanalytical chem-istry at the University of Arizona. Hisresearch has focused on a variety of micro-scope-based systems, including epifluores-cent and TIRF microscopic characterizationof novel biosensing and drug screening plat-forms using microarrays of stabilized lipidbilayers with embedded transmembraneproteins. At the end of 2010 he began work-ing as an Application Scientist at Photomet-rics and has since set up a lab containingmultiple microscopes and electro-opticaltest systems for data acquisition and analy-sis. He has also provided research and analy-sis for developers working with originalequipment manufacturers and attends sev-eral microscopy courses a year where heteaches various aspects of imaging to acad-emic research personnel.

A B S T R A C TIn this article, Part 3 of a four part series, thenoise sources for CCD, EMCCD, and scientificgrade CMOS cameras are introduced andtheir impact on measurements described.The major noise sources are combined withsignals calculated from a microscope/samplesystem to generate signal-to-noise ratios. Tocompare sensor performance, these ratiosare plotted as a function of increasing expo-sure time, a commonly adjusted user para-meter, for the three sensor types at the samepixel size and also with different pixel sizescharacteristic of each sensor.

K E Y W O R D Slight microscopy, digital cameras, CCD,EMCCD, CMOS, noise, signal-to-noise ratio,imaging, life sciences

A U T H O R D E TA I L SJames Joubert, Applications Scientist,Photometrics and QImaging3440 East Britannia DriveTucson, AZ 85706-5006, USATel: +1 520 889 9933Email jjoubert@photometrics.com

Microscopy and Analysis September 2011

DIGITAL CAMERAS PART3

I N T R O D U C T I O NParts 1 and 2 of this series [1, 2] provided anintroduction to the three most common cam-era technologies, CCD, EMCCD, and CMOS sen-sors, and compared their performance withmetrics ranging from sampling requirementsto light throughput at the detector. Through-out this series, the discussion has focused onutilizing optical parameters of an imaging sys-tem in the selection of a camera for particularbio-imaging applications. Here, in Part 3, the focus shifts to noise para-

meters with an introduction and discussion ofvarious noise sources. In this installment, thenoise properties of different scientific camerasare combined with the photon throughputmodel developed in Part 2 to generate signal-to-noise ratio (SNR) profiles for the three sen-sor types as a function of exposure time. TheSNR of an image is a well-accepted metric ofimage quality and it is used in this discussion toallow quantitative comparison of the sensors. In Part 4, in an effort to identify which sen-

sor would be best employed for particularapplications, the SNR analysis will beexpanded to compare sensor performance forapplications with different levels of signal (e.g.low-light level applications versus high-lightlevel applications).

N O I S EThe concept of noise is often misunderstood.This term is often used to represent almost anyerror in the measured number of photons � ata pixel in an image. However, not all errorsshould be considered as noise. When an erroris deterministic, it is not noise. Noise is a prob-abilistic phenomenon where there is uncer-tainty in the occurrence of the event beingmeasured. Examples of such phenomena inmicroscopy and imaging include the emissionof photons during fluorescence, the detectionof photons by the sensor, and the reading outof photoelectrons during the digitizationprocess. The uncertainty leads to variationsfrom one measurement to the next, and thisvariation is the noise inherent in the camera

Digital Camera Technologies for Scientific Bio-Imaging.Part3:NoiseandSignal-to-NoiseRatiosJames Joubert 1, Yashvinder Sabharwal 2 and Deepak Sharma 1

1. Photometrics and QImaging, Tucson, AZ, USA. 2. Solexis Advisors LLC, Austin, TX, USA

MICROSCOPY AND ANALYSIS SEPTEMBER 2011 1

other noise sources and the image quality isnegligibly affected by dark noise and readnoise.

D A R K N O I S EDark current is the signal that electrons gener-ate by thermal excitation instead of by photoexcitation. Just as the amount of signalgenerated increases with longer exposures tolight, dark current also increases with longexposures. Additionally, larger pixels increasethe likelihood of dark current electrons beinggenerated. Being thermally generated, darkcurrent can be reduced by cooling. From animage processing perspective, dark current canbe subtracted out using a dark image. How-ever, the dark noise, the inherent random fluc-tuation in this dark current cannot, and isapproximately equal to the square root of thedark current [4]. The SNR analysis providedlater in this article includes the exposure timefor the very reason that dark noise will have anincreased effect for longer exposure times.

R E A D N O I S E : T H E D I F F E R E N C EB E T W E E N C C D A N D C M O S

CCDThe third type of noise associated with a cam-era is read noise, and this is the primary sourceof noise at very low light levels. In CCD imag-ing sensors, datasheets typically list a singleread noise for the CCD. In fact, this is an aver-age value since read noise typically follows aGaussian distribution across all the pixels in thesensor. This is characteristic of a single datadigitizer with a single Gaussian noise distribu-tion associated with it (Figure 1). To obtain thisspecification, the read noise is usually charac-terized by measuring the standard deviationof a bias image, an image with zero exposuretime and no incident light. This value is inintensity units, also called grey levels or ana-log-to-digital units (ADUs), but is typically con-verted to a standard unit of electrons by mul-tiplying by the camera’s gain factor. The gaincan be measured with a standard mean-vari-ance test. For a CCD sensor this average readnoise obtained from a bias image and a meanvariance falls at the center of the left curve inFigure 1, which is also at the peak of the sym-metric Gaussian distribution.

CMOSPixels in recently developed scientific gradeCMOS cameras produce a different type ofnoise distribution, one that follows a non-Gaussian skewed distribution of read noisevalues across a chip. The blue diamond curvesin Figure 1 represent the best-fit Gaussiancurve for the data set and demonstrate howclosely the read noise distribution of a CCDsensor on the left matches a normal Gaussiandistribution while the skewed distribution of ascientific CMOS sensor on the right does not.Because of the scientific grade CMOS cam-

era’s skewed distribution, comparisons of sci-entific grade CMOS cameras can be difficult,and so a choice of which read noise value touse must be made. Two possibilities are theaverage (mean) read noise measured with a

mean variance and a bias or the modal (peak)value of the skewed distribution. The standardaverage value takes the noisier pixels in theskewed end of the distribution into accountsomewhat and thus is higher than the modalvalue, which does not. For example, for the sci-entific CMOS shown in Figure 1, the standardaverage read noise value for this camera is 33%higher than the modal value. Additionally, thistailing means a significant number of pixels willhave a read noise higher than average.To further complicate matters, the amount

of tailing varies among different scientificCMOS cameras. To quantify this, the read noisedata can be compared against a standardGaussian distribution to determine the per-centage of total pixels that fall outside thistypical Gaussian distribution. As expected, theCCD read noise distribution follows a Gaussiandistribution with less than 1.5% of the totalpixels falling outside the Gaussian distribution(Figure 1, left). On the other hand, the tailingin the scientific CMOS data causes this per-centage of pixels outside the Gaussian to be42%, or more than a third of the pixels (Figure1, right). This large number of tailing pixels isa complication that should be consideredwhen comparing CMOS cameras to CCDs forlow-to-medium light imaging, where readnoise dominates. At high light levels, wherephoton shot noise dominates, the skewedread noise is much less of an issue.The tailing in the skewed distribution mani-

fests itself in scientific grade CMOS cameraimages in several ways, such as ‘salt-and-

pepper noise’ (see Figure 2) which appears asrandom bright pixels and dark pixels superim-posed on the image and a bar-code effect ofvertical lines of different levels of dark grayintensity appearing at random spacing acrossthe image. These noise types specific to the scientific

grade CMOS result in part to the fundamen-tally different way in which the pixels are readout compared to a CCD (Figure 3). In CCDs thephotoelectrons produced on each pixel arepassed through the same serial register andthen read out using one readout amplifier.This leads to the reduced variability seenamong the chip’s pixels. Scientific CMOS, how-ever, has a separate readout amplifier for eachindividual pixel, and the pixels are output witha separate amplifier and analog-to-digital con-vertor for each column. Furthermore, some sci-entific CMOS cameras switch between two dif-ferent amplifiers when reading out the pixelswithin a single image. The end result isincreased variability from pixel to pixel and,more noticeably, from column to column,manifesting itself in the bar code column noisementioned above. The trade-off is theincreased speed achievable by scientific CMOSwith multiple amplifiers. The salt-and-pepper noise, or random tele-

graph noise, also results in part from defects inindividual pixels combined with the use of cor-related double sampling (CDS) [5]. Defects inthe pixel semiconductor can trap electrons,creating more than one level of electron cur-rent such that double sampling between dif-

Figure 2: Salt-and-pepper speckle noise in a scientificCMOS bias image. The higher concentration ofbright and dark speckles is readily apparent. Thehigh amount of speckling corresponds to the longtail in the read noise distribution.

MICROSCOPY AND ANALYSIS SEPTEMBER 20112

Figure 1: Plot of read noise distribution for standard CCDs (left) and for scientific CMOS (right).

DIGITAL CAMERAS PART3

ferent levels can cause either bright pixels ordark pixels, depending on the how the twosamples are taken.Certain pixels with more defects create more

current-level variation, and thus have largerswings in signal and larger standard devia-tions. These pixels are what skew the readnoise distributions to high noise values, as seenin Figures 1 and 4. Because certain pixels arenoisier than others, the location of noisy pixelson the chip is somewhat predictable. However,since these noisy pixels are spread throughoutthe chip, they are impossible to avoid andimpossible to predict when a ‘salt or pepper’state will occur.

S I G N A L - T O - N O I S E R AT I O ( S N R )Having an expression for the total number ofdetected photons from Part 2 of the series andthe expression for the total noise, we arrive atthe signal-to-noise ratio, which is an oftenused metric to describe the quality of theimage being acquired. In typical situations,microscopists take exposure times rangingfrom 10 ms to 1 s. Therefore, the SNR calcula-tions presented in this section use exposuretimes within this range. Figure 5 providesimages characterized by increasing SNR forvisual reference. It shows increasing SNRstaken from a CCD camera using a test card.Equation 2 outlines the signal-to-noise ratio

calculation. The sources of noise used in thiscalculation are read noise �r , shot noise �n ,and dark current noise �d , which are the dom-inant sources of noise in CCD and CMOS cameras:

It was previously mentioned that the shotnoise is a function of the signal level. Equation

Figure 4: CMOS noise distribution andindividual pixel response due torandom telegraph (salt-and-pepper) noise. Defects in pixelscreate two states with differentsignals. Double sampling andsubtraction of the two samplescreates a high, an average, anda low signal so a pixel will fluc-tuate rapidly among these threesignals over time (i.e. frame-to-frame). Different pixels have dif-ferent defect numbers and dif-ferent amounts of variation,leading to a read noise distribu-tion skewed to higher noise val-ues.

MICROSCOPY AND ANALYSIS SEPTEMBER 2011 3

Figure 3: Sampling architecture of CCD and CMOS cameras. CCDs (left) sample through one amplifier and thus have a single read noise source. CMOS sensors(right) sample using a different amplifier for each pixel and for each row, introducing a variety of read noise sources.

2 shows that as the signal becomes smaller andsmaller, the shot noise will correspondingly falland approach the read noise. Eventually theread noise becomes the dominant noise sourcelimiting the SNR. In extremely low-lightmicroscopy applications, an alternate technol-ogy, the electron multiplication CCD (EMCCD)has been developed to overcome this problem.Electron multiplication technology provides theability to amplify the detected photons by aknown factor before digitization, allowing thesignal to be brought up above the read noise.This electronic amplification is achievedthrough a process called impact ionization.Impact ionization is also a probabilistic processwhere the exact factor of multiplication in theregister of the CCD can vary. This variation addsanother noise source known as the excess-noise

factor �. This excess-noise factor only affectsthe sources of noise which must be digitizedand not the noise induced by the digitizationprocess itself. In other words, the shot noise anddark current are multiplied by the excess noisefactor as they are subject to the multiplicationprocess. As a result the SNR equation is modi-fied for an EMCCD, as shown in Equation 3:

P U T T I N G I T A L L T O G E T H E RClearly there are a number of variables thatultimately affect the SNR of the image beingacquired. With the model that we have devel-oped in this series, we can incorporate all ofthese variables to provide a graphical inter-pretation of the SNR. Most quantitative light

SNRCCD =�=

� (2)� Ö �d

2+ �r

2+ �n

2

SNREMCCD =�=

� (3)� Ö �r

2 + �2 .�n

2 + �2 .�d

2

MICROSCOPY AND ANALYSIS SEPTEMBER 20114

microscopy applications have used CCD andEMCCD sensors. However, the recent emer-gence of scientific grade CMOS sensor tech-nology suggests that these sensors may beviable for such scientific applications as well.As a result, this analysis evaluates these threesensor categories. By plotting the SNR as afunction of the exposure time for the acquiredimage, the impact of dark noise with increas-ing exposure time is included in the analysis. Again, as mentioned in Part 2, the calcula-

tions assume a sample labeled with enhancedcyan fluorescent protein (ECFP, � = 3300 cpsm)having a concentration of 200 nM in the sam-ple. These calculations further assume a 60�,1.4 NA oil-immersion objective. To show howthe different noise sources of each sensor cat-egory affect the SNR, Figure 6 plots the SNR foreach category of sensor assuming that all sen-sors have the same pixel size and QE. Readnoise values characteristic of each class of sen-sor (3.5 e- for scientific CMOS, 6 e- for CCD, and<0.5 e- for EMCCD) and other noise sources areincluded. For SNR levels below around 3, theEMCCD class of sensor will perform the bestbecause it has the lowest read noise of allthree and the excess noise factor is also stillminimal. As the exposure time increases andthe detected signal increases, the excess noisefactor starts to increase the total noise and thescientific CMOS class of sensor demonstratesthe best performance. For very long exposuretimes, the CCD and scientific grade CMOS areequivalent as the shot noise, which is indepen-dent of sensor, then dominates. The previous discussion was purely an acad-

emic exercise intended to demonstrate howthe different sources of noise make the differ-ent sensor classes better or worse in terms ofSNR depending on the parameters of theacquisition. If the actual pixel sizes of the dif-ferent sensors and their QEs are considered,then the resulting SNR profiles are shown inFigure 7. In this analysis, the 3.5 µm scientificCMOS with a 0.5� coupler was also includedsince it was shown in Part 2 that this configu-ration could be used without sacrificing reso-lution. Alternatively, a 40�, high NA objectivecould be used without a coupler with the 3.5µm scientific CMOS sensor to increase the sig-nal while still Nyquist sampling.To tie the pixel analysis together, Figure 7

combines the signal-to-noise ratios for the 14µm-pixel EMCCD sensor, the 6.5 µm-pixel CCDsensor and the 3.5 µm-pixel CMOS sensor.These were selected due to their accurate rep-resentation of the majority of each respectivesensor family. Since the small pixel of theCMOS sensor will sufficiently sample whenusing a 0.5X coupler in the optical system, itwas also used in this graph to show the bene-fit in the signal-to-noise ratio.Figure 7 provides a fascinating result. The

EMCCD sensor maintains its superior SNR asexposure time is increased because the muchlarger pixel size allows it to capture signifi-cantly more photons. Similarly, the CCDpeforms better than the scientific CMOSbecause of its relatively larger pixel size. Thescientific grade CMOS with its very small pixelhas the worst SNR. However, if the CMOS sen-

Figure 7: SNR comparison for different sensors and with 3.5 µm-pixel sensor with a 0.5X coupler.

Figure 6: Simplified SNR comparison for different sensors with 14 µm pixels and the same QE typical of front-illumination.

sor is used with the 0.5� coupler, then itseffective pixel area is increased by a factor of4. This increase in effective area coupled withlower read noise provides better performancethan the CCD and the scientific CMOS withoutthe coupler.

C O N C L U S I O N SUtilizing imaging and radiometric analysisbased on the parameters of magnification,immersion media, and numerical aperture, thenumber of detected incident photons per sec-ond on sensor can be determined. Combiningthis with the known properties of the differentsensors such as quantum efficiency, read noise,pixel size, and dark current, we can extend theoptical analysis into a camera performanceanalysis. With the incorporation of the noiseproperties of the sensor into the model, it ispossible to calculate the signal-to-noise ratioand hence get an estimate of image qualitywhich can be used to compare different sen-sors. These comparisons are intended to pro-vide guidelines when looking to purchase a

Figure 5: Comparison of SNRs of 3:1, 12:1 and 18:1.

camera for microscopy applications. In Part 4 of the series, the SNR analysis will be

extended to consider how variations in thelight level of the object drive camera selection.Images from the different sensors at these SNRvalues will be presented along with thenumerical analysis.

R E F E R E N C E S1. Sabharwal, Y. Digital Camera Technologies for Scientific Bio-

Imaging. Part 1: The Sensors. Microscopy and Analysis 25(4):S5-S8 (AM), 2011.

2. Sabharwal, Y., Joubert, J., Sharma, D. Digital CameraTechnologies for Scientific Bio-Imaging. Part 2: Samplingand Signal. Microscopy and Analysis July 2011. microscopy-analysis.com/light/news-features/latest-features

3. Joubert, J. and Sharma, D. Using CMOS Cameras for LightMicroscopy. Microscopy Today 19(4):22-29, 2011.

4. Janesick, J. R. 2001. Scientific charge-coupled devices. SPIEPress, Bellingham, Washington.

5. Martin-Gonthier, P. and Magnan, P. RTS noise impact inCMOS image sensors readout circuit. 16th IEEE Int. Conf. onElectronics, Circuits and Systems, Tunisia. 2009.

©2011 John Wiley & Sons, Ltd