Intercomparison of a Correlated-Photon-Based Method to Measure Detector Quantum Efficiency

Intercomparison of a correlated-photon-basedmethod to measure detector quantum efficiency

Alan Migdall, Stefania Castelletto, Ivo Pietro Degiovanni, and Maria Luisa Rastello

We report on the absolute calibration of photodetector quantum efficiency by using correlated photonsources, performed independently at two laboratories, the National Institute of Standards and Technol-ogy and the Istituto Elettrotecnico Nazionale �IEN�. The goal is to use an interlaboratory comparisonto demonstrate the inherent absoluteness of the photon correlation technique by showing its indepen-dence from the particular experimental setup. We find that detector nonuniformity limited this com-parison rather than uncertainty inherent in the method itself. The ultimate goal of these investigationsis development of a robust measurement protocol that allows the uncertainties of individual measure-ments to be determined experimentally and verified operationally. Furthermore, to demonstrate thegenerality of the procedure, the IEN measurement setup was also used to calibrate a fiber-coupledavalanche photodiode module. Uncertainties are evaluated for the detector both with and without fibercoupling and differences are discussed. The current IEN setup using a thinner and higher transmit-tance nonlinear crystal for the generation of correlated photons shows a significant improvement inoverall accuracy with respect to previously reported results from IEN �Metrologia 32, 501–503 �1996��.© 2002 Optical Society of America

OCIS codes: 030.5630, 040.5570, 120.3940, 120.4800, 120.5630.

1. Introduction

Recently a technique based on correlated photons ob-tained through parametric downconversion �PDC�has been studied for the absolute calibration of pho-ton counters. The interest in this technique is es-tablishment of inherently absolute measurements atvery low light levels, i.e., in the photon-counting re-gime. This technique has proved successful for theabsolute calibration of photomultipliers and ava-lanche photodiodes �APDs�.1–7 Although reports ofthis method have so far consisted of demonstrationsand feasibility studies, much less emphasis has beengiven to systematic studies of uncertainty and inde-pendent verifications of that uncertainty. Withoutsuch efforts the impressive potential of this methodwill not be fully realized as a true metrological tech-nique that can be used conveniently and with confi-

A. Migdall is with the Optical Technology Division of the Na-tional Institute of Standards and Technology, 100 Bureau Drive,Stop 8441, Gaithersburg, Maryland 20899-8441. S. Castelletto�[email protected]�, I. P. Degiovanni, and M. L. Rastello are with theIstituto Elettrotecnico Nazionale G. Ferraris, Strada delle Cacce91 10135, Turin, Italy.

Received 1 June 2001; revised manuscript received 7 December2001.

0003-6935�02�152914-09$15.00�0© 2002 Optical Society of America

2914 APPLIED OPTICS � Vol. 41, No. 15 � 20 May 2002

dence. The goal of this research is to provide some ofthis missing framework.

In the PDC process a pump field with angular fre-quency �p generates, by interaction with a ��2� non-linear crystal, correlated pairs of signal and idlerphotons under the constraints of conservation of en-ergy and wave-vector momentum:

�p � �s � �i, kp � ks � ki, (1)

where �s and �i are signal and idler frequencies andkp, ks, and ki are pump, signal, and idler wave vec-tors, respectively.

These conservation rules lead to pairs of photonsthat are strongly correlated both spatially and tem-porally. Using these rules with available crystals,one can produce signal and idler pairs that areemitted noncollinearly with the pump, allowing foreasy optical discrimination and making these pho-ton pairs useful for measuring the quantum efficiencyof photodetectors operating in the photon-countingregime.1–6,8

When two correlated PDC emission channels cor-responding to signal and idler photon propagationdirections are appropriately selected, the detection ofone photon of a PDC pair guarantees with certaintythe presence of the second photon along the corre-lated direction. Selecting these two channels and di-

recting them to two photon counters �A and B�, wegive the mean count rates at both channels �NA, NB�and in coincidence NC, respectively, by

NA � �A N, NB � �B N, (2)

NC � �A�B N, (3)

where �A and �B denote the counting efficiency of twophotodetectors, A and B, respectively, and N is therate of correlated pair production. Thus the quan-tum efficiencies are found directly:

�A �NC

NB, �B �

NC

NA. (4)

Because in practice7,9 it is difficult to arrange exactlythat each detector sees only photons correlated to theother, we have to dedicate the channels to particularaims. One detector is the detector-under-test�DUT�, while the other acts simply as a trigger toindicate when a correlated photon can be expected atthe DUT. For the trigger channel �A in this case� ashort range of wavelengths, defined by a narrow-bandwidth interference filter, and an iris is used �seeFig. 1�, while for the second channel �B�DUT� thespectral bandpass and collection iris are larger, en-suring that all photons correlated to those arriving atA fall on B. This is crucial to a simple understand-ing of the ultimate accuracy of the technique. Con-sequently the second relation in Eq. �4� is rewrittenas

�DUT �1

TB

NC

Ntrigger, (5)

where TB is the transmittance of the portion of theoptical path, B, that is not included in DUT itself.

We report on the absolute calibration of the sameAPD operating as a single photon counter �referred toas DUT-NIST� performed independently in two lab-oratories, the National Institute of Standards andTechnology �NIST� and the Istituto ElettrotecnicoNazionale �IEN�. Similar experimental setups havebeen used, and a procedure of measurement is pro-

posed to determine empirically the accuracy limits ofthe technique.

The aim here is to demonstrate by comparison theinherent absoluteness of the measurements and theirindependence of the particular PDC generation andtrigger detection setups and to highlight the system-atic effects limiting the uncertainty. Once this isdone a measurement protocol can be developed tohelp move this technique from the realm of simpledemonstrations into the world of metrology.

In addition to the above the same setup used forcomparison at IEN was also used to calibrate a fiber-coupled APD �DUT-IEN� to demonstrate the gener-ality of the procedure. Uncertainty evaluations areshown for both DUT calibrations and experimentalsetups, and differences and similarities are pre-sented.

2. Experimental Setup for Laboratory Comparison

The arrangements for the quantum efficiency mea-surements at NIST and IEN were generally similar�Fig. 1�. A linearly polarized argon-ion laser operat-ing at 351.1 nm was used to pump a nonlinear crys-tal, NLC. A half-wave plate ��2� was used to allowrotation of the polarization of the pump beam. Thisenabled the PDC process to be turned off, because thephase-matching condition permits only one pump po-larization to be downconverted. This was used todetermine scatter and dark count rates.

At IEN the nonlinear crystal used was a 5-mm-longLiIO3 crystal, housed in a sealed holder filled withdry nitrogen. The crystal was cut and tilted forphase matching at 51.7° and was mounted to allowrotation about the normal to the crystal surface.The output window of the crystal housing and theoutput surface of the crystal produced a total reflec-tive loss of �4.1 0.1�%, as measured at 633 nm.Standard uncertainties �k � 1� are used throughoutthis paper.10 This level of reflectance is lower thanexpected for bare surfaces but higher than expectedfor typical antireflection-coated surfaces. This oc-curred because the output surfaces were antireflec-tion coated but not optimized for the 633-nm light ofour measurements. The crystal presented negligi-ble absorption of �0.2% over the 5-mm length at 633nm.

At NIST a bare KDP crystal 5 mm long was used.The bare KDP crystal presented a 4.1% reflectanceper surface at normal incidence. The crystal absorp-tion was found to be negligible ��0.05%�. Similardownconversion geometries were used in both labo-ratories with the downconverted light of interest �633and 789 nm� emitted between 3° and 5°.

Both the trigger and the DUT detectors were APDphoton-counting modules equipped with activequenching circuits and built-in discriminators.These modules produce nearly square pulses 8 nswide and 2 V in amplitude. The distances from thedetectors to the source were chosen in both laborato-ries to be 1 m for the DUT and 2 m for the trigger.Both detectors were mounted on translation-tiltstages.

Fig. 1. Experimental setup for absolute quantum efficiency mea-surement comparison with correlated photons at 632.8 nm �DUT�and 789 nm �trigger�: Ar , pump laser at 351 nm, FDUT, Ftrigger,interference filters at 632.8 and 789 nm, respectively. Irises IDUT

and Itrigger are set according to procedure. DUT was in turn NISTSPCM-AQ-231 and IEN SPCM-AQ-152. The box around the DUTand its optics indicates that is considered as a unit.

20 May 2002 � Vol. 41, No. 15 � APPLIED OPTICS 2915

The detector calibrated in the comparison �DUT-NIST� was a single-photon APD with a sensitive area500 �m in diameter with a built-in active quenchingcircuit �EG&G SPCM-AQ-231�.11 The DUT and theoptics �LDUT, FDUT� were from NIST: LDUT was acollection lens with a 25-mm focal length, mounted 25mm from the DUT sensitive area; FDUT was an in-terference filter peaking at 633 nm with a 10-nmFWHM. IDUT was an iris with a variable diameterfrom 1.5 to 10 mm. For the comparison the DUTwas mounted with its collection lens, spectral filter,and collection iris as a unit that could be translatedhorizontally and vertically as well as tilted. TheNIST setup used a trigger detector unit identical tothe DUT-NIST.

At IEN the trigger detector was similar but notidentical to the DUT: It was an EG&G ModelSPCM-AQ-152-FC with a sensitive area of �0.025mm2 �180 �m in diameter� and dark counts below 50counts�s. This detector was coupled to a smalllength �1 m� of multimode optical fiber. The PDCsignal was coupled into the fiber with a 20� micro-scope objective �Ltrigger�. The trigger beam was spec-trally limited by an interference filter peaked at 789nm and with a 3-nm FWHM.

Coincidences and single counts were measured inboth experiments by nearly identical electronics.The output signal from the trigger detector was sentto the start input of the time-to-amplitude-converter�TAC� circuit. The DUT output was delayed andsent to the stop input of the TAC. The TAC outputwas sent to a multichannel analyzer that recordedhistograms of interarrival times of the DUT and trig-ger events. Correlated photon pairs are seen in thehistogram as a peak whose width is due to the com-bined time jitter of the detectors and the electronics.This peak is on top of a flat background resultingfrom uncorrelated output pulses of detectors. Truecoincidences are found by counting the events withina fixed time window around this peak and subtract-ing the flat background level within this same timewindow �referred to as accidental coincidences�.The coincidence window must be set wide enough tocontain all the true coincidences: To achieve uncer-tainties much below 1% it must be set many times theFWHM of the coincidence peak12 owing to the longtails of the peak. At IEN the window was �3.88 0.01� ns, while the peak FWHM was 0.54 ns.

Correction for accidental counts must be measuredor calculated. At NIST two windows were set on themultichannel analyzer, one to record the total coin-cidences and a larger one away from the peak todetermine the rate of accidental counts. At IEN ac-cidental counts were calculated. We have provedthe theoretical formula for the accidental coincidencecounts in Ref. 13.

To show the versatility of the procedure, we alsocalibrated a fiber-coupled APD �DUT-IEN� identicalto the trigger detector of the IEN comparison setup.DUT-IEN is a package consisting of an interferencefilter centered at 632.8 nm with a bandpass FWHM of10 nm, microscope objectives, and multimode fiber as

described above. Attention was paid to the fiber-coupling stability and alignment of both detectors.Losses due to the fiber and the coupling lenses werenot determined individually because we consideredthem to be part of the DUT detector.

3. Measurement Procedure

To obtain high reproducibility, allowing comparablemeasurement results from the two laboratories, weattempted to establish an optimal and robust proce-dure. High-accuracy measurements can be achievedif the system is designed to maximize the collection ofall photons correlated to those seen by the triggerdetector. Collection system losses are of two types:conventional transmittance losses due to reflectanceand absorptance of the optical components in theDUT optical path or geometric ones, such as thosedue to limiting irises and detector misalignment.

The first loss type can be handled straightforward-ly; the transmittance of optical components can bedirectly measured with high accuracy and�or thelosses can be calculated. For the IEN experimentthe losses due to the crystal were measured with aHe–Ne laser: We accounted for reflection losses onthe output window and the absorption loss inside thecrystal. Assuming that PDC-generated lighttraverses on average half of the crystal length, weobtained a crystal transmittance of 0.959 0.002.Conventional transmittance losses due to the collec-tion lens and interference filter were the same in bothexperimental setups, because the lens–filter–detector package was calibrated as a whole.

More difficult to analyze were the geometric losses.They can be divided into two types. First and mosttrivially the DUT may be misaligned with the centerof path of photons correlated to those seen by thetrigger. Second, losses in the DUT collection pathcan be due to the spread of emission positions anddirections of photons correlated to those seen by thetrigger detector. The causes of this spreading,which have been treated elsewhere,14 are due to suchthings as the finite diameter of the pump beam andthe finite length of the nonlinear crystal. The finitespectral bandwidth of light seen by the DUT that iscorrelated to the trigger is determined by the spectralband of the light seen by the trigger through theenergy conservation rule. Thus it is important thatany frequency-selective element in the DUT opticalpath is broad enough to include all correlated fre-quencies. The finite spread of frequencies corre-sponds to a finite spread of angles, so that the triggercollection angle also puts constraints on the geomet-ric collection of the DUT.

A. Detector Alignment

The detector-alignment procedure is as follows:First, the trigger detector position is translated radi-ally across the cone of downconverted light to maxi-mize the single-photon signal. This centers thedetector on the central wavelength of the spectralfilter. The DUT must then be centered radially andtangentially along the downconverted light cone on


the light correlated to the trigger. Because the de-tector package includes a collection lens, centeringthe DUT package on the correlated beam involvesiterative optimization of its translational positionand its angular orientation. This procedure consistsof stopping down the collection lens iris before trans-lationally maximizing the correlated signal. Thenthe detector�lens package is tilted about the lens po-

sition, allowing the detector to be positioned at thefocused spot of light. These two steps are repeateduntil no further gains are seen.

A check of the trigger position must be performedby translational scan to verify that the maximumcorrelated signal occurs at the maximum of the singletrigger counts. Thus, by successive iterative scansof both detectors, we achieve maximum overlap of thetwo detectors on the correlated pairs. Figure 2shows the final results of the alignment procedurewith IDUT fully open �11.7-mrad collection angle� andItrigger with a 4-mm diameter �2-mrad collection an-gle� for the IEN setup. The procedure describedabove was used to calibrate DUT-IEN. The result-ing DUT and trigger translational scans are shown inFig. 3 �IDUT fully open with a collection angle of 9.4mrad limited by the objective aperture�. In this casethe procedure was used to optimize the fiber couplingto correlated photons. It is clear from Fig. 3 that theradial position of DUT is more critical than the trig-ger position, which presents a larger flat region at themaximum quantum efficiency level. This is mainlybecause of the narrower DUT collection angle withrespect to Fig. 2. Figure 4 shows the quantum effi-ciency, and DUT counts for a radial scan of DUT-IENposition for two different tilt angles of the packageconsisting of the filter and fiber-coupling optical sys-tem in the IEN setup. Note that, while the tilt has

Fig. 2. DUT-NIST quantum efficiency as the DUT-NIST isscanned radially across the cone of downconversion light in theIEN setup �F�: The value of quantum efficiency is corrected fortransmittance of the crystal, dark counts, and accidental counts.�, the DUT count rate.

Fig. 3. Measurement of DUT-IEN performed at IEN as a trigger detector is moved �a� radially and �b� tangentially to the cone ofdownconverted light, while �c� and �d� show the same results except that the DUT is moved instead: F, quantum efficiency, �, triggercount rate in �a� and �b� and the DUT count rate in �c� and �d�.


a significant effect on the DUT singles count rate dueto shifts in the filter transmittance passband, it hasvery small effect on the resulting quantum efficiencydetermination because the DUT filter passband ex-ceeds the spectral range of the photons correlated tothe trigger. The quantum efficiency values reportedare corrected for the following effects present in theIEN experimental setup: dark counts, accidental co-incidence counts, TAC dead time, and optical lossesin the crystal.15

B. Collection-Angle Verification

A further check of the alignment of the DUT andtrigger was obtained by scanning both detectors ver-sus collection angles to optimize the correlated signal.Figure 5�a� shows a scan of quantum efficiency versuscollection angle for the DUT-NIST in the NIST setup.The apparent quantum efficiency of the DUT is seento level off to better than 0.25% for a DUT collectionangle greater than 6 mrad. This is consistent with atrigger detector collection angle of 2.2 mrad. A com-plementary measurement �Fig. 5�b�� was made byfixing the DUT collection angle at 6.5 mrad �the startof the level region of Fig. 5�a�� and scanning the trig-ger collection angle. A drop in apparent quantumefficiency is seen as the trigger collection angle ex-ceeds 2.2 mrad, causing the angular range of thecorrelated photons to exceed the collection range ofthe DUT.

The same measurement was performed at IEN.Figure 6 shows the quantum efficiency versus theDUT collection angle. The quantum efficiency isseen to level out at a collection angle of �4.7 mrad fora trigger collection angle of 2 mrad. The smalldownward slope of quantum efficiency with a highercollection angle is due to an increasing detector deadtime as the DUT singles counts continue to risenearly linearly with the collection angle. This levelof variation �0.8%� is higher then those seen atNIST. This difference is likely due to a higher DUTdeadtime and higher DUT count rates with respect tothe trigger at IEN: In fact the maximum DUT countrate was 250 kHz, while the trigger was 2.2 kHz.

C. Determination of the True Trigger Rate

The simple formula given in Eq. �5� has to be modifiedto account for the presence of unwanted counts. Infact each detector is affected by background counts,resulting from stray light unrelated to the downcon-version pairs and electronic noise �dark counts�.The measurement of dark counts plus stray light ismade with a wave plate in the pump beam. Thiswave plate can be used to rotate the polarization ofthe pump beam by 90°, which effectively turns off thecreation of photon pairs, because the phase-matchingconstraints allow only one polarization orientation ofthe pump beam to produce downconverted light.The advantage of this scheme is that, while the pro-duction of photon pairs is stopped, all other scattered

Fig. 4. Quantum efficiency �Œ, F� and DUT counts �‚, E� valuesfor two tilting positions of the DUT-IEN detector as it is scannedradially.

Fig. 5. �a� Apparent quantum efficiency of the DUT-NIST and itssingles count rate shown as the DUT collection lens iris is variedwith the trigger detector collection angle of 2.2 mrad. �b� Appar-ent quantum efficiency of the DUT and trigger singled count rateshown as the trigger collection lens iris is varied with the DUTdetector collection angle fixed at 6.5 mrad. The quantum effi-ciency is not corrected for crystal losses.


light remains the same, allowing an excellent deter-mination of the total scattered-light level.

Figure 7�a� shows the trigger count rate as thepump polarization was scanned �in the NIST setup�.The minimum level, an indication of the scattered-light count rate, was found to be �0.020 0.006�% ofthe maximum. A similar measurement was per-formed at IEN, yielding a minimum trigger rate of�0.003 0.080�% �see Fig. 7�b��.

Care must be taken with this technique to avoidoverestimating the scatter level. If the pump beamis not pure linear polarization at the wave plate, thedownconversion process will not be completelyturned off at the minimum point of the curve and theapparent scattered�dark level will be too high. Thiswas checked by also monitoring the coincidence rateat the minimum point of the curves in Fig. 7. Withthe NIST setup we found that the minimum coinci-dence rate was �0.03 0.01�% of the maximum rate,while at IEN it was �0.005 0.003�%, both acceptablylow levels.

D. Quantum Efficiency Stability

A stability test was performed at NIST and IEN.Figure 8�a� shows the NIST quantum efficiency mea-surements exhibiting a mean drift of �0.07% and a0.3% repeatability at one point on the detector sur-face over a 7-h period. That the quantum efficiencydetermination remained nearly constant, even as thetrigger rate drifted by 4%, highlights the overall ro-bustness of this primary standard method: Thequantum efficiency is independent of trigger countrates, as expected.

The same measurements were performed at IENon a fiber-coupled APD. Figure 8�b� shows the tem-

poral variation of the trigger counts and the quantumefficiency. The observed trigger drift was 0.7% over1.5 h, while the quantum efficiency drift was muchless. We used the 0.3% fluctuations over 1.5 h as anestimate of the standard uncertainty �k � 1� of quan-tum efficiency measurements. As with the NISTmeasurements this empirically supports the claimthat measurement of quantum efficiency by the cor-related photon method is independent of the triggerdetector quantum efficiency or variations of its quan-tum efficiency.

Fig. 6. Quantum efficiency of the DUT-NIST measured at IEN, F,and its singles count rate, �, shown as the DUT collection lens irisis varied with the trigger detector collection angle of 2 mrad.Quantum efficiency is not corrected for crystal losses. The spot onthe detector surface to be measured was not reproducibly chosen,so the difference in quantum efficiency maximums in this figureand that shown in Figs. 5�a� and 5�b� is most likely due to varia-tions of quantum efficiency over the detector surface. As we see inFig. 10 this variation can be large.

Fig. 7. �a� Trigger, F, and coincidence, �, count rates shown asthe pump polarization is rotated �in the NIST setup�. The mini-mum trigger rate is 0.02% of the maximum signal �after subtract-ing for detector dark counts�, while the coincidence rate falls to alevel of 0.03%. �b� The same measurement performed at IENyielding similar results.


E. Spatial Uniformity of DUT-NIST

At both IEN and NIST the spatial uniformity of theDUT-NIST sensitive area was determined by tiltingthe detector–filter–lens as a unit. Because the lenswas near the center of the tilt motion, while the APDwas farther away, a tilt of the entire unit effectivelyscanned the detector relative to the focused spot ofcorrelated light at the detector surface. Manualscans of the detector showed large quantum efficiencyvariations with extremes of 0.194–0.242 �see Fig. 9for measurements made with the IEN setup�. Note

that these variations are in stark contrast to the lowvariations that can be achieved with high-performance analog Si detectors.16 The detectorwas not specifically scanned through its center, so theobserved detector width is likely to be smaller thanits diameter. Note that Fig. 2 shows a similar shapebecause translation of the DUT package also has theeffect of scanning the correlated light spot across thedetector. To investigate this variation in detail, anautomated system was subsequently built at NIST totake complete raster scans of the detector efficiency.For this scan the detector was separated from thelens and the filter mount and moved separately, elim-inating the possibility of any unwanted optical effectsfrom tilting optics. Figure 10 shows the result atNIST: The maximum quantum efficiency is 40%larger than the minimum value. The edges indicatethat the full width of the correlated spot is no largerthan 50 �m. The large variation seen here is con-sistent with the results of the simple manual tiltingobtained at IEN �Fig. 9� and that, although we werenot able to make a rigorous comparison, we canclearly see qualitative agreement and some quanti-tative agreement between the measurements in thetwo laboratories. For more rigorous interlaboratorycomparisons a detector with better spatial uniformitywould be clearly desirable.

4. Uncertainty Evaluation

Because of the poor spatial response uniformity ofDUT, the measurements in the two laboratoriescould not be directly compared to provide an indepen-dent test of the measurements. As a result we haveinstead used two methods to quantify the measure-ment uncertainty. One method relies on statisticalevaluation, while the other is determined by experi-mental means. The two methods produce consistentresults.

The statistical uncertainty is deduced by applyingthe uncertainty propagation law to the model ofmeasurement as described in Ref. 15, calculatedaccording to Ref. 17. In Table 1 we report the rel-ative uncertainty budget of the quantum efficiency

Fig. 8. �a� Stability of the quantum efficiency at one point on thedetector surface as the trigger count rate falls, measured atNIST. This highlights the robustness of the quantum efficiencydetermination. The relative standard deviation of the quantumefficiency measurements was 0.3%. �b� Short-term measurementof DUT-IEN made at IEN. Here the 0.3% relative fluctuationsare of the order of the estimated uncertainty, meaning that trigger-count drifts have little effect on the measurement.

Fig. 9. Variation of quantum efficiency, F, and DUT-NIST countrate, �, as the package filter–lens–detector is tilted �measured inthe IEN setup�.


measurements made with the IEN setup of theDUT-NIST and DUT-IEN detectors �for a singlelocation on the detector active area� at comparablecount rates. Here the total uncertainty is calcu-lated, taking account of the statistical correlation co-efficient,

�Ntrigger, NC�

��NCNtrigger� � �NC��Ntrigger��u2�NC�u2�Ntrigger��

1�2 , (6)

that contributes to the reduction of the total uncer-tainty, where u2�x� � �x2� � �x�2 is the variance ofa generic variable x. Equation �6� means that fluc-tuations of the trigger and coincidence rates are cor-related as expected, because fewer �or extra� countsin the trigger channel have a significant probability ofyielding fewer �or extra� counts in the coincidencechannel. Thus the total uncertainty can be smallerthan the largest single component �as seen in thesecond column of Table 1�.

Note that in the case of the DUT-NIST calibrationat IEN the noise associated with the trigger counts,due to a somewhat unstable fiber coupling, wasgreater than for the case of DUT-IEN calibration,resulting in a greater measurement uncertainty inthe first case.

An alternative method for evaluating uncertaintyis shown in Table 2. The uncertainty budget isgiven for quantum efficiency measurements of theDUT-NIST in the IEN and NIST setups, where thefinal uncertainties are deduced by experimentalmeans, by using, for example, the variations as seenin Figs. 5, 6, and 8 and the results in Fig. 7. Notethat the uncertainty associated with DUT-NIST inthe IEN setup turns out to be lower if evaluated by

Table 1. Uncertainty Budget for Calibrations of DUT-NIST andDUT-IEN Made in an IEN Setupa

Uncertainty Component

Relative UncertaintyContribution �k � 1� �%�

DUT-IEN DUT-NIST

Trigger counts 0.33 1.13Dark counts 0.02 0.25Coincidence counts 0.45 2.01Optical losses 0.46 0.46DUT counts �0.01 �0.01Coincidence window �0.01 �0.01Residual dead time 0.02 0.02

Total uncertaintyStatistical correlations excluded 0.72 2.36Statistical correlations included 0.56 1.87

aThe relative uncertainty is evaluated with a Gaussian propa-gation model that accounts for statistical correlation as describedin Ref. 15.

Note: There is a statistical correlation between trigger andcoincidence counts results as a negative contribution to the totaluncertainty by Eq. �6�. This correlation was empirically evalu-ated as 0.46 and 0.68 for DUT-NIST and DUT-IEN, respectively.The total uncertainty excluding statistical correlations �i.e., simplequadrature sum� is given for comparison on the next to the lastrow.

Table 2. Uncertainty Budget for Calibrations of DUT-NIST Performed inthe NIST and IEN Setups

Uncertainty Component

Relative Uncertaintycontribution �k � 1� �%�

NIST Setup IEN Setup

DUT iris test result 0.25 0.80Trigger noise 0.08 1.70Stability test result 0.30 1.11Optical losses �0.1 0.80Pump polarization purity test result 0.007 0.35

Total uncertainty 0.40 2.35Total DUT spatial nonuniformity 40 25

Note: Here the uncertainty was determined empirically accord-ing to the procedure described in this research. The last rowshows the measured spatial variation of the DUT-NIST. Thislevel of variation clearly limits how well measurements made inthe different setups can be compared.

Fig. 10. Spatial maps of �a� quantum efficiency and �b� raw countsat 633 nm �these efficiencies include crystal transmittance losses�as DUT-NIST was scanned across the downconverted light beamat NIST.


the statistical method rather than by the empiricalone �1.87% versus 2.35%�. This last method mayoverestimate uncertainty because it does not includepossible statistical correlations.

5. Conclusions

We have shown the results of calibrating an ava-lanche photodiode from NIST in setups at IEN andNIST by using a correlated photon technique. Aprocedure has been sketched for a interlaboratorycomparison to minimize and empirically quantifysystematic effects. The results show qualitativeconsistency between the two laboratories. At thistime the overall uncertainty is limited by the spatialuniformity of the detector under test rather than themeasurement method itself. A measurement of thisnonuniformity has been given.

We performed a further calibration of an IEN fiber-coupled avalanche photodiode with the same experi-mental setup, following the procedure established,yielding an improved uncertainty relative to a previ-ous calibration done at IEN. We have studied con-tributions to the uncertainty of this kind ofmeasurement. We have established that pump la-ser instability contributes little to the final uncer-tainty, highlighting the inherent absolute nature ofthe measurement method. The procedure is cur-rently under test, and improvement in both labora-tories and a measurement protocol is underdevelopment.

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Documents

Intercomparison of a Correlated-Photon-Based Method to Measure Detector Quantum Efficiency