Open Access
Add to BibSonomyAbstract
We introduce a technique for measuring detection efficiency that is traceable to the primary standard, the cryogenic radiometer, through a reference silicon photodiode trap detector. The trap detector, used in conjunction with a switched integrator amplifier, can measure signals down to the 0.1 pW (3 x 105 photons second−1) level with 0.1% uncertainty in a total integration time of 300 seconds. This provides a convenient calibration standard for measurements at these levels across the optical spectrum (UV – near IR). A second technique is also described, based on correlated photons produced via parametric down-conversion. This can be used to directly measure detection efficiency in the photon counting regime, and provides a route for expanding the formulation of the candela in terms of photon flux to enable it to address the needs of emerging quantum optical technologies and applications. The two independent techniques were cross-validated by a comparison carried out at 702.2 nm, which showed agreement to within 0.2%.
©2011 Optical Society of America
1. Introduction
The few photon research community is striving to utilize and detect fewer and fewer photons in applications ranging from low level signalling from space and the study of single molecule dynamics to quantum information processing where control of single and entangled photons are required. We describe two independent techniques that were used to measure the detection efficiency of a Perkin-Elmer channel photomultiplier (CPM), as well as the low power reference detector implemented within these measurements.
The cryogenic radiometer [1,2], the primary standard for optical radiation, typically operates at the 1 mW – 2 mW power level. Traceability to this standard is normally provided by a reference trap detector [3,4] which, to avoid nonlinearity issues, must operate at irradiance levels not exceeding 1 mW cm−2. A transimpedance amplifier (TIA) is conventionally used to convert the generated photocurrent into a voltage. Measurements are possible at low power levels, however these are limited by the noise floor of the trap detector and TIA. The TIA does not perform optimally when coupled with a low shunt resistance detector at high V/I gain due to its noise gain [5] which is proportional to the ratio between its large value feedback resistor and the detector’s shunt resistance. A switched integrator amplifier (SIA) has been shown to have a lower noise equivalent power (NEP) compared to a TIA when used with a three element silicon photodiode trap detector in dark conditions. The measured NEP of the SIA and trap combination [6] was as low as 25 fW/Hz½ (8 x 104 photons s−1Hz-½) while the NEP of the TIA and trap was at the level of 45 fW Hz-½. As reported in [7], AC measurements using chopped light can reduce the noise floor using a frequency compensated TIA to about 23 fW/Hz½. To measure absolute radiant flux, an absolute traceable calibration of the lock-in amplifier must be carried out, with the consequent introduction of additional uncertainty contributions such as the lock-in nonlinearity at the level of 0.1% [8]. The combination of trap plus SIA provides all the advantages of using a trap detector, without the need for ancillary lock-in instrumentation, and is therefore a more suitable transfer standard for calibrating detectors in the few photon regime. There are currently no reference transfer standards for this regime and it is the goal of national metrology institutes to develop traceability to standards for few photon applications.
The work reported here was part of a European consortium project [9] aimed to provide traceability for optical radiation measurements over the dynamic range from a single photon up to mW of optical power. The correlated photon technique was used to bridge the gap between the high power and the single photon regimes. This technique has been used in a number of configurations [10–12 and references therein]. The technique is inherently absolute and therefore could be used to establish optical radiation detector scales at low photon flux, and provide an independent route for the expanding the formulation of the candela, the SI unit of optical power, to include one based on photon number [13,14]. This would allow the candela to address the needs of emerging quantum optical technologies and applications, and is in line with proposed redefinitions for four of the seven SI base units – the kilogram, ampere, Kelvin and mole – in terms of fundamental constants in a quantum-based SI system. Although the technique is inherently absolute it must be validated if it is to be used within the framework of the reformulation of the SI unit. A conventional technique was therefore developed by NPL and CMI to validate the correlated photon technique with a target uncertainty level of the order of 0.1%. Development of the switched integrator amplifier [5,6] meant that it was now possible to access much lower light levels with a reference trap detector and this ensemble has been tested and implemented in a technique for measuring detection efficiency. A channel photomultiplier was chosen as the device under test due to its large active area (~5 mm diameter) compared with a single-photon avalanche diode (~200 μm diameter). This simplified the measurement using the conventional method since the trap detector has a small collection angle (f/10) and therefore a beam that had to be strongly focused down to 200 μm could not be accommodated by the reference trap detector.
2. Measurement of the detection efficiency of a photon counting device based on a conventional technique
The technique uses an optical beam to alternately underfill a reference detector and the detector under test (DUT). The reference detector measures the power in the beam, hence the detection efficiency (DE) of the DUT can be calculated from its response to the same beam.
Previous measurements [15,16] described set-ups that required the use of neutral density filters to attenuate the beam into the low power regime, and a monitor channel to correct for signal instability. The attenuation of the filters had to be measured, and long settling times were required after any change to the set-up which involved exposing the experimental area to ambient light. The reference detectors used were single element silicon photodiodes that reflect approximately 30% of the signal, requiring many correction factors to be assessed.
The measurement technique reported here uses a trap detector as the reference standard. This detector is the workhorse of high power optical radiation measurements due to a number of salutary features: with only 0.4% reflectance loss, it also has near unit external quantum efficiency over optical wavelengths, low spatial non-uniformity (~0.02%), and low polarization sensitivity. In combination with the SIA, the trap detector is able to measure levels as low as 5 pW with an uncertainty better than 0.1% in a total integration time of 20 seconds, removing the need for neutral density filters to switch from the high power regime to the low power regime. The SIA used in this work was developed at CMI and has been fully characterized for its noise and amplification performance [5]. The SIA was operated with a gain of 1011 VA−1 with an external PTFE integration capacitor of 1 pF.
2.1. Experimental details: Conventional Technique
Figure 1 and Fig. 2 illustrate the experimental set-up. The light from a halogen lamp, operating from a 12 V current stabilized power supply, was fed to the integrating sphere via a fiber optic bundle. A neutral density filter (Ealing Optics CG08) attenuated the light (~9% transmittance). A 12 nm band pass filter positioned at the input port of the integrating sphere selected the bandpass of interest, centered at 702.2 nm, chosen for the comparison with the correlated photon technique. Enclosures were used to ensure that the only light getting to the detector area should be the light from the two output ports of the sphere. The photon counter had a dark count rate of < 10 counts per second (cps). The count level with the shutter closed was about 50 cps, therefore we could be confident that we had a very low level of background radiation. The purpose of the integrating sphere was to provide a uniform patch of light out of both ports. Apertures of 1 mm diameter were attached to these output ports. A detector with a linear response can be placed at the second output port and used to correct for instabilities in the source and carry out measurements at power levels below the minimum level measurable by the reference detector by relating these levels back to the level measured with the reference detector. A polarizer was used to select vertically polarized light, the same polarization as that of the photons used in the correlated photons measurement.
Fig. 1 Experimental set-up for measurement of detection efficiency, top view, ND = neutral density filter, IS = integrating sphere, L = lens, P = polarizer, SIA = switch integration amplifier.
In order to reduce the effect of the spatial non-uniformity of the DUT response, a lens magnification of x2 formed a 2 mm diameter image of the aperture which underfilled the photon counter. The standard deviation in DUT output from repeated centring of this image on the photon counter was 0.02% of the mean value.
The signal stability had a relative standard error of the mean (SEOM) of 0.008% over 1.5 hours, which was well within the target uncertainty for the measurement (order of 0.1%), hence a monitor channel was not considered necessary. The duration of the measurement depended on the signal level – the lower the signal the greater the number of samples read.
A motorized stage moved the reference detector and then the photon counter into the beam over a number of cycles. An automated shutter was used to account for the background signal.
2.2. Data analysis
The detection efficiency ηCPM is the ratio of the count rate measured by the CPM photon counter NCPM to the equivalent count rate measured by the trap detector, Ntrap, where the trap detector [4] has a known DE determined from its calibration against the cryogenic radiometer Eq. (1).
A photo-current was created in the trap by the incident optical power P, and the SIA converted this into a voltage, Vout which was measured, Eq. (2):
where R (AW−1) was the responsivity of the trap, and GSIA (VA−1) was the gain of the SIA.Ntrap is related to P by the standard relationship given by Eq. (3):
where h is Planck’s constant, c is the speed of light, and λ denotes wavelength.These equations lead to Eq. (4) which describes the DE of the photon counting detector:
The above expression is valid for measurement at a single wavelength. In our experiment, the measurements spanned the spectral range transmitted by the 12 nm bandpass filter, and the responses of the two detectors exhibited differing spectral variations. It was therefore necessary to relate the effective detector responses over the bandpass range to the required responses at 702.2 nm. Although both detectors viewed the same spectral light distribution, the spectral behaviour of the bandpass filter, the source and the responses of the detectors must be taken into account in order to obtain a value for the photon counter DE at 702.2 nm.
We defined the correction factor Θtrap which relates the calibrated trap responsivity at 702.2 nm, Rcal(702.2), to the effective trap responsivity averaged over the spectral extent of the bandpass filter, Reff by Eq. (5):
where L(λ) was the spectral output of the halogen lamp source, FA(λ) was the spectral transmittance of the bandpass filter and Rth(λ) is the theoretical responsivity of an ideal trap with external quantum efficiency, ε equal to one [4] Eq. (6).where e is the elementary charge.Evaluating Eq. (5) gives: Θtrap = 0.9981. The spectral output of the halogen lamp source was measured with a diode array spectrometer. This was measured after the experiments were carried out, and it is known that the output of such spectral sources are prone to vary with time. Since we could not be certain of the lamp spectrum at the time of the experiment, we made the extreme assumption that the lamp output was constant in wavelength and re-evaluated Eq. (5). The change in Θtrap was 0.03%, and this factor was included in the uncertainty budget for Θtrap. Θtrap also changed by less than 1 part in a 104 when estimated spectral variations associated with the sphere and transfer optics were taken into account. The significant spectral variation came from the transmittance of the bandpass filter. The CPM exhibited a strong spectral dependency, as shown in Figs. 3a and 3b.
Fig. 3 Fit to typical data of the relative detection efficiency of the channel photomultiplier supplied by Perkin Elmer (Fig. 3a), the full spectral range is in Fig. 3b.
Similarly, we defined the correction factor ΘCPM that relates the CPM detection efficiency at 702.2 nm, η(702.2), to the effective CPM responsivity, ηeff, over the spectral extent of the bandpass filter FA(λ), by Eq. (7):
where Nph(λ) is the lamp spectral distribution given in Eq. (6) but expressed in photons s−1, ηrel(λ) is the relative variation of detection efficiency of the CPM vs. wavelength (Fig. 3), NCPMeff was the measured number of counts sec−1, and NCPM_702.2 would be the number of counts sec−1 at 702.2 nm. For ηrel(λ) we used representative data from the manufacturer, as it was the best available at the time. In order to assess the impact of uncertainty of this data on the correction factors θCPM (Eq. (7) and θcc (Eq. (18) we evaluated the respective sensitivity coefficients and found them to be less than 0.0001.Evaluating Eq. (7) gives: ΘCPM = 1.0145. In this case, the significant spectral variation came both from the bandpass filter and the detector response. In our experiment we measured an effective detection efficiency ηCPMeff since Eq. (4) takes the form, Eq. (8):
Therefore, the response of the photon detector at 702.2 nm is expressed by Eq. (9):
where the subscript ‘CPMconventional’ is used to distinguish this value from the value obtained using the correlated photon technique.2.3. Linearity measurements
It is very important to assess the linearity of all detectors [17]. Trap detectors are typically linear in their response to irradiance levels below 1 mW cm−2, however photon counters tend to suffer from non-linear effects [18], see Fig. 4 . This often means that at high photon fluxes the photon counter is unable to register all of the counts due to its own dead time [19]. The correlated photon measurements were typically carried out at <10,000 cps (the available photons for detection) and the conventional measurements at 100,000 cps.
In order to determine the linearity correction factor, in situ measurements, Fig. 5 , were taken at different flux levels. The flux level was controlled by inserting different neutral density filters in the light housing – negating the need to open up the main experimental area and exposing the detectors to light. This was more robust than altering the voltage supply to the lamp since changing the voltage will affect the stability of the lamp.
From this data we approximated the loss in detection efficiency of the photon counter with the increase of the photon flux using a linear relationship. Using this approximation we calculated the ratio of the two detection efficiencies, corrected for detector non-linearity, at the different flux levels used in the conventional and correlated techniques respectively.
2.4. Assessment of uncertainties
The most significant uncertainty in the conventional technique arose from the noise of the channel photomultiplier. Table 1 shows that this noise did not originate from the source as the reference detector had a lower noise level. The trap detector spectral responsivity was calibrated against the cryogenic radiometer. The gain calibration for the SIA at the level of 1011 VA−1 was obtained by calibration of its integration capacitor value at a favorable high input current (typically 10 nA) followed by conversion to higher gain through accurate determination of the SIA integration periods (for further details see [5,6])
Table 1. Assessment of the Uncertainties of the Conventional Technique
3. Measurement of the detection efficiency using correlated photons
Correlated photons are produced through the process of parametric down-conversion (PDC). A high-energy photon in a suitable non-linear crystal will very occasionally spontaneously decay into two lower energy photons, referred to as signal and idler photons, under the constraints of energy and momentum conservation [20]. Our correlated photon measurement of detection efficiency was based on non-collinear type I down-conversion in a barium beta-borate (BBO) crystal. Down-conversion occurs all along the pump path through the crystal. The down-converted photons of a given wavelength are emitted with the same polarisation orthogonal to the pump polarisation, and in a cone emanating from the point of down-conversion. Figure 6 shows down-conversion from the centre of the BBO crystal, leading to a circular distribution for each wavelength in a plane perpendicular to the pump direction (z-axis). Correlated pairs (anti-correlated in frequency/wavelength) are denoted using identical symbols. For simplicity, only pairs in the vertical axis are marked.
Fig. 6 Type I down-conversion in BBO; matching shapes represent different correlated photon pairs, with the crosses representing degenerately down-converted photons.
The emission time, direction, wavelength and polarization can be deduced for the idler from the measured properties of the signal photon. Use of this technique for detection efficiency measurements was originally developed by Burnham and Weinberg [21], and independently by Klyshko [22], and has since been widely reported [10–12]. A schematic of the measurement set-up is shown in Fig. 7 . The signal photon was taken as going to the trigger, and the idler photon as going to the DUT. For specific details about this measurement set-up see Cheung et al. [13]
Fig. 7 Schematic of set-up for detection efficiency measurements using correlated photons, F = filter, PBS = polarizing beam splitter, HWP = half wave plate, NLC = non linear crystal,, L = lens, DUT = Device Under Test, TRIG = trigger detector, D = delay unit. The whole apparatus sits in a light tight enclosure
A narrow bandpass filter was used to select the ‘trigger’ wavelength in the trigger arm and, through the phase matching conditions, this determined the ‘idler’ wavelength and bandwidth. When the trigger detector (TRIG) registered a photon it heralded the arrival of its twin on the DUT. Photons lost due to detection inefficiency and optical elements in the trigger channel only impacted on the overall efficiency of the measurement, what was crucial was to determine whether the DUT registered every twin of every photon detected by the trigger.
The trigger detector (TRIG) was a Perkin-Elmer single photon counting module (SPCM-AQR14). The device under test (DUT) was the Perkin-Elmer channel photomultiplier CPM-962 measured using the conventional technique. The signal from each detector was split, and sent to an EG&G 994 dual counter, and also to the coincidence counter (EG&G 9308 picosecond time analyser) via a bespoke TTL-NIM converter [23]. The signal from the trigger detector was connected to the START input of the coincidence counter. The signal from the DUT was delayed using an electrical delay unit before reaching the STOP input of the coincidence counter to overcome the dead time of the coincidence counter and detectors.
Counting the coincidences and count rates from both detectors was carried out simultaneously. The user defined the number of triggers, and counting on both counters was carried out until the coincidence counter registered the set number of triggers on the start channel. An offset of 60 ns was set to account for the dead time of the electronics and a span of 80 ns set the duration over which stop signals were registered. Once that window of time had elapsed, or a stop signal had been received, a new window would be opened by the next trigger start signal. A histogram of events was collected into 65536 time-intervals, 1.22 ps wide, and binned into 1024 bins of width 78 ps (Fig. 8 ).
The DE of the DUT is expressed as Eq. (10):
where Nc is the number of coincidences acquired by the coincidence counter and NTRIG is the count rate from the trigger detector reported by the dual rate counter. More correctly, this is the DE from the point of down-conversion to the detector. To extract the detection efficiency of the detector, the losses due to optical elements in the DUT path must be characterised and the number of accidental and false triggers evaluated [12,13,24–27], Eq. (11).where Ac = the number of accidental coincidences due to uncorrelated photons, dark counts and stray light; TDUT = the transmittance in the DUT channel; NTRIGGER = the number of photons detected by the trigger; NFALSE = the number of false triggers due to dark counts and stray light. Note that one need only count coincidences and individual count rates. It is not necessary to know the detection efficiency of the trigger detector, making this technique inherently absolute.The area under the curve in Fig. 8 allowed Nc to be calculated. Ac was determined by looking at the underlying level of events occurring either side of the peak. A thorough analysis of how this background correction was carried out is described in reference [13]. NTRIGGER was a user-defined number, 4 x 106 in this case. NFALSE was determined by repeating the experiment with the down-conversion turned off using the half wave plate to rotate the pump polarization so that PDC did not occur but the pump beam was still incident on the crystal and false triggers could be counted. Since the coincidence rate should have been close to zero, the number of triggers set was much lower to reduce the measurement time, typically 5 x 103. The count rate was then used to calculate the number of false triggers that would have been received in the time taken to collect 4 x 106 triggers when PDC was occurring.
TDUT included the transmittance of the down-conversion medium, focussing optics and filters, as well as losses due to aperturing or misalignment (Eq. (12). The transmittance of these components can be measured with high accuracy using existing facilities at NPL [12,28–30].
where td = transmittance of the down-conversion medium from point of down-conversion; tf = transmittance of any focusing optics; tλ = transmittance of any spectral selection element; tb = transmittance of any pump and pump-scatter blocking filter, applicable in the absence of tλ; tg = incomplete collection of heralded photons due to geometrical aperturing or misalignment.3.1. Characterizing the optical losses
3.1.1 The down-conversion crystal (td)
The correlated photons emerged at different points of the output surface of the crystal at approximately 6° from normal incidence. Losses due to reflections off this surface were minimised by using anti-reflection coatings. Spatial transmittance and reflectance measurements of the down-conversion crystal were carried out on the NPL spatial uniformity facility, using the same 12 nm bandpass filter centred at 702.2 nm that was used in the conventional measurements to filter the broad-band source, and with the crystal mounted at 6° to the incident beam, and for vertically polarised light, the same polarisation as the correlated photons. The spectral transmittance of the crystal was measured on the NPL Cary 5 spectrometer facility to correct the bandpass-limited measurements to a value at 702.2 nm.
The transmittance over the 8 mm x 8 mm area of the crystal is shown in Fig. 9 . The uncertainty in each value was 0.002, and the average external transmittance Td over the central 3 mm x 3 mm area was 0.979 ± 0.002. The reflectance at the exit face was measured to be 0.004 ± 0.00025, hence the fraction of photons transmitted after multiple internal reflections was negligible. The down-conversion efficiency is of the order of 10−7, therefore pump depletion can be considered as being only due to crystal absorption. If pump absorption is ignored, the centre of the crystal thickness can be taken as the mean point of down-conversion, and the transmittance of the signal photons from the point of down-conversion until they exit the crystal is given by the square root of the internal transmittance value 0.987, multiplied by the transmittance through the exit face 0.996, which came to 0.989 ± 0.002. Calculation, including taking account of pump absorption at 351 nm, was found to differ from this approximation by 1 part in 105, with an uncertainty of less than 1 part in 104 due to the uncertainty in the pump absorption coefficient.
Fig. 9 Transmittance of the crystal, measured at 700 nm, at 6° to the incident beam. The values to the right are the values when the crystal is out of the beam. The colour bar represents transmittance.
There was also an uncertainty caused by the non-uniform transmittance of the crystal, since there was a variation in the location of where exactly the correlated photons were emitted. This was because the photons could have been created at any point along the crystal thickness, and also because of the imprecision in re-positioning the pump beam. The pump beam had a width of ~2 mm, and the cone of down-conversion, having traversed a crystal thickness of 2 mm became ~2.4 mm in diameter. The pump beam could be placed to within 0.5 mm of the centre of the crystal face. The down-conversion could therefore occur within a 3.5 mm diameter patch centred on the crystal. This uncertainty was taken to be the standard deviation of the √Td values, 0.001, giving the overall value for the transmittance experienced by the down-converted signal photons as 0.9894 ± 0.0023. The variation in transmittance appeared to reside in the anti-reflection coatings, since the reflectance measurements showed similar scale structure to the transmittance measurements, but inverted.
3.1.2 The focusing lenses (tf)
The lenses were characterised using a double lens technique developed at NIST [30] and adapted for measurements at NPL (Fig. 10 ). A double lens technique was used to allow a trap detector to measure the transmittance. The source of radiation could be either laser based (relative uncertainty = 0.06%) or monochromator based [31].
Fig. 10 Schematic of set-up for the measurement of lens transmittance, SF = spatial filter,BS = beam splitter, MS = motorized shutter.
The source of radiation was a mode-locked, stabilised Ti-sapphire laser, of wavelength 702.2 nm. The measured transmittance of the lens was 0.96317 ± 0.0006.
3.1.3 Geometrical alignment (tg)
As in the conventional technique, a 2 mm diameter beam, which just underfilled the photon counter, was obtained by positioning the detector behind the focal plane of the detector lens. The DUT was centred on this beam and measurements were carried out to check that all the coincident photons were received. This was done by varying the aperture on the DUT. Once the number of coincidences started to plateau with respect to increasing aperture size it was clear that all the coincidences were being collected. The count rate on the device under test should continue to increase, albeit more slowly, as it will continue to register more uncorrelated photons as the aperture increases. In Fig. 11a the DUT singles rate starts to plateau later than the DUT coincidence rate. The uncertainty in losses due to geometrical misalignment was inferred from the standard deviation of the points across the coincidence plateau (Fig. 11b).
Fig. 11 a. Geometric alignment (measurements Spring 2008), Fig. 11b is a close up of the data points over which the relative variation is taken as the uncertainty in the geometric alignment.
3.1.4 Wavelength dependence due to system geometry
It was necessary to consider the geometry of the down-conversion process, which is wavelength dependent. The spectral variation of the down-converted power at signal wavelength λs, integrated over all solid angles, and in the spectral window δλs about λs, is given by Eq. (13) [32].
where Pp is the pump power and the p, s and i subscripts refer to pump, signal and idler, respectively. For a given pump wavelength, in terms of photon number, Eq. (13) becomes Eq. (14)The pump beam was incident normal to the entrance face of the BBO crystal. Signal photons at a specific wavelength λs would propagate in a cone with axis the pump direction and apex at the point of down-conversion. This gave rise to signal photons distributed on a circle centered on the pump axis of radius rs and thickness δλs in a plane perpendicular to the pump direction. The angular distribution within this cross section (shaded area of Fig. 12 ) is uniform for type I down-conversion.
Fig. 12 Down-conversion geometry viewed along pump axis. The dashed line represents the down-conversion wavelength of interest, λs, the shaded area represents the spread of the down-conversion wavelength, δλs.
The phase-matching condition would produce a distribution of signal wavelengths and give rise to a distribution of circle radii. Down-conversion would occur at all points along the pump path through the crystal, and the radius rs for a given signal wavelength would therefore increase as the point of down-conversion moved towards the entrance face of the crystal, leading also to a distribution of circle radii for signal photons of a given wavelength. Similar arguments apply to the idler photons.
The pump, signal, and idler photons would all suffer absorption by the crystal. The fraction ϕs,j of each circle of down-conversion corresponding to a signal wavelength λs and point of down-conversion zj in the crystal which is intercepted by the trigger aperture was weighted by the factors tpj, tsj and tcs. tpj is the internal transmittance of the length zj of the crystal at the pump wavelength. tsj is the internal transmittance of the crystal at λs for the distance [dj = (l-zj)/cos(αs)] traversed by the signal photon, where l is the length of the crystal and αs is the angle the idler photon makes with the pump within the crystal. tcs is the transmittance through the anti-reflection coating. The small variations in uniformity of the crystal/anti-reflection coating have been previously discussed, where they led to an uncertainty in the overall transmittance of the idler photons, and were not considered in this calculation. There was a wavelength variation in tcs due to the anti-reflection coating, while the wavelength variation in tsj was insignificant.
Nsap(λ), the spectral variation of the signal photons intercepted by the circular aperture in front of the trigger optics, expressed in photons s−1, is given by Eq. (15):
The initial position of the circular aperture was taken as being aligned normal to and centred on the signal photons of wavelength 702.2 nm originating from exactly halfway along the pump path through the crystal [zj=1/2]. The trigger aperture of diameter 6 mm was positioned 1.0 m from the exit face of the crystal, and therefore defined a solid angle of view of 2.8 x 10−5sr, with apex at the point at which the idler exited the crystal. The intersection of the solid angle of view cone with a plane perpendicular to the pump (where each down-converted wavelength is distributed in a circle) and passing through the centre of the aperture forms an ellipse (Fig. 13 ) [33]. The in-plane intersection of this ellipse with the circle of down-conversion, corresponding to λs, defined the geometric filtering produced by the detector aperture. For each λs and zj, the points of intersection of the circle and ellipse were calculated, and hence the angles subtended by the arc of the circle intercepted by the ellipse. These values, as fractions of 2π radians, yielded the fractions ϕs,j of the total power at each λs which entered the aperture [34].
The trigger aperture was aligned so that the number of counts Strig was maximised (Eq. (16), where
and ηdt(λ) describes the relative DE of the trigger detector. Strig was evaluated for the initial assumed position of the aperture, and then re-evaluated as the aperture position was translated about its plane of orientation. The position at which Strig was a maximum was then taken to be the ‘true’ position for the evaluation of Nsap(λ). The calculation confirmed that the limiting spectral filtering for the trigger was the band pass filter, since Nsap ranged from 678 nm to 720 nm. The larger solid angle of view (4.5 x 10−4 sr) for the DUT meant that its limiting spectral filtering was also due to its band pass filter.3.1.5 Optical losses due to spectral filtering (tλ)
Spectral filtering played a significant role in the final determination of the detection efficiency. A 4 nm band pass filter was used in the trigger arm, and the same 12 nm band pass filter that was used in the conventional measurements was used in the DUT arm.
A simplistic model would just account for the transmittance losses due to the band pass filter on the DUT arm, however it was the trigger band pass filter that imposed a band pass on the DUT arm since only some of the photons that were transmitted by the DUT filter were correlated with those detected on the trigger arm. The transmittance profiles of the band pass filters were measured on an NPL calibrated Cary 5 spectrometer at normal incidence and at off-normal angles of incidence. Figure 14 shows the transmittance profile of both filters measured at normal incidence. The uncertainties in the transmittance values were given by the NPL uncertainty budget for a standard measurement on the Cary 5 spectrometer.
Fig. 14 Transmittance profile of the DUT and trigger band pass filters measured at normal incidence using the NPL calibrated Cary 5 spectrometer.
The transmittance value used in the determination of the detection efficiency was taken as the average of the DUT band pass weighted with the trigger band pass over the 4 nm (full width half maximum), Eq. (17):
The detection of coincident photons in the idler beam was triggered by the detection of their heralding twins in the signal beam, the spectral distribution of which was given by Nsap(λ)FIEN (λ), where FIEN (λ) described the spectral transmittance of the 4 nm band pass filter used in the trigger arm. This spectral weighting, when applied to the idler photons, became because of the frequency (wavelength) anti-correlation of the down-converted photons, where denotes reflection about the 702.2 nm degenerate wavelength. A coincident idler photon was only sought when its signal twin had been detected, hence the absolute values of were not important, only their relative spectral distribution. was the spectral transmittance of the 12 nm band pass filter used in the idler (DUT) arm.
3.2 Evaluation of detection efficiency at 702.2 nm
The correlated photon technique required a similar consideration of the detector spectral response as for the conventional technique (Eq. (7)). The correction factor, Θcc, for the coincidence counting technique is given by Eq. (18).
where ηrel(λ) is the relative DE of the CPM vs. wavelength (Fig. 3) and determines the bandpass of photons correlated with the triggers (see section 3.1.5). ηeff_cc is the measured DE, corresponding to ηDUT in Eq. (12), and ηcc(702.2) is the required DE at 702.2 nm. Evaluation of Eq. (18) showed that even if Nsap was assumed to be wavelength independent, the change in θcc was not significant.3.3 Reproducibility
The value of the reproducibility came from the standard deviation of the measurements carried out over several days, each after realignment by different operators.
3.4. Uncertainty budget
The evaluation of Eq. (11) for one particular set of measurements is presented in Table 2 , and the final averaged value from five sets of measurements is presented in Table 3 .
Table 2. Uncertainties for Final Set-up (Winter 2009) of Correlated Photon Technique
Table 3. Final Value from Winter 2009 Measurements
4. Results
The final results for the DE evaluated at 702.2 nm by the two independent techniques are presented in Table 4 .
Table 4. Final results of Comparison (†Uncertainty Dominated by Reproducibility of Those Measurements, *Corresponds to 2009)
The winter results were obtained using the improved final measurement for the conventional technique (Fig. 1), incremental improvements having been made subsequent to the Spring and Summer measurements. Notably, the channel photomultiplier required a long settling time, dependent on ambient lighting conditions prior to measurement. The measurement set-up was designed to be non-interactive so that once the detector was aligned, the experimental area could be sealed up for light tightness. Once the settling time had elapsed, a week of measurements could commence without any change to the lighting levels within the experimental area. Coupled to this, it was also possible to measure the linearity of the detector in situ. It is interesting to note that the detection efficiency of the photon counter has varied over the course of the year, and that the variation has been observed with both techniques.
5. Conclusion
The use of the trap detector in conjunction with SIA has enabled the absolute calibration of the detection efficiency of a photon counter, traceable to the cryogenic radiometer, with an uncertainty of 0.2% at a flux level of 1 pW, corresponding to 3 x 106 photons s−1, at 702 nm. Furthermore, the detection efficiency was determined by two entirely independent techniques and experimental set-ups, with an agreement of 0.14(46)%. This compares well with the value of 0.14% previously reported in an earlier comparison of calibrations using correlated photons and a transfer standard traceable to cryogenic radiometry [12], but where the comparison was carried out using the same experimental set-up, and the same beam of correlated photons for both measurements. These authors also reported a variation in detection efficiency over the period of their measurements.
The correlated photon technique enables an intrinsically absolute measurement of detection efficiency, without the need of a reference standard. It is important to evaluate the optical losses each time a measurement is made. The dominant uncertainties in Table 3 arose from the characterization of the DUT filter, the crystal, and the collection of all heralded photons. A filter with a flatter response in the spectral region anti-correlated with the trigger filter and a crystal with more robust and uniform coatings would lead to more accurate characterization, while spatial mapping may also lead to greater certainty that all heralded photons are intercepted, enabling the uncertainties (0.18%) quoted by other authors [12],to be achieved. Polyakov and Migdall have recently published a review of this area [35]. This cross-validation demonstrates that the combination of trap and switched integrator amplifier is well-suited for use as a low power transfer standard – currently no such standards exist for the photon counting regime. It is particularly advantageous to have extended the trap detector, the reference standard at high photon flux, to low photon flux since trap detectors are very well understood. The technique based on this new low power transfer standard has low uncertainty, 0.2%, and is being extended for use with a monochromator so that detection efficiency can be measured at different wavelengths.
Acknowledgements
The research within the EURAMET joint research project leading to these results has received funding from the European Community’s Seventh Framework Programme, ERA-NET Plus, under Grant Agreement No. 217257.
The NPL authors would like to acknowledge the support of the UK National Measurement Office, and the provision of the trigger filter by L'Istituto Nazionale di Ricerca Metrologica (iNRiM), Italy.
The CMI authors gratefully acknowledge the financial support of the Czech Office for Standards, Metrology and Testing – Ministry of Industry and Trade.
References and links
1. J. E. Martin, N. P. Fox, and P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21(3), 147–155 (1985). [CrossRef]
2. N. P. Fox and J. P. Rice, “Absolute radiometers,” in Experimental methods in the physical sciences, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Elsevier Academic Press, 2005), pp. 35–96.
3. E. F. Zalewski and C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22(18), 2867–2873 (1983). [CrossRef] [PubMed]
4. N. P. Fox, “Trap detectors and their properties,” Metrologia 28(3), 197–202 (1991). [CrossRef]
5. J. R. Mountford, G. Porrovecchio, M. Smid, and R. Smid, “Development of a switched integrator amplifier for high-accuracy optical measurements,” Appl. Opt. 47(31), 5821–5828 (2008). [CrossRef] [PubMed]
6. G. Porrovechio, M. Smid, J. R. Mountford, J. Y. Cheung, C. J. Chunnilall, and M. G. White, “Sub picowatt absolute light radiation measurement technique with a trap detector and switched integrator amplifier,” (In preparation).
7. G. P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic design of a tunnel-trap Si radiometer,” J. Res. Natl. Inst. Stand. Technol. 105, 813–818 (2000).
8. E. Theocharous, “Absolute linearity characterization of lock-in amplifiers,” Appl. Opt. 47(8), 1090–1096 (2008). [CrossRef] [PubMed]
10. A. N. Penin and A. V. Sergienko, “Absolute standardless calibration of photodetectors based on quantum two-photon fields,” Appl. Opt. 30(25), 3582–3588 (1991). [CrossRef] [PubMed]
11. G. Brida, S. Castelletto, I. P. Degiovanni, C. Novero, and M. L. Rastello, “Quantum efficiency and dead time of single-photon counting photodiodes: a comparison between two measurement techniques,” Metrologia 37(5), 625–628 (2000). [CrossRef]
12. S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007). [CrossRef] [PubMed]
13. J. Y. Cheung, C. J. Chunnilall, E. R. Woolliams, N. P. Fox, J. R. Mountford, J. Wang, and P. J. Thomas, “The quantum candela: a re-definition of the standard units for optical radiation,” J. Mod. Opt. 54(2-3), 373–396 (2007). [CrossRef]
14. J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and 'the candela': evolution in the classical and quantum world,” Metrologia 47(5), R15–R32 (2010). [CrossRef]
15. S. D. Biller, N. A. Jelley, N. M. D. Thorman, N. P. Fox, and T. H. Ward, “Measurements of photomultiplier single photon counting efficiency for the Sudbury Neutrino Observatory,” Nucl. Instrum. Methods Phys Res. A 432(2-3), 364–373 (1999). [CrossRef]
16. A. R. Beaumont, J. Y. Cheung, C. J. Chunnilall, J. Ireland, and M. G. White, “Providing reference standards and metrology for the few photon - photon counting community,” Nucl. Instrum. Methods Phys. Res. A 610(1), 183–187 (2009). [CrossRef]
17. E. Theocharous, “How Linear is Your Photodetector?” in Europhotonics tech briefs(2007), pp. 33–35.
18. E. Theocharous, M. A. Itzler, J. Y. Cheung, and C. J. Chunnilall, “The characterisation of the linearity of response and spatial uniformity of response of two InGaAs/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46(11), 1561–1567 (2010). [CrossRef]
19. G. H. Rieke, Detection of light: from the ultraviolet to the submillimeter (Cambridge University Press, 1994).
20. J. E. Midwinter and J. Warner, “The effects of phase matching method and of uniaxial crystal symmetry on the polar distribution of second-order non-linear optical polarization,” Br. J. Appl. Phys. 16(8), 1135–1142 (1965). [CrossRef]
21. D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25(2), 84–87 (1970). [CrossRef]
22. D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. 7(5), 591–595 (1977). [CrossRef]
23. J. Peck, L. L. C. Impeccable Instruments, and T. N. Knoxville, USA (Private Communication) 2004).
24. M. Ware and A. L. Migdall, “Single photon detector characterization using correlated photons: the march from feasibility to metrology,” J. Mod. Opt. 51, 1549–1557 (2004).
25. J. Y. Cheung, C. J. Chunnilall, and J. Wang, “Radiometric applications of correlated photon metrology,” Proc. SPIE 5551, 220–230 (2004). [CrossRef]
26. J. Y. Cheung, M. P. Vaughan, J. R. M. Mountford, and C. J. Chunnilall, “Correlated photon metrology of detectors and sources,” Proc. SPIE 5161, 365–376 (2004). [CrossRef]
27. S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B 19(6), 1247–1258 (2002). [CrossRef]
28. W. S. Hartree, E. Theocharous, and N. P. Fox, “A wavelength tunable, quasi-cw laser source for high accuracy spectrometric measurement in the 200 nm to 500 nm region,” Proc. SPIE 4826, 104–112 (2003). [CrossRef]
29. E. Usadi and L. Crane, “Laser-based spectrophotometry at NPL,” Proc. SPIE 5192, 36–45 (2003). [CrossRef]
30. J. Y. Cheung, J. L. Gardner, A. Migdall, S. Polyakov, and M. Ware, “High accuracy dual lens transmittance measurements,” Appl. Opt. 46(22), 5396–5403 (2007). [CrossRef] [PubMed]
31. G. Porrovechio, M. Smid, and J. Y. Cheung, “Monochromator-based technique for measuring the focal length of lenses at different wavelengths,” (In preparation).
32. E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurements of second-order nonlinear optical coefficients from the spectral brightness of parametric fluorescence,” Opt. Lett. 19(3), 168–170 (1994). [CrossRef] [PubMed]
33. Appolonius, Conics (c. 200 B.C.).
34. G. Brida, M. Genovese, and C. Novero, “On the measurement of photon flux in parametric down-conversion,” Eur. Phys. J. D 8(2), 273–275 (2000). [CrossRef]
35. S. V. Polyakov and A. Migdall, “Quantum radiometry,” J. Mod. Opt. 56(9), 1045–1052 (2009). [CrossRef]
