Improvement of the detection efficiency calibration and homogeneity measurement of Si-SPAD detectors
© The Author(s) 2016
Received: 22 July 2016
Accepted: 23 November 2016
Published: 1 December 2016
Silicon single-photon avalanche diodes (Si-SPADs) are the most used devices for measuring ultra-weak optical radiant fluxes in many quantum technology fields, such as quantum optics, quantum communication, quantum computing, etc. In all these fields, the detection efficiency is the main parameter, which has to be accurately known for achieving reliable measurements. In this paper we present the improvements performed on the setup described in López et al. (J Mod Opt 62:S21–S27, 2015) for determining the detection efficiency of Si-SPAD detectors with a low measurement uncertainty. The improvement arises from the precise alignment of the Si-SPAD detector and the low deviation reached between the total calculated filter transmission and the individual filter transmission measurements (≤0.05%) performed with an integrating sphere with attached Si-photodiode as standard detector.
The relative standard uncertainty of the Si-SPAD detection efficiency measurement achieved is now as low as ~0.16%. Furthermore, the investigation of the detection efficiency homogeneity of two commercial Si-SPAD detectors from different manufacturers and with different sensor diameters is also presented. The obtained homogeneity is ≤2.2% within a region of diameter of 40 μm.
The detailed analysis presented in this paper shows the potential for achieving low measurement uncertainties for Si-SPAD detector calibration even in the low photon flux range. The low uncertainties are only to be realized for reproducible measurement conditions, i.e. in specific for equal beam sizes and beam shapes and well as for an irradiation of equal active areas of the detector. This, however, will be difficult to obtain when measurements are performed at different national metrology institutes.
Nowadays, Silicon single-photon avalanche diodes (Si-SPADs) are gaining more and more importance in a variety of different quantum technology fields, i.e. experimental quantum optics, quantum cryptography, quantum computing, as well as in medicine, 3D-imaging, biology, telecommunications and astrophysics (Knill et al. 2001; O’Brien 2007; O’Brien et al. 2009). In all these fields, the detection efficiency is a key parameter required to efficiently measure the optical radiant flux at photon levels; i.e. the detection efficiency must be determined using standard detectors or procedures that are traceable to primary reference standards.
There are two approaches mostly used for determining the detection efficiency of Si-SPAD detectors: one is based on the detector subtitution technique, which uses a strongly attenuated laser and a reference detector (López et al. 2015; Dhoska et al. 2015a, b; Kück et al. 2014) and the other one based on the two-photon correlation technique (Polyakov et al. 2006). The latter has the advantage that it does not require a reference detector; however, the effect of multiple photon events at photon-counting level has to be considered. The lowest uncertainty so far reported using this approach is 0.18%. Nevertheless, even when the achieved uncertainty is similar to those reported using the detector substitution technique (u = 0.16–0.3%) (López et al. 2015; Müller et al. 2012), the latter is mostly preferred by most of the national metrology institutes, since it uses a calibrated reference detector traceable to the primary reference standard (cryogenic radiometer) for the optical radiant power measurement; and thus, the traceability to a national primary standard is in this way fully assured. For this reason, the setup used to determine the detection efficiency of Si-SPAD detectors at Physikalisch-Technische Bundesanstalt (PTB), the German National Metrology Institute, is based on this approach, which uses the double attenuator technique (López et al. 2015). In this case, a standard detector (Si-Photodiode) is used to calibrate two attenuators required to attenuate the laser radiant power impinging on the Si-SPAD detector. These measurements are performed in situ subsequently; thus, the total attenuation is calculated by multiplying the two attenuation values. Knowing the total filter attenuation, the total optical power impinging on the Si-SPAD detector can be calculated and compared with the count rate generated by the Si-SPAD detector. From these measurements the detection efficiency of the Si-SPAD detector is determined. Using this measurement procedure, the detection efficiency was determined with a relative standard uncertainty of approx. 0.3% (López et al. 2015). The major uncertainty contribution to this measurement arose from the uncertainty associated to the measurement of the filter transmission, which is obtained from the deviation between the individual and combined transmission measurement carried out with an analog standard Si-photodiode (López et al. 2015; Dhoska et al. 2015a, b; Kück et al. 2014).
In this paper, we present the recent improvements carried out to this setup for achieving a low uncertainty for the Si-SPAD detection efficiency calibration. These consist in improving the filter transmission measurement and in implementing an accurate and automatic alignment procedure of the Si-SPAD detector. Furthermore, the mapping of the quantum detection efficiency homogeneity is also presented.
Two different types of Si-SPAD detectors with different sensor diameters were used in the experiments: a Single Photon Counting Module (SPCM) (Perkin-Elmer SPCM-AQR) with a sensor diameter of ϕ D1 = 180 μm (http://www.pas.rochester.edu/~advlab/APD_SPCM_AQR.pdf) and a Si-SPAD (Micro Photon Device PDM) with a sensor diameter of ϕ D2 = 50 μm (http://www.micro-photon-devices.com/Docs/Datasheet/PDM.pdf). The operating temperature of the Si-SPAD detectors was 24 °C.
Si-SPAD alignment procedure
It should be noted that the centroid algorithm does not need to fit any specific model, therefore, it can also be used for determining the diameters and centers of the Gaussian beam profiles obtained in the second step.
Detection efficiency homogeneity procedure
The homogeneity of the detection efficiency of the Si-SPAD detector is determined by scanning the active area of the Si-SPAD sensor with a laser beam of a diameter of approx. 10 µm; i.e. focusing the laser beam with an objective lens and scanning it as described in the previous section. However, in this case a monitor detector is used for correcting the possible fluctuation of the laser optical power which may occur during the measurement. The scanning is carried out with a step resolution of 5 µm over the complete active area of the sensor.
Filter transmission procedure
Si-SPAD alignment position
Results obtained from the three scans performed with the SPCM-AQR Si-SPAD detector at different z-positions
Based on these scans and the determined data, the optimum (x,y,z)-position for the Si-SPAD detector is calculated to x center = 235.11 mm, y center = 6.28 mm and z = 14.6 mm using Eqs. (1)–(3). As expected, the scan profile at this z-position corresponds dominantly to a rectangular profile, see Fig. 3c.
Results obtained from the three scans performed with the PDM Si-SPAD detector at different z-positions
In Fig. 5a, the homogeneity of the detection efficiency of the Si-SPAD PerkinElmer SPCM-AQR, obtained for the mean detection efficiency within the circled region 1 (diameter: 120 µm), is ≤0.85%. However, the homogeneity is improved by selecting smaller regions, i.e. for the region 2 with a diameter of 40 µm the homogeneity obtained is ≤0.3%. Figure 5b shows the homogeneity obtained for the PDM detector. Here the homogeneity obtained for region 1 (diameter: 40 µm) and region 2 (diameter: 20 µm) is ≤2.2% and ≤0.13%, respectively.
Detection efficiency and its associated uncertainty
Measurement uncertainty budget for determining the detection efficiency of the Si-SPAD detector (Perkin-Elmer SPCM-AQR)
Planck constant, h
2.52 × 10−7
Speed of light, c
Amplification factor, A 1
Amplification factor, A 2
2.08 × 10−6
Amplification factor, A 3
2.08 × 10−6
Ratio V 1/V Mon1, Q 1
Ratio V 2/V Mon2, Q 2
Ratio V 3/V Mon3, Q 3
Ratio CR/V MonSPAD, Q 4
Spectral responsivity of integrating sphere with Si-diode, s Si
Factor for the use of two filters, F filt
Combined uncertainty, u c
Summary and conclusion
In this paper, the improvement of the measurement setup for the detection efficiency calibration of Si-SPAD detectors was described. These improvements are based on the optimization of the Si-SPAD detector positioning, which is now performed in a completely automated way. Furthermore, the uncertainty contribution due to the filter transmission measurement is practically negligible by using an integrating sphere, which diminishes the back reflection into the measurement setup. The overall relative standard measurement uncertainty for the estimation of the Si-SPAD detection efficiency is now 0.16% instead of 0.3% as in López et al. (2015). However, this value has to be validated by independent measurements and comparisons with other national metrology institutes. The detailed analysis presented in this paper shows the potential for achieving low measurement uncertainties in determining the Si-SPAD detection efficiency even in the low photon flux range.
The homogeneity of the detection efficiency was also investigated. It was shown, that it strongly depends on the beam size impinging on the detector and the regions of its active area. However, the homogeneity can be improved by selecting small regions of the sensor active area, e.g. for a region with diameter of 20 µm, the obtained homogeneity is ≤0.13%. Nevertheless, the low uncertainties are only to be realized for reproducible measurement conditions, i.e. in specific for equal beam sizes and beam shapes and well as for an irradiation of equal active areas of the detector. This, however, will be difficult to obtain when measurements are performed at different national metrology institutes.
KD developed the Si-SPAD alignment position method and the detection efficiency calibration. HH and BR performed the configuration of the measurement setup. ML developed the filter transmission method and homogeneity. TK has made the analysis of the uncertainty of the detection efficiency. SK determined the direction of progress of the entire study. All authors read and approved the final manuscript.
This research work has been supported by the project “Single-Photon Sources for Quantum Technology” (SIQUTE) with Researcher Mobility Grant (RMG) EXL01-RMG1 of the European Metrology Research Programme (EMRP). The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.
The authors declare that they have no competing interests.
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