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Table A3 Uncertainty budget for the detection efficiency measurement performed by NPL for a mean photon number \(\mu =0.105\)

From: A study to develop a robust method for measuring the detection efficiency of free-running InGaAs/InP single-photon detectors

Measurand Value Standard Uncertainty Type of distribution Sensitivity coefficient Contribution Contribution (%)
Planck’s constant, h, [J s] 6.6260701510−34 J s 0 Rectangular 1.6691032 0 0
Wavelength, λ, [m] 1.550510−6 m 110−11 m Rectangular −71,348.53 −7.1310−7 1.3410−5
Speed of light, c, [m/s] 299.79245810−6 m s−1 0 Standard 3.6910−10 0 0
InGaAs SPAD Count rate, \(\rho _{\mathit{click}}\), [s−1] 2156 s−1 4.870 s−1 Standard 9.1010−5 4.4310−4 5.18
InGaAs SPAD Dark Count rate, \(\rho _{\mathit{Dark},\mathit{click}}\), [s−1] 920 s−1 3.0 s−1 Standard −8.8510−5 −2.8210−4 2.09
Power meter light measurement, \(P_{\mathrm{cal}}\), (W) 1.03510−9 W 4.51210−12 W Standard −1.07108 −4.8110−4 6.10
Power meter dark measurement, \(P_{\mathrm{Dark}}\), (W) −3.08110−12 W 5.54410−13 W Standard 1.07108 5.9110−5 0.09
Attenuation factor, α 38,815 569 Standard 2.8510−6 1.6210−3 69.34
Power meter correction factor, \(F_{\mathrm{cal}}\) 0 −1.78510−4 Rectangular −0.111 1.9710−5 0.01
Connect/disconnect fibre factor, \(F_{\mathrm{fconn}}\) 1 0.005 Rectangular 0.111 5.5310−4 8.07
InGaAs SPAD Dead time, D, [s] 10.22010−6 s 5.9010−9 s Rectangular 284.50 1.6810−6 7.4210−5
Laser frequency, \(f_{\mathit{laser}}\), [s−1] 110,000 s−1 63.509 s−1 Rectangular −1.1810−8 −7.4710−7 1.4810−5
Power meter calibration factor, \(F_{\mathrm{cal}}\) 1.013 5.16610−3 Standard −0.109 −5.6410−4 8.39
Scaling factor, S 0.99731 1.12010−3 Rectangular −0.111 −1.2410−4 0.41
Power meter instability factor, \(F_{\mathrm{stab}}\) 0 0.001 Standard −0.111 −1.1110−4 0.32
Responsivity instability factor, \(F_{\lambda }\) 0 5.010−6 Rectangular −0.111 −5.5310−7 8.0710−6
Detection efficiency, η 0.1107 0.0019 Standard    
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