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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