Calibration and comparison of detection efficiency for free-space single-photon avalanche diodes at 850 nm

Jeongwan Jin; Thomas Gerrits; Angela Gamouras

doi:10.1364/AO.461154

Applied Optics
Vol. 61,
Issue 17,
pp. 5244-5249
(2022)
•https://doi.org/10.1364/AO.461154

Calibration and comparison of detection efficiency for free-space single-photon avalanche diodes at 850 nm

Jeongwan Jin, Thomas Gerrits, and Angela Gamouras

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Jeongwan Jin, Thomas Gerrits, and Angela Gamouras, "Calibration and comparison of detection efficiency for free-space single-photon avalanche diodes at 850 nm," Appl. Opt. 61, 5244-5249 (2022)

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Abstract

A detection efficiency measurement system for free-space single-photon detectors has been established at the National Research Council (NRC) Canada. This measurement apparatus incorporates an 850 nm fiber laser source and utilizes a double-attenuation and substitution calibration technique. Detection efficiency calibrations of silicon single-photon avalanche photodiodes (SPADs) at incident photon rates in the range of $1.0 \times {10^5}$ photon counts per second (Cts/s) (36 fW) to $2.1 \times {10^6} \,{\rm{Cts}}/{\rm{s}}$ (734 fW) are SI-traceable through the substitution configuration with a silicon transfer standard detector, calibrated directly using the NRC absolute cryogenic radiometer. The measurement approach taken by the NRC was compared with the SPAD calibration technique implemented at the National Institute of Standards and Technology (NIST) in the United States. The count-rate-dependent detection efficiency of a silicon SPAD was measured at NIST and compared with results from the same SPAD measured at NRC within the range of incident photon rates from $1 \times {10^5}\; {\rm{Cts}}/{\rm{s}}$ to $5 \times {10^5} \;{\rm{Cts}}/{\rm{s}}$. Comparison of the calibration results shows agreement between the two laboratories within the combined measurement uncertainties.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Source	Magnitude (%)
Cryogenic radiometer effects	0.011
Measurement repeatability	0.131
TSD temperature variation ( $\pm 1^{\circ} C$ )	0.001
TSD photocurrent measurement	0.004
Wavelength calibration ( $\pm 0.05 n m$ )	0.003
Spectral bandwidth effects	0.000
Combined uncertainty ( $k = 1$ )	0.132

Measurand	Unit	Measured Value	Uncertainty	Type	Uncertainty (%)
Speed of light (c)	$m \cdot s^{- 1}$	$2.99792458 \times 10^{8}$
Planck constant (h)	$J \cdot s$	$6.62607015 \times 10^{- 34}$
Wavelength ( $λ$ )	$m$	$850.63 \times 10^{- 9}$	$6.00 \times 10^{- 11}$	B	0.01
TSD spectral responsivity (s)	$A \cdot W^{- 1}$	$4.53 \times 10^{- 1}$	$5.98 \times 10^{- 4}$	A	0.13
Amplification ( $A_{0}, A_{1}, A_{2}$ )	$V \cdot A^{- 1}$	$1.00 \times 10^{9}$	$5.00 \times 10^{6}$	B	0.50
Ratio $V_{0} / V_{0, M o n}$ ( $Q_{0}$ )	1	$1.14 \times 10^{1}$	$8.38 \times 10^{- 3}$	A	0.07
Ratio $V_{1} / V_{1, M o n}$ ( $Q_{1}$ )	1	$2.25 \times 10^{- 1}$	$7.53 \times 10^{- 4}$	A	0.34
Ratio $V_{2} / V_{2, M o n}$ ( $Q_{2}$ )	1	$2.64 \times 10^{- 2}$	$7.31 \times 10^{- 4}$	A	2.76
Ratio $N_{SPAD} / V_{SPAD,Mon}$ ( $Q_{3}$ )	$V^{- 1} \cdot s^{- 1}$	$2.25 \times 10^{6}$	$8.05 \times 10^{3}$	A	0.32
Detection efficiency ( $η_{d e t}$ )	1	$5.09 \times 10^{- 1}$	$1.45 \times 10^{- 2}$	A
Combined uncertainty ( $k = 1$ ), $u (η_{d e t}^{N R C})$					2.85

NRC			NIST			Normalized Error
SPAD Signal (Cts/s)	Detection Efficiency	Standard Uncertainty	SPAD Signal (Cts/s)	Detection Efficiency	Standard Uncertainty	Unmediated $E r r$	Relative to CRV $E r r_{N R C}$ $E r r_{N I S T}$
494352	0.527	0.004	490879	0.524	0.003	0.24	0.12	0.08
446310	0.516	0.005	439989	0.526	0.003	0.92	0.47	0.27
331550	0.524	0.006	326821	0.529	0.003	0.36	0.20	0.08
294975	0.535	0.006	292509	0.529	0.003	0.41	0.24	0.08
273072	0.538	0.007	270240	0.529	0.003	0.59	0.36	0.10
187470	0.537	0.009	179168	0.530	0.003	0.37	0.24	0.04
169977	0.564	0.011	151944	0.531	0.003	1.47	0.97	0.12
124033	0.525	0.013	121060	0.532	0.003	0.26	0.17	0.01
102895	0.509	0.015	84364	0.533	0.003	0.80	0.55	0.04

Source	Magnitude (%)
Cryogenic radiometer effects	0.011
Measurement repeatability	0.131
TSD temperature variation ( $\pm 1^{\circ} C$ )	0.001
TSD photocurrent measurement	0.004
Wavelength calibration ( $\pm 0.05 n m$ )	0.003
Spectral bandwidth effects	0.000
Combined uncertainty ( $k = 1$ )	0.132

Measurand	Unit	Measured Value	Uncertainty	Type	Uncertainty (%)
Speed of light (c)	$m \cdot s^{- 1}$	$2.99792458 \times 10^{8}$
Planck constant (h)	$J \cdot s$	$6.62607015 \times 10^{- 34}$
Wavelength ( $λ$ )	$m$	$850.63 \times 10^{- 9}$	$6.00 \times 10^{- 11}$	B	0.01
TSD spectral responsivity (s)	$A \cdot W^{- 1}$	$4.53 \times 10^{- 1}$	$5.98 \times 10^{- 4}$	A	0.13
Amplification ( $A_{0}, A_{1}, A_{2}$ )	$V \cdot A^{- 1}$	$1.00 \times 10^{9}$	$5.00 \times 10^{6}$	B	0.50
Ratio $V_{0} / V_{0, M o n}$ ( $Q_{0}$ )	1	$1.14 \times 10^{1}$	$8.38 \times 10^{- 3}$	A	0.07
Ratio $V_{1} / V_{1, M o n}$ ( $Q_{1}$ )	1	$2.25 \times 10^{- 1}$	$7.53 \times 10^{- 4}$	A	0.34
Ratio $V_{2} / V_{2, M o n}$ ( $Q_{2}$ )	1	$2.64 \times 10^{- 2}$	$7.31 \times 10^{- 4}$	A	2.76
Ratio $N_{SPAD} / V_{SPAD,Mon}$ ( $Q_{3}$ )	$V^{- 1} \cdot s^{- 1}$	$2.25 \times 10^{6}$	$8.05 \times 10^{3}$	A	0.32
Detection efficiency ( $η_{d e t}$ )	1	$5.09 \times 10^{- 1}$	$1.45 \times 10^{- 2}$	A
Combined uncertainty ( $k = 1$ ), $u (η_{d e t}^{N R C})$					2.85

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Applied Optics