Absolute linearity measurement of photodetectors using sinusoidal modulated radiation

Tamer F. Refaat; David G. Johnson

doi:10.1364/AO.51.004420

Applied Optics
Vol. 51,
Issue 19,
pp. 4420-4429
(2012)
•https://doi.org/10.1364/AO.51.004420

Absolute linearity measurement of photodetectors using sinusoidal modulated radiation

Tamer F. Refaat and David G. Johnson

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Tamer F. Refaat and David G. Johnson, "Absolute linearity measurement of photodetectors using sinusoidal modulated radiation," Appl. Opt. 51, 4420-4429 (2012)

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Abstract

A method is presented for characterizing the linearity of photodetectors based on time-domain analysis of response to sinusoidal excitation. Nonlinearity is quantified solely from the output distortion. Relative response is converted to absolute response by including two calibration points. For low signal level, one calibration point is required, while using dark current as the second point. The response is mapped over a wider range using a series of overlapping sinusoids for calibration transfer. The method is demonstrated with a relatively linear photodiode and a nonlinear phototransistor. A Michelson interferometer is used to generate sinusoidal modulation of a laser source. Results demonstrate the potential of the proposed technique.

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Detector	$A [{mm}^{2}]$	$V_{B} [V]$	$P_{c} [μW]$	$V_{c} [mV]$	$ℜ_{c} [V / W]$	$G [V / A]$
Photodiode	$1.1 \times 1.1$	$- 1.0$	6.40	256.00	$4.00 \times 10^{4}$	$10^{5}$
Phototransistor	$0.8 \times 0.8$	$- 0.2$	3.50	296.00	$8.47 \times 10^{4}$	$10^{3}$

Signal record	1	2	3
Upper voltage limit, $V_{H} [V]$	0.71	1.29	1.50
Lower voltage limit, $V_{L} [V]$	0.19	0.57	1.17
Four-Parameters Sinusoidal Fitting:
Frequency, $f [Hz]$	$9992.92 \pm 5.22$	$9980.09 \pm 5.48$	$9998.05 \pm 13.2$
Amplitude, $V_{a} [mV]$	$279.88 \pm 1.92$	$388.38 \pm 3.65$	$198.12 \pm 9.19$
Offset, $V_{o} [mV]$	$450.88 \pm 1.75$	$933.26 \pm 4.03$	$1347.18 \pm 9.43$
Mean Root-Mean-Square error [mV]	4.46	4.45	5.44
Polynomial Fit:
Nonlinearity polynomial order, $N$	3	1	2
Root-Mean-Square error [mV]	0.52	0.75	0.79
Responsivity Parameters:
$ℜ_{0} [A / W^{0}]$	0.00	$- 2.70 \times 10^{- 3}$	$- 2.47 \times 10^{- 3}$
$ℜ_{1} [A / W^{1}]$	$3.94 \times 10^{4}$	$4.05 \times 10^{4}$	$4.04 \times 10^{4}$
$ℜ_{2} [A / W^{2}]$	$1.03 \times 10^{8}$	---	$2.44 \times 10^{5}$
$ℜ_{3} [A / W^{3}]$	$- 2.91 \times 10^{12}$	---	---
Radiation power offset, $P_{o} [μW]$	11.20	23.09	33.30
Radiation power amplitude, $P_{a} [μW]$	6.89	9.58	4.81

Signal record	1	2	3	4	5
Upper voltage limit, $V_{H} [V]$	0.49	0.90	1.18	1.36	1.49
Lower voltage limit, $V_{L} [V]$	0.20	0.45	0.88	1.17	1.36
Four-parameters Sinusoidal Fitting:
Frequency, $f [Hz]$	$9999.87 \pm 4.21$	$9998.97 \pm 9.05$	$9997.18 \pm 10.96$	$9999.65 \pm 10.29$	$10003.81 \pm 11.4$
Amplitude, $V_{a} [mV]$	$154.33 \pm 0.24$	$235.02 \pm 1.20$	$161.47 \pm 5.78$	$109.35 \pm 3.34$	$79.03 \pm 2.43$
Offset, $V_{o} [mV]$	$356.24 \pm 0.38$	$691.25 \pm 3.44$	$1040.90 \pm 4.86$	$1266.23 \pm 4.20$	$1429.24 \pm 3.68$
Mean Root-Mean-Square error [mV]	8.48	9.67	5.81	4.89	4.71
Polynomial Fit:
Nonlinearity polynomial order, $N$	4	3	3	6	6
Root-Mean-Square error [mV]	0.48	1.02	0.82	0.44	0.41
Responsivity Parameters:
$ℜ_{0} [A / W^{0}]$	0.00	0.117275	0.38198	$6.36 \times 10^{3}$	$- 3.03 \times 10^{5}$
$ℜ_{1} [A / W^{1}]$	$1.26 \times 10^{5}$	$5.89 \times 10^{4}$	$1.91 \times 10^{4}$	$- 1.20 \times 10^{9}$	$4.88 \times 10^{10}$
$ℜ_{2} [A / W^{2}]$	$- 1.76 \times 10^{10}$	$- 1.18 \times 10^{9}$	$7.92 \times 10^{8}$	$9.41 \times 10^{13}$	$- 3.27 \times 10^{15}$
$ℜ_{3} [A / W^{3}]$	$1.98 \times 10^{15}$	$1.53 \times 10^{13}$	$- 1.70 \times 10^{13}$	$- 3.94 \times 10^{18}$	$1.17 \times 10^{20}$
$ℜ_{4} [A / W^{4}]$	$- 9.22 \times 10^{19}$	---	---	$9.25 \times 10^{22}$	$- 2.34 \times 10^{24}$
$ℜ_{5} [A / W^{5}]$	---	---	---	$- 1.16 \times 10^{27}$	$2.51 \times 10^{28}$
$ℜ_{6} [A / W^{6}]$	---	---	---	$6.05 \times 10^{30}$	$- 1.12 \times 10^{32}$
Radiation power offset, $P_{o} [μW]$	4.73	12.63	23.94	31.74	37.40
Radiation power amplitude, $P_{a} [μW]$	2.80	6.36	5.62	3.93	2.41

Detector	$A [{mm}^{2}]$	$V_{B} [V]$	$P_{c} [μW]$	$V_{c} [mV]$	$ℜ_{c} [V / W]$	$G [V / A]$
Photodiode	$1.1 \times 1.1$	$- 1.0$	6.40	256.00	$4.00 \times 10^{4}$	$10^{5}$
Phototransistor	$0.8 \times 0.8$	$- 0.2$	3.50	296.00	$8.47 \times 10^{4}$	$10^{3}$

Signal record	1	2	3
Upper voltage limit, $V_{H} [V]$	0.71	1.29	1.50
Lower voltage limit, $V_{L} [V]$	0.19	0.57	1.17
Four-Parameters Sinusoidal Fitting:
Frequency, $f [Hz]$	$9992.92 \pm 5.22$	$9980.09 \pm 5.48$	$9998.05 \pm 13.2$
Amplitude, $V_{a} [mV]$	$279.88 \pm 1.92$	$388.38 \pm 3.65$	$198.12 \pm 9.19$
Offset, $V_{o} [mV]$	$450.88 \pm 1.75$	$933.26 \pm 4.03$	$1347.18 \pm 9.43$
Mean Root-Mean-Square error [mV]	4.46	4.45	5.44
Polynomial Fit:
Nonlinearity polynomial order, $N$	3	1	2
Root-Mean-Square error [mV]	0.52	0.75	0.79
Responsivity Parameters:
$ℜ_{0} [A / W^{0}]$	0.00	$- 2.70 \times 10^{- 3}$	$- 2.47 \times 10^{- 3}$
$ℜ_{1} [A / W^{1}]$	$3.94 \times 10^{4}$	$4.05 \times 10^{4}$	$4.04 \times 10^{4}$
$ℜ_{2} [A / W^{2}]$	$1.03 \times 10^{8}$	---	$2.44 \times 10^{5}$
$ℜ_{3} [A / W^{3}]$	$- 2.91 \times 10^{12}$	---	---
Radiation power offset, $P_{o} [μW]$	11.20	23.09	33.30
Radiation power amplitude, $P_{a} [μW]$	6.89	9.58	4.81

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Applied Optics