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.

© 2012 Optical Society of America

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References

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  1. S. Yang, I. Vayshenker, X. Li, T. Scott, and M. Zander, “Optical detector nonlinearity: simulation,” NIST Technical Note 1376 (1995).
  2. C. Sanders, “Accurate measurements of and corrections for nonlinearities in radiometers,” J. Res. Natl. Inst. Stand. 76A, 437–453 (1972).
  3. L. Coslovi and F. Righini, “Fast determination of the nonlinearity of photodetectors,” Appl. Opt. 19, 3200–3203 (1980).
    [CrossRef]
  4. J. Fischer and L. Fu, “Photodiode nonlinearity measurement with an intensity stabilized laser as a radiation source,” Appl. Opt. 32, 4187–4190 (1993).
    [CrossRef]
  5. K. Mielenz and K. Eckerle, “Spectrophotometer linearity testing using the double-aperture method,” Appl. Opt. 11, 2294–2303 (1972).
    [CrossRef]
  6. R. Frehlich, “Estimation of the nonlinearity of a photodetector,” Appl. Opt. 31, 5926–5929 (1992).
    [CrossRef]
  7. A. Schaefer, E. Zalewski, and J. Geist, “Silicon detector nonlinearity and related effects,” Appl. Opt. 22, 1232–1236 (1983).
    [CrossRef]
  8. “IEEE Standard for Digitizing Waveform Recorders,” IEEE Std, 1057–1994 (Institute of Electrical and Electronics Engineers, 2001).
  9. “IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters,” IEEE Std, 1241–2000(Institute of Electrical and Electronics Engineers, 2000).
  10. T. Furtak, “Sinusoidal radiation chopper for modulation of the maximum available light intensity,” Appl. Opt. 16, 803–804 (1977).
  11. P. Griffiths and J. De Haseth, Fourier Transform Infrared Spectrometry (Wiley-Interscience, 2007).
  12. According to the binomial theorem, it is possible to expand (x+y)n into a sum of the form ∑k=0n(nk)·xn−k·yk, where (nk) is the binomial coefficient defined by the integer value of the factorial relation n!/k!·(n−k)!.
  13. The function cos(θ)n can be expanded in the form 2−n·∑k=0n(nk)·cos[(n−2·k)·θ] indicating a highest harmonic content of n.
  14. T. Refaat, G. Halama, and R. De Young, “Comparison between super low ionization ratio and reach through avalanche photodiode structures,” Opt. Eng. 39, 2642–2650 (2000).
    [CrossRef]
  15. T. Larason, S. Bruce, and A. Parr, “Spectroradiometric detector measurements: Part I—Ultraviolet detectors and Part II—Visible to near-infrared detectors,” (NIST Special Publication, 1998) 250–241.

2000 (1)

T. Refaat, G. Halama, and R. De Young, “Comparison between super low ionization ratio and reach through avalanche photodiode structures,” Opt. Eng. 39, 2642–2650 (2000).
[CrossRef]

1993 (1)

1992 (1)

1983 (1)

1980 (1)

1977 (1)

1972 (2)

K. Mielenz and K. Eckerle, “Spectrophotometer linearity testing using the double-aperture method,” Appl. Opt. 11, 2294–2303 (1972).
[CrossRef]

C. Sanders, “Accurate measurements of and corrections for nonlinearities in radiometers,” J. Res. Natl. Inst. Stand. 76A, 437–453 (1972).

Bruce, S.

T. Larason, S. Bruce, and A. Parr, “Spectroradiometric detector measurements: Part I—Ultraviolet detectors and Part II—Visible to near-infrared detectors,” (NIST Special Publication, 1998) 250–241.

Coslovi, L.

De Haseth, J.

P. Griffiths and J. De Haseth, Fourier Transform Infrared Spectrometry (Wiley-Interscience, 2007).

De Young, R.

T. Refaat, G. Halama, and R. De Young, “Comparison between super low ionization ratio and reach through avalanche photodiode structures,” Opt. Eng. 39, 2642–2650 (2000).
[CrossRef]

Eckerle, K.

Fischer, J.

Frehlich, R.

Fu, L.

Furtak, T.

Geist, J.

Griffiths, P.

P. Griffiths and J. De Haseth, Fourier Transform Infrared Spectrometry (Wiley-Interscience, 2007).

Halama, G.

T. Refaat, G. Halama, and R. De Young, “Comparison between super low ionization ratio and reach through avalanche photodiode structures,” Opt. Eng. 39, 2642–2650 (2000).
[CrossRef]

Larason, T.

T. Larason, S. Bruce, and A. Parr, “Spectroradiometric detector measurements: Part I—Ultraviolet detectors and Part II—Visible to near-infrared detectors,” (NIST Special Publication, 1998) 250–241.

Li, X.

S. Yang, I. Vayshenker, X. Li, T. Scott, and M. Zander, “Optical detector nonlinearity: simulation,” NIST Technical Note 1376 (1995).

Mielenz, K.

Parr, A.

T. Larason, S. Bruce, and A. Parr, “Spectroradiometric detector measurements: Part I—Ultraviolet detectors and Part II—Visible to near-infrared detectors,” (NIST Special Publication, 1998) 250–241.

Refaat, T.

T. Refaat, G. Halama, and R. De Young, “Comparison between super low ionization ratio and reach through avalanche photodiode structures,” Opt. Eng. 39, 2642–2650 (2000).
[CrossRef]

Righini, F.

Sanders, C.

C. Sanders, “Accurate measurements of and corrections for nonlinearities in radiometers,” J. Res. Natl. Inst. Stand. 76A, 437–453 (1972).

Schaefer, A.

Scott, T.

S. Yang, I. Vayshenker, X. Li, T. Scott, and M. Zander, “Optical detector nonlinearity: simulation,” NIST Technical Note 1376 (1995).

Vayshenker, I.

S. Yang, I. Vayshenker, X. Li, T. Scott, and M. Zander, “Optical detector nonlinearity: simulation,” NIST Technical Note 1376 (1995).

Yang, S.

S. Yang, I. Vayshenker, X. Li, T. Scott, and M. Zander, “Optical detector nonlinearity: simulation,” NIST Technical Note 1376 (1995).

Zalewski, E.

Zander, M.

S. Yang, I. Vayshenker, X. Li, T. Scott, and M. Zander, “Optical detector nonlinearity: simulation,” NIST Technical Note 1376 (1995).

Appl. Opt. (6)

J. Res. Natl. Inst. Stand. (1)

C. Sanders, “Accurate measurements of and corrections for nonlinearities in radiometers,” J. Res. Natl. Inst. Stand. 76A, 437–453 (1972).

Opt. Eng. (1)

T. Refaat, G. Halama, and R. De Young, “Comparison between super low ionization ratio and reach through avalanche photodiode structures,” Opt. Eng. 39, 2642–2650 (2000).
[CrossRef]

Other (7)

T. Larason, S. Bruce, and A. Parr, “Spectroradiometric detector measurements: Part I—Ultraviolet detectors and Part II—Visible to near-infrared detectors,” (NIST Special Publication, 1998) 250–241.

S. Yang, I. Vayshenker, X. Li, T. Scott, and M. Zander, “Optical detector nonlinearity: simulation,” NIST Technical Note 1376 (1995).

“IEEE Standard for Digitizing Waveform Recorders,” IEEE Std, 1057–1994 (Institute of Electrical and Electronics Engineers, 2001).

“IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters,” IEEE Std, 1241–2000(Institute of Electrical and Electronics Engineers, 2000).

P. Griffiths and J. De Haseth, Fourier Transform Infrared Spectrometry (Wiley-Interscience, 2007).

According to the binomial theorem, it is possible to expand (x+y)n into a sum of the form ∑k=0n(nk)·xn−k·yk, where (nk) is the binomial coefficient defined by the integer value of the factorial relation n!/k!·(n−k)!.

The function cos(θ)n can be expanded in the form 2−n·∑k=0n(nk)·cos[(n−2·k)·θ] indicating a highest harmonic content of n.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the experimental setup used for detector linearity measurement. The monochromatic radiation source is modulated by a free-running Michelson interferometer enclosed in the NICOLET 6700. Characterization results presented for the detection system consisting of the detector, preamplifier, and digital oscilloscope. Incident and reflected beam traces are separated for clarity.

Fig. 2.
Fig. 2.

Samples of the measured output signal records from (a) the photodiode and (b) the phototransistor at different radiation levels. The lowest signal level is selected to intersect the calibration voltage. Higher signals are selected to cover the operating range, with adequate overlap for calibration transfer. The signals are also compared with the background.

Fig. 3.
Fig. 3.

Sample records for (a) the photodiode and (b) the phototransistor consist of five cycles. 500 data points (dots) in the record mark the voltage states due to digitizer quantization. For comparison, the results of the four-parameter sinusoidal fit are plotted as continuous curves.

Fig. 4.
Fig. 4.

Demonstration of the data points selection criteria. The collected data (15,000 points) representing the voltage states are plotted against the normalized power as gray dots. The scattering of the normalized power at each voltage state is due to the measurement uncertainty. Selection of the data point depends on satisfying the sinusoidal distribution function. Selection of the normalized power value is based on the comparison between the arithmetic and Gaussian means at each voltage state. The data are shown for phototransistor Signal Record 4.

Fig. 5.
Fig. 5.

Gaussian fit of normalized power distribution at a given voltage state for a certain signal record. The normalized power distribution is obtained by constructing a 50 bin histogram. Data are shown for phototransistor Signal Record 5 at voltage state of 1.197 V.

Fig. 6.
Fig. 6.

Comparison between the ideal and measured sinusoidal distribution functions. The ideal distribution function was obtained by applying Eq. (17) to the amplitude and offset voltages obtained from the sinusoidal fit. The measured distribution was obtained by tracking the number of occurrence of each voltage state relative to the record length. Data are shown for phototransistor Signal Record 3.

Fig. 7.
Fig. 7.

Output voltage variation with respect to the calculated normalized power (symbols) and the polynomial fitting (curves) for (a) the photodiode and (b) the phototransistor. Data represent all signal records covering the whole test range for both devices.

Fig. 8.
Fig. 8.

Averaged fast Fourier transform for the five-cycle samples records, obtained for (a) the photodiode and (b) the phototransistor. The nonlinearity order N is determined for each signal record by setting its value to the highest observed harmonic [13].

Fig. 9.
Fig. 9.

Output voltage versus incident radiation power, defining the response function, for both detectors under study.

Fig. 10.
Fig. 10.

Nonlinearity versus incident radiation power for both detectors. Nonlinearity is calculated using Eq. (1).

Tables (3)

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Table 1. Calibration Results for the Detectors Considered in This Studya

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Table 2. Statistical and Characterization Results for the Photodiodea

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Table 3. Statistical and Characterization Results for the Phototransistora

Equations (17)

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Δ=R(P)RcRc;Rc=R(Pc).
V(P)=n=0NRn·Pn;VLVVH,
P(t)=Po+Pa·ρ(t),
ρ(t)=cos(2π·f·t+ϕ),
f=2·v/λ.
V(t)=n=0NRn·m=0n(nm)·Ponm·Pam·ρ(t)m.
V(ρ)=n=0Nan·ρn,
an=Pan·k=nN(kn)·Rk·Pokn.
V(P)=n=0NanPan·m=0n(nm)·(Po)nm·Pm.
Rn=k=nN(kn)·ak·(Po)knPak.
Pa=(Pc2Pc1)(ρc2ρc1),
Po=(Pc1·ρc2Pc2·ρc1)(ρc2ρc1).
k=0Nak·εk=R0;ε=PoPa,
Pa=Pc(ρcε),
Po=ε·Pc(ρcε).
Vf(t)=Vo+Va·cos(2π·f·t+ϕ)Vf(ρ)=Vo+Va·ρ(t),
pdf(V)=real{1π·Va2(VVo)2}.

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