Abstract

In applications where low signal-to-noise ratios are encountered, the use of phase-sensitive detection (PSD) is highly advantageous and is applied widely. However, the characteristics of lock-in amplifiers that utilize the PSD technique, such as the linearity of the output and the gain of these instruments, have not been extensively evaluated. The author proposes a method for measuring the linearity characteristics of lock-in amplifiers and describes how this method was used to measure the linearity factor of three nominally identical commercially available digital lock-in amplifiers. The results of this study show that the linearity factor of these lock-in amplifiers can deviate from unity by more than 0.1% over a factor of 2 change in output. Moreover, the linearity characteristics of these lock-in amplifiers vary from one instrument to the next. The linearity characteristics were shown to be independent of the reference frequency, the time constant, and the temporal profile of the signal being analyzed. However, they were found to be dependent on the sensitivity settings of these instruments. The linearity characteristics of these instruments were observed not to change with time. This implies that, where the uncertainty contribution due to the nonlinearity of a lock-in amplifier is significant, the nonlinearity can be evaluated by using the method described in this article and can be used to apply corrections.

© 2008 Optical Society of America

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References

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  1. E. Theocharous, “The establishment of the NPL infrared relative spectral responsivity scale using cavity pyroelectric detectors,” Metrologia 43, S115-S119, (2006).
    [CrossRef]
  2. D. P. Blair and P. H. Sydenham, “Phase sensitive detection as a means to recover signals buried in noise,” J. Phys. E 8, 621-627, (1975).
    [CrossRef]
  3. E. Theocharous, J. Ishii, and N. P. Fox, “Absolute linearity measurements on HgCdTe detectors in the infrared,” Appl. Opt. 43, 4182-4188 (2004).
    [CrossRef] [PubMed]
  4. C. L. Sanders, “Accurate measurements of and corrections for nonlinearities in radiometers,” J. Res. Nat. Bur. Stand. Sect. A 76, 437-453 (1972).
  5. The output of digital lock-in amplifiers represents the root mean square value of the fundamental (reference) frequency component of the electrical signal being analyzed; so the output of a lock-in amplifier depends on the temporal profile of the electrical signal being analyzed. The sensitivity settings are calibrated for input signals of a square-wave temporal profile. The effective gain defines the lock-in amplifier sensitivity for that particular temporal profile of the signal being analyzed.
  6. L. P. Boivin, “Automated absolute and relative spectral linearity measurements on photovoltaic detectors,” Metrologia 30, 355-360 (1993).
    [CrossRef]
  7. E. Theocharous, “Reply to comments on 'Absolute linearity measurements on a PbS detector in the infrared',” Appl. Opt. 46, 6495-6497 (2007).
    [CrossRef] [PubMed]
  8. E. Theocharous, “Absolute linearity measurements on PbS detectors in the infrared,” Appl. Opt. 45, 2381-2386(2006).
    [CrossRef] [PubMed]
  9. E. Theocharous, “Absolute linearity measurements on a PbSe detector in the infrared,” Infrared Phys. Technol. 50, 63-69 (2007).
    [CrossRef]
  10. W. Budde, “Physical detectors of radiation,” in Optical Radiation Measurements (Academic Press, 1983), Vol. 4, pp. 70-82.
  11. I. Vayshenkev, S. Yang, and R. Swafford, “Nonlinearity of high-power optical power meters at 1480 nm,” Appl. Opt. 45, 1098-1101 (2006).
    [CrossRef]
  12. E. Theocharous, “How linear is the response of your detector?,” Europhoton. Mag. , February 2007, pp. 33-35.
  13. E. Theocharous, N. P. Fox, V. I. Sapritsky, S. N. Mekhontsev, and S. P. Morozova, “Absolute measurements of black-body emitted radiance,” Metrologia 35, 549-554 (1998).
    [CrossRef]

2007

E. Theocharous, “Reply to comments on 'Absolute linearity measurements on a PbS detector in the infrared',” Appl. Opt. 46, 6495-6497 (2007).
[CrossRef] [PubMed]

E. Theocharous, “Absolute linearity measurements on a PbSe detector in the infrared,” Infrared Phys. Technol. 50, 63-69 (2007).
[CrossRef]

2006

2004

1998

E. Theocharous, N. P. Fox, V. I. Sapritsky, S. N. Mekhontsev, and S. P. Morozova, “Absolute measurements of black-body emitted radiance,” Metrologia 35, 549-554 (1998).
[CrossRef]

1993

L. P. Boivin, “Automated absolute and relative spectral linearity measurements on photovoltaic detectors,” Metrologia 30, 355-360 (1993).
[CrossRef]

1975

D. P. Blair and P. H. Sydenham, “Phase sensitive detection as a means to recover signals buried in noise,” J. Phys. E 8, 621-627, (1975).
[CrossRef]

1972

C. L. Sanders, “Accurate measurements of and corrections for nonlinearities in radiometers,” J. Res. Nat. Bur. Stand. Sect. A 76, 437-453 (1972).

Appl. Opt.

Europhoton. Mag.

E. Theocharous, “How linear is the response of your detector?,” Europhoton. Mag. , February 2007, pp. 33-35.

Infrared Phys. Technol.

E. Theocharous, “Absolute linearity measurements on a PbSe detector in the infrared,” Infrared Phys. Technol. 50, 63-69 (2007).
[CrossRef]

J. Phys. E

D. P. Blair and P. H. Sydenham, “Phase sensitive detection as a means to recover signals buried in noise,” J. Phys. E 8, 621-627, (1975).
[CrossRef]

J. Res. Nat. Bur. Stand. Sect. A

C. L. Sanders, “Accurate measurements of and corrections for nonlinearities in radiometers,” J. Res. Nat. Bur. Stand. Sect. A 76, 437-453 (1972).

Metrologia

E. Theocharous, “The establishment of the NPL infrared relative spectral responsivity scale using cavity pyroelectric detectors,” Metrologia 43, S115-S119, (2006).
[CrossRef]

E. Theocharous, N. P. Fox, V. I. Sapritsky, S. N. Mekhontsev, and S. P. Morozova, “Absolute measurements of black-body emitted radiance,” Metrologia 35, 549-554 (1998).
[CrossRef]

L. P. Boivin, “Automated absolute and relative spectral linearity measurements on photovoltaic detectors,” Metrologia 30, 355-360 (1993).
[CrossRef]

Other

The output of digital lock-in amplifiers represents the root mean square value of the fundamental (reference) frequency component of the electrical signal being analyzed; so the output of a lock-in amplifier depends on the temporal profile of the electrical signal being analyzed. The sensitivity settings are calibrated for input signals of a square-wave temporal profile. The effective gain defines the lock-in amplifier sensitivity for that particular temporal profile of the signal being analyzed.

W. Budde, “Physical detectors of radiation,” in Optical Radiation Measurements (Academic Press, 1983), Vol. 4, pp. 70-82.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the layout of the NPL linearity measurement facility.

Fig. 2
Fig. 2

Linearity factor, as a function of output voltage, for the silicon detector, transimpedance amplifier combination. Error bars for this and subsequent figures represent the standard deviation of at least 8 measurements of the linearity factor.

Fig. 3
Fig. 3

Linearity factor as a function of output voltage for three different lock-in amplifiers, all with 0.2 V sensitivity.

Fig. 4
Fig. 4

Linearity factor of third lock-in amplifier as a function of output voltage for three different sensitivity settings. Also shown are the fourth-order polynomials fitted to the data points.

Fig. 5
Fig. 5

Linearity factor as a function of output voltage for the third lock-in amplifier at 0.2 V sensitivity, for two different modulation frequencies.

Fig. 6
Fig. 6

Linearity factor as a function of output voltage for the third lock-in amplifier at 0.2 V sensitivity for 1 and 0.3 s time constants.

Fig. 7
Fig. 7

Linearity factor as a function of output voltage for the third lock-in amplifier at 0.2 V sensitivity for two different temporal profiles.

Equations (1)

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L ( V A + B ) = V A + B ( V A + V B ) ,

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