APPENDIX E
FIGURES OF MERIT FOR INFRARED PHOTODETECTORS

The key figure of merit that is usually employed is the specific detectivity D*, which describes the smallest detectable signal (Accetta and Shumaker, 1993). D* can be viewed as a measure of the temporal noise in the detector. D* is defined through the following procedure.

  1. Define the responsivity, R, for photodetectors as the ratio of the root mean square output voltage to the input signal power of the root mean square.

  2. Define the noise-equivalent power (NEP) in watts as the incident flux required to give output voltage equal to the noise voltage:

    NEP = Vn /R (watts),

    where Vn is the RMS noise voltage

  3. The detectivity is given by:

    D = 1/NEP (W-1)

  4. The specific detectivity, D*, is the detectivity D for a 1-Hz bandwidth and a 1-cm2 area:

D* = D (A×Δ f )1/2 W-1 cm. sec-1/2

D* is independent of the detector area, A, and bandwidth, Δ f, if the noise is proportional to (A×Δ f )1/2· This area dependence is found if radiation fluctuations dominate the noise or if A is varied by connecting together several small identical detectors; the bandwidth dependence is found if the spectral response is flat over the relevant frequency range. The specific detectivity, D*, is a normalized measure related to the inverse of the smallest signal that can be detected.

Noise from the background places a fundamental limit on detectivity. A background limited photodetector with a wavelength-independent response at 300 K has a D* of 1.8 × 1010 W /(sec1/2 cm) for a hemispheric field of view.

For a single detector, D* is clearly a relevant figure of merit. In order to maximize D*:

  • reduce all noise except for unavoidable radiative background noise; and

  • increase the quantum efficiency as much as possible.

The typical figure of merit for arrays is the noise-equivalent temperature difference which is the smallest temperature difference that can be resolved. Typical error-correction algorithms that calibrate by illuminating the array uniformly at two different temperatures eliminate inhomogeneity caused by linear time-independent and spectrally independent variations. However, non-linearities in the detector response, variations in the spectral response between detectors, and temporal variations (drifts and 1/ f noise have all been shown to lead to residual spatial nonuniformity that under many operating conditions is substantially larger than the temporal noise described by D*. Spatial noise cannot be averaged out by time integration (Mooney et al., 1989). Therefore, nonuniformity is particularly important under conditions of substantial illumination and for staring arrays, because the large data rates place strong constraints on correction algorithms.



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Expanding the Vision of Sensor Materials APPENDIX E FIGURES OF MERIT FOR INFRARED PHOTODETECTORS The key figure of merit that is usually employed is the specific detectivity D*, which describes the smallest detectable signal (Accetta and Shumaker, 1993). D* can be viewed as a measure of the temporal noise in the detector. D* is defined through the following procedure. Define the responsivity, R, for photodetectors as the ratio of the root mean square output voltage to the input signal power of the root mean square. Define the noise-equivalent power (NEP) in watts as the incident flux required to give output voltage equal to the noise voltage: NEP = Vn /R (watts), where Vn is the RMS noise voltage The detectivity is given by: D = 1/NEP (W-1) The specific detectivity, D*, is the detectivity D for a 1-Hz bandwidth and a 1-cm2 area: D* = D (A×Δ f )1/2 W-1 cm. sec-1/2 D* is independent of the detector area, A, and bandwidth, Δ f, if the noise is proportional to (A×Δ f )1/2· This area dependence is found if radiation fluctuations dominate the noise or if A is varied by connecting together several small identical detectors; the bandwidth dependence is found if the spectral response is flat over the relevant frequency range. The specific detectivity, D*, is a normalized measure related to the inverse of the smallest signal that can be detected. Noise from the background places a fundamental limit on detectivity. A background limited photodetector with a wavelength-independent response at 300 K has a D* of 1.8 × 1010 W /(sec1/2 cm) for a hemispheric field of view. For a single detector, D* is clearly a relevant figure of merit. In order to maximize D*: reduce all noise except for unavoidable radiative background noise; and increase the quantum efficiency as much as possible. The typical figure of merit for arrays is the noise-equivalent temperature difference which is the smallest temperature difference that can be resolved. Typical error-correction algorithms that calibrate by illuminating the array uniformly at two different temperatures eliminate inhomogeneity caused by linear time-independent and spectrally independent variations. However, non-linearities in the detector response, variations in the spectral response between detectors, and temporal variations (drifts and 1/ f noise have all been shown to lead to residual spatial nonuniformity that under many operating conditions is substantially larger than the temporal noise described by D*. Spatial noise cannot be averaged out by time integration (Mooney et al., 1989). Therefore, nonuniformity is particularly important under conditions of substantial illumination and for staring arrays, because the large data rates place strong constraints on correction algorithms.

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Expanding the Vision of Sensor Materials The operating temperature is an important consideration. Refrigeration becomes more costly and difficult as the operating temperature is lowered. For many applications the detector operating temperature should be high enough so that relatively low-cost refrigeration (such as liquid nitrogen at 77 K) can be used. This requirement of 77 K operation eliminates the possible use of extrinsic silicon detectors, which must be cooled to less than 30 K, from many applications. REFERENCES Accetta, J.S., and D.L. Shumaker, eds. 1993. The Infrared and Electro-Optical Systems Handbook, Vol. PM10. Society of Photo-optical Instrumentation Engineers. Bellingham, Washington: SPIE Press. Mooney, J.M., F.D. Shepherd, W.S. Ewing, J.E. Murguia, and J. Silverman. 1989. Responsivity nonuniformity limited performance of infrared staring cameras. Optical Engineering 28(11):1151–1161.