Calculation of NET

Calculation of NET (Noise Equivalent Temperature)
for a Thermal (Black) Pyroelectric IR Detector

The NET (Noise Equivalent Temperature) is defined as the minimum detectable temperature such that the signal from the detector through the optics is equal to its noise (SNR = 1).

Noise Equivalent Power (NEP) is the minimum detectable power which a detector can measure with a S/N of 1.
D Star (D*) is the specific detectivity accounting for the size of the detection element.

When characterizing the NET we must define the optical power on the detector's active area in terms of a minimum temperature difference or DT causing that power difference or excitance.

The excitance (MBB814) as a function of temperature and wavelength in the 8 to 14 micron interval from a 300 K BB is found below:

C₁ = 3.7413 x 10¹²
C₂= 1.4388,
T_bb = 300 °K
Lower Wavelength 8 x 10⁴ cm
Upper Wavelength 14 x 10⁴ cm, ε = .999

M B B 814 = [\int_{A}^{B} C_{1} \cdot (\frac{1}{L^{5}}) (e x p (\frac{C_{2}}{L \cdot T b b}) - 1)^{- 1} \cdot \frac{C_{2}}{L \cdot T b b^{2}} \cdot \frac{1}{(e x p (\frac{C_{2}}{L \cdot T b b}) - 1)} d L] \cdot ε

MBB814 = 3.285 x 10⁶Watts/cm²

Detector and Optical Considerations
(Typical MWA 4110 1 mm Dia. LTO with Rv and Vn @10Hz 1Hz. BW)

\begin{array}{c} R v = 2500 \frac{V}{W} V n; R v = 6 \cdot 10^{- 6} V / s q r t . H z .; N E P = \frac{V n}{R v} \\ N E P = 2.4 * 10^{- 10}; F_{n u m b e r} = - 1.2 d d = .1 A d = \frac{d d^{2}}{4} \cdot 𝜋 \\ A d = 0.008 D s t a r = \frac{R v \sqrt{A d}}{V n}; D s t a r = 3.693 \cdot 10^{10} \end{array}

Solving with a SNR of "1" we find the NET

N E T = \frac{F_{n u m b e r}^{2} \cdot N E P}{M B B 814 \cdot A d \cdot S N R} N E T = 0.0134 ° K

Alternately we can find the NET using Dsta

N E T = \frac{F_{n u m b e r}^{2}}{(\sqrt{A d}) M B B 814 \cdot D s t a r \cdot S N R} N E T = 0.0134 ° K

In conclusion one can see that a typical 1 mm dia. MWA 4110 LTO Pyroelectric detector chopped at 10 Hz. with an F# 1.2 is capable of achieving an NET of 13.4 mK