NETD – Thermal Sensitivity

Noise Equivalent Temperature Difference is defined as the smallest temperature difference that a thermal camera or pyrometer can distinguish. In other words, NETD characterizes the thermal sensitivity of an infrared camera or pyrometer: it quantifies how small a temperature contrast the system can detect above its internal noise floor.

Engineers sometimes confuse NETD with overall measurement uncertainty. NETD is not a complete “uncertainty” of temperature measurement. Rather, NETD is the contribution of random noise to the temperature reading. Likewise, NETD should not be used to characterize drift or stability over minutes.

The NETD is not the same as absolute error, bias, or overall repeatability including drift. It also differs from the minimum resolvable temperature difference (MRTD), which involves spatial resolution and target recognition thresholds, and from non-uniformity or inhomogeneity (IETD), which describes the pixel-to-pixel variations. NETD is purely about how much the reading fluctuates from frame to frame on a uniform target.

Formally, the NETD is the share of measurement uncertainty caused by high-frequency temporal noise. It is defined as the temperature difference of a blackbody that yields a signal-to-noise ratio of 1 for the thermographic camera. For an individual detector element, NETD is reported as a standard uncertainty with 68.3% confidence (coverage factor k = 1). NETD does not include the slow drift of the image mean; such components must be removed during testing.

NETD for pyrometers for thermal cameras according to Standardized Measurement (VDI/VDE 5585)

Mathematically, NETD can be obtained by measuring the temporal noise of the thermal or pyrometer camera under uniform illumination. In practice, measurement readings are often pooled into a histogram, and the histogram’s standard deviation is used to check for an expected normal distribution. While for a pyrometer, a single timeseries is analyzed, for thermal camera each pixel must be considered.

The German technical guideline VDI/VDE 5585 Blatt 1 (2018) defines NETD and prescribes the method for measuring it using thermographic cameras. The VDI 5585-1 specifies two standard methods for NETD measurement, to accommodate different camera designs. Both methods assume the camera has already been non-uniformity-corrected and it also requires the blackbody to be very stable.

Method A (Frame-wise standard deviation): The infrared camera observes a stable, uniform blackbody at a fixed temperature. At least 100 consecutive frames are recorded at the desired integration time and frame rate. For each pixel element, the temporal standard deviation of its temperature signal is computed. The NETD is then taken as the average of those pixel-wise standard deviations. This procedure is equivalent to plotting a histogram of the pixel values over time and taking its RMS width.

The following equation, where N>100 is the number of data points [math]T_i[/math] is the temperature value of each data point, calculates the standard deviation per pixel. Each NETD is mapped in a matrix and for a general information on the NETD, each pixel-wise NETD is averaged.

[math]NETD_{A}=\sigma=\sqrt{\sum_{i=1}^N}\left(T_{i}-T_{mean}\right)^{2}[/math] with [math]T_{mean}=\frac{1}{N}\sum_{i=1}^NT_{i}[/math]

Method B (Two-Frame Differential): This faster method works when the camera produces only processed temperature frames or when taking many frames is impractical. The camera captures two successive images of the uniform source under identical conditions. The pixel-by-pixel difference between the two images is formed. The NETD is calculated from these differences using the following formula.
The mean NETD for an infrared camera can be computed from the following set of equations, where [math]n_h[/math] is the horizontal number of pixels, and [math]n_v[/math] is the vertical number of pixels in the image.

[math]NETD_{B}=\frac{\sqrt{2}}{2}\sqrt{\sum_{i=1}^{n_{h}}\sum_{j=1}^{n_{v}}\frac{\left(\triangle T_{i,j}-\triangle T_{i,j_{mean}} \right)}{n_{h}n_{v}}^{2}}[/math]

with  [math]\triangle T_{i,j}=T_{i,j}\left(t\right)-T_{i,j}\left(t+\triangle T\right)[/math]

and [math]\triangle T_{i,j_{mean}}=\frac{1}{N}\sum_{i,j=1}^N T\left(i,j\right)[/math]

This effectively computes the standard deviation of the pixel differences with a √2 factor. Because subtracting two identical images yields only noise, this method provides the ensemble NETD. It is defined in VDI 5585 as an alternative when per-pixel time series are not available.

Factors Influencing NETD

NETD is not a fixed absolute property of a thermal camera or pyrometer; it depends strongly on the test conditions and camera settings. Key factors include:

• Scene temperature: NETD typically decreases at higher scene temperatures, all else equal. Because infrared sensors respond to radiance, the NETD depends on the radiance temperature of the source. In practice, NETD is usually specified at a given scene temperature. The thermal derivative (dR/dT) of a blackbody is higher at higher temperatures. Thus, for the same detector noise in volts, a 100 °C target yields a larger signal change per degree than a 25 °C target. Figure 1 illustrates this with a PI 640i thermal camera.

• Integration time and frame rate or sampling rate: The infrared sensor’s integration or exposure time per frame determines how much signal is collected. Longer integration increases signals and tends to reduce the effect of readout noise, thereby lowering NETD. In practice, doubling the integration time can roughly reduce NETD by [math]√2[/math], until other noises (like 1/f flicker noise) become dominant. See Figure 2, which illustrates this effect with a PI640 target at an ambient black body.

• Optics: The lens and optics control how much infrared energy reaches the detector. A faster lens, lower f/#, admits more light, lowering NETD. A slower lens, higher f/#, raises NETD. The NETD scales roughly proportional to the f-number: for example, a thermal camera good NETD at f/1.0 might have substantially worse NETD at f/1.3, even if the detector and camera are the same, because the f/1.3 lens collects less radiation.
• Detector temperature and camera stabilization: For uncooled microbolometers, the sensor temperature can drift with ambient or self-heating. If the detector’s operating temperature rises, its dark noise typically increases, which in turn worsens NETD.
• Signal processing: The raw detector noise can be reduced by on-chip or post-processing such as frame averaging, filtering, or “bad-pixel” replacement. In NETD reporting, it must be stated whether any temporal averaging is used. Manufacturers often apply digital averaging to improve effective NETD by [math]√N[/math]

For comparability, VDI/VDE 5585 specifies how NETD must be measured and reported. The scene radiation temperature must accompany the NETD value, the measuring time, such as frame rate and/or integration time, and any image averaging. For systems with interchangeable optics or filters, specify the exact lens and filter. If the camera has switchable measuring temperature ranges, indicate which range was active. Providing these parameters enables reproducible tests and like-for-like comparisons

NETD in Image Quality

In imaging terms, a lower NETD yields higher contrast (visibility) of small thermal features; higher NETD produces noisier-looking images where subtle temperature variations are obscured. For applications like fault detection, medical thermography, or target identification, a lower NETD usually means better performance. A camera with NETD=50 mK can, in principle, discern a 0.05 K difference between two identical-looking objects, whereas one with NETD=100 mK needs a 0.1 K difference for the same SNR. NETD refers specifically to temporal noise – random fluctuations from frame to frame – not spatial nonuniformity across the array. VDI 5585 explicitly defines NETD as the uncertainty contribution due to high-frequency temporal noise.

In other words, NETD is the random “grain” of the image over time. By contrast, drift or bias instability refers to slow changes in offset or gain, which NETD does not capture. Drift is a low-frequency effect and is treated as a different performance parameter.

Figure 4 illustrates a face with different NETD levels. The face was averaged to have a very low NETD, in a second step more noise is added again to simulate different NETD level in order to get an impression of it. The noise on the uniform background becomes more prominent but features in the face are still very visible even at higher NETD values. Only at very high noise levels, details in the face are more difficult to make out.

Figure 5 illustrates a video of a hand at different noise levels with the same process. Here the images have not been down sampled or averaged.