Detector Sizing and NETD for a Small Target at Distance
You must detect a 20 mm overheated terminal on a 400 V panel from 8 m away. Candidate imager A: 160×120 microbolometer, 8–14 µm, 25° FOV, NETD 80 mK, IFOV computed from a 160-pixel horizontal array. Candidate imager B: 320×240, same FOV, NETD 50 mK. Both have ±2 °C accuracy. The terminal is expected to be 15 K above its surroundings. Site rules require the imager to resolve the target with at least 3 pixels across its smallest dimension for a reliable temperature measurement, and at least 1 pixel for detection only.
1. Compute the IFOV and pixel coverage for each imager and state which meets the 3-pixel criterion.
Read the worked answer
IFOV ≈ FOV / number of horizontal pixels (small-angle approximation):
- Imager A: 25° / 160 = 0.156° per pixel. In radians: 0.156 × π/180 ≈ 2.73 mrad. At 8 m, pixel footprint = 2.73 mrad × 8 m ≈ 21.8 mm.
- Imager B: 25° / 320 = 0.078° per pixel ≈ 1.36 mrad. At 8 m, footprint ≈ 10.9 mm.
Target is 20 mm:
- A: 20 / 21.8 ≈ 0.9 pixel across - below even the 1-pixel detection criterion; the target is sub-pixel and its energy is spread over the surrounding pixels (spatial averaging).
- B: 20 / 10.9 ≈ 1.8 pixels - meets detection (≥1 px) but fails the 3-pixel measurement criterion (needs ~3 px, i.e., footprint ≤ 6.7 mm, requiring ~3× the resolution or ~1/3 the distance).
Neither imager supports a reliable temperature measurement of this target at 8 m under the stated rule. B supports detection only.
2. Given the 15 K rise and the NETD values, what can each imager actually tell you, and what would you change?
Read the worked answer
NETD is the noise-equivalent temperature difference - the smallest signal distinguishable from noise at a stated scene temperature and averaging. With a 15 K rise:
- A (NETD 80 mK = 0.08 K): signal-to-noise ≈ 15/0.08 ≈ 188 - radiometrically ample if the target filled a pixel. It does not (0.9 px), so the pixel signal is diluted by the surrounding background; the apparent rise is roughly the target fraction of the pixel times 15 K, i.e., well under 15 K and mixed with background. Detection is marginal, measurement impossible.
- B (NETD 50 mK): S/N ≈ 300, and at 1.8 px the target dominates the central pixel but still does not meet the 3-px rule; a measurement would carry a large spatial-averaging error.
Options:
- Move closer - to meet 3 px with B, distance ≤ ~2.7 m (3 × 10.9 mm ≈ 32.7 mm footprint at 8 m scaled: 8 m × 6.7/20 ≈ 2.7 m).
- Use a narrower-FOV lens (telephoto) to shrink IFOV.
- Accept detection-only and confirm with a contact method (clamp meter, contact probe) at the identified terminal.
- Do not report a temperature from a sub-3-pixel target; report a relative severity and flag the spatial-resolution limitation in the report.