Payloads and mission data

Why this matters

The aircraft is only a carrier; the mission’s results come from the payload. The night search in this case needs a thermal camera, and users will ask “how far away can it see a person?” Sellers often answer with a single number. An engineer must be able to compute it and know the assumptions behind it. The drone knowledge base’s payload unit recommends choosing sensors from the required output and understanding calibration, ground sample distance and the accuracy of processed results.

Field of view per pixel

Each camera pixel sees a small angle called the IFOV (instantaneous field of view), equal to the pixel size $p$ divided by the focal length $f$. Looking down from height $H$, the ground area per pixel (GSD) is $H\cdot \text{IFOV}$. The examples in this module use the real specification of the thermal camera in the DJI Zenmuse H20T: 640×512 pixels, 12 µm pixel pitch, 13.5 mm focal length, and a gimbal angular vibration range of ±0.01°, as listed on the manufacturer’s specification page. This gives an IFOV of about 0.889 mrad.

The Johnson criteria

Johnson (1958) tested how many line pairs (cycles) of detail across a target are needed to perform each task with 50% probability. The widely used values are 1.0 line pair for detection (knowing an object is there), 4.0 for recognition (knowing it is a person or a vehicle) and 6.4 for identification (telling who or which model) (Perić and colleagues, 2019). One line pair takes two pixels. The critical dimension of a standard 1.8 m × 0.5 m person is $\sqrt{1.8\times 0.5}\approx 0.95$ m, and of a vehicle 2.3 m.

import math

PITCH, FOCAL = 12e-6, 13.5e-3                   # m, pixel pitch and focal length
IFOV = PITCH / FOCAL                            # rad
JOHNSON = {"detection": 1.0, "recognition": 4.0, "identification": 6.4}   # line pairs
TARGETS = {"person": math.sqrt(1.8 * 0.5), "vehicle": 2.3}               # m, critical dimension

print(f"IFOV {IFOV * 1000:.3f} mrad, GSD at 90 m {90 * IFOV * 100:.1f} cm")
for name, dc in TARGETS.items():
    ranges = {k: dc / (2 * n * IFOV) for k, n in JOHNSON.items()}
    print(f"{name:<8} (Dc {dc:.2f} m): " + ", ".join(f"{k} {r:,.0f} m" for k, r in ranges.items()))

IFOV 0.889 mrad, GSD at 90 m 8.0 cm
person   (Dc 0.95 m): detection 534 m, recognition 133 m, identification 83 m
vehicle  (Dc 2.30 m): detection 1,294 m, recognition 323 m, identification 202 m

Gimbal and blur

During the exposure, if the camera rotates at angular rate $\omega$, the image moves by $\omega t$, or $\omega t/\text{IFOV}$ pixels. If the aircraft moves at speed $v$, the ground image moves by $vt/\text{GSD}$ pixels. Blur above about 1 pixel destroys the detail that the Johnson calculation assumes. The gimbal reduces camera rotation caused by aircraft vibration and tilting.

import math

IFOV = 12e-6 / 13.5e-3                          # rad
IFOV_DEG = math.degrees(IFOV)
print(f"gimbal vibration 0.01 deg = {0.01 / IFOV_DEG:.2f} pixel")
for rate in (0.5, 2.0):                         # deg/s of residual rotation after the gimbal
    for ms in (10, 20, 40):
        print(f"rate {rate} deg/s, exposure {ms} ms: {rate * ms / 1000 / IFOV_DEG:.2f} px")
    print(f"  longest exposure for 1 px at {rate} deg/s: {IFOV_DEG / rate * 1000:.0f} ms")

H, V = 90, 16                                   # height m, speed m/s
gsd = H * IFOV
for ms in (5, 10):
    print(f"forward motion at {V} m/s, {H} m, {ms} ms: {V * ms / 1000 / gsd:.1f} px")

gimbal vibration 0.01 deg = 0.20 pixel
rate 0.5 deg/s, exposure 10 ms: 0.10 px
rate 0.5 deg/s, exposure 20 ms: 0.20 px
rate 0.5 deg/s, exposure 40 ms: 0.39 px
  longest exposure for 1 px at 0.5 deg/s: 102 ms
rate 2.0 deg/s, exposure 10 ms: 0.39 px
rate 2.0 deg/s, exposure 20 ms: 0.79 px
rate 2.0 deg/s, exposure 40 ms: 1.57 px
  longest exposure for 1 px at 2.0 deg/s: 25 ms
forward motion at 16 m/s, 90 m, 5 ms: 1.0 px
forward motion at 16 m/s, 90 m, 10 ms: 2.0 px

Choosing a payload to fit the question

Fahlstrom and colleagues and Barnhart and colleagues recommend starting from the user’s question and then choosing the payload. “Where are people trapped?” needs a thermal camera plus a zoom camera to confirm. “How wide is the flood?” needs a mapping camera with accurate positions. “How far has the water dropped?” may need a height model from photogrammetry or LiDAR. Every image needs a correct time and position, or users will place things in the wrong location, as covered in UAT 311.

Module lab

Common mistakes

Summary

• IFOV = pixel size / focal length, and GSD = height × IFOV
• The Johnson criteria use 1.0, 4.0 and 6.4 line pairs across the critical dimension for detection, recognition and identification
• Blur comes from camera rotation and aircraft motion and should stay below about 1 pixel
• Computed ranges are geometric limits and must be confirmed by field tests

Check your understanding

1. Pixel size 17 µm and focal length 19 mm. What is the IFOV?
2. IFOV 1 mrad at 100 m height. What is the GSD?
3. IFOV 1 mrad and a 1 m critical dimension. What is the Johnson detection range?
4. A rotation rate of 1°/s, IFOV 0.05° and a 20 ms exposure give how many pixels of blur?
5. Why can a thermal camera’s real range be shorter than the computed range?