UAV Payloads #03
How High, How Fine? Working Back from GSD to Payload Specification
"We need to be able to see clearly."
That sentence cannot be turned into a purchase order. Does seeing clearly mean knowing there is a person there, or making out their clothing or what they are holding? These two differ in focal length by more than six times, and in price by even more.
Turning it into numbers takes only four steps: target size → pixels needed → allowed ground sample distance → focal length. The only empirical values used are one set of Johnson criteria; every other step is a division.
1. Ground sample distance: how much ground one pixel covers
The patch of ground that one camera pixel corresponds to is called the ground sample distance (GSD). The formula has only three variables:
GSD = H × p ÷ f
H is the altitude, p the pixel pitch and f the focal length. For a longwave infrared camera at 122 m altitude with 12 µm pixels and a 25 mm focal length:
GSD = 122 × 12×10⁻⁶ ÷ 25×10⁻³ = 0.0586 m = 58.6 mm
The middle step, p ÷ f, is called the instantaneous field of view (IFOV), in radians; 12 µm ÷ 25 mm = 480 µrad. It is a property of the camera itself, independent of altitude, so calculating it first and then multiplying by altitude makes conversions much quicker.
Note that GSD is not "the smallest thing you can see". One pixel can only tell you the average brightness of that patch of ground; to "make out" something you need several pixels. That is the next section.
2. How many pixels: the Johnson criteria
In 1958, John Johnson of the U.S. Army published a set of experimental results relating "what an observer can achieve" to "how many line pairs can be resolved across the target". The results are still in use today, known as the Johnson criteria:
| Level | Line pairs needed | Pixels | Meaning |
|---|---|---|---|
| Detection | 1.0 ± 0.25 | 2.0 px | Something is there |
| Orientation | 1.4 ± 0.35 | 2.8 px | Which way it is facing |
| Recognition | 4.0 ± 0.8 | 8.0 px | A person, not an animal |
| Identification | 6.4 ± 1.5 | 12.8 px | Distinguishing detailed differences between targets of the same class (such as clothing or handheld objects) |
These pixels have to span the target's critical dimension, the actual size in the direction that needs to be resolved. For a person it is usually taken as 0.75 m (a conservative choice; the geometric mean of height and shoulder width gives about 0.94 m, with correspondingly longer range). Dividing the critical dimension by the number of pixels needed gives the allowed GSD:
3. The 400 ft ceiling caps the altitude
The drone chapter of Taiwan's Civil Aviation Act stipulates that flight altitude must not exceed 400 ft, about 122 m, above ground or water. This rule caps the H in GSD = H × p ÷ f: when operating at the ceiling, the only ways to raise the interpretation level are a longer focal length or a sensor with a smaller pixel pitch.
Put an uncooled longwave infrared core of 640 × 512 with 12 µm pixels (active area 7.68 × 6.14 mm) at 122 m, and calculate where each focal length lands:
| Focal length | IFOV | GSD | Ground coverage width | Achievable for a person |
|---|---|---|---|---|
| 9 mm | 1333 µrad | 163 mm | 104.1 m | Detection |
| 13 mm | 923 µrad | 113 mm | 72.1 m | Detection |
| 19 mm | 632 µrad | 77.1 mm | 49.3 m | Recognition |
| 25 mm | 480 µrad | 58.6 mm | 37.5 m | Identification (no margin) |
| 35 mm | 343 µrad | 41.8 mm | 26.8 m | Identification |
Look at the trade-off in the last two columns: going from 13 mm to 35 mm takes the interpretation level from detection to identification, but the width covered in a single pass drops from 72 m to 27 m; covering the same area takes 2.7 times as much flight path, and whether the battery lasts is another question.
Be especially careful with the 25 mm row: a GSD of 58.6 mm exactly equals the identification threshold of 58.6 mm. It looks as if it meets the target, but it actually has zero margin. The Johnson criteria assume sufficient contrast between target and background, and when the background temperature is close to body temperature (for example during thermal crossover around dawn and dusk, or on ground that has baked in the sun), when the air is humid, or when the target is partly hidden by vegetation, real performance is worse. To identify reliably at 122 m, go for 35 mm.
4. Speed is part of the payload specification too
Calculating the focal length is not the end of it. While the camera is integrating, the aircraft is moving forward, and the ground is smeared across the image:
smear = ground speed × integration time
Visible cameras can shorten the integration time with an electronic shutter; uncooled longwave infrared cannot. An uncooled microbolometer relies on thermal equilibrium, with a thermal time constant of about 8 to 12 ms. The detector responds exponentially to temperature changes, so this time can be approximated as the exposure time, and there is no electronic shutter to shorten it.
| Ground speed | Smear | Multiple of GSD | Verdict |
|---|---|---|---|
| 3 m/s | 30 mm | 0.72 | Acceptable |
| 4 m/s | 40 mm | 0.96 | Borderline |
| 8 m/s | 80 mm | 1.91 | Drops one interpretation level |
| 15 m/s | 150 mm | 3.59 | Detection level only |
The conclusion is a little counterintuitive: you pay for a 35 mm long lens to achieve identification, fly too fast, and your actual interpretation capability may drop back to recognition, so the money spent on the long lens is wasted. To really make use of the 35 mm resolution, ground speed must stay below about 4.2 m/s (about 15 km/h), much slower than most people's intuitive inspection speed.
Visible cameras are not entirely immune either. Under the same conditions of 122 m, a 25 mm lens and an 11.7 mm GSD, a 1/500 s exposure at a ground speed of 10 m/s produces 20 mm of smear, 1.7 GSDs; to keep it within one pixel, the shutter needs at least 1/1000 s. In good daylight this is not a problem, but at dusk or on overcast days you have to trade off between shutter speed, gain and image quality.
5. A complete walk-through
Putting the four steps together with a real question: "Find and recognize a person lost in the mountains, at the legal altitude ceiling."
- Target critical dimension: a person, taken as 0.75 m.
- Interpretation level: "find and recognize" = recognition, needing 8 pixels.
- Allowed GSD: 0.75 ÷ 8 = 0.0938 m = 93.8 mm.
- Allowed IFOV: 93.8 mm ÷ 122 m = 769 µrad.
- Minimum focal length: 12 µm ÷ 769 µrad = 15.6 mm. Choose the standard 19 mm.
- Coverage width: 7.68 mm ÷ 19 mm × 122 m = 49.3 m. For 30 % side overlap, the line spacing is 34.5 m.
- Speed limit: GSD 77.1 mm ÷ 10 ms = 7.7 m/s.
- Search rate: with 49.3 m coverage, 34.5 m spacing and 7.7 m/s, about 0.96 km² per hour (34.5 m × 7.7 m/s × 3600 s = 956 340 m²).
That last number is the answer a search and rescue commander really needs: one aircraft, with one battery change, covers less than one square kilometer in an hour. If the search area is 20 km², you know how many aircraft and how many sorties are needed, or whether to step down to detection only (a 13 mm lens, 72 m coverage, a speed limit of 11.3 m/s, raising the search rate to about 2.0 km²/hr) to gain speed. The value of working back the specification is not in calculating the focal length, but in turning "can it be done" into numbers that can be discussed.
6. A checklist
- Is the target's critical dimension written down? In which direction?
- Is the interpretation level detection, recognition or identification? Who decides at acceptance?
- Does the calculated GSD leave margin? Exactly at the line should not count as a pass.
- Once coverage width is converted to line spacing and search rate, does the mission time hold up?
- Has the speed limit been calculated? Is it written into the flight planning parameters?
- Is the altitude the regulatory ceiling or the mission requirement? When they differ, the lower one applies.
- Have the gimbal stability requirements of a long lens been calculated? See Gimbal Stability Is Not the Angle on the Datasheet.
