DRI range calculator — detection, recognition, identification

Estimate detection, recognition and identification range for thermal and visible cameras with a Johnson-style criterion and an optional signal limit.

640×512 LWIR · 12 µm · NATO target (2.3 m)
75 mm
25300
Detection—
Recognition—
Identification—
— wide at 1 km · open the DRI tool

Detection, Recognition, and Identification (DRI)

Target A
Advanced pixel assumptions

Pixels across the critical dimension per task — a simplified Johnson geometric pixel-count model (≈1.5 / 6 / 12 at 50%). A first-order engineering estimate, not a universal DRI standard; the geometric probability assumption scales these values.

Environmental / Signal limit optional

Optional simplified signal-limited screening estimate from contrast, atmospheric attenuation and sensor sensitivity — not a validated DRI model. It computes a separate signal range for each task (detection, recognition, identification) and never changes the geometric pixels-on-target; the final range per task is the lower of its geometric and signal limits. The task thresholds are illustrative, editable assumptions, not calibrated performance limits.

Estimated DRISimplified Johnson-style geometric estimate · 50% probability
Detection
—
Geometric-limited
Recognition
—
Geometric-limited
Identification
—
Geometric-limited
Geometric sampling limitsimplified Johnson-style criterion
TaskRange
Detection—
Recognition—
Identification—
Environmental / signal limitoptional
Enable the Environmental / Signal limit below to add a task-specific signal range.
Critical dim. (A / B)
—
HFOV × VFOV
—
IFOV
—
How this is calculated

The geometric and signal limits are computed independently for each task, and the final per-task range is the lower of the two, so the result is auditable.

Geometric sampling limit (per task N = 1.5 / 6 / 12):

R = (critical dimension × focal length) ÷ (N × pixel pitch)

Environmental / signal limit — computed separately for each task. Thermal, using |ΔT| and the task's required SNR:

|ΔT| · e−σR · MTF ≥ SNRtask × NETD  ⟹  R = ln( |ΔT|·MTF ÷ (SNRtask·NETD) ) ÷ σ

Visible/EO uses the same form with initial contrast C and the task's minimum remaining contrast Cmin,task: R = ln( C ÷ Cmin,task ) ÷ σ. If the signal is already below threshold at zero range the task range is zero ("below signal threshold"); if σ = 0 and the threshold is met there is no atmospheric limit in the model. NETD and atmosphere affect these signal limits only — never the geometric pixels-on-target.

All DRI outputs are first-order estimates, not guaranteed real-world performance, and should not be interpreted as measured or validated system range. Actual range depends on target contrast, atmospheric transmission, optics MTF, sensor sensitivity, image processing, stabilization, display and observer/algorithm performance.

Engineering assumptions

Projection: Rectilinear   ·   Lens distortion: Not modelled

Geometric model: No atmospheric degradation   ·   Signal / environment model: Optional first-order screening

Optical MTF: Not modelled unless used in signal screening   ·   Stabilization: Not modelled

  1. 1Sensor library. A curated convenience library — specs are unverified; check the datasheet before relying on a preset. NETD values are selected nominal assumptions ("typically < X mK" under stated conditions and variant), not guaranteed values; detector and module specifications can differ. "Format" rows are generic optical-format approximations (no specific part, no band), so they don't appear under the VIS / LWIR filters.
  2. 2Geometric probability assumption. Scales the geometric pixel requirement only — it does not change the signal model's contrast/SNR thresholds, which are independent illustrative assumptions. Actual discrimination probability depends on target characteristics, contrast, sensor performance, image processing and observer/task conditions; a calibrated probability claim would require validating the complete system model, not just a geometric multiplier.
  3. 3Critical dimension. A representative target dimension or feature relevant to the selected task. This value drives the geometric range calculation; overall width and height describe the target's scale but do not directly affect the calculated range. Choose the critical dimension based on the target, viewing angle and task; built-in values are preliminary engineering assumptions. V1 uses one representative critical dimension, while advanced analysis could use task-specific dimensions.
  4. 4A/B comparison. A/B comparison uses the same sensor and environmental signal assumptions for both targets. The geometric range changes with each target's critical dimension; differences in target contrast or thermal signature are not modelled separately.
  5. 5Environmental / signal probability assumption. Scales the signal thresholds for a more or less demanding screening assumption — it does not change the geometric pixel requirement. These thresholds, and this scaling, are illustrative and not calibrated. System-level prediction needs MRTD/MRT or validated sensor/atmospheric modelling.

DRI calculator — detection, recognition & identification range

This calculator estimates the maximum range at which an imaging system can detect, recognise and identify a target, from the sensor, lens and a representative target dimension. It reports a per-task range for detection, recognition and identification, and shows whether each one is limited by geometric sampling or by an optional signal/environmental ceiling.

DRI is the standard language for specifying surveillance and targeting sensors. "Detection" means a target is present; "recognition" means its class is distinguishable (a vehicle vs a person); "identification" means the specific type is resolved. The simplified geometric model produces shorter recognition and identification ranges because these tasks require progressively more spatial information across the target's critical dimension.

How DRI range is calculated

The estimate is a four-step first-order model:

  1. Target critical dimension. A representative target dimension for the selected task.3 Library values are preliminary engineering assumptions.
  2. Geometric sampling limit (always active) = ( critical dimension × focal length ) ÷ ( N × pixel pitch ), where N is the pixels-across requirement (≈1.5 / 6 / 12 at 50% probability, scaled by the probability assumption2). This is a simplified Johnson-style pixel criterion — a first-order engineering estimate, not a universal DRI standard. It produces task-specific detection, recognition and identification ranges.
  3. Optional environmental / signal limit. A separate model (target/background contrast, atmospheric attenuation and sensor sensitivity) that produces a task-specific signal range for detection, recognition and identification from editable per-task thresholds. Contrast and atmosphere affect this limit only, never the geometric pixels-on-target.
  4. Final limiting range. For each task, the lower of the two: Detection = min(Geometric D, Environmental), Recognition = min(Geometric R, Environmental), Identification = min(Geometric I, Environmental). Each band shows whether it was limited by Geometric or Environmental / Signal.

Worked example

A 640 × 512 / 12 µm LWIR sensor, 50 mm lens, against a 2.3 m NATO target at 50% probability:

Detection (1.5 px) = (2.3 · 0.050) ÷ (1.5 · 12×10⁻⁶) ≈ 6.4 km Recognition (6 px) ≈ 1.6 km Identification (12 px) ≈ 0.8 km

These are the geometric limits. With the Environmental / Signal limit off, they are the final estimate (each band Geometric-limited). Turning it on computes a separate signal range per task; in worse atmosphere, or for a harder task with a higher threshold, a task's signal range can drop below its geometric range, flipping that band to Environment-limited (or "No signal" if the threshold is never met).

Frequently asked questions

What is the Johnson criteria?
The Johnson criteria relate the number of resolvable cycles (or pixels) across a target's critical dimension to the probability of detection, recognition and identification. The original formulation is expressed in cycles across the target (detection ~1, recognition ~3–4, identification ~6, depending on the formulation). This calculator uses a simplified pixel-count interpretation with baseline values of approximately 1.5 / 6 / 12 pixels at its 50% probability assumption — a first-order engineering estimate, not a universal DRI standard.
Do atmosphere and target/background contrast affect the geometric DRI limit?
No — they do not change the geometric pixel projection, which depends only on target size, focal length and pixel pitch. But they can reduce the usable signal, so they can impose the separate Environmental / Signal ceiling. That is why the calculator keeps them as an optional second limit rather than folding them into the pixel count.
What critical dimension should I use?
The critical dimension is a representative target dimension or feature relevant to the selected task — it comes from the target and task definition, not from a universal "Johnson" table. It drives the geometric range calculation; overall width and height describe the target's scale but do not directly affect the calculated range. The built-in library pre-fills preliminary engineering values (for example the 2.3 m NATO target for reference, or ~0.75 m for a standing person). Choose the value based on the target, viewing angle and task.
How does NETD affect detection range?
NETD (noise-equivalent temperature difference) sets the thermal contrast floor: the apparent temperature difference must stay above roughly SNR × NETD to be usable. A lower NETD extends the contrast-limited range but does not change the geometric limit. That is why this tool reports the Environmental / Signal limit as a separate figure rather than merging it into the geometric range.
What atmospheric conditions does it assume?
The environmental limit uses a Beer–Lambert transmission model with an editable attenuation coefficient. For visible/EO, the Koschmieder relation (V ≈ 3.912/σ) relates that coefficient to a rough meteorological visibility — a simplified model with real-atmosphere limitations. For thermal/LWIR the coefficient is a user-supplied illustrative value: thermal transmission depends on wavelength, humidity and weather and is not the same as visible-light visibility. As conditions worsen, each task's signal range drops and can become the binding limit for that task.
Why is identification range shorter than detection?
The simplified geometric model produces shorter recognition and identification ranges because these tasks require progressively more spatial information — more pixels across the critical dimension. With the default 12 vs 1.5 pixel criteria, the geometric identification range is one-eighth of the detection range. This ratio is a property of the simplified model, not a universal DRI relationship — which is why long-range ID drives the most demanding optics and sensor choices.

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