Pixels on target calculator — GSD & target sampling vs range

Field of view

Sensor1

Sensor width (mm)

Sensor height (mm)

Horizontal pixels

Vertical pixels

Pixel pitch (µm, for IFOV)

Focal length (mm)

Distance (m)

Coverage at distance

Scene coverage (degrees)

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Scene coverage (meters)

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IFOV (central)

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How this is calculated

Field of view. For each axis, the angle the sensor sees:

FOV = 2 · arctan( sensor dimension ÷ (2 · focal length) )

Scene coverage. How much real-world width, height and diagonal the frame spans at the set distance:

coverage = 2 · distance · tan( FOV ÷ 2 )

IFOV (central). The exact rectilinear angular width of one pixel at the centre of the field:

IFOV = 2 · arctan( pixel pitch ÷ (2 · focal length) )

Angular sampling. The average angular size per pixel across the whole image (FOV ÷ pixel count). This is close to, but not identical with, the central IFOV — it is an image-average, shown here in µrad/px.

Model limits. Rectilinear (pinhole) projection. Real lenses vary across the field and add their own MTF and chromatic effects — treat this as first-order geometry.

Engineering assumptions

Projection: Rectilinear · Lens distortion: Not modelled · Atmosphere: Not modelled / simplified

Optical MTF: Not modelled · Stabilization: Not modelled · Ground: Flat horizontal plane

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.

Target sampling

Sensor1

Sensor width (mm)

Sensor height (mm)

Horizontal pixels

Vertical pixels

Target

Target width (m)

Target height (m)

Distance (m)

Focal length (mm)60 mm

Min Max

HFOV × VFOV

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Pixels on target (H×V)

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Scene (W×H)

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Pixel density

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Ground sample dist.

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Target angular size

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Target fills

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How this is calculated

Field & coverage. At the selected focal length, each axis uses FOV = 2·arctan(sensor ÷ (2·f)) and coverage = 2·distance·tan(FOV/2).

Pixels on target. How many pixels span the target on each axis:

pixels = ( target dimension × focal length ) ÷ ( range × pixel pitch )

This direct form is equivalent to target size ÷ ground sample distance, and uses the same geometry as the DRI tool. Both horizontal and vertical are shown on the preview.

Model limits. Rectilinear geometry only, assuming a front-facing target of the entered width and height. Oblique aspect angle, partial occlusion and target depth reduce the actual projected pixels. Resolvable detail also depends on optical MTF, focus accuracy, atmosphere and display, so pixels-on-target is a geometric ceiling, not resolvable detail.

Engineering assumptions

Projection: Rectilinear · Lens distortion: Not modelled · Atmosphere: Not modelled / simplified

Optical MTF: Not modelled · Stabilization: Not modelled · Ground: Flat horizontal plane

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.

Target sampling calculator — pixels on target vs range

This calculator tells you how many pixels a target of known size occupies at a given range and focal length — one of the most useful first-order metrics for judging whether a target is adequately sampled. It also returns the target's angular size, the ground sample distance (GSD), pixel density and how much of the frame the target fills, for both the horizontal and vertical axes.

Pixels-on-target is a useful first-order measure of spatial sampling. Sweep focal length and range to see whether the target reaches the required pixel count.

How pixels-on-target is calculated

The direct geometric form, identical to the relationship used by the DRI tool so the two stay consistent:

Pixels on target = ( target dimension × focal length ) ÷ ( range × pixel pitch ) — evaluated separately for width and height.
Ground sample distance (GSD) = scene width ÷ horizontal pixel count — the real-world size one pixel covers at the target.
Target angular size = 2 · arctan( target dimension ÷ (2 · range) ) — how large the target appears in object space.

Worked example

A 7.0 m × 3.0 m truck, imaged by a 1920 × 1080 / 2.9 µm sensor with a 50 mm lens at 800 m:

Pixels wide = (7.0 · 0.050) ÷ (800 · 2.9×10⁻⁶) = 151 px Pixels tall = (3.0 · 0.050) ÷ (800 · 2.9×10⁻⁶) = 65 px GSD ≈ 4.6 cm/px · Angular size = 8.75 mrad

At 151 × 65 pixels the target is strongly sampled geometrically. Under a simplified Johnson-style pixel-count model the smaller 65-pixel dimension already exceeds even the 12-pixel identification threshold — but actual identification still depends on target aspect, contrast, optics, atmosphere, motion and processing. Halving the focal length to 25 mm would roughly halve the pixel counts to about 75 × 32 px, still well-sampled geometrically.

Frequently asked questions

How many pixels on target do I need?

For a simplified Johnson-style pixel-count interpretation, this calculator uses approximately 1.5 pixels for detection, 6 for recognition and 12 for identification at 50% probability. These are first-order engineering values, not universal DRI standards, and scale up for higher confidence. The DRI tool applies these thresholds formally; this tool gives you the raw pixel count so you can judge against whichever requirement applies.

What is ground sample distance (GSD)?

GSD is the real-world distance that one pixel covers at the target — for example 4.6 cm/px means each pixel maps to a 4.6 cm square on the ground. Smaller GSD means finer detail. It is the inverse view of pixels-on-target: a 1 m feature at 4.6 cm/px spans about 22 pixels.

Does this account for atmosphere or optical blur?

No — this is a pure geometric sampling calculation. Real resolvable detail is further limited by optical MTF, focus, atmospheric turbulence and transmission, motion and display. Pixels-on-target is the geometric ceiling; actual performance sits below it. The DRI tool adds an optional Environmental / Signal limit on top of the geometry.

Why show both horizontal and vertical pixel counts?

Targets are rarely square and pixels may not be either. A 7 m-wide, 3 m-tall vehicle spans far more pixels horizontally than vertically, and recognition often depends on resolving the smaller dimension. Showing both lets you check the limiting axis rather than assuming a single figure.

Detection, Recognition, and Identification (DRI)

Camera type

Sensor1

Horizontal pixels

Vertical pixels

Pixel pitch (µm)

Focal length (mm)

Geometric probability assumption (×1.0)2

Target A

Target

Overall width (m)

Overall height (m)

Critical dimension (m)3

Compare a second target

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.

Detection (px)

Recognition (px)

Identification (px)

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.

Apply Environmental / Signal limit

Environmental / signal probability assumption (×1.0)5

Target–background ΔT (K)

Atmos. attenuation σ (km⁻¹)

Sensor NETD (mK)

Apply optional signal attenuation factor

Advanced signal assumptions

Required SNR per task — illustrative assumptions, not calibrated. Higher demands → shorter range. Uses |ΔT| so a cooler-than-background target still has contrast.

SNR — Detection

SNR — Recognition

SNR — Identification

Typical values

Atmos. attenuation σ (km⁻¹):
A user-supplied illustrative LWIR coefficient — thermal transmission depends on wavelength, humidity and weather, so it is not equivalent to visible-light meteorological visibility. Enter a value from your own band- and condition-specific data; the EO ranges (0.2 clear → ~0.8 fog) are only a rough starting point.

Target–background ΔT:
~2 K day vehicle vs background, ~0.5–1 K low-contrast, ~5–10 K hot engine/exhaust.

NETD:
Sets the thermal contrast floor only — not a complete system-sensitivity model (spatial, temporal, spectral and processing effects are not captured).

SNR:
A configurable first-order threshold, not a universal DRI criterion. ≈ 5 is commonly associated with a Rose-type detection criterion; lower values are a more permissive screening assumption. The defaults (2.5 / 4 / 6) are placeholders for demonstrating increasingly demanding tasks.

Signal attenuation factor:
An optional single scalar on contrast, not a computed MTF at a defined spatial frequency. ~0.7 well-focused, ~0.4–0.5 modest, ~0.2 near the resolution limit.

Estimated DRISimplified Johnson-style geometric estimate · 50% probability

Detection

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Geometric-limited

Recognition

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Geometric-limited

Identification

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Geometric-limited

Geometric sampling limitsimplified Johnson-style criterion

Task	Range
Detection	—
Recognition	—
Identification	—

Environmental / signal limitoptional

Enable the Environmental / Signal limit below to add a task-specific signal range.

Critical dim. (A / B)

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HFOV × VFOV

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IFOV

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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 ≥ SNR_task × NETD ⟹ R = ln( |ΔT|·MTF ÷ (SNR_task·NETD) ) ÷ σ

Visible/EO uses the same form with initial contrast C and the task's minimum remaining contrast C_min,task: R = ln( C ÷ C_min,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

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.
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.
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.
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.
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.

Pixels-on-target calculator

Field of view

Target sampling

Target sampling calculator — pixels on target vs range

How pixels-on-target is calculated

Worked example

Frequently asked questions

Detection, Recognition, and Identification (DRI)

Need the real system, not just the numbers?