Field of view and pixel density: a worked DORI example
Calculate scene width and a starting focal length, then test the recorded result.
Updated
Installation and acceptance
Treat this as an initial optical estimate. Perspective, lens distortion, focus, compression, noise and motion can reduce useful detail. Use the actual recorded pixel dimensions after any crop or dewarping. Place a measurable target at the critical plane and assess a moving subject under expected light. Keep the standard edition, lens setting, stream configuration and accepted footage in the design record.
Calculate at the target plane
Let N be recorded horizontal pixels, W the scene width in metres at the target and P the horizontal pixel density in px/m. Then P = N/W and W = N/P. Use the width at the actual person or plate, not the foreground width. For a rectilinear view with horizontal angle θ, W = 2D × tan(θ/2), where D is distance to the plane perpendicular to the optical axis. These relationships describe sampling geometry, not optical resolution or recognition accuracy.
For N = 3840 and a planning density P = 250 px/m, W = 15.36 m. At D = 20 m, θ = 2 × atan(15.36/40) ≈ 42°. If the recorded stream is reduced to 1920 pixels without changing the view, density falls to 125 px/m. Upscaling that recording back to 3840 does not recreate the missing detail.
Translate field of view into a candidate lens
Use the manufacturer’s actual horizontal field of view for the selected aspect ratio and lens setting. Sensor cropping, distortion, focus distance and lens design change the result. Select a candidate within the documented lens range and confirm the installed scene width; do not round the calculation into an unsupported model specification.
Separate spatial detail from motion detail
A scene can satisfy a pixel-density target and still fail because the target moves during exposure. For transverse speed v in m/s, exposure t in seconds and density P in px/m, approximate image smear is b = v × t × P pixels, locally near the measured plane. At v = 2 m/s, t = 1/50 s and P = 250 px/m, smear is about 10 pixels; at 1/250 s it is about 2 pixels. This simplified estimate excludes camera vibration and perspective changes.
Frame rate and exposure time are different. Raising frames per second does not by itself remove blur from each frame. Shorter exposure requires sufficient light or other image-quality trade-offs. Validate a moving target in the exported recording, including night illumination, rather than judging a paused live image of an empty scene.