Focal Length and Effective Focal Length (EFL)

In paraxial optics, effective focal length (EFL) is the distance from a system principal plane to its focal point and describes the optical power of the complete lens. In a multi-element lens, principal planes may lie inside or outside the element group, so EFL is not the barrel length and is not necessarily the distance from the first element to the sensor. For finite object distance, the thin-lens approximation 1/f = 1/u + 1/v is useful; real multi-element systems must follow the manufacturer’s optical convention and data.

For a fixed sensor half-width Y′, a distant object, and an approximately rectilinear projection, the half field angle is θ ≈ arctan(Y′/f), so the full angle is about 2θ. Halving focal length does not exactly double angle because the relationship is an arctangent, but it substantially widens coverage. Shorter focal lengths can also make edge distortion, relative-illumination falloff, and edge-resolution challenges more significant.

For a sensor with a 6.4 mm active horizontal dimension, estimated horizontal FOV is about 77.3° with a 4 mm lens and 43.6° with an 8 mm lens for distant objects. This is a geometric estimate: actual values depend on EFL, distortion, focus distance, and the manufacturer’s FOV convention. Validate with the intended working distance and measured coverage.

Start with object distance and required scene width, then estimate a focal-length range from the active sensor format. Check minimum focus distance, image-circle coverage, distortion, F-number, edge MTF, mechanical length, and edge illumination. For measurement or localization, do not optimize for coverage alone; check pixel density at the edge and residual error after distortion correction.