F-Number and Light Throughput

Key Takeaways

F/# = f/D, where f is effective focal length and D is typically the entrance-pupil diameter; a smaller F-number is generally a faster system.
Under ideal conditions, image-plane irradiance scales approximately with 1/(F/#)²; each full stop changes exposure by about a factor of two.
A faster lens gathers more light but often raises design, manufacturing, alignment, and aberration-control difficulty.

Definition and equation

The F-number (F/#) is commonly written N = f/D, where f is effective focal length and D is the entrance-pupil diameter as viewed from object space. In systems with vignetting, internal stops, or complex pupils, geometric F/# can differ from T-stop, which accounts for transmission. Sensor output also depends on lens transmission, spectrum, microlens efficiency, exposure time, and illumination.

Throughput from F1.4 to F16

Ideal on-axis irradiance is approximately proportional to 1/N². The geometric ratio between F1.4 and F16 is therefore about (16/1.4)² ≈ 131. In photographic exposure terms that is about seven stops, or roughly 128×. Real lenses add transmission losses, vignetting, stop-position, and field effects, so this ratio is not a promise of actual sensor output.

Fast lenses, manufacturing, and tilt

A low F-number produces a wider ray cone. Correcting spherical aberration, coma, astigmatism, chromatic aberration, and field curvature across that cone is difficult; designs often need larger elements, more complex construction, tighter tolerances, and higher cost. Tilt at the lens or image plane can put one side in focus and the other out. Fast systems often have tighter focus tolerances because depth of focus is smaller, but allowable tilt depends on focal length, pixel size, working distance, aberrations, and focus position—not F/# alone.

System trade-offs

For low light, a faster aperture may help, but also check depth of field, edge performance, flare, and sensor chief-ray-angle compatibility. Stopping down can improve some aberrations and increase depth of field, while an excessively small aperture reduces high-frequency response through diffraction. Choose the operating aperture against system exposure, DOF, MTF, and tolerance requirements.

Related Products

Lens Selection & Engineering Support Align aperture, sensor, and illumination requirements. MIPI Camera Module A low-latency camera-module path for embedded systems. USB Camera Module A convenient option for rapid evaluation and integration.

Application Scenarios

Robot Vision & Perception Balance aperture and image quality for motion and lighting. Healthcare & Assisted Living Evaluate low-light imaging and depth-of-field needs. Smart Home & Spatial Awareness Balance indoor coverage and low-light imaging.