F-Number (f/N): Lens Aperture Ratio for Exposure Control
The f-number, written f/N, describes the ratio between a lens’s focal length and the diameter of its entrance pupil. Because exposure depends on the amount of light reaching the sensor, f-number provides a convenient, dimensionless way to compare lenses of different focal lengths. Dropping the f-number by one full stop (for example, from f/4 to f/2.8) doubles the transmitted light, while halving it (from f/4 to f/2) quadruples the throughput. Increasing f-number reduces exposure and increases depth of field. Mastering the f-number scale is therefore central to photography, cinematography, microscopy, and remote sensing.
This explainer reviews the mathematical basis of the f-number, charts its historical development from Waterhouse stops to modern electronically controlled apertures, and outlines measurement practices that keep exposure settings consistent across devices. Links to the luminance article and the deep sky exposure planner support practical workflows spanning studio photography to astrophotography.
Definition and Mathematical Relationships
From aperture diameter to exposure
The f-number N equals f / D, where f is focal length and D is the entrance pupil diameter. Exposure at the sensor is proportional to (1 / N²) for a given shutter speed and scene luminance. Photographers use a standard f-number sequence—f/1.0, f/1.4, f/2, f/2.8, f/4, and so on—where each step represents a factor of √2 in aperture diameter and a doubling or halving of light. When converting between systems, ensure focal lengths are specified in millimetres and that teleconverters or speed boosters are accounted for, as they change the effective f-number.
Depth of field and diffraction considerations
Depth of field depends on f-number, subject distance, and acceptable circle of confusion. Stopping down (larger N) increases depth of field, beneficial for landscape photography or microscopy. However, diffraction causes resolution loss as f-number increases beyond the sensor’s pixel pitch-limited optimum. Balancing depth of field with diffraction requires understanding sensor characteristics and evaluating modulation transfer functions. The spectral radiance guide highlights how wavelength affects diffraction thresholds.
Historical Development of the F-Number Scale
From Waterhouse stops to modern apertures
Early cameras used interchangeable plates with circular openings—Waterhouse stops—to control exposure. By the late nineteenth century, lens makers adopted the f-number to standardise aperture markings across focal lengths. The Royal Photographic Society promoted the system to avoid confusion caused by proprietary scales. In the twentieth century, iris diaphragms with overlapping blades allowed continuous aperture control, while modern lenses pair these mechanisms with electromagnetic actuators for precise, repeatable f-number settings.
Cinema and exposure metering evolution
Motion-picture production introduced T-stops, which adjust f-number markings for actual light transmission losses. Exposure meters, both handheld and in-camera, calibrate to the f-number scale, measuring scene luminance in cd·m⁻² or foot-lamberts and recommending f-number and shutter settings. Digital cameras embed exposure metadata (EXIF) that records f-number, aiding post-production workflows and scientific reproducibility. When reporting results, specify whether values reflect f-number or T-stop measurements to maintain clarity.
Measurement Techniques and Calibration
Verifying aperture accuracy
Manufacturers verify f-number accuracy using integrating spheres, collimators, and photometric benches that measure throughput. Advanced users can validate lenses by comparing exposure changes against a calibrated light meter or by imaging a uniform light source and analysing histogram shifts. Temperature, mechanical tolerances, and aperture blade hysteresis can introduce variability, so document testing conditions and repeat measurements across focus settings.
Integrating f-number in exposure workflows
Exposure planning tools combine f-number with shutter speed, ISO sensitivity, and scene luminance. Astrophotographers consult the deep sky exposure planner to ensure f-number and exposure length deliver sufficient signal without saturating stars. Solar observers use the eclipse visibility calculator to coordinate safe aperture settings with certified filters and short exposures.
Applications Across Imaging Disciplines
Photography, cinematography, and microscopy
Still photographers adjust f-number to shape creative outcomes: wide apertures isolate subjects with shallow depth of field, while narrow apertures keep landscapes sharp from foreground to infinity. Cinematographers coordinate f-number across multi-camera shoots to maintain consistent exposure and bokeh characteristics, often favouring T-stops for absolute accuracy. Microscopists match objective numerical aperture to f-number equivalents, balancing resolution, contrast, and illumination intensity.
Remote sensing and astrophotography
Earth observation satellites and telescopes operate at fixed f-numbers determined by optical design. Low f-numbers support wide-field surveys like Pan-STARRS, while high f-numbers enhance spectral resolution for instruments such as spectrographs. Integrating f-number with magnitude limits, as discussed in the apparent magnitude article, ensures exposure strategies align with scientific objectives.
Importance of Consistent Reporting
Metadata and documentation
When publishing imagery or datasets, include f-number, focal length, sensor size, exposure time, ISO, and filter information. Provide calibration references for light meters or photometric standards used. For laboratory imaging, document illumination spectra, polarisation state, and measurement geometry to enable replication. The candela guide offers notation conventions that harmonise lighting and imaging reports.
Communicating exposure decisions
Translating f-number into intuitive exposure guidance helps teams coordinate fieldwork. Use exposure value (EV) charts, share target histograms, and connect f-number to practical scenarios—such as sunrise landscape shooting or indoor event coverage. Outreach materials can reference the light pollution calculator to demonstrate how sky brightness affects astrophotography settings.