Foot-Lambert (fL): Screen Luminance Unit for Displays and Cinema
The foot-lambert (fL) is a legacy luminance unit widely used in cinema and display engineering to specify how bright a screen appears to a viewer. This guide defines the unit, traces its historical adoption by film and projection standards, and shows how to convert foot-lambert targets into the SI luminance unit of candela per square metre. Pair it with the lambert explainer and the cd/m² reference to keep photometric documentation coherent across eras.
Definition and SI Conversion
The foot-lambert expresses luminance for a perfectly diffusing (Lambertian) surface that emits or reflects one lumen per square foot into one steradian. It can be written as:
1 fL = 1 lm·ft⁻²·sr⁻¹ = (1/π) cd·ft⁻². Converting to SI luminance uses the exact foot-to-metre relationship. Because 1 ft = 0.3048 m, the conversion factor is 1 fL ≈ 3.426 26 cd/m². Conversely, 1 cd/m² equals about 0.291 9 fL. When specifying targets, always provide both units and document any rounding to avoid confusion in procurement or calibration reports.
Historical Development
Cinema and broadcast adoption
The foot-lambert gained prominence during the early twentieth century as motion-picture projection matured. The Society of Motion Picture Engineers (now SMPTE) specified screen luminance targets in foot-lamberts to standardise theatre experiences across venues. Classic cinema targets hovered around 16 fL on-axis for white fields, with tolerance bands to account for lamp ageing, screen gain, and projection geometry. Television and broadcast engineering later inherited the same unit for studio monitors, especially in North America.
Transition toward SI luminance
As SI photometry became the global norm, manufacturers began listing display brightness in candela per square metre. Yet foot-lambert references persist in archival standards, cinema handbooks, and maintenance manuals. Understanding the conversion ensures continuity when upgrading projectors, comparing legacy audits, or translating film preservation guidelines into modern laboratory documentation.
Key Concepts and Measurement Practice
Lambertian assumptions
Foot-lambert values assume a Lambertian diffuser, meaning luminance is constant with viewing angle. Real screens deviate through gain, hot-spotting, or directional coatings. When measuring fL, document screen gain, observation angle, and projector alignment so that comparisons remain meaningful. For high-gain screens, report both peak luminance and average field luminance to avoid overstating perceived brightness.
Instrument calibration
Luminance meters use photopic filters and cosine-corrected optics to approximate human vision. Calibration against traceable cd/m² standards is essential; some instruments allow the display of foot-lamberts internally, but the calibration chain is still rooted in SI. Recording calibration certificates and the conversion factor used keeps audits defensible when reports cross international boundaries.
Applications in Practice
Cinema projection. Theatre technicians measure on-screen luminance in foot-lamberts to verify compliance with SMPTE recommendations. They adjust lamp power, lens transmission, and screen reflectance to restore target fL after lamp ageing or screen cleaning. Display engineering. Manufacturers comparing modern HDR panels with legacy studio monitors still translate peak cd/m² values into fL for archival compatibility. Simulation and VR. Visual system designers express luminance budgets in fL when matching virtual environments to film-based references.
Why the Foot-Lambert Still Matters
The foot-lambert survives because cinema, broadcast, and archival display standards were built around it. Engineers and conservators still encounter fL targets when retrofitting theatres, validating film scans, or maintaining heritage equipment. Mastering the unit enables consistent communication between SI-centric photometry teams and legacy documentation, ensuring that luminance-critical work remains accurate, traceable, and comparable over time.