What Is Etendue and Why It Limits UV Spot Lamp Brightness
There is a ceiling on how much UV power a spot lamp can concentrate onto a small area, and no amount of optical engineering can overcome it. This ceiling exists because of a conserved quantity in optics called etendue — and understanding it resolves a category of questions that confuse engineers new to UV curing system design: why can't a brighter LED be used to achieve a brighter spot? Why does adding lenses not always increase irradiance? And why does a larger light guide not automatically produce more power at the cure surface? What Etendue Is Etendue (pronounced ay-TAHN-doo) is a measure of the spatial extent and angular divergence of a light beam combined into a single quantity: the source area multiplied by the solid angle of the emission cone, which is set by the numerical aperture of the optic. Etendue has a critical property: in a lossless optical system, it can never decrease. Lenses, mirrors, and light guides can redistribute light — trading area for angle — but they cannot reduce total etendue. In real systems with optical losses, etendue can only stay the same or increase. The Consequence for Spot Lamp Design For a UV LED emitting from a given chip area with a given emission angle, the etendue of its output is fixed. The optical system — light guide, coupling lenses, cure head optics — can transform this etendue (large area/small angle in one configuration, small area/large angle in another) but cannot reduce it. This means there is a fundamental limit to how small a spot can be produced at the cure surface while maintaining a given total power: reducing spot size requires increasing beam divergence, which reduces irradiance per unit area as the cone angle steepens. More concretely: if a UV LED has a chip area of 1 mm² and emits into a 90° full-angle cone, attempting to focus this output to a 0.1 mm² spot with a lens would require the exit beam to carry 10 times the original etendue — physically impossible without loss. Why Brighter LEDs Do Not Always Solve the Problem Increasing LED power — a higher-drive-current chip or a larger array — increases total emitted UV power. But if the chip is larger to accommodate that power, its source area increases, and so does its etendue. A 4× higher-power LED with 4× the chip area has 4× the etendue but not 4× the radiance (power per unit area per unit solid angle, also called brightness). Radiance — not total power — is the quantity that determines how bright a spot can be at the cure surface, a distinction covered in more depth in how UV LED spot lamps deliver pinpoint curing accuracy. The relevant figure of merit for spot lamp use is therefore radiance — watts per square millimeter per steradian — not rated total power. Etendue and Light Guide Coupling When a UV LED is coupled to a light guide, the etendue of the LED must fit within the etendue…