Eyewear Filter Heating
Temperature rise of a laser eyewear filter or lens at the beam centre, absorbed at the face or through the thickness, and the time until it softens.
Educational only — not compliance-grade
These pages implement the published exposure limits for the cases each one states, but they are educational tools: no laser safety officer has signed them off.
- Do not use these results alone for PPE selection, NHZ / NOHD approval, controlled-area sign-off, enclosure/interlock approval, or formal classification.
- Always verify against ANSI Z136.1, IEC 60825-1, your local procedures, and the responsible laser safety officer / CLSO.
EN 207 tests eyewear against a CW beam for 5 s (50 pulses for pulsed lasers).
An absorbing filter at its design wavelength takes nearly all of it (the rest is reflected); a clear lens a fraction of a percent.
Temperature rise at the beam centre after 5.00 s
730 K
755 °C against T_g = 145 °C: the filter softens
Time to reach T_g (145 °C)
87.9 ms
Largest absorbed power for 5.00 s
313 mW
Absorbed now: 1.90 W
Mean irradiance on the filter, P/(πd²/4)
10.2 W/cm²
Rise against exposure time (log scales); dashed: the rise that takes the material from 25 °C to its glass transition.
Heat conduction from a Gaussian beam into a laterally infinite plate with insulated faces (Carslaw & Jaeger). Absorbed near the front face, the rise is √2 P/(π1.5K w) · arctan(√(8κt)/w) while the heat stays within the thickness (it tends to Lax's P/(√(2π) K w)), plus the heat reflected by the back face; absorbed evenly, it is P/(4πKL) · ln(1 + 8κt/w²). w is the 1/e² radius, κ = K/(ρc).
The rise is proportional to the absorbed power. No cooling by air or the frame is included, so long exposures are overstated. Plastics soften at their glass transition (polycarbonate ≈ 145 °C, PMMA ≈ 105 °C), and dyes can bleach before that; glass can crack from thermal stress at a far smaller rise than its 557 °C transition. These are estimates: eyewear is rated by test (EN 207 LB numbers), and the rating on the frame takes precedence.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Gaussian beam heating a laterally infinite plate with insulated faces, absorbed at the face or evenly in depth; constant properties and no cooling, so long exposures err high. Not modelled: thermal stress, dye bleaching.
- Carslaw, H. S. & Jaeger, J. C. (1959). Conduction of Heat in Solids, 2nd ed. Oxford University Press. Instantaneous point source and the method of images.
- Lax, M. (1977). Temperature rise induced by a laser beam. J. Appl. Phys. 48, 3919–3924. doi:10.1063/1.324265
- EN 207:2017, Personal eye-protection equipment – Filters and eye-protectors against laser radiation (5 s CW test).