Diffused laser energy follows the inverse square law, meaning the irradiance (energy intensity) decreases significantly as it moves further away from the point of diffusion.
The simplified formula for irradiance is:
I = P / r²
Where:
I = Irradiance (W/cm²),
P = Laser Power (W),
r = Distance from the point of diffusion or point of surface interaction (cm).
Practical Explanation:
As laser energy travels outward from the point of diffusion, it spreads over an expanding area, becoming progressively less intense with distance.
Energy Diffusion Visualization:
Real-World Considerations:
Surface Interaction: When a laser hits a rough, non-reflective surface, typically up to 80% of the energy may be absorbed or scattered, further reducing the effective energy needing containment.
Assumptions:
Applicability to Typical Diffused Energy Scenarios: While this simplified irradiance equation accurately represents most typical scenarios involving diffused energy after a laser beam interacts with surfaces, it does not apply to situations where the laser remains highly collimated or tightly focused along its entire path. However, as soon as a collimated or focused beam interacts with a surface and begins to diffuse, the equation becomes fully applicable.
Simplified Equation: For clarity and conservative estimation, this calculation simplifies the irradiance equation by omitting factors such as 2π or 4π in the denominator. By excluding these factors, the simplified formula provides a more conservative (higher) estimate of irradiance compared to precise calculations involving spherical or cylindrical beam distributions.
Beam Size Not Considered: The calculation provided does not factor in beam size. Our direct-hit testing conditions (200–300 W/cm² at a 5mm beam size) represent highly concentrated laser energy. The simplified irradiance calculation used here illustrates general diffusion over distance and does not replicate these direct-hit, concentrated test conditions.
Uniform Energy Distribution: This calculation assumes the laser energy spreads evenly as it moves outward.
No Energy Loss Considered: The calculations provided do not factor in the typical energy reduction from surface interactions.
Visualization:
To visualize how laser barriers and curtains effectively contain diffused energy in typical use-cases, please reference the illustration below:
