Laser Brightness (Irradiance) Calculator
How to Use the Calculator:
This calculator helps you estimate the irradiance (often perceived as brightness) of a laser beam at a specific distance from the laser source.
- Laser Power (P): Enter the output power of your laser. You can find this on the laser's specification sheet. Select the correct unit (milliwatts or watts).
- Initial Beam Diameter (D₀): This is the diameter of the laser beam as it exits the laser aperture (usually specified at the 1/e² intensity points). Enter this value in millimeters (mm).
- Full Angle Beam Divergence (θ): This measures how much the beam spreads out with distance. It's typically given in milliradians (mrad) as a full angle. Check your laser's datasheet for this value.
- Distance to Target (z): Enter the distance from the laser aperture to the point where you want to calculate the irradiance, in meters (m).
After entering all values, click the "Calculate Irradiance" button. The results, along with a step-by-step breakdown of the calculation, will appear below the calculator form.
Important Notes:
- This calculator assumes a circular Gaussian beam profile and uses a common linear approximation for beam divergence.
- The "brightness" calculated here is irradiance (power per unit area), a physical quantity. True perceptual brightness also depends on the laser's wavelength and the human eye's sensitivity, which are not considered in this simplified model.
- Always handle lasers with extreme caution and follow all safety guidelines. Never look directly into a laser beam or point it at others.
Theory: Laser Irradiance
Irradiance (E) is defined as the power (P) of electromagnetic radiation incident per unit area (A) on a surface. It's a measure of the concentration of laser light and is typically expressed in units like Watts per square meter (W/m²) or Watts per square centimeter (W/cm²).
For a laser beam, the irradiance decreases as the beam travels away from the source because the beam spreads out due to divergence, increasing its cross-sectional area.
Assumptions:
- The laser beam has a circular profile (often Gaussian, though this model uses a simplified geometric spread).
- The beam divergence is constant and symmetrical.
- The calculations are for the irradiance at the center of the beam, assuming uniform power distribution across the calculated beam spot for simplicity. In reality, Gaussian beams have higher intensity at the center.
Formulas Used:
1. Convert Inputs to Base Units:
Power (P_W) in Watts: P_input / 1000 (if mW) or P_input (if W) Initial Diameter (D0_m) in meters: D0_mm / 1000 Full Divergence Angle (θ_rad) in radians: θ_mrad / 1000 Distance (z_m) in meters (as input)2. Beam Diameter at Distance z (D_z):
The diameter of the beam at a distance 'z' from the laser aperture is calculated using the initial diameter and the full angle beam divergence.
D_z_m = D0_m + (z_m * θ_rad)3. Beam Radius at Distance z (w_z):
The radius is half of the diameter.
w_z_m = D_z_m / 24. Beam Area at Distance z (A_z):
The cross-sectional area of the beam (assuming a circular spot).
A_z_m² = π * (w_z_m)²(where π ≈ 3.14159)
5. Irradiance (E):
The power per unit area.
E_Wm² = P_W / A_z_m²The results are then converted to other common units like W/cm² and mW/cm² for convenience.