The Laser Safety Calculator is an interactive tool that evaluates the nominal safety distance for a laser system. Specific for photonic insecticides optical units designed to track and shoot target insects. (https://www.photonicinsecticides.com) It computes key parameters such as the Rayleigh range and the distance behind the focal point where the energy density on a target (simulated by an extremely small "eye" aperture) falls below a specified safety threshold. This allows users to determine the Nominal Ocular Hazard Distance (NOHD) for a given laser configuration.

The calculator uses several input parameters, adjustable via interactive sliders:

• Max Focal Length: Maximum focal length (from 0.5 m to 10 m).
• Selected Focal Length: A specific focal length value within the above range for which output values are computed.
• Wavelength: Laser wavelength in nanometers.
• M² (Beam Quality): A factor representing the beam quality.
• Beam Radius (w_in): The input beam radius at the lens in millimeters (adjustable up to 50 mm).
• Laser Power: The laser output power in Watts.
• Exposure Time: The duration for which the laser is on (in seconds, minimum 0.001 s).

For worst-case analysis, the eye is simulated as an infinitely small aperture (set to 1×10⁻¹⁰ m) to capture the highest concentration of the Gaussian beam distribution.

The safety calculator performs the following computations. The formulas are embedded as screenshots, so they render nicely:

1. Rayleigh Range Calculation

   The Rayleigh range (denoted as z_R) is calculated with the formula:

   

   where:

   • M² is the beam quality factor.
   • λ is the wavelength (in meters).
   • f is the focal length (in meters).
   • w_in is the input beam radius (in meters).

2. Beam Waist Calculation

   The beam waist at the focal point (denoted as w₀) is given by:

   

3. Beam Radius as a Function of Distance

   The beam radius w(x), at a distance x behind the focal point, is determined by:

   

4. Power Enclosed in a Circular Aperture

   The fraction of beam power captured by a circular aperture (representing the "eye") is computed using:

   

5. Energy Density Calculation

   The energy density E (in J/m²) delivered to the eye over an exposure time t is calculated as:

   

   where:

   • P is the laser power.
   • t is the exposure time.
   • r is the eye radius.

6. Nominal Safety Distance

   The safe distance x behind the focal point is determined by iterating until the energy density falls below 10,000 J/m². The Nominal Safety Distance is then calculated as: Nominal Safety Distance = f + x

This project is written in Python 3.x. You will also need:

• NumPy – for numerical calculations
• Matplotlib – for plotting and interactive sliders

Install them via pip:

pip install numpy matplotlib
python laser_safety_calculator.py

Below are example screenshots of the program in action:

As we can see from the screenshots above, by increasing the initial beam size, we can make the nominal safety zone very small.

As we can see from the screenshots above, when putting the focal point at 10 meter, for example if we want to shoot up from a cart below a tree, up into the canope, where certain insects may be present, or may have put their eggs, the nominal safety zone is still a very workable number. We can make the nominal saferty zone so small because we are free to increase our initial beam size. These optics will be more expensive, but are possible.

The results demonstrate that the nominal safety zone is not much wider for a 1.3 m focal point. Even with an 10 m focal point, the safety distance remains feasible when combined with additional safety sensors. This indicates that the laser system can be made safe across a range of configurations with appropriate sensor integration and safety measures.