Audience Safe Distance
Estimate projector distance needed to meet a caller-supplied irradiance limit.
Description
A circular expanding-beam estimate finds a radius large enough to meet a supplied average irradiance limit.
A circular expanding-beam estimate finds a radius large enough to meet a supplied average irradiance limit. Distance uses the tangent of a half-angle divergence.1
Estimate projector distance needed to meet a caller-supplied irradiance limit.
When to use Audience Safe Distance
Use this tool to estimate projector distance needed to meet a caller-supplied irradiance limit.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Audience Safe Distance and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter averagePowerWatts, initialBeamRadiusMeters, halfAngleDivergenceRadians, maximumIrradianceWPerM2 using the field table and calculation rules, then run the tool.
- Read requiredBeamRadiusMeters, minimumDistanceMeters. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| averagePowerWatts | Average projector power (W) | number; minimum: 0 | Required |
| initialBeamRadiusMeters | Initial beam radius (m) | number; minimum: 0 | Required |
| halfAngleDivergenceRadians | Beam half-angle divergence (rad) | number; minimum: 0 | Required |
| maximumIrradianceWPerM2 | Caller maximum irradiance (W/m²) | number; minimum: 0 | Required |
Enter nonnegative power/radius and positive divergence radians/limit. Return radius and minimum distance. Use a physically meaningful divergence with positive tangent.
requiredRadius=sqrt(P/(πlimit)); distance=max(0,(requiredRadius−initialRadius)/tan(divergence)) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| requiredBeamRadiusMeters | Required beam radius (m) | number; minimum: 0 |
| minimumDistanceMeters | Minimum distance (m) | number; minimum: 0 |
{
"input": {
"averagePowerWatts": 3.141592653589793,
"initialBeamRadiusMeters": 0,
"halfAngleDivergenceRadians": 0.7853981633974483,
"maximumIrradianceWPerM2": 1
},
"output": {
"requiredBeamRadiusMeters": 1,
"minimumDistanceMeters": 1.0000000000000002
}
}Limitations and assumptions
The angle is not restricted to a physical interval. No exposure limit is derived, and the result does not certify audience safety or cover pulsed and scan-failure hazards.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Audience-Scan Exposure: Calculate accumulated scan exposure and compare it with a caller-supplied limit. For a complementary task, use Nominal Ocular Hazard Distance: Estimate nominal ocular hazard distance with a simple expanding circular-beam irradiance model.
References
-
Audience Safe Distance — tool.io
Similar or alternative tools
- Audience-Scan Exposure
Calculate accumulated scan exposure and compare it with a caller-supplied limit.
- Nominal Ocular Hazard Distance
Estimate nominal ocular hazard distance with a simple expanding circular-beam irradiance model.