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Integrating Sphere Calculator

Calculate sphere multiplier, throughput, detector signal, and temporal response for integrating sphere designs.

An integrating sphere spatially homogenizes light through multiple Lambertian reflections, producing a uniform radiance at any port regardless of the input beam's angle or spatial profile. The sphere multiplier M = ρ / (1 − ρ(1 − f)) quantifies this enhancement, where ρ is wall reflectance and f is the fractional port area — the two parameters that dominate sphere performance. This calculator offers two modes: Sphere Response computes surface area, port fraction, sphere multiplier, wall irradiance, sphere radiance, and uniformity error for a given sphere diameter, coating (Spectralon, BaSO₄, Infragold, or custom), and port configuration; Detector Signal adds source flux, detector port index, and responsivity to return throughput efficiency, photocurrent, and temporal response. Use this tool when designing a sphere for power measurement, source calibration, or reflectance standards.

Sphere Parameters
Sphere Geometry
Surface area Aₛ
70685.8mm²
Surface area Aₛ
706.9cm²
Total port area
1013.4mm²
Port fraction f
0.0143
Port fraction f
1.434%
Sphere Performance
Sphere multiplier M
28.781
Wall irradiance E (1 mW)
0.4072W/m²
Sphere radiance L (1 mW)
0.1296W·m⁻²·sr⁻¹
Uniformity error δ
42.105%
Abridged Optics — v1.0Calculations assume uniform Lambertian wall coating and identical circular ports. Real spheres may deviate due to baffles, self-absorption, and non-ideal coating.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.