Absolute Photopic Luminance: Bridging Radiometry and Human Perception

Physical sensors measure radiant energy in watts. Human eyes, however, possess retinal cone cells with highly wavelength-dependent spectral responsivities.

A laser emitting 1 watt of radiant power at 555 nm appears blindingly bright to a human observer, while a 1 watt laser at 400 nm (violet) or 720 nm (deep red) appears dim, and a 1 watt laser at 800 nm (infrared) is completely invisible.

The Photopic Luminous Efficiency Function V(\lambda)

In 1924, the Commission Internationale de l'Éclairage (CIE) standardized the photopic luminous efficiency function V(\lambda). It peaks at exactly 555 nm with a conversion factor of 683 lumens per watt:

\Phi_v = 683 \int_{380}^{780} \Phi_e(\lambda) V(\lambda) d\lambda

Where:

• \Phi_e(\lambda) is spectral radiant flux in W/nm
• V(\lambda) is the dimensionless eye sensitivity curve
• \Phi_v is total luminous flux in lumens

export function computeLuminousFlux(spd: Float32Array): number {
  let totalLumens = 0;
  const K_M = 683.002; // lm/W at 555nm

  for (let i = 0; i < 81; i++) {
    const wavelength = 380 + i * 5;
    const vLambda = getVLambda(wavelength);
    const watts = spd[i] * 5; // bin width = 5nm
    totalLumens += watts * vLambda * K_M;
  }

  return totalLumens;
}