Equal radiant power under visual weighting

An original declared model makes the distinction visible without substituting invented numbers for the photopic luminous efficiency function. Define a triangular weight

w (λ) = max (0, 1 - \frac{∣ λ - 555 nm ∣}{150 nm}), Φ_{v} = (683 lm W^{- 1}) \int w (λ) Φ_{e, λ} (λ) d λ .

This

w

is an illustrative function, not a fit or table of

V

. Three ideal spectral lines, each carrying radiant flux

1 mW

, at

450

,

555

and

650 nm

3/10

,

1

and

11/30

. Their model weighted outputs are respectively

0.2049

,

0.6830

and approximately

0.25043 lm

. These are model calculations, not standard luminous fluxes or measured data. For mixtures of these lines the model outputs add, just as the integral adds independent spectral contributions.

Figure 1.
Equal radiant fluxes give different outputs under a declared spectral weight
. Original triangular weighting model, not CIE data. Each ideal line carries $1 mW$ ; its drawn height represents line power, not a finite spectral density. The lower bars apply the stipulated $683 lm W^{- 1}$ model scale. The model demonstrates the mechanism without supplying calibration data for actual photometry. Details.

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