Stockman and Sharpe luminosity function

Sharpe, Stockman, Jagla & Jägle (2005) 2-deg V*(l) luminous efficiency function

Units	0.1 nm steps	1 nm steps	5 nm steps
Quantal (log)
Energy (log)
Energy (linear)

Data key

Columns

Quantal

Logarithmic

1. Wavelength (nm)
2. log 2-deg photopic luminous efficiency, V₂*(l)

Energy

Logarithmic

1. Wavelength (nm)
2. log 2-deg photopic luminous efficiency, V_2e*(l)

Linear

1. Wavelength (nm)
2. 2-deg photopic luminous efficiency, V_2e*(l)

Notes

    Based on the linear combination of the Stockman and Sharpe (2000) M- and L-cone spectral sensitivities that best fits experimentally-determined 25-Hz, 2° diameter, heterochromatic (minimum) flicker photometric data obtained from 40 observers (35 males, 5 females) of known genotype, 22 with the serine variant L(ser180), 16 with the alanine L(ala180) variant and 2 with both variants of the L-cone photopigment. The matches, from 425 to 675 nm in 5-nm steps, were made on a 3 log troland xenon white (correlated color temperature of 5586 K, but tritanopically metameric with CIE D₆₅ standard daylight for the Stockman & Sharpe (2000) L- and M-cone fundamentals) adapting field of 16° angular subtense, relative to a 560 nm standard. Both the reference standard and test lights were kept near flicker threshold so that, in the region of the targets, the total retinal illuminance averaged 3.19 log trolands. The new function is extrapolated to wavelengths shorter than 425 nm and longer than 675 nm using the Stockman & Sharpe (2000) cone fundamentals. The quantal luminous efficiency function is:

  or

relative to the quantal cone fundamentals and having unity peak sensitivities.  Functions are tabulated at 0.1, 1 or 5 nm steps.  The 0.1 and 1 nm functions were obtained by the interpolation of the 5 nm functions using a cubic spline.  Functions are normalized to peak at unity at the nearest 0.1 nm step. The l_max for quantal efficiencies is 545.6 nm.

The same function, but energy based, and given in terms of the energy based cone fundamentals and renormalized to unity peak sensitivities:

  or

The different weight simply reflects the unity renormalization required after the cone fundamentals are converted from quanta to energy units. The l_max for energy-based efficiencies is 555.5 nm.

NB This is a update of the preliminary estimate of V₂*(l), given previously in Stockman & Sharpe (2000) and previously tabulated here. The preliminary estimate, which had an L-cone weight of 1.50,  was based on the first 22 of the 40 observers used to obtain the final estimate.

References

Stockman, A., & Sharpe, L. T. (2000). Spectral sensitivities of the middle- and long-wavelength sensitive cones derived from measurements in observers of known genotype. Vision Research, 40, 1711-1737.

Sharpe, L. T., Stockman, A., Jagla, W. & Jägle, H.(2005). A luminous efficiency function, V*(l), for daylight adaptation. Journal of Vision, 5, 948-968.

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