Incorrect log function in the pupil diameter computation of "Barten (1999)" contrast sensitivity function.

[xmsguan]

colour/colour/contrast/barten1999.py

Line 131 in 491b6ef

return as_float(5 - 3 * np.tanh(0.4 * np.log(L * X_0 * Y_0 / 40**2)))

The np.log function should be replaced by np.log10
See Beau's work at JOV that traces the log function back to the work by Crawford (1936)

With np.log10, the Barten (flat) curve in the example should evaluate instead to:
[0.021876435681538915, 0.014184813713158736, 0.00952448986054018, 0.006680496306613172, 0.004924641286022344, 0.0038228778810919495, 0.003118856932347983, 0.002662754642667843, 0.002367458781369199, 0.0021814667512135366]

With np.log10, the Barten (flat) and Barten (ramp) curves, evaluated at X0=60, L = [0.001, 0.01, 0.1, 1.0, 10.0, 100.0] are:

Barten (flat):
[0.06299067646573944, 0.021876435681538915, 0.008678146175280605, 0.004311183591087381, 0.0027590747863252907, 0.0021814667512135366]

Barten (ramp):
[0.12598135293147888, 0.04375287136307783, 0.01735629235056121, 0.008622367182174762, 0.0055181495726505814, 0.004362933502427073]

which fit closer to Figure 33 of ITU BT.2246 and also Figure 4 of the following paper:

S. Miller, M. Nezamabadi, S. Daly, "Perceptual Signal Coding for More Efficient Usage of Bit Codes," SMPTE Meeting Presentation, 2012

[KelSolaar]

Thanks a lot @xmsguan!

@nick-shaw and I always wondered why we could not get closer to Miller et al. figure and ITU BT.2246. Admittedly I would not have figured out as it is not specified in Barten's thesis.

Cheers,

Thomas