  We use radiances collected from space by the Infrared Atmospheric Sounder
Interferometer (IASI) when looking down at ocean surfaces during the day to
remotely determine the probability distribution of wave slopes. This is
achieved by using about 300 channels between 3.6 and 4.0 $\mu$m and a
physically-based approach which properly takes the contribution of the
reflected solar radiation into account. Based on about 150 million
observations, the same number of wave-slope probabilities are retrieved for
wind speeds up to 15 m/s. We revisit and discuss the methodology proposed by
Cox and Munk (CM) to derive their celebrated wave-slope probability
distribution function (pdf) from photographs of the sun glitter. We propose an
original and robust approach for accurate retrievals of the 7 parameters
appearing in the Gram-Charlier representation of the pdf. Our results for the
mean square slopes are fully compatible with those of CM, and with the more
recent results by Br\'eon and Henriot, but our lower uncertainties enable us to
point out departures from the linear wind-speed dependencies and a slight
overestimation of the upwind MSS described by the linear fit of CM at moderate
wind speed. Our skewness and kurtosis coefficients show clear influences of the
wind speed, with a steady decrease of the former and the alongwind kurtosis
coefficient being maximal at moderate wind speeds, features that CM could not
point out due to the limitations of their measurements. We revisit the
renormalization procedure employed by CM to obtain the complete variances from
truncated pdf and show that it imposes stringent conditions on the kurtosis
coefficients that allow us to determine them accurately, with wind-dependent
values specific to the local sea state.
