The fit is to the form P1*e^(thickness*P2/wavelength**4)



postscript

My interpretation is this:

P1 says something about the absorption. Note that the second sample is 5x thicker than the first, and that 0.9663**5 = 0.84, which is very close to the P1 of the thicker sample. This suggests that the absorption is a uniform 4% per 2 cm.

P2 (or clarity parameter C) is the value that addresses the Rayleigh scattering. The magic value here is 103 and 111 for the two samples, respectively. The fact that the numbers are so close indicates that they describe the same scatterer (which of course they are), and that the sample quality is very good on my scale (200 and up for the old Swedish aerogel, and ~100 is the best I've ever seen).

<< postscript The family of curves om the left are of the function A*exp[-L*C/lambda**4], where L is the sample thickness in cm, C=110.E8 is the clarity of the aerogel, and A is an absorption loss term, taken as 1.5% per cm, uniform in wavelength: A=100-1.5*L. If the absorption is small, this approximation is OK. Note that the lower part of each curve is dominated by the Rayleigh scattering, and only when you reach the top does the absorption start playing a role. Therefore, if you want to measure absorption at 500nm, you should take a transmission spectrum of a thin sample, 10mm or less, and for 400nm, 2mm or less etc. The bottom frame is for a different clarity, and reproduces curves from this paper.

<< ps On the left I reproduce on the same scale the reflection spectra measured be Sean (see reflectivity paper, and an update. This shows that if we use the new Tyvek, we could make use of photons down to about 275nm.