To use the moon as the calibration source, we need to know the brightness temperature in the center of moon as a function of its phase. Mangum(1992) worked out such a function on the basis of a model developed by Krotikov, Troitskii(1964), and Linsky(1966,1973). Which assume that the lunar surface is smooth and uniform with temperature- and depth-independent thermal properties. It has been proved that the main uncertainty, resulting from the assumption, will not affect the brightness temperature too much.
Krotikov, V.D.,and Troitskii, V.S. 1964, Soviet Phys
Linsky, J.L. 1966, Icarus, 5, 606
Linsky, J.L. 1973, Apjs, 25, 163
Mangum, J. G. 1993, publication of the Astronomical Society of the Pacific 105,117
Polarization of Moon thermal emission
There are two different cases of reflection polarization. In one case the electric vector in is parallel to the plane of incidence, called the p polarization. In the other case the electric vector is perpendicular to the plane of incidence, called the s polarization.
If we define and , Fresnel's formulas are:
andwhere n is indices of refraction.
Then ep=1- rp and es=1- rs are the fractions which will be absorbed. Suppose that all the absorbed energy will be emitted later, the emissivity will be equal to absorbability. So, the polarization = (es^2-ep^2)/(es^2+ep^2).
Asumeing that Moon surface is smooth and given a value of n (or dielectric constsnt ), we can predict the polarization of thermal emission:
But this can't be observed by SPARO, since SPARO has a beam size~5'. The following graph shows the averaged polarization over the beam:
Comparing with the polarization observed by SPARO on 4/25/2000, it seems showing that Moon surface has a dielectric constant ~ 1.3
Here is a comparison of dielectric constants at different wave length, note that the blue ones include some compensation for roughness:
From i to o are the "reflection" measurements :
i, j, l, and m : Evans (1963,64)
k : Davies (1966)
n : Rea (1964)
o : Tyler (1968)
J. W. M. Baars, 1965,AJ,70Q,132B
David D. Cudaback,1969,AJ,538
F. D. Drake, 1969,AJ,539
J. L. Margot, D. B. Cambell,1996, LPS,XXVII and XXVIII
P. E. Clegg, B. S. Carter, 1970, Mon. Not. R. astr. Soc. 148. 261
Richard Barvainis, Dan P. Clemens,1988,AJ,95,510
P. H. Moffal, 1972, Mon. Not. R. astr. Soc. 161. 139