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integration of tabulated data in spherical coordinates


My experiment (a goniometer) is aimed at measuring the light reflected
by a surface for several geometric configurations; to describe the 
whole upper hemisphere, in spherical coordinates (radius, latitude,
longitude), the observation angle is in the range 0-90 degrees in
latitude, and 0-360 degrees in longitude. To determine the albedo of the
surface, I need to integrate these reflectance measurements over the

First, I used Sph_Scat to perform a spherical gridding of my data with a
better angular resolution (5 degrees in latitude and longitude, instead
of the 10 degrees of the measurements).

But my problem is that I did not find any IDL routine that integrates
the volume formed by a surface defined by tabulated data (my
measurements) in spherical coordinates (radius, latitude, longitude).

Has anyone solved this problem before, or have any ideas on to do it?