# How to estimate the necessary sample volume ?

## Cold Surface Spectroscopy Facility

The necessary sample volume to fullfill the photometric constraints mainly depends on several parameters:

• grain size (diameter) , Dg
• porosity, P
• reflectance level at the most transparent wavelength, Rm
• maximum angle of emergence angle of observation, e_max
• range of azimut of the observations

We use the following rules of thumb (validated on several typical samples) to determine the minimum depth, d, and the minimum diameter, D, of the sample (and thus the minimum volume V) in order to guarant that the measurements fullfil the photometric constraints (@ > 99.9%) of an infinitely deep and extended surface (i.e. bottom or side effects < 0.1%) over the whole measured wavelength range and the complete set of illumination/viewing geometries.

Thickness mini (d):

• for Rm > 0.7:              d > 100 * Dg             (i.e. ~ 100 grains deep)
• for 0.3 < Rm < 0.7:     d > 50 * Dg               (i.e. ~ 50 grains deep)
• for Rm < 0.3:              d > 20 * Dg               (i.e. ~ 20 grains deep)

Diameter mini (D) (in cm):

• D >  2 / cos(e_max) + d

Volume mini (V) (in cm3, for a cylindrical sample):

• V >  d * pi/4 * (2 / cos(e_max) + d)^2

if the measurements are performed only in the principal plane (azimut 0° and 180°) then the sample may be rectangular with sizes L x l (in cm) :

• L > 2 / cos(e_max) + d
• l >  2 + d

Volume mini (V) (in cm3, for a rectangular sample):

• V >  d * (2 / cos(e_max) + d) * (2 + d)

Notes:

• the Visible albedo A can be used as a first proxy, if the reflectance in the Near-IR is unknown, but frequently dark materials are bright in the NIR !
• The calculation is for a powder with typical porosity of 30-50%. If porosity is higher, increase volume accordingly