Uncollected scattering in a radiometric energy balance

Uncollected scattering in a radiometric energy balance is outgoing scattered radiation that falls outside the measured channels. Assigning every missing joule to optical absorption then overestimates the absorbed energy. The radiometric energy balance must count disjoint transmitted, reflected, scattered and absorbed terms for the same interval.

For an original collection model, stipulate $100\mu \mathrm{J}$ incident, $30\mu \mathrm{J}$ transmitted and $20\mu \mathrm{J}$ specularly reflected. A separate scattered-light receiver collects $q=10\mu \mathrm{J}$. If its calibrated capture fraction is $c=0.25$, the scattered energy is $q/c=40\mu \mathrm{J}$, leaving $10\mu \mathrm{J}$ absorbed. If all that is known is $0.20\le c\le 0.50$, scattering can range from $20$ to $50\mu \mathrm{J}$ and absorption from $0$ to $30\mu \mathrm{J}$. One receiver reading cannot determine both the total scattering and its capture fraction.

The fraction $c$ is an energy fraction, not automatically the receiver's fraction of solid angle. Converting geometrical coverage into an energy fraction also needs the scattering distribution.

An integrating sphere provides broad angular collection through repeated diffuse reflection. Actual reflectance/transmittance arrangements depend on port geometry, baffles and whether the specular component is included. The primary guide describes excluding that component through a port and using baffles to prevent direct viewing of the illuminated sample.^[ref] The apparatus therefore needs its own response calibration; calling a receiver integrating does not establish perfect collection.