Radiometric energy balance

A radiometric energy balance accounts for radiant energy crossing the specified measurement boundary during a specified interval. For a passive optic, suppose the relevant transient has finished, no electromagnetic energy remains stored, and no additional energy source is present. Incident radiation is partitioned into all outgoing radiation and energy transferred to matter. Resolving outgoing paths givesThe channels must be disjoint: a scattering term cannot include energy already counted by a reflection or transmission collector. The definition of radiant energy concerns radiation emitted, transferred or received, so the location and collection geometry belong in each term.^[ref]

For an original example, inject $10\mu \mathrm{J}$ and measure $6\mu \mathrm{J}$ in the transmitted path plus $2\mu \mathrm{J}$ in the specular reflection. Calling the missing $2\mu \mathrm{J}$ absorbed is premature. If a separate collector finds $1.5\mu \mathrm{J}$ of diffuse outgoing radiation outside those channels, the inferred absorbed energy is only $0.5\mu \mathrm{J}$. The uncollected scattering in a radiometric energy balance would otherwise be misidentified as optical absorption.

A physical check compares calibrated incident and outgoing energy readouts while controlling apertures, backgrounds and the observation window. The scattered component may need a different collection geometry from the specular beam. Energy absorbed by matter can remain stored or later leave as heat or radiation; a more general control-volume balance must explicitly include storage, other heat transfer and work. It must not count absorbed energy twice by also treating the same material-energy increase as an independent loss.

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.