= Isotropic radiance field
{title2=$L_{\rm e}(\boldsymbol\omega)=L_0$}
An \b[isotropic radiance field] has the same <radiance> in every direction at the specified point: $L_{\rm e}(\boldsymbol\omega)=L_0$. Angular isotropy is a local property; it does not by itself assert that $L_0$ is the same at every spatial position. Integrating this constant field gives the orientation-independent one-sided <irradiance> $\pi L_0$. The <spherical irradiance> article derives the corresponding all-direction value using its projected-area convention.<International Lighting Vocabulary by CIE>[Entries17-21-053 and17-21-054 note2, receiving-surface and small-sphere geometries]{ref}
An original counterexample shows why a few equal detector readings do not establish isotropy. Send six ideal narrow beams toward a point along the positive and negative Cartesian axes. Give every beam a normal-incidence irradiance $q=1\,\mathrm{W\,m^{-2}}$. A one-sided planar receiver with unit normal $\mathbf n$ then records
$$
E(\mathbf n)=q\bigl(|n_x|+|n_y|+|n_z|\bigr).
$$
The three axis-aligned receiver orientations all give $q$. However, a normal along $(1,1,1)/\sqrt3$ gives $\sqrt3q\approx1.732\,\mathrm{W\,m^{-2}}$. Three mutually perpendicular measurements therefore agree even though the idealized field is strongly directional. Finite narrow beams approximate this construction.
An <angular isotropy test with planar irradiance measurements> must sample enough orientations to test its stated angular model. A <collimated light> source and a rotating receiver can check angular response before such a test. Detector-area projection and the instrument's own angular sensitivity must be distinguished from variation in the incident field.
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