= Etendue bench measurement
A proposed <optical bench> test uses a steady illuminated diffuse patch, a relay made from two <optical lens> elements, interchangeable centred circular stops, and a calibrated <optical power meter> large enough to collect the whole output bundle. Start with small cone <angles> so an ordinary relay approximates the <area-angle tradeoff>. Measure the patch's image <diameter> and the accepted angular extent at both conjugate planes; the <transverse magnification> gives the spatial scale, but does not by itself measure <etendue>.
Map the local <radiance> with a baffled <photodiode> on translation and rotation stages, using two small aligned holes to select a narrow known <solid angle>. Keep the sampled position fixed while scanning direction, calibrate the sampling footprint and angular response, and repeat at several positions. Numerically integrate $n^2\cos\theta\,dA\,d\Omega$ over the occupied samples, and integrate $(L/n^2)dG$ to predict the collected <radiant flux>. This checks the filled-cone assumption instead of inferring it from two outer dimensions.
Compare the relay without a stop and with a stop of $0.6$ times the illuminated <diameter> in the same plane. The uniform-bundle prediction is a <radiant flux> ratio of $0.36$, with unchanged local <radiance> in the surviving samples. Cover the input for a dark reading, monitor source drift, repeat the open-stop reading, check detector linearity with calibrated <optical attenuators>, and enlarge the collecting detector or scan it to check for missed <light rays>. Lens losses, angular response, illumination gradients, alignment errors and <diffraction> can spoil the ideal prediction; their effects must be measured separately. This is a procedure to try, with predicted readouts, not purported experimental data.
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