A new method to measure the effect of the backscatter into the beam monitor chambers in linear accelerators is introduced from first principles. The technique, applicable to high-energy photon beams, is similar to the well-known telescopic method although here the heavy blocks are replaced by a very small, centred block on the shadow tray, thus the name 'ecliptic method'. This effect, caused mainly by backscattering from the secondary collimators, is known to be an output factor constituent and must be accounted for when detailed calculations involving the machine's head are required. Since its magnitude is generally small, experimental errors might obscure the behaviour of the phenomenon. Consequently, the procedure introduced goes along with an uncertainty assessment. Our theory was confirmed via measurements in cobalt-60 beams, where the studied effect does not contribute to the output factor. Measurements were also performed on our Saturne 41 linear accelerator and the results were qualitatively similar to those described elsewhere. The collimation systems were studied separately by varying one jaw setting while keeping the other at its maximum value. In the light of these results, we deduced an algorithm that can correlate the former data with the effect of backscattering to the beam monitor chambers for any rectangular field within 0.5%, which is of the order of the experimental uncertainty (0.6%). As we show, the experimental procedure is safe, simple, not invasive for the linac and requires only basic dosimetry equipment.