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From our equation in the previous slide, the response is the average radiance multiplied by the throughput. The average throughput does not change because the solid angle subtended by the aperture and the area of the sensor are the same. Since the radiance is constant on the wall, the response of the sensor will be the same.

Also noted was that if the wall was a point light source, then the radiance would not be constant. Instead, it would fall off proportional to 1/R^2.


Another way to think about this is that the area of the wall is increasing, but the solid angle subtended by the sensor coming from the wall is decreasing by the same ratio. Also to add on to the part about point light sources, if the distance become so large that the area on the wall is no longer increasing (i.e. the area exceeds the bounds of the wall) then the response of the sensor can change.


Since the wall has constant radiance, the answer differs if it's not constant or it becomes a spotlight source.


The sensor essentially accumulates all the light and averages it. When we move the sensor back, the area on the wall increases. This is a bigger source of light, sending to a smaller solid angle.