There is some confusion because in photography, two different things are called "exposure".Please elaborate.
An exposure, as I understand it, is a collection of photons,
What you describe is photometric exposure, and it's just one variable. What's even worse, it's different for different parts of the sensor, depending on which scene you are shooting.
What I describe is two-variable camera exposure, the amount of time (shutter speed) and solid angle (aperture) you want your sensor to expose to photons from. It can be combined into a single exposure value (EV), which can be used to convert scene luminance into photometric exposure of the sensor.
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