What is "photometric exposure," and how is it related to what is commonly called "exposure" and "exposure values"?
I have also seen the term "radiometric exposure" used to describe a similar property.
Radiometric exposure measures how much energy reaches a unit of surface in an unit of time, with no regard to wavelengths that carry the energy.
For photometric exposure, different weights are assigned to different wavelengths in order to mimic sensitivity of human eye to different wavelengths; for that purpose, a luminosity function has been agreed upon based on studies on visual photoreception. According to the function, energy of 555 nm (green) waves is assigned the highest weight and wavelengths outside visual spectrum are excluded by using weight of 0.
Unless based on the "human eye" attached to photographer, any exposure metering is based on calculations based on metered radiometric exposure. The metering device can then use a luminosity function to decide what the applicable exposure would be.
The luminosity function applied can be either based on the generic one (giving photometric exposure), or a custom one - either simplified (like measuring only green), or based on data about specific imaging media (an infrared or X-ray image would need to apply different weights to wavelengths for optimal metering). Since the function is more or less known in advance, radiometric exposure metering does not have to be sensitive to all wavelengths, just those that have some weight assigned in luminosity function.
From this Wikipedia page, my understanding is that the photometric exposure is the total amount of light (illumination) integrated over a period of time, as sensed by the imaging medium.
The radiometric exposure is similar, but expressed in terms of energy instead. This is merely the time integral of the power-per-area (energy flux) of the light sensed by the sensor.
To my understanding, the photometric exposure is directly proportional to the photographic EV (exposure value) integrated over time to produce the image "exposure" as we use this term. Ev signifies the brightness of an object, and over Tv period generates an image on the sensor. The illuminance (Ev in the article) is just the same, and integrating it over time gives the photometric exposure.