Mistakes I perceived:
the emitter is always at normal incidence to the detector's view angle
no it isn't
radiance measured at the emitter is the same as radiance measured at the detector
this doesn't mean the radiance is the same when measured from a DIFFERENT ANGLE
it means the radiance doesn't change over DISTANCE
also it means radiance is the same for both combinations of terms:
- solid angle of emitter and projected area of detector
- solid angle of detector and projected area of emitter
The key point is that the cosine term in the definition of radiance does not use the detector's surface normal but the emitter's surface normal
it can use either, see my point above
apparent size of the source is quite clearly constant due to the nature of your setup
no it isn't, the apparent size of the source is SMALLER for the angled detector
you calculated radiance using the following terms:
- power is constant, since the emitter is obviously still emitting the same amount of light in both cases
- area is constant, as the emitter's surface area hasn't changed
- solid angle is constant, because the emitter is held facing the detector at normal incidence in both cases
but you missed PROJECTED AREA (or the cosine term)
Therefore, measured radiance is the same in both cases
not once you factor in the projected area term you missed
but for all practical purposes ™ it’s a point and a direction
no it isn't
you can't just ignore the differential projected area and solid angles ... otherwise what's the point in defining radiance at all?
you CAN simplify like this inside a video game using the simplified Lambertian dot product lighting we use ... but not in Radiometry and definitely not in the example I gave!
that is actually the WHOLE POINT of my post, to clarify why this is the case!
Assuming the receiver is left and the emitter right in your images
Irradiance at every point of the receiver is smaller for the angled configuration
but the emitter is on the left
so irradiance at the detector is the same
as the flux is the same and the detector area is the same
Think about what happens when you aim the emitter perpendicular to the receiver, the projected area goes to zero and no light moves towards the receiver so radiance is zero, as expected
your logic is flawed
when the emitter is perpendicular there is nothing to discuss, nothing to measure ...
it is the same as if I removed the emitter completely!
you are making the assumption that because the radiance is zero when perpendicular
that it must change from 1 to 0 as the viewing angle increases
this makes no sense
if instead you considered what happened at a viewing angle of 89.99999999 degrees - then you would have seen my point!
The orientation of the emitter doesn't matter since it's defined to emit equally in all directions
it doesn't matter when considering intensity or power ... it DOES matter when measuring radiance
as the differential projected area is LESS
Edited by skytiger, 06 May 2013 - 05:33 PM.