A question on Source4 photometrics

For some reason this question has fascinated me so I got one of our Optical Design Engineers involved and this is what he has to say about the matter:

Okay, here is what is going on.  The equation used by the student is correct for a source that radiates uniformly in all directions, such as a bare HPL lamp.  In a 19-deg S4 light fixture, the center (or maximum) candela is 243,000, but decreases as you move off-axis.  You can see this in the candela plot on the data-sheet.

A better approximate equation to use is this one from the High End website:

P=2.1 R^2 (E1 + 0.5 E0).

Using the data from the 19-degree data sheet, at 25 ft, the field diameter is 8 ft, and the center Illuminance is 392 fc (this is E0).  E1 is at the edge of the field, which is 1/10^th the center value, by definition.  This yields P=7900 lumens.

As you can see, this is not very accurate.  At ETC, we measure lumens using a sophisticated photometric camera made by Radiant Imaging.   The camera grabs a 512x512 image of the beam and computes the field lumens using geometric and photometric equations.

I hope this covers it for you :-)

- Mike

Thank you. I agree with you that the general equation the student was using assumes a completely uniform field. I can see that since the light distribution is (in a perfect world)  cosine, with the highest candela values at the centre, then one need to take that into account and integrate values working out from the centre to the 1/10th peak spot.

Again thank you.

Thank you. I agree with you that the general equation the student was using assumes a completely uniform field. I can see that since the light distribution is (in a perfect world)  cosine, with the highest candela values at the centre, then one need to take that into account and integrate values working out from the centre to the 1/10th peak spot.

Again thank you.