The proper way of calculating lux / cd / candlepower

[EasyB]

I will say again that the phenomenon that Enderman is explaining makes sense, but actual measurements disagree with the proposed model.

@EasyB

I have to say that this possible effect has caused me some confusion regarding my understanding of throw and how to predict it, so I did some measurements to see what is actually happening.

My test light was a UF-1504, with 62mm diameter lens and XPL HI V2 1A. I put in a 8x7135 driver to keep the output more constant with time. I measured the lux at three different distances measured from the lens.

dlux__cd
6.05m7230_264.6Kcd
8.34m3840_267.1Kcd
10.29m2530__267.9Kcd

These measurements are consistent with measuring the distance right from the lens and not at some point behind the lens.

Plugging the 10.29m measurement (the beam size at this distance was 36cm) into the calculator you linked (after converting units), results in:
divergence distance behind aperture: 2.14m
candlepower: 390.9Kcd

The calculator results are not consistent with my measurements and how they vary with distance. There are certainly some things in your explanation of the effect that make sense, but actual measurements tell a different story.

A different effect could have caused your conflicting results when you measured the lux at 1m and 2m. At small distances like 1m, the lens might not be filled with the image of the LED, from the point of view of the lux meter. Moving farther back to where the lens is filled would then result in a larger throw number.

Below is a graphical representation of the data and the two models: measuring the distance from the lens and measuring the distance from 2.14m behind the lens, as the calculator predicted.

This plot shows the measured lux vs distance. The blue diamonds are the data points in the quote above that I measured. I estimate the uncertainty at about 100lux. The red line is the lux according to the inverse square law, measured from the lens. The equation is lux=265000cd/(d^2). The blue line is the predicted lux when the distance is measured from 2.14m behind the lens, as the calculator predicts for the measurement. The equation is lux=390900cd/((d+2.14m)^2). The two lines cross at 10.29m because that is the measurement that was input to the calculator.

The two models predict different lux numbers and the measurements are consistent with measuring distance from the lens and not from a point behind the lens.