Fisheye camera method for spatial non-uniformity corrections in luminous flux measurements with integrating spheres

This paper presents a fisheye camera method for determining spatial non-uniformity corrections in luminous flux measurements with integrating spheres. Using a fisheye camera installed into a port of an integrating sphere, the relative angular intensity distribution of the lamp under test is determined. This angular distribution is used for calculating the spatial non-uniformity correction for the lamp when combined with the spatial responsivity data of the sphere. The method was validated by comparing it to a traditional goniophotometric approach when determining spatial correction factors for 13 LED lamps with different angular spreads. The deviations between the spatial correction factors obtained using the two methods ranged from $-0.15$ % to 0.15%. The mean magnitude of the deviations was 0.06%. For a typical LED lamp, the expanded uncertainty ($k = 2$ ) for the spatial non-uniformity correction factor was evaluated to be 0.28%. The fisheye camera method removes the need for goniophotometric measurements in determining spatial non-uniformity corrections, thus resulting in considerable system simplification. Generally, no permanent modifications to existing integrating spheres are required.