By distinguishing six areas (four on the sphere plus both sides of the screen) according to possible mutual exchanges and direct illumination, the approach leads for any given source to sets of six equations between the unknown illumination levels of these areas. From one of them defining the measurement, correction factors, restricted to the effect of the screen, are deduced for the comparison between a standard and an unknown lamp. Applied to the controversial case of the photometry of a fluorescent lamp, the method shows that its direction is irrelevant provided that both lamps are centered at the same place. The screen should be small. The paper demonstrates serious errors in the photometric method in which the luminance of the back of the screen is measured.
L. Morren, "Method for Assessing the Effect of the Screen in an Integrating Sphere, with an Application to the Photometry of a Tubular Lamp," Appl. Opt. 10, 2621-2628 (1971)