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## Various planes of observation 

Both the simulation and the measurement using a spectro-goniometer follow a radial symmetry with the OLED in the centre of rotation, mimicking a spherical surface of observation. However, for many conceivable applications this does not represent a very realistic model. Therefore, as introduced earlier, the analysis of the beam-shaping performance is carried out using a planar, diffusive screen (see Fig. 1b). A subsequent image analysis allows us to obtain the brightness distribution. The results of spectro-goniometer and imaging screen measurements are in direct correlation to each other via an azimuthal transformation, as sketched in Fig. 4a. This case, where the projection source is in the centre of the sphere, is called gnomonic projection. Assuming the OLED to be a point source and the aperture of the spectrometer as d A at the distance R , the corresponding area on the screen is d A $^{′}$, which is at a distance r from the spheres north pole ( θ$_{north pole}$ = 0 $^{◦}$). Because the diameter of d A is much smaller than R , it can be interpreted as the surface element in spherical coordinates and analogue d A ′ in planar coordinates. Simple calculation yields for the irradiance E : 

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