content_image/303552.jpg content_image/303553.jpg content_image/303554.jpg content_image/303555.jpg content_image/303556.jpg content_image/303557.jpg
## 4 Gnomonic Transformation 

As written in the main text, the transition between the spectro-goniometer and the planar screen is described by an azimuthal transformation, precisely a gnomonic projection. Treating the OLED as a point source, the emitted light symmetric with respect to the azimuthal angle ϕ , the detector at a distance R , and its aperture d A being much smaller then R , which than is equal to the surface element in spherical coordinates: 

<img src='content_image/303552.jpg'>

Using the same notation as in the main text, the respective area on the flat screen, can be written as the surface element in polar coordinates d A $^{′}$, which is at a distance r from the sphere’s north pole: 

where the relation between r and R is given as: 

<img src='content_image/303553.jpg'>

<img src='content_image/303554.jpg'>

With this the transformation between the two measurement systems is straightforwardly obtained: 

<img src='content_image/303555.jpg'>

With the definition of the irradiance E as the derivative of the photonflux d Φ with respect to the detecting surface dA , one gets: 

<img src='content_image/303556.jpg'>

As the aperture of the detector is constant, assuming a cylindrical symmetry, rather than a spherical, appears to be ap- propriate. This results in: 

<img src='content_image/303557.jpg'>

In Fig. 10, the measured brightness distribution on the screen (black) is compared to the integrated irradiance, obtained using the spectro-goniometer (non-filled red dots). Especially in the side emission, a strong difference in the shape is obvious. The contrast between 0 $^{◦}$-emission and the maximum is way higher in the case of the goniometer. Furthermore, the profile peaks around 60 ◦ compared to 40 ◦ on the screen. When multiplying the goniometer profile with cos $^{2}$( θ ) , those data resemble the black line very well. Both the contrast and the maximum angle is reproduced. In forward emission direction, the drop of intensity coincides, as well. Actually, it is surprising that the cosine of the angle to the power of two gives the best results, as a power between two and three was expected to model the transformation most realistically. Obviously, some 

