## 4 Discussion  
The introduced superpixel method was implemented in the presented optical setup. This technique enables arbitrary complex modulation with one phase-only SLM. Therefore, a high-fidelity mode generation is possible. Hence, the supported fiber modes can be directly excited at the fiber input. A theoretical maximum of the presented technique of \(F_{\mathrm{theoretical}}=0.9943\) was derived. During the experiment, a value of \(F=0.9509\) could be achieved, which corresponds to \(95.6\%\) of \(F_{\mathrm{theoretical}}\). The main part of occurring deviations in the simulation can be explained with the overlaying diffraction grating on the superpixel pattern to reduce the influences of undesired polarizations of light or unmodulated light. This leads to a trade-off between the size of the superpixel and the grating. The selective mode excitation is followed by a challenging alignment procedure, which could be managed by developing specific adjustment methods. A DH-based decomposition technique that is used to analyze the propagated light with respect to containing fiber modes was introduced. Hence, one row of the acquired TM can be obtained in a single-shot and reduces the measurement effort by a factor of 4 in relation to phase-shifting-based acquisition methods or factor \(N\) in relation to correlation filter methods. Presently, the bottle neck regarding the TM acquisition time is the SLM's frame rate (best performance at approximately 20 Hz). Eventually, a TM measurement of an approximately 1 cm long piece of MMF was conducted. At these  
Figure 10: Measured TM of one linear polarization direction of a MMF. During the experiment, constant laboratory conditions were guaranteed.  
propagation distances, mode coupling effects are weakly developed, so that a TM resembles a diagonal matrix so long as laboratory conditions are constantly complied. The major power of the resulting TM, which is shown in Figure 10, is clearly distributed over the diagonal elements. Hence, a proof of the presented principle could be accomplished. However, TM entries off the diagonal have a value significantly greater than background noise and need to be discussed. By using a piece of MMF, which has a length of approximately 1 cm, it was intended to reduce the scattering property of the investigated sample. Yet, the utilized laser with \(\lambda_{0}=~{}532\) nm propagates with approximately 20,000 waves through the waveguide, which is still enough to come upon manufacturing imperfections. In Table 1, the fiber properties with the given tolerances are listed. Both the core diameter and the NA have a tolerance of more than 10%--these are imperfect conditions. In [11], the authors obtained similar results: the simulated phase distribution after propagation through an approximately 10 cm piece of step-index MMF did not fit the experimental results until they superimposed the ideal refractive index profile with Zernike polynomials. As a consequence, the person who works with MMFs should address manufacturing imperfections. The presented results open the door to fast TM acquisition procedures of highly mod MMFs using MDM. In such procedures, the amplitude and phase relations are determined to understand the mode scrambling processes inside the MMF affecting the TM.