## 2 Procedure of Operation  
TM measurements are commonly performed using an SLM that displays different masks to imprint a desired field distribution on an incident Gaussian beam [10; 11; 12; 13; 14]. For a few-mode fiber, inaccuracies in mode generation are still manageable, since deviations are not likely to overlap with any other mode, because there are only a few other modes in the fiber. For this reason, the power that does not overlap with the desired mode simply leads to a loss rather than an unwanted mode excitation [7]. MMFs are significantly more sensitive to undesired mode excitation. As more modes are in the MMF's mode domain, it is more probable that power that does not overlap with the desired mode is overlapping with another. For this reason, it is necessary to ensure an accurate generation of the fiber modes with the SLM and accurately control various modes in the MMF. In Section 2.1,an algorithm to create phase masks is explained, that allows the generation of arbitrary light fields combining a sequence of SLM pixels, which form a superpixel.  
The accuracy of mode excitation is accompanied with the need of an appropriate alignment of the optical setup, which is shown in Figure 1. Hence, a step-by-step instruction is presented in Section 2.2, which shows how an accurate alignment can be achieved.  
The light, which exits the MMF, has to be investigated with regard to containing fiber modes. To analyze the received light, one needs access to the complex light field distribution consisting of amplitude and phase information. DH is one promising approach to measure these light properties in a single-shot. In Section 2.3, an algorithm that decomposes the holographically measured light field into the fiber's mode domain is introduced.  
Figure 1: Experimental scheme. The laser beam is coupled to a single mode fiber (SMF), collimated by a collimation package (CP) and widened by a beam expander (BE). A polarizing beam splitter (PBS) and a half-wave plate (HWP) filter the laser beam at a linear polarization, matching the SLM required modulation polarization. Beamsplitter 1(BS1) splits the laser beam into reference and object beam, which is reflected at the SLM plane after being modulated by the SLM pixels. Lens 1 (L1) executes an optical Fourier Transform (FFT) to the modulated laser beam, so a pinhole (IB) filters the first diffraction order in the Fourier plane. L2 executes an optical inverse Fourier Transform (IFFT). L3 and microscope objective 1 (MO1) image the filtered beam onto the fiber facet of the MMF. To yield excitation conditions as precise as possible, the incidence angle of the beam is tuned by two mirrors M3 and M4. The light, that is propagated through the MMF is imaged on camera 2 (CMOS2) with a telescope composed of MO2 and L6. The hologram, which is generated by the interference between the light field that exits the MMF and the reference beam is captured by CMOS2. The reference beam is cleaned up with L7, IB2 and L8. Afterwards, the reference beam is directed onto CMOS2 with M1, M2 and BS4. For proper alignment, the sub-setups in the yellow boxes are used and are explained in detail in Section 2.2. Laser: 532 nm Laser Quantum torus; SMF: THORLABS P3-460B-FC-5; CP: collimator PAF-A4A; BE: beam expander GBE10-A 10x; HWP: half-wave plate; SLM: HOLOEYE Pluto-2; M1-M6: protected silver mirrors PF10-03-P01; BS1-BS5: 50:50 beam splitter cubes BS013; PBS: polarizing beam splitter cubes PBS251; IB1-2: pinholes D368; L1-L8: lenses f1 = 250 mm, f2 = 60 mm, f3 = 160 mm, f4 = 80 mm, f5 = 180 mm, f6 = 300 mm, f7 = 60 mm, f8 = 160 mm; MO1: 80x Mitutoyo Plan Apo SL; MO2: Olympus PLN 40x; MMF: THORLABS FG025 JJA; BB: beam block; CMOS1 and CMOS2: IDS UI348 xLE-M.