In this Letter, we propose a simple optical architecture based on phase-only programmable spatial light modulators, in order to characterize general processes on photonic spatial quantum systems in a d>2 Hilbert space. We demonstrate the full reconstruction of typical noises affecting quantum computing, such as amplitude shifts, phase shifts, and depolarizing channels in dimension d=5. We have also reconstructed simulated atmospheric turbulences affecting a free-space transmission of qudits in dimension d=4. In each case, quantum process tomography was performed in order to obtain the matrix χ that fully describes the corresponding quantum channel, E. Fidelities between the states are experimentally obtained after going through the channel, and the expected ones are above 97%.Instituto de Física La Plata