Fig. 2: Schematics of SPIM variants.
a illustrates the quadrature method26. The amplitude-modulating mask was divided into two regions, encoding vectors {ξi} and {ηi} respectively. Spin configurations {ϕi} are encoded identically in the two regions on the SLM, but with one arbitrary spin having a phase shift of π/2 relative to all other spins. b illustrates the correlation function method27. The SLM encodes both the spin configurations {ϕi} and the Mattis vector elements {ξi} by rotating each ϕi by an angle \(\arccos ({\xi }_{i})\). A function G in the coupling matrix is first inverse Fourier transformed into a distribution function g(u) where u is the spatial coordinate in the focal plane, and then digitally integrated with intensity measurement I to produce the Hamiltonian H. c illustrates the linear combination method28. The coupling matrix is decomposed into a linear combination of many Mattis-type matrices. Each Mattis-type matrix is individually implemented and the intensity measurements from all linear components are summed digitally to produce the overall Hamiltonian.
