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Thermographic NDE is based on the interaction of thermal waves with inhomogeneities. These inhomogeneities are related to sample geometry or material composition. Although thermography is suitable for a wide range of inhomogeneities and materials, the fundamental limitation is the diffusive nature of thermal waves and the need to measure their effect radiometrically at the sample surface only. The propagation of the thermal waves from the heat source to the inhomogeneity and to the detection surface results in a degradation in the spatial resolution of the technique. A new concerted ansatz based on a spatially structured heating and a joint sparsity of the signal ensemble allows an improved reconstruction of inhomogeneities. As a first step to establish an improved thermographic NDE method, an experimental setup was built based on structured 1D illumination using a flash lamp behind a mechanical aperture. As a follow-up to this approach, we now use direct structured illumination using a 1D laser array. The individual emitter cells are driven by a random binary pattern and additionally shifted by fractions of the cell period. The repeated measurement of these different configurations with simultaneously constant inhomogeneity allows for a reconstruction that makes use of joint sparsity. With analytical-numerical modelling or numerical FEM simulations, we study the influence of the parameters on the result of non-linear reconstruction. For example, the influence of the illumination pattern as a variable heat flux density and Neumann boundary condition for convolution with the constant Green's function can be studied. These studies can be used to derive optimal conditions for a measurement technique.