  Thermographic photothermal super resolution reconstruction enables the
resolution of internal defects/inhomogeneities below the classical limit which
is governed by the diffusion properties of thermal wave propagation. Based on a
combination of the application of special sampling strategies and a subsequent
numerical optimization step in post-processing, thermographic super resolution
has already proven to be superior to standard thermographic methods in the
detection of one-dimensional defect/inhomogeneity structures. In our work, we
report an extension of the capabilities of the method for efficient detection
and resolution of defect cross sections with fully two-dimensional structured
laser-based heating. The reconstruction is carried out using one of two
different algorithms which are proposed within this work. Both algorithms
utilize the combination of several coherent measurements using convex
optimization and exploit the sparse nature of defects/inhomogeneities as is
typical for most nondestructive testing scenarios. Finally, the performance of
each algorithm is rated on reconstruction quality and algorithmic complexity.
The presented experimental approach is based on repeated spatially structured
heating by a high power laser. As a result, a two-dimensional sparse
defect/inhomogeneity map can be obtained. In addition, the obtained results are
compared with those of conventional thermographic inspection methods which make
use of homogeneous illumination. Due to the sparse nature of the reconstructed
defect/inhomogeneity map, this comparison is performed qualitatively.
