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The optical transmission matrix (TM) characterizes the transmission properties of a sample. We show a novel experimental procedure for measuring the TM of light waves in a slab geometry based on sampling the light field on a hexagonal lattice at the Rayleigh criterion. Our method enables the efficient measurement of a large fraction of the complete TM without oversampling while minimizing sampling crosstalk and the associated distortion of the statistics of the matrix elements. The procedure and analysis described here is demonstrated on a clear sample which serves as an important reference for other systems and geometries such as dense scattering media.

The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is measured. While conventional experimental methods suffer from sampling effects and optical aberrations, we use a basis of Bessel modes of the first kind to faithfully recover the singular values, eigenvalues and eigenmodes of light propagation through a finite thickness of air.

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