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Cosmic shear - the weak gravitational lensing effect generated byfluctuations of the gravitational tidal fields of the large-scale structure -is one of the most promising tools for current and future cosmologicalanalyses. The spherical-Bessel decomposition of the cosmic shear field ("3Dcosmic shear") is one way to maximise the amount of redshift information in alensing analysis and therefore provides a powerful tool to investigate inparticular the growth of cosmic structure that is crucial for dark energystudies. However, the computation of simulated 3D cosmic shear covariancematrices presents numerical difficulties, due to the required integrations overhighly oscillatory functions. We present and compare two numerical methods andrelative implementations to perform these integrations. We then show how togenerate 3D Gaussian random fields on the sky in spherical coordinates,starting from the 3D cosmic shear covariances. To validate our field-generationprocedure, we calculate the Minkowski functionals associated with our randomfields, compare them with the known expectation values for the Gaussian caseand demonstrate parameter inference from Minkowski functionals from a cosmicshear survey. This is a first step towards producing fully 3D Minkowskifunctionals for a lognormal field in 3D to extract Gaussian and non-Gaussianinformation from the cosmic shear field, as well as towards the use ofMinkowski functionals as a probe of cosmology beyond the commonly usedtwo-point statistics.

3D cosmic shear: numerical challenges, 3D lensing random fields generation and Minkowski Functionals for cosmological inference