The spatial distribution of beams with orbital angular momentum in the far field is known to be extremely sensitive to angular aberrations, such as astigmatism, coma and trefoil. This poses a challenge for conventional beam optimization strategies when a homogeneous ring intensity is required for an application. We developed a novel approach for estimating the Zernike coefficients of low-order angular aberrations in the near field based solely on the analysis of the ring deformations in the far field. A fast, iterative reconstruction of the focal ring recreates the deformations and provides insight into the wavefront deformations in the near field without relying on conventional phase retrieval approaches. The output of our algorithm can be used to optimize the focal ring, as demonstrated experimentally at the 100 TW beamline at the Extreme Light Infrastructure - Nuclear Physics facility.

In order to reach the highest intensities, modern laser systems use adaptive optics to control their beam quality. Ideally, the focal spot is optimized after the compression stage of the system in order to avoid spatio-temporal couplings. This also requires a wavefront sensor after the compressor, which should be able to measure the wavefront on-shot. At PHELIX, we have developed an ultra-compact post-compressor beam diagnostic due to strict space constraints, measuring the wavefront over the full aperture of 28 cm. This system features all-reflective imaging beam transport and a high dynamic range in order to measure the wavefront in alignment mode as well as on shot.

The set N of all null geodesics of a globally hyperbolic $(d + 1)$-dimensional spacetime $(M, g)$ is naturally a smooth $(2d - 1)$-dimensional contact manifold. The sky of an event x in M is the subset X of N consisting of all null geodesics through x, and is an embedded Legendrian submanifold of N diffeomorphic to $S^{(d - 1)}$. It was conjectured by Low that for $d = 2$ two events x and y are causally related if and only if X and Y are linked (in an appropriate sense). We use the contact structure and knot polynomial calculations to prove this conjecture in certain particular cases, and suggest that for $d = 3$ smooth linking should be replaced with Legendrian linking.

We made aperture masking optical interferometry experiments using up to 30 apertures and with a tip-tilt correction of wavefront error. We examined the performance of minimum redundant configurations of 11–30 sub-apertures on the pupil plane mask. These configurations have two advantages; the redundancy noise is as small as realized in non-redundant masking method, and the uv-coverage is as high as in speckle interferometry enabling to get reconstructed images without mask exchange. We also examined the effect of tip-tilt wavefront correction within a telescope pupil in front of the aperture masking optics. The light coherency between sub-apertures was shown to increase by the correction.