Context. Integrated superconducting spectrometers (ISSs) for wide-band submillimeter (submm) astronomy use quasi-optical systems for coupling radiation from the telescope to the instrument. Misalignment in these systems is detrimental to the system performance. The common method of using an optical laser to align the quasi-optical components requires an accurate alignment of the laser to the submm beam from the instrument, which is not always guaranteed to a sufficient accuracy. Aims. We develop an alignment strategy for wide-band ISSs that directly uses the submm beam of the wide-band ISS. The strategy should be applicable in both telescope and laboratory environments. Moreover, the strategy should deliver similar quality of the alignment across the spectral range of the wide-band ISS. Methods. We measured the misalignment in a quasi-optical system operating at submm wavelengths using a novel phase and amplitude measurement scheme that is capable of simultaneously measuring the complex beam patterns of a direct-detecting ISS across a harmonic range of frequencies. The direct detection nature of the microwave kinetic inductance detectors in our device-under-test, DESHIMA 2.0, necessitates the use of this measurement scheme. Using geometrical optics, the measured misalignment, a mechanical hexapod, and an optimisation algorithm, we followed a numerical approach to optimise the positioning of corrective optics with respect to a given cost function. Laboratory measurements of the complex beam patterns were taken across a harmonic range between 205 and 391 GHz and were simulated through a model of the ASTE telescope in order to assess the performance of the optimisation at the ASTE telescope. Results. Laboratory measurements show that the optimised optical setup corrects for tilts and offsets of the submm beam. Moreover, we find that the simulated telescope aperture efficiency is increased across the frequency range of the ISS after the optimisation.

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We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the brutus N-body code to include post-Newtonian pairwise terms up to 2.5 order, and the first order Taylor expansion to the Einstein-Infeld-Hoffmann equations of motion. The degree to which our system is relativistic depends on the scaling of the total mass (the unit size was 1 parsec). Using the brutus method of convergence, we test for time-reversibility in the conservative regime, and demonstrate that we are able to obtain definitive solutions to the relativistic three-body problem. It is also confirmed that the minimal required numerical accuracy for a successful time-reversibility test correlates with the amplification factor of an initial perturbation, as was found previously for the Newtonian case. When we take into account dissipative effects through gravitational wave emission, we find that the duration of the resonance, and the amount of exponential growth of small perturbations depend on the mass scaling. For a unit mass , the system behavior is indistinguishable from Newton’s equations of motion, and the resonance always ends in a binary and one escaping body. For a mass scaling up to , relativity gradually becomes more prominent, but the majority of the systems still dissolve in a single body and an isolated binary. The first mergers start to appear for a mass of , and between and all systems end prematurely in a merger. These mergers are preceded by a gravitational wave driven in-spiral. For a mass scaling , all systems result in a gravitational wave merger upon the first close encounter. Relativistic three-body encounters thus provide an efficient pathway for resolving the final parsec problem. The onset of mergers at the characteristic mass scale of potentially leaves an imprint in the mass function of supermassive black holes.@en