Reducing beam tracking complexity using a phase ramp and Fresnel lens when steering beams using spatial light modulators.

Steering multiple laser beams using spatial light modulators (SLMs) creates unwanted diffraction and reflections that are not modulated by the SLM, which can make beam tracking difficult. A novel, to the best of our knowledge, and simple beam steering methodology is proposed, which aims at reducing the influence of this clutter while maintaining tracking performance. The beam(s) are deliberately defocused before steering with a superposition of a phase ramp and Fresnel lens (PRFL) phase screen on the SLM. As a result, the non-modulated reflections and diffracted light are decreased in relative intensity to the steered beam, in turn allowing simple and standard peak intensity and center of gravity (CG) algorithms for tracking. Hardware demonstration shows tracking performance using the PRFL remained on-par with more complex filtering approaches while adding no additional hardware. This method has potential to improve the communication performance of multi-beam laser communication terminals.

Intercomparison of flux-, gradient-, and variance-based optical turbulence (C n2) parameterizations.

For free-space optical communication or ground-based optical astronomy, ample data of optical turbulence strength (C n2) are imperative but typically scarce. Turbulence conditions are strongly site dependent, so their accurate quantification requires in situ measurements or numerical weather simulations. If C n2 is not measured directly (e.g., with a scintillometer), C n2 parameterizations must be utilized to estimate it from meteorological observations or model output. Even though various parameterizations exist in the literature, their relative performance is unknown. We fill this knowledge gap by performing a systematic three-way comparison of a flux-, gradient-, and variance-based parameterization. Each parameterization is applied to both observed and simulated meteorological variables, and the resulting C n2 estimates are compared against observed C n2 from two scintillometers. The variance-based parameterization yields the overall best performance, and unlike other approaches, its application is not limited to the lowest part of the atmospheric boundary layer (i.e. the surface layer). We also show that C n2 estimated from the output of the Weather Research and Forecasting model aligns well with observations, highlighting the value of mesoscale models for optical turbulence modeling.

Π-ML: a dimensional analysis-based machine learning parameterization of optical turbulence in the atmospheric surface layer.

Turbulent fluctuations of the atmospheric refraction index, so-called optical turbulence, can significantly distort propagating laser beams. Therefore, modeling the strength of these fluctuations (C n2) is highly relevant for the successful development and deployment of future free-space optical communication links. In this Letter, we propose a physics-informed machine learning (ML) methodology, Π-ML, based on dimensional analysis and gradient boosting to estimate C n2. Through a systematic feature importance analysis, we identify the normalized variance of potential temperature as the dominating feature for predicting C n2. For statistical robustness, we train an ensemble of models which yields high performance on the out-of-sample data of R2 = 0.958 ± 0.001.

Actuation profiles to form Zernike shapes with a thermal active mirror.

In EUV lithography, the absorption of EUV light causes wavefront distortion that deteriorates the imaging process. An adaptive optics system has been developed ["Adaptive optics to counteract thermal aberrations," Ph.D. thesis (TU Delft, 2013)] to correct for this distortion using an active mirror (AM). This AM is thermally actuated by absorbing an irradiance profile exposed by a projector onto the AM. Due to thermal conductivity and bimorph-like deformation of the AM, the relation between actuation profile and actuated shape is not trivial. Therefore, this Letter describes how actuation profiles are obtained to generate Zernike shapes. These actuation profiles have been obtained by a finite-element-based optimization procedure. Furthermore, these actuation profiles are exposed to the AM, and the resulting deformations are measured. This Letter shows actuated Zernike shapes with purities higher than 0.9 for most actuation profiles. In addition, superimposed actuation profiles resulted in superimposed Zernike shapes, showing linearity needed to apply modal wavefront correction. Therefore, this approach can be used to obtain actuation profiles for this AM concept, which can be used for highly precise wavefront correction.