The low beam divergence of free space optical communications offer increased data rates that are not restricted by interference. Both single and multi-Beam laser communication terminals (SBTs and MBTs) require efficient algorithms for tracking multiple beams with sub-millirad accuracy and between 100Hz - 1kHz control bandwidths. In addition, MBT tracking systems track the full frame in order to acquire and track multiple beams in multiple places on the detector at once. To our knowledge, no suitable algorithms exist that offer multi-beam tracking for MBTs which simultaneously allow beams to move and (dis)appear randomly. We propose a novel multi-beam tracking algorithm using computationally inexpensive temporal-based techniques inspired by multiple target tracking. This method leverages frame association based on directional beam behavior and statistical analysis for accurate beam classification and labeling. Experimental results using commercially available hardware show that our algorithm can track 1000 beams with over 99% precision at 1 ms per frame overhead, utilizing a 1.8 GHz processor. The tracked beam location is within 1 pixel of the true center. An analytical model of the algorithm was derived from mixed replacement urn problems and complete homogeneous symmetric polynomials. Combining these yielded in a, to our knowledge, new probability distribution we coined CombiTron. Our temporal-based tracking technique significantly enhances MBT performance with minimal computational overhead. This approach can be useful to applications outside of multi-beam tracking, including single beam tracking. The theory matches simulations and experiments, allowing for accurate estimation of tracking performance and requirements.

The spatial diversity and beam shaping are key approaches to mitigating the effects of atmospheric turbulence on laser beam propagation through free space. This study investigates the propagation characteristics of an annular beam array in atmospheric turbulence for uplink satellite links using the extended Huygens-Fresnel principle and the Rytov method. Analytical derivations are presented for various optical parameters, including received intensity, kurtosis parameter, beam footprint size, Strehl ratio, beam wander, scintillation index, and bit error rate (BER), to evaluate the beam performance under turbulence conditions. The findings indicate that converting a Gaussian beam into an annular shape enhances performance, with further improvements observed as the number of beams increases.

Laser satellite communication technologies are promising next-generation communications systems, offering higher data rates, more secure links, and cost-effective operations. One of the remaining challenges to tackle for ensuring sufficient link availability is atmospheric turbulence. While turbulence effects on laser links can be partly compensated for with corrective technologies and algorithms, these methods would benefit from better knowledge of turbulence profiles on the communications channel, both for system design or real-time assistance during operations. As state-of-the-art turbulence profilers are not designed to measure profiles from a laser beam on a moving satellite, this paper proposes a line-of-sight turbulence profiling tool tailored for laser satellite communications. Speckle-based turbulence observation and reconstruction via machine learning uses surrogate learning to build a model that can reconstruct optical turbulence profiles (C_n²(h)) from a single shot measurement of a speckle pattern. In this paper, the first modeling results of this flexible approach demonstrate that eight-layer turbulence profiles can be reconstructed from simulated single speckle images of a star with less than 10% error on the Fried parameter.

To support the development of free-space-optical (FSO) communication technologies, an end-to-end physical layer model of a satellite communication service was developed. This service involves physical processes spanning multiple time scales: hours (relative platform dynamics), minutes (link selection, atmospheric attenuation), milliseconds (atmospheric turbulence, platform disturbances), and nanoseconds (photon and bit transportation). The modified multi-scale method (MMM) was used to combine the physics of these processes and to model an end-to-end global FSO communication service between an airborne platform and a satellite constellation. The method provides a better understanding of physical interdependencies, allows performance analysis on multiple time scales, and enables valuable insight into where to optimize such a service. The results show realistic performance metrics when compared to other smaller-scale models and demonstrations. The MMM can be used as a mission performance indicator of an end-to-end satellite communication service.

Intersatellite free-space optical communications are the backbone of the future highspeed global communication networks. In orbit, thermo-mechanical loads create perturbations that detriment the performance of these links. Among these perturbations, the transmitter pointing jitter and optical aberrations are of special relevance. We present an analysis of the coupled effects of transmitter pointing jitter and optical aberrations on intersatellite free space optical communications. A mathematical model is presented to evaluate the performance of average bit error probability, probability of outage, and reliability on intersatellite free space optical communication links subjected to these perturbations. Furthermore, the optimum non-aberrated truncated Gaussian beams are obtained for each of these performance parameters for different telescope architectures. The results demonstrate that the performance parameters are highly sensitive to the optimal far-field irradiances. These optimum operation points are then perturbed by Seidel aberrations to study the effect of these aberrations in the system. The results show that optical communication terminals are most sensitive to coma aberrations, mainly due to the induced apparent angle of arrival on the beacon beam. Finally, Monte Carlo simulations of combinations of Seidel aberrations show a strong dependency on the telescope architecture of the sensitivity of the communication performance parameter to the magnitude of the optical aberrations.

One of the most ambitious goals of modern astronomy is to uncover signs of extraterrestrial biological activity, primarily achieved through spectroscopic analysis of light emitted by exoplanets to identify specific atmospheric molecules. Most exoplanets are indirectly identified through techniques like transit or Doppler shift of the host star's flux. Long-term surveys have yielded statistical insights into the occurrence rates of different planet types based on factors such as radius/mass, orbital period, and the spectral type of the host star, initial estimates of terrestrial planets within the habitable zone have also emerged. However, the difficulty of detecting light from these exoplanets leaves much unknown about their nature, formation, and evolution. As the number of rocky exoplanets around nearby stars rises, questions about their atmospheric composition, evolutionary trajectory, and habitability increase. Direct measurement of an cxoplanct's atmospheric composition through its spectral signature in the infrared can provide answers. Measuring the infrared spectrum of these planets poses significant challenges due to the star/planet contrast and very small angular separation from their host stars. Previous research showed that space-based telescopes are mandatory, and unless large primary mirrors (>30m in diameter) can be sent into space, intcrfcrometric techniques become essential. Combining light from distant telescopes with interferometric techniques allows access to information at minimal angular separation, operating within the diffraction limit of individual telescopes. Successful demonstrations of on-ground nulling interferometry open a new era for such space-based missions. They are vital to sidestep and tackle these scientific questions. We recently initiated a new study with the European Space Agency to explore the design parameters and the performances related to an interferometric concept based on a single spacecraft and sparse multiple sub-apertures. Launch constraints are linked to the use of an Ariane 6 launch vehicle. Our parametric study covers a range of 1-4 m for the diameter of the telescope and a 10-60 m baseline. The most promising concept working in the infrared range (3-20μm) will be highlighted. This study is conducted by TUDelft in cooperation with KULeuven, CSL/ULiege, and Amos with the support of the European Space Agency.

In this study, we examine the propagation characteristics of vortex-Gaussian beams in atmospheric turbulence for uplink free-space optical (FSO) links. Using the extended Huygens–Fresnel principles, we analytically derive key parameters, including the received intensity, second-order and fourth-order intensity moments, the Strehl ratio, the kurtosis parameter, and the effective beam spot radius. Then, we used phase-screen simulations to analyze the behavior of the scintillation index. Our findings demonstrate that vortex beams offer superior Strehl ratio performance compared to the Gaussian beam and exhibit greater resilience to atmospheric turbulence variations. Furthermore, the vortex beams exhibit kurtosis values below 3 and have a larger effective beam spot radius compared to Gaussian beams. Additionally, vortex beams exhibit a lower scintillation index compared to the Gaussian beam at longer propagation distances.

We investigate Gaussian beam propagation from the ground to a LEO satellite, analyzing beam footprint, Strehl ratio, scintillation index, and bit-error rate under atmospheric turbulence with adaptive optics (AO) applied at the transmitter.

Laser satellite communications is a growing market for telecommunications services and secure communications. Due to the small footprint of the beam, it provides security, and it can serve as inherently safe communication, using the quantum properties of light, i.e. quantum communications, and quantum key distribution. For quantum communications, the detector sensitivity is of utmost importance. Hence, detector technologies such as Superconducting Nanowire Single Photon Detector (SNSPD), are designated to support optical communications. In this research, we estimate the efficacy of SNSPD arrays for optical downlinks to earth. In this paper, we investigate how spatial resolution of the SNSPD and the spatiotemporal statistics of the incoming turbulence can be matched, in order to effectively use SNSPD arrays. We simulated the downlink using a split-step approach, using a receiver aperture of 1 m and a Fried parameter of 50 and 12.5 cm (D/r₀ is 2 and 8). We obtained the average intensity, the scintillation index, the probability density function (PDF) and the power spectral density (PSD) using 4000 samples. We project instantaneous images on the SNSPD, to estimate how the PSD is distributed. We conclude that stronger turbulence conditions could improve detection performance, because the point spread function (PSD) is wider, and the incident light is distributed over more pixels.

When using Radio Frequency aboard small satellites, for high data rates, this would need large antennas, violating constraints related to size, weight, and power. As an alternative, Free Space Optical Communication (FSOC) uses laser beams, operating in the optical and infrared frequency domain, in order to transmit data through the atmosphere between satellites and ground stations. However, implementing FSOC systems on (small) satellites remains challenging. In this paper, we investigate the role of phase shifting in FSOC systems. The functionality of these phase shifters is used for modulation, beam steering using optical phased arrays, and phase stabilization of the transmit and receive beams. This is where Photonic Integrated Circuit (PIC)-based platforms could offer a solution. Their extremely compact form factor makes them ideal for space applications. Phase shifters embedded within PIC-based platforms offer a known solution by allowing dynamic manipulation of the phase of light. A specific setup, namely the use of hybrid AOMs, looks promising as other phase shifting techniques can suffer from several issues, such as being thermal sensitive, having non-linear effects and possible material degradation in the long-Term. As these devices come with their own challenges, this work identifies these shortcomings and focuses on the analysis and design of an efficient low-power miniaturized RF driving system, in combination with the design of an efficient hybrid AOM setup for phase shifting in a PIC environment.

Tip-tilt pre-compensation adds a significant performance improvement for uplink optical communications channels, such as optical feeder-links. Besides the large contribution of tip-tilt to the wavefront disturbances, tip-tilt aberrations are less sensitive for the point ahead angle than higher order aberrations. Nevertheless, reciprocity between downlink and uplink is not perfect, resulting in residual pointing errors. One effect is the difference in beam shape: the downlink can be considered as a plane wave, whereas the uplink typically is a Gaussian beam. To improve reciprocity between up and donwlink, I propose to use a Gaussian apodization filter inn the part of the downlink beam that is used for measuring tip-tilt. This idea is tested using a numerical wave propagation simulation. In this simulation the reduction of beam wander is 13% and 20% is observed in the direction of the point ahead angle, and its transversal direction respectively. Also, it reduced the scintillation index by 8%. This yielded an improvement of the optical link by 1.5 dB at a probability of 10^-3,.

Traditional laser communication terminals are limited to point-to-point links, which constrains their scalability and flexibility for global networks that require simultaneous connections with multiple targets. While multiple single-beam terminals can expand capacity, this approach multiplies Size, Weight, Power, and Cost (SWaPC), limiting scalability. Multi-beam laser communication terminals offer a promising alternative, though the design of an effective beam steering system remains a key challenge. This paper explores the design process of such a system, providing an overview of multi-beam steering literature as well as an comparison and trade-off of existing space-borne multi-beam steering technologies. It also analyzes insights from related fields such as terrestrial laser communications, LiFi, single-beam laser communication, optical cross-connects, radio links, and multiple target tracking. Key system functions are identified and visualized in a function flow diagram, and various design options are evaluated, culminating in a design options tree which serves as a design recipe. Two application scenarios, involving high and low target densities, demonstrate that steering systems based on micro-mirror arrays and spatial light modulators present significant advantages over alternatives. This study offers a comprehensive framework for designing multi-beam steering systems for space-based laser communication terminals.

One of the most ambitious goals of modern astronomy is to uncover signs of extraterrestrial biological activity, primarily achieved through spectroscopic analysis of light emitted by exoplanets to identify specific atmospheric molecules. Most exoplanets are indirectly identified through techniques like transit or Doppler shift of the host star's flux. Long-term surveys have yielded statistical insights into the occurrence rates of different planet types based on factors such as radius/mass, orbital period, and the spectral type of the host star. Initial estimates of terrestrial planets within the habitable zone have also emerged. However, the difficulty of detecting light from these exoplanets leaves much unknown about their nature, formation, and evolution. As the number of rocky exoplanets around nearby stars rises, questions about their atmospheric composition, evolutionary trajectory, and habitability increase. Direct measurement of an exoplanet's atmospheric composition through its spectral signature in the infrared can provide answers. Measuring the infrared spectrum of these planets poses significant challenges due to the star/planet contrast and very small angular separation from their host stars. Previous research showed that space-based telescopes are mandatory, and unless large primary mirrors (>30m in diameter) can be sent into space, interferometric techniques become essential. Combining light from distant telescopes with interferometric techniques allows access to information at minimal angular separation, operating within the diffraction limit of individual telescopes. Successful demonstrations of on-ground nulling interferometry open a new era for such space-based missions. They are vital to sidestep and tackle these scientific questions. We recently initiated a new study with the European Space Agency to explore the design parameters and the performances related to an interferometric concept based on a single spacecraft and sparse multiple sub-apertures. Launch constraints are linked to the use of an Ariane 6 launch vehicle. Our parametric study covers a range of 1-4 m for the diameter of the telescope and a 10-60 m baseline. The most promising concept working in the infrared range (3-20μm) will be highlighted. This study is conducted by TUDelft in cooperation with KULeuven, CSL/ULiège, and Amos with the support of the European Space Agency.

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.

For free-space optical communication or ground-based optical astronomy, ample data of optical turbulence strength (C 2 n) 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 2 n is not measured directly (e.g., with a scintillometer), C 2 n 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 2 n estimates are compared against observed C 2 n 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 2 n 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.

We present a machine learning-based measure-correlate-predict approach that predicts a multi-year time-series of optical turbulence strength (Cn2) with high accuracy (r = 0.78 at 16 locations) based on a single year of in-situ Cn2 measurements and reanalysis data.

Turbulent fluctuations of the atmospheric refraction index, so-called optical turbulence, can significantly distort propagating laser beams. Therefore, modeling the strength of these fluctuations (𝐶2𝑛) 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 𝐶2𝑛. Through a systematic feature importance analysis, we identify the normalized variance of potential temperature as the dominating feature for predicting 𝐶2𝑛. 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.

For the next generation of very high throughput communication satellites, free-space optical (FSO) communication between ground stations and geostationary telecommunication satellites is a potential solution to overcome the limitations of RF links. To mitigate atmospheric turbulence effects, TNO proposes Adaptive Optics (AO) to apply uplink pre-correction. As a successor of Optics Feeder Link Adaptive Optics (OFELIA) breadboard [1], [2], the Terabit Optical Communication Adaptive Terminal (TOmCAT) project phase 2 aims to demonstrate the AO precorrection technology for a terabit Optical Ground Station (OGT) in a ground-to-ground link field test over 10 km. Within this demonstrator an upgraded version of the OFELIA breadboard is used as optical bench for the AO (pre-)correction, but moreover the demonstrator enables the (future) integration of equipment for the final OGT configuration including the Beam Multiplexer (BMUX) and communication equipment. Apart from the OGT demonstrator, the overall layout of the field test has been upgraded, including the test site and the Ground Support Equipment (GSE), with the goal to create a better understanding of the encountered link phenomena and the instant (turbulence) conditions at which it was measured. New additions to the GSE are several weather stations placed along the link path to quantify the local turbulence and to relate the measured link performance to the instant turbulence conditions. The test campaign is split in two successive field tests: First the AO Demonstrator evaluates the upgraded AO pre-correction performance with a single non-modulated link, followed by the OGT Demonstrator which will include the multiplexing of multiple uplink channels and RF end-to-end modems to prove the technical feasibility of supporting a terabit communication link. This paper covers the design of the AO demonstrator and GSE, the field test layout and the preliminary results for the AO demonstrator field test. For the downlink correction the residual Wave Front Error (WFE) is presented. The pre-correction performance is depicted in the uplink transmission loss and scintillation, all as function of the encountered turbulence conditions.

A 10 km ground-To-ground field test of a Terabit/s Optical Feeder Link demonstrator has been carried out. The demonstrator aimed for end-To-end communication performance with the use of Adaptive Optics pre-correction to mitigate the atmospheric turbulence disturbances of the FSO channel. It further includes the multiplexing of multiple uplink channels and RF end-To-end modems to prove the technical feasibility of supporting a Terabit/s communication link. The field test-performed in July 2022-demonstrates error free communication for over 10 minutes. This achievement proves the feasibility of a digital transparent communication architecture for the Terabit/s Feeder link application. The field test results are presented jointly with a companion paper [1] which focusses on the communication aspects. The Adaptive Optics (AO) pre-correction performance is analyzed against the atmospheric turbulence strength and the number of corrected AO modes. The encountered turbulence conditions during the field test caused irradiance fluctuations in the strong fluctuation regime. The field test results show a significant AO wavefront error correction on the downlink. For the uplink irradiance levels, a modest advantage of pre-correcting higher wavefront modes is found against the pre-correction of only the tip-Tilt modes. Finally, with respect to the uplink fading characteristics, the AO pre-correction leads to a reduction of the mean-fade time of approximately 20-30%, compared to AO tip-Tilt pre-correction only.

Optical feeder links (OFLs) benefit from the vast amount of bandwidth available in the THz-regime of the electromagnetic spectrum, and can be considered as enablers for future terabit-per-second satellite systems. A particular challenge for OFLs is to mitigate the effects of fading, caused by a combination of turbulence-induced scintillation, beam wander and pointing errors. The conventional solution is to exploit temporal diversity by a combination of interleaving and forward error correction (FEC). In this study we present an overview of fading mitigation techniques for latency-constrained coherent ground-to-satellite OFL and contribute a generic model which combines various diversity schemes including temporal, spatial, frequency and site diversity. To unlock spatial diversity, multi-beam space-time block coding and multi-beam, multi-λ are proposed and simulated. Though space-time block coding (STBC) provides more diversity gain, it requires accurate timing synchronization at the transmitter and channel state information at the receiver. Temporal, frequency and site diversity all rely on some form of interleaving and the potential diversity, pros and cons of each of these diversity techniques are covered in the presented study. In general, with a strict latency constraint and a tight link budget, frequency diversity, spatial diversity - either by STBC or multi-beam multi-λ - and site diversity can be effective methods to mitigate the effects of fading and close the link budget.