Adaptive Optics System Research Articles

The clinical outcome of treating elderly distal radius fractures by long volar locking plate with the elimination of irreducible metaphyseal comminuted volar cortical fragments: a retrospective case series

Background: In severe comminuted metaphyseal distal radius fracture (DRF) of elderly patients, after maintaining only radiological parameters of the radius using long volar locking plates (VLPs), we inevitably eliminated a few volar cortical fragments of metaphysis. Here, we report the final radiological and clinical outcomes of our method. Methods: For the patients who were treated between 2014 and 2018, the demographic factors, the preoperative radiologic factors, area of the eliminated volar cortical fragment, and final radiologic parameter, were evaluated. Clinical outcomes and ranges of active motion were evaluated. Results: In total, 31 patients were included. The mean patient age was 77.3 years and the mean eliminated cortical area was 3.30 cm2. At the final follow-up, the mean volar tilt, radial inclination, articular step-off, and ulnar variance were 10.35°, 20.00°, 0.58 mm, and 0.71 mm, respectively. There were no definitive correlations between bone mineral density, fragment area, the largest cortical fragment diameter ratio and differences in final and immediate postoperative measurements of these radiological parameters, respectively. Visual analog scale and disabilities of the arm, shoulder, and hand (DASH) scores were satisfactory, and the mean arcs of flexion-extension and pronation-supination were 124.35° and 133.23°. Clinical outcomes were not significantly different according to the AO system category. Conclusions: For maintenance of radiological parameters of the radius, long VLPs are useful in older patients with DRFs who exhibit volar metaphyseal comminution, despite concurrent ulnar fractures. Inevitable elimination of irreducible free comminuted cortical fragments when filling the defect does not affect final radiological and clinical outcomes. Level of evidence: Level IV, case series.

Homodyne detection efficiency analysis of coherent lidar based on a hybrid algorithm

Atmospheric turbulence-induced phase variations affect the homodyne detection efficiency of the coherent lidar, which further affects the performance of the lidar. Adaptive optics (AO) is an effective method to correct turbulence-induced wavefront aberrations. In this paper, a coherent lidar wavefront correction technique based on a hybrid algorithm of stochastic parallel gradient descent (SPGD) and simulated annealing (SA) is proposed on the basis of a theoretical analysis. The simulation results verify that the hybrid algorithm can significantly improve the efficiency of homodyne detection in coherent lidar. The results show that the hybrid algorithm has the characteristics of fast convergence speed and strong correction ability. The conclusion of this paper provides a reference for the design of the coherent lidar AO system.

Enhanced Neural Architecture for Real-Time Deep Learning Wavefront Sensing.

To achieve real-time deep learning wavefront sensing (DLWFS) of dynamic random wavefront distortions induced by atmospheric turbulence, this study proposes an enhanced wavefront sensing neural network (WFSNet) based on convolutional neural networks (CNN). We introduce a novel multi-objective neural architecture search (MNAS) method designed to attain Pareto optimality in terms of error and floating-point operations (FLOPs) for the WFSNet. Utilizing EfficientNet-B0 prototypes, we propose a WFSNet with enhanced neural architecture which significantly reduces computational costs by 80% while improving wavefront sensing accuracy by 22%. Indoor experiments substantiate this effectiveness. This study offers a novel approach to real-time DLWFS and proposes a potential solution for high-speed, cost-effective wavefront sensing in the adaptive optical systems of satellite-to-ground laser communication (SGLC) terminals.

Design considerations for wavefront sensing with self-referencing interferometers in adaptive optics systems

In this work, we show the design and implementation of wavefront sensing with a self-referencing interferometer (SRI). The SRI is developed to aid adaptive optics (AO) control, via deformable mirrors, in correcting wavefront error from atmospheric turbulence in (laser-based) free-space optical communication links. The SRI is used here given its potential to outperform more common wavefront sensors in functioning over weak through strong turbulence conditions. In this study, we identify and analyse the key parameters in the SRI’s optical design and show guiding principles for its subsequent image processing.

Commissioning of the MIRAC-5 Mid-infrared Instrument on the MMT

Abstract We present results from commissioning observations of the mid-IR instrument, MIRAC-5, on the 6.5 m MMT telescope. MIRAC-5 is a novel ground-based instrument that utilizes a state-of-the-art GeoSnap (2–13 µm) HgCdTe detector with adaptive optics support from MAPS to study protoplanetary disks, wide-orbit brown dwarfs, planetary companions in the contrast-limit, and a wide range of other astrophysical objects. We have used MIRAC-5 on six engineering observing runs, improving its performance and defining operating procedures. We characterize key aspects of MIRAC-5's performance, including verification that the total telescope, atmosphere, instrument, and detector throughput is approximately 10%. Following a planned dichroic upgrade, the system will have a throughput of 20% and background limiting magnitudes (for SNR = 5 and 8 hr exposure times) of 18.0, 15.6, and 12.6 for the L’, M’, and N’ filters, respectively. The detector pixels experience 1/f noise but, if the astrophysical scene is properly modulated via chopping and nodding sequences, it is less than 10% the Poisson noise from the observed background in an 85 Hz frame. We achieve close to diffraction-limited performance in the N-band and all bands are expected to reach diffraction-limited performance following the adaptive optics system commissioning. We also present an exposure time calculator calibrated to the on-sky results. In its current state, MIRAC-5 will be capable of achieving several scientific objectives including the observation of warm wide-orbit companions. Once the adaptive optics is commissioned and a coronagraph installed in 2025, MIRAC-5 will have contrast-limited performance comparable to JWST, opening new and complementary science investigations for close-in companions.

Wavefront Correction for Extended Sources Imaging Based on a 97-Element MEMS Deformable Mirror.

Adaptive optics (AO) systems are capable of correcting wavefront aberrations caused by transmission media or defects in optical systems. The deformable mirror (DM) plays a crucial role as a component of the adaptive optics system. In this study, our focus is on analyzing the ability of a 97-element MEMS (Micro-Electro-Mechanical System) DM to correct blurred images of extended sources affected by atmospheric turbulence. The RUN optimizer is employed as the control method to evaluate the correction capability of the DM through simulations and physical experiments. Simulation results demonstrate that within 100 iterations, both the normalized gray variance and Strehl Ratio can converge, leading to an improvement in image quality by approximately 30%. In physics experiments, we observe an increase in normalized gray variance (NGV) from 0.53 to 0.97 and the natural image quality evaluation (NIQE) from 15.35 to 19.73, representing an overall improvement in image quality of about 28%. These findings can offer theoretical and technical support for applying MEMS DMs in correcting imaging issues related to extended sources degraded by wavefront aberrations.

Laboratory demonstration of single-camera PPPP wavefront sensing using neural networks

Laser guide stars in astronomical adaptive optics systems have the focus anisoplanatism problem, especially for telescopes larger than 4 m in diameter. The Projected Pupil Plane Pattern (PPPP) offers an alternative solution by projecting a collimated laser beam across the telescope’s entire pupil. One significant challenge is dealing with gain-related issues, necessitating the use of two beam profiles obtained simultaneously from two different distances from the telescope pupil. In this work, we explore the integration of a convolutional neural network (CNN) with experimental data emulating PPPP. We investigate how CNNs can significantly simplify the PPPP design by enabling operation with a single beam profile. These results permit the development of the PPPP concept to use a single beam profile without distance-gain degeneracy. In this work, it is shown that a 10% residual error can be achieved for test data randomly chosen over the SNR range of 4 to 12.

Three Years of High-contrast Imaging of the PDS 70 b and c Exoplanets at Hα with MagAO-X: Evidence of Strong Protoplanet Hα Variability and Circumplanetary Dust

We present 3 yr of high-contrast imaging of the PDS 70 b and c accreting protoplanets with the new extreme AO system MagAO-X as part of the MaxProtoPlanetS survey of Hα protoplanets. In 2023 and 2024, our sharp (25–27 mas FWHM), well-AO-corrected (20%–26% Strehl), deep (2–3.6 hr) images detected compact (r ∼ 30 mas; r ∼ 3 au) circumplanetary disks (CPDs) surrounding both protoplanets. Starlight scattering off the front edge of these dusty CPDs is the likely source of the bright compact continuum light detected within ∼30 mas of both planets in our simultaneously obtained continuum 668 nm filter images. After subtraction of contaminating continuum and point-spread function residuals with pyKLIP angular differential imaging and spectral differential imaging, we obtained high-contrast ASDI Hα images of both planets in 2022, 2023, and 2024. We find the Hα line flux of planet b fell by (8.1 ± 1.6) × 10−16 erg s−1 cm−2, a factor of 4.6 drop in flux from 2022 to 2023. In 2024 March, planet b continued to be faint with just a slight 1.6× rise to an Hα line flux of (3.64 ± 0.87) × 10−16 erg s−1 cm−2. For c, we measure a significant increase of (2.74 ± 0.51) × 10−16 erg s−1 cm−2 from 2023 to 2024, which is a factor of 2.3 increase. So both protoplanets have recently experienced significant Hα variability with ∼1 yr sampling. In 2024, planet c is brighter than b: as c is brightening and b generally fading. We also tentatively detect one new point source “CC3” inside the inner disk (∼49 mas; at PA ∼ 295°; 2024) with orbital motion roughly consistent with a ∼5.6 au orbit.

Low probability of intercept (LPI) free-space optical communication with wavelength diversity in strong atmospheric turbulence regime

In physical-layer security and cryptography we are concerned with the security of the transmitted data, while in low probability of intercept (LPI) communication with protecting the privacy of the end users. In our recent publications related to LPI communications and radars over free-space optical (FSO) links we proposed to hide the constant-amplitude modulated data, imposed on thermal source beam, in ambient solar radiation to protect the end users privacy and at the same time improve the reliability and security, while reducing the detectability of transmitted signal by the adversary Willie. In order to study both LPI and covert communication concepts we have developed an FSO communication testbed at the University of Arizona campus with a 1.5 km-long FSO link. Here we present results of our FSO experiments, where we conducted both LPI and covert communications at data rates ranging from 125 Mb/s to 10 Gb/s, wherein the information beam is kept completely hidden under the ambient solar radiations as random thermal noise. To improve the system reliability to atmospheric turbulence effects we make use of wavelength diversity method as a low-cost, easy to implement and far more practical alternative to conventional adaptive optics systems.

Design and Experimental Validation of a Model-Free Controller for Beam Stabilization in Adaptive Optics Systems

Design and Experimental Validation of a Model-Free Controller for Beam Stabilization in Adaptive Optics Systems

Cascade adaptive optics with a second stage based on a Zernike wavefront sensor for exoplanet observations

Context. Over the past decade, the high-contrast observation of disks and gas giant planets around nearby stars has been made possible with ground-based instruments using extreme adaptive optics (XAO). These facilities produce images with a Strehl ratio higher than 90% in the H band, in median observing conditions and high-flux regime. However, the correction leaves behind adaptive optics (AO) residuals, which impede studies of fainter or less massive exoplanets. Aims. Cascade AO systems with a fast second stage based on a Pyramid wavefront sensor (PWFS) have recently emerged as an appealing solution to reduce the atmospheric wavefront errors. Since these phase aberrations are expected to be small, they can also be accurately measured by a Zernike wavefront sensor (ZWFS), a well-known concept for its high sensitivity and moderate linear capture range. We propose an alternative second stage that relies on the ZWFS to correct for the AO residuals. Methods. We implemented the cascade AO with a ZWFS-based control loop on the ESO’s GPU-based High-order adaptive OpticS Testbench (GHOST) to validate the scheme in monochromatic light. We emulated the XAO first stage in different observing conditions (wind speed, seeing) and determined the corresponding operation parameters (e.g., number of controlled modes, integrator gain, loop calibration) that lead to stable loop operation and good correction performance. Our strategy was assessed in terms of corrected wavefront errors and contrast gain in the images with a Lyot coronagraph to probe its efficiency. Results. In median wind speed and seeing, our second-stage AO with a ZWFS and a basic integrator was able to reduce the atmospheric residuals by a factor of 6 and increase the wavefront error stability with a gain of 2 between open and closed loop. In the presence of non-common path aberrations, we also achieved a contrast gain of a factor of 2 in the coronagraphic images at short separations from the source, proving the ability of our scheme to work in cascade with an XAO loop. In addition, it may prove useful for imaging fainter or lighter close-in companions. In more challenging conditions, contrast improvements are also achieved by adjusting the control loop features. Conclusions. Our study validates the ZWFS-based second-stage AO loop as an effective solution to address small residuals left over from a single-stage XAO system for the coronagraphic observations of circumstellar environments. Our first in-lab demonstration paves the way for more advanced versions of our approach with different temporal control laws, non-linear reconstructors, and spectral widths. This would allow our approach to operate in high-contrast facilities on the current 8–10 m class telescopes and Extremely Large Telescopes to observe exoplanets, all the way down to Earth analogs around M dwarfs.

High strehl and high contrast for the ELT instrument METIS

The Mid-infrared ELT Imager and Spectrograph (METIS) is a first-generation instrument for the Extremely Large Telescope (ELT), Europe’s next-generation 39 m ground-based telescope for optical and infrared wavelengths, which is currently under construction at the European Southern Observatory (ESO) site at Cerro Armazones in Chile. METIS will offer diffraction-limited imaging, low- and medium-resolution slit spectroscopy, and coronagraphy for high-contrast imaging between 3 and 13 microns, as well as high-resolution integral field spectroscopy between 3 and 5 microns. The main METIS science goals are the detection and characterisation of exoplanets, the investigation of proto-planetary disks, and the formation of planets. The Single-Conjugate Adaptive Optics (SCAO) system corrects atmospheric distortions and is thus essential for diffraction-limited observations with METIS. SCAO will be used for all observing modes, with high-contrast imaging imposing the most demanding requirements on its performance. The Final Design Review (FDR) of METIS took place in the fall of 2022; the development of the instrument, including its SCAO system, has since entered the Manufacturing, Assembly, Integration and Testing (MAIT) phase. Numerous challenging aspects of an ELT Adaptive Optics (AO) system are addressed in the mature designs for the SCAO control system and the SCAO hardware module: the complex interaction with the telescope entities that participate in the AO control, wavefront reconstruction with a fragmented and moving pupil, secondary control tasks to deal with differential image motion, non-common path aberrations and mis-registration. A K-band pyramid wavefront sensor and a GPU-based Real-Time Computer (RTC), tailored to the needs of METIS at the ELT, are core components. This current paper serves as a natural sequel to our previous work presented in Hippler et al. (2018). It reflects all the updates that were implemented between the Preliminary Design Review (PDR) and FDR, and includes updated performance estimations in terms of several key performance indicators, including achieved contrast curves. We outline all important design decisions that were taken, and present the major challenges we faced and the main analyses carried out to arrive at these decisions and eventually the final design. We also elaborate on our testing and verification strategy, and, last not least, comprehensively present the full design, hardware and software in this paper to provide a single source of reference which will remain valid at least until commissioning.

Ultrafast adaptive optics for imaging the living human eye

Adaptive optics (AO) is a powerful method for correcting dynamic aberrations in numerous applications. When applied to the eye, it enables cellular-resolution retinal imaging and enhanced visual performance and stimulation. Most ophthalmic AO systems correct dynamic aberrations up to 1−2 Hz, the commonly-known cutoff frequency for correcting ocular aberrations. However, this frequency may be grossly underestimated for more clinically relevant scenarios where the medical impact of AO will be greatest. Unfortunately, little is known about the aberration dynamics in these scenarios. A major bottleneck has been the lack of sufficiently fast AO systems to measure and correct them. We develop an ultrafast ophthalmic AO system that increases AO bandwidth by ~30× and improves aberration power rejection magnitude by 500×. We demonstrate that this much faster ophthalmic AO is possible without sacrificing other system performances. We find that the discontinuous-exposure AO-control scheme runs 32% slower yet achieves 53% larger AO bandwidth than the commonly used continuous-exposure scheme. Using the ultrafast system, we characterize ocular aberration dynamics in six clinically-relevant scenarios and find their power spectra to be 10−100× larger than normal. We show that ultrafast AO substantially improves aberration correction and retinal imaging performance in these scenarios compared with conventional AO.

Transfer learning enhanced convolutional neural network for efficient monitoring of a rate-adaptive coherent transmission system

With the demand for capacity and the complex evolution of network topology, flexible coherent communication transceivers are being considered for deployment in a short reach (< 40 km) scenario. The probability constellation shaping (PCS)-based system provides the capability to continuously change the data rate of communication systems, thus calling for the need to monitor both the link rate and the network performance. In this work, a transfer learning (TL)-enhanced entropy and performance estimation scheme is developed to monitor a rate-continuous coherent optical transmission system with various signal-to-noise ratios (SNR). The scheme is demonstrated over a 40-km coherent transmission system with a line rate varying from 128 to 192 Gbps. The entropy is varied from 4 to 6 bits with an interval of 0.05 bits, corresponding to a fine-grained rate of 1.6 Gbps. The mean absolute error (MAE) of entropy tasks reaches 0.158 bits with TL, while that of SNR tasks is reduced to 0.44 dB with TL (for 6 bits of entropy). Our solution allows fine-grained monitoring of link rate and SNR for future adaptive optical communication systems.

Angle‐Based Neuromorphic Wave Normal Sensing

AbstractAngle‐based wavefront sensing has a rich historical background in measuring optical aberrations. The Shack–Hartmann wavefront sensor is widely employed in adaptive optics systems due to its high optical efficiency and high robustness. However, simultaneously achieving high sensitivity and large dynamic range is still challenging, limiting the performance of diagnosing fast‐changing turbulence. To overcome this limitation, angle‐based neuromorphic wave normal sensing, which serves as a differentiable framework developed on the asynchronous event modality is proposed. Herein, it is illustrated that the emerging computational neuromorphic imaging paradigm enables a direct perception of a high‐dimensional wave normal from the highly efficient temporal diversity measurement. To the best of available knowledge, the proposed scheme is the first to successfully surpass the spot‐overlapping issue caused by the curvature constraint in classical angle‐based wavefront sensing setups under challenging dynamic scenarios.

Super-oscillation sub-diffraction focusing with emulated atmospheric turbulence

The super-oscillation (SO) phenomena successfully applied to super-resolution optical telescopes have yet to study the existence of atmospheric turbulence (AT). In this paper, we first experimentally investigate the sub-diffraction focusing of the SO light field in the atmospheric-like turbulence. The 137-element adaptive optics (AO) system is utilized to correct the dynamic wavefront aberration produced by the AT and obtain the AO closed-loop RMS of the residual wavefront error ∼λ/15. For a proofed telescope (clear aperture 12 mm and focal length 1000 mm) @λ=632.8 nm, the FWHM of the experimental SO spot under the modest AT (wavefront error RMS ∼0.57λ) is about 0.79 times of the Airy spot compared with the non-AT result of 0.76 times, while the strong AT (wavefront error RMS ∼1.35λ) erases the sub-diffraction focusing effect of the SO field and the average side-lobe intensity increases significantly. This study is promising for super-resolving telescope, synthetic aperture for visible imaging, etc.

Adaptive Threshold Wave Front Sensing for Portable Adaptive Optics System Driven by Hybrid Parallel Technique

Our Portable Adaptive Optics (PAO) system designed for high-contrast imaging of exoplanets with current 2–4 m class telescopes achieves a correction speed of nearly 1000 Hz, utilizing a Shack–Hartmann Wave Front Sensor (WFS) in a 9 × 9 sub-aperture configuration. As we look towards adapting the PAO system for larger telescopes, an increase in the number of sub-apertures in the WFS and enhanced precision in wave front detection are imperative. Originally programmed in LabVIEW, our initial PAO software is based on a traditional centroid calculation module for nighttime wave front sensing and lacks adaptive processing of background noise. To address these limitations and to boost the PAO system's performance and accuracy in wave front detection, we propose a compressive neural network (Th-Net) combined with a specialized hybrid parallel programming approach for wave front detection. Our experimental results indicate that this hybrid parallel technique and Th-Net significantly enhance the PAO system's operational speed and wave front detection precision under uneven background noise. This work paves the way so that a duplicable and low-cost PAO system can be used for direct imaging of exoplanets with large telescopes.

Performance comparison of the Shack-Hartmann and pyramid wavefront sensors with a laser guide star for 40 m telescopes

Context. Upcoming giant segmented mirror telescopes will use laser guide stars (LGS) for their adaptive optics (AO) systems. Two options of wavefront sensors (WFSs) are the Shack-Hartmann wavefront sensor (SHWFS) and the pyramid wavefront sensor (PWFS). Aims. In this paper, we compare the noise performance of the PWFS and the SHWFS. We aim to identify which of the two is best to use in the context of a single or tomographic configuration. Methods. To compute the noise performance, we extended a noise model developed for the PWFS to be used with the SHWFS. To do this, we expressed the centroiding algorithm of the SHWFS as a matrix-vector multiplication, which allowed us to use the statistics of noise to compute its propagation through the AO loop. We validated the noise model with end-to-end simulations for telescopes of 8 and 16 m in diameter. Results. For an AO system with only one WFS, we found that given the same number of subapertures, the PWFS outperforms the SHWFS. For a 40 m telescope, the limiting magnitude of the PWFS is around one magnitude higher than the SHWFS. When using multiple WFS and a generalized least-squares estimator to combine the signal, our model predicts that in a tomographic system, the SHWFS performs better than the PWFS (with a limiting magnitude that is higher by a 0.3 magnitude. When using sub-electron RON detectors for the PWFS, the performance quality is almost identical for the two WFSs. Conclusions. We find that when using a single WFS with LGS, PWFS is a better alternative than the SH. For a tomographic system, both sensors would give roughly the same performance.

Spectroscopy using a visible photonic lantern at the Subaru Telescope: Laboratory characterization and the first on-sky demonstration on Ikiiki (α Leo) and ‘Aua (α Ori)

Context. Photonic lanterns (PLs) are waveguide devices enabling high-throughput single-mode spectroscopy and high angular resolution. Aims. We aim to present the first on-sky demonstration of a PL operating in visible light, to measure its throughput and assess its potential for high-resolution spectroscopy of compact objects. Methods. We used the SCExAO instrument (a double-stage extreme adaptive optics system installed at the Subaru Telescope) and FIRST mid-resolution spectrograph (R 3000) to test the visible capabilities of the PL on internal source and on-sky observations. Results. The best averaged coupling efficiency over the PL field of view was measured at 51% ± 10%, with a peak at 80%. We also investigated the relationship between coupling efficiency and the Strehl ratio for a PL, comparing them with those of a single-mode fiber (SMF). Findings show that in the adaptive optics regime a PL offers a better coupling efficiency performance than an SMF, especially in the presence of low-spatial-frequency aberrations. We observed Ikiiki (α Leo – mR = 1.37) and ‘Aua (α Ori – mR = −1.17) at a frame rate of 200 Hz. Under median seeing conditions (about 1 arcsec measured in the H band) and large tip or tilt residuals (over 20 mas), we estimated an average light coupling efficiency of 14.5% ± 7.4%, with a maximum of 42.8% at 680 nm. We were able to reconstruct both star’s spectra, containing various absorption lines. Conclusions. The successful demonstration of this device opens new possibilities in terms of high-throughput single-mode fiber-fed spectroscopy in the visible. The demonstrated on-sky coupling efficiency performance would not have been achievable with a single SMF injection setup under similar conditions, partly because the residual tip or tilt alone exceeded the field of view of a visible SMF (18 mas at 700 nm). This emphasizes the enhanced resilience of PL technology to such atmospheric disturbances. The additional capabilities in high angular resolution are also promising but still have to be demonstrated in a forthcoming investigation.

Long-term changes of sodium column abundance at 24.6°S above the Atacama Desert in Chile

Aims. The utilisation of artificial laser guide star (LGS) obviates the necessity for a prominent natural guide star (NGS) within adaptive optics (AO) systems. High-power lasers are fundamental components of most AO systems today. The generation of an LGS relies on the excitation of sodium (denoted by its symbol Na) atoms situated in the upper atmosphere. Therefore, the sodium vertical column density (denoted as CNa) is a crucial parameter. Beyond ensuring the optimal and stable performance of an AO system, knowledge of the return flux from an LGS is imperative during the design phase, aiding in the accurate specification of both the LGS and the AO system. The availability of sodium in the upper atmosphere has been the focal point of diverse studies, exhibiting a pronounced dependence on the specific observatory site. Furthermore, it is well established that CNa varies across multiple timescales, including hours, nights, months, seasons, and even several years. As many of the world’s largest telescopes are located in the Atacama Desert in northern Chile, our objective is to provide CNa statistics pertinent to this specific region. Methods. We used telemetry data from the AO systems operational at the Paranal Observatory (24.6°S, 70.4°W): Ground Atmospheric Layer Adaptive Corrector for Spectroscopic Imaging (GALACSI) and Ground layer Adaptive Optics system Assisted by Lasers (GRAAL). We combined these data with measurements from two space instruments: SCanning Imaging Absorption Spectrometer for Atmospheric CHartographY (SCIAMACHY) and Optical Spectrograph and Infrared Imaging System (OSIRIS), as well as with simulated data from the Whole Atmosphere Community Climate Model (WACCM). We carefully analysed and compared these datasets to develop a statistical model for the temporal variations of CNa. Results. We validated the use of the AO telemetry data from Paranal systems to retrieve the CNa. The near-continuous measurements encompassing the period from mid-2017 to the end of 2023 facilitated the determination of monthly and yearly abundance and variability of Na in the mesopause region. Throughout the complete years of measurement, the annual and semi-annual variations exhibit consistent characteristics that align with previously documented findings in atmospheric studies. Through meticulous comparison and the fitting of various long-term datasets, we formulated a model depicting the evolution of CNa over time. The validity of our data processing and model is scrutinised, and the results obtained for the Paranal latitude exhibit noteworthy concordance with the findings of other studies.