Search

ESO is in the process of upgrading one of the two FORS (FOcal Reducer/low dispersion Spectrograph) instruments - a multi-mode (imaging, polarimetry, long-slit, and multi-object spectroscopy) optical instrument mounted on the Cassegrain focus of Unit Telescope 1 of ESO's Very Large Telescope. FORS1 was moved from Chile to Trieste, and is undergoing complete refurbishment, including the exchange of all motorised parts. In addition, new software is developed, based on the Extremely Large Telescope Instrument Control Software Framework, as the upgraded FORS1 will be the first instrument in operations to use this framework. The new Teledyne e2V CCD has now been procured and is undergoing testing with the New Generation Controller at ESO. In addition, a new set of grisms have been developed, and a new set of filters will be purchased. A new internal calibration unit has been designed, making the operations more efficient., Comment: This paper is dedicated to the memory of our former colleague, Mario Nonino, who passed away prematurely. Proceedings for the SPIE Astronomical Telescopes and Instrumentation 2024

Fully-unsupervised Person and Vehicle Re-Identification have received increasing attention due to their broad applicability in surveillance, forensics, event understanding, and smart cities, without requiring any manual annotation. However, most of the prior art has been evaluated in datasets that have just a couple thousand samples. Such small-data setups often allow the use of costly techniques in time and memory footprints, such as Re-Ranking, to improve clustering results. Moreover, some previous work even pre-selects the best clustering hyper-parameters for each dataset, which is unrealistic in a large-scale fully-unsupervised scenario. In this context, this work tackles a more realistic scenario and proposes two strategies to learn from large-scale unlabeled data. The first strategy performs a local neighborhood sampling to reduce the dataset size in each iteration without violating neighborhood relationships. A second strategy leverages a novel Re-Ranking technique, which has a lower time upper bound complexity and reduces the memory complexity from O(n^2) to O(kn) with k << n. To avoid the pre-selection of specific hyper-parameter values for the clustering algorithm, we also present a novel scheduling algorithm that adjusts the density parameter during training, to leverage the diversity of samples and keep the learning robust to noisy labeling. Finally, due to the complementary knowledge learned by different models, we also introduce a co-training strategy that relies upon the permutation of predicted pseudo-labels, among the backbones, with no need for any hyper-parameters or weighting optimization. The proposed methodology outperforms the state-of-the-art methods in well-known benchmarks and in the challenging large-scale Veri-Wild dataset, with a faster and memory-efficient Re-Ranking strategy, and a large-scale, noisy-robust, and ensemble-based learning approach., Comment: This paper has been submitted for possible publication in an IEEE Transactions

ESCAPE (European Science Cluster of Astronomy and Particle physics ESFRI research infrastructures) is a project to set up a cluster of ESFRI (European Strategy Forum on Research Infrastructures) facilities for astronomy, astroparticle and particle physics to face the challenges emerging through the modern multi-disciplinary data driven science. One of the main goal of ESCAPE is the building of ESAP (ESFRI Science Analysis Platform), a science platform for the analysis of open access data available through the EOSC (European Open Science Cloud) environment. ESAP will allow EOSC researchers to identify and stage existing data collections for analysis, share data, share and run scientific workflows. For many of the concerned ESFRIs and RIs, the data scales involved require significant computational resources (storage and compute) to support processing and analysis. The EOSC-ESFRI science platform therefore must implement appropriate interfaces to an underlying HPC (High Performance Computing) or HTC (High Throughput Computing) infrastructure to take advantage of it. This poster describes the analysis done to identify the main requirements for the implementation of the interfaces enabling the ESAP data access and computation resources integration in HPC and HTC computation infrastructures in terms of authentication and authorization policies, data management, workflow deployment and run., Comment: Will appear in Proceedings ADASSXXX ASP Conference Series

We are in the era of the Big Data. In Astronomy and Astrophysics, the massive amounts of data generated are, as of today, in the Peta-scale if not already in the Exa-scale. In the near future, we will see the data collected size and complexity grow further constantly, setting new challenges for data processing, reduction and analysis. This will pose new needs in terms of software and hardware solutions but also in terms of new models for resource management, access and sharing. In Astronomy and Astrophysics, in the environment of the International Virtual Observatory Alliance (IVOA), a big work has already been done with regards to data, gaining complete data FAIRness. In this paper, a model is proposed, based on the IVOA architecture, for software and hardware solutions for data analysis. The goal of this model is to build a cloud to access Astronomy and Astrophysics resources following the FAIR principles., Comment: Will appear in Proceedings ADASSXXXII ASP Conference Series

In unconstrained scenarios, face recognition and person re-identification are subject to distortions such as motion blur, atmospheric turbulence, or upsampling artifacts. To improve robustness in these scenarios, we propose a methodology called Distortion-Adaptive Learned Invariance for Identification (DaliID) models. We contend that distortion augmentations, which degrade image quality, can be successfully leveraged to a greater degree than has been shown in the literature. Aided by an adaptive weighting schedule, a novel distortion augmentation is applied at severe levels during training. This training strategy increases feature-level invariance to distortions and decreases domain shift to unconstrained scenarios. At inference, we use a magnitude-weighted fusion of features from parallel models to retain robustness across the range of images. DaliID models achieve state-of-the-art (SOTA) for both face recognition and person re-identification on seven benchmark datasets, including IJB-S, TinyFace, DeepChange, and MSMT17. Additionally, we provide recaptured evaluation data at a distance of 750+ meters and further validate on real long-distance face imagery.

The EU ESCAPE project is developing ESAP, ESFRI 1 Scientific Analysis Platform, as an API gateway that enables the seamless integration of independent services accessing distributed data and computing resources. In ESCAPE we are exploring the possibility of exploiting EGI's OpenStack cloud computing services through ESAP. In our contribution we briefly describe ESCAPE and ESAP, the the use cases, the work done to automate a virtual machine creation in EGI's OpenStack cloud computing, drawbacks and possible solutions., Comment: Will be published in ADASS XXXII Proceedings - Astronomical Society of the Pacific Conference Series

End-to-end simulations play a key role in the analysis of any high-sensitivity CMB experiment, providing high-fidelity systematic error propagation capabilities unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data, or as a random realization independent from the data. We refer to these as Bayesian and frequentist simulations, respectively. We show that the two options lead to significantly different correlation structures, as frequentist simulations, contrary to Bayesian simulations, effectively include cosmic variance, but exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties, and we argue that they therefore also have different and complementary scientific uses, even if this dichotomy is not absolute. Before BeyondPlanck, most pipelines have used a mix of constrained and random inputs, and used the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. BeyondPlanck represents the first end-to-end CMB simulation framework that is able to generate both types of simulations, and these new capabilities have brought this topic to the forefront. The Bayesian BeyondPlanck simulations and their uses are described extensively in a suite of companion papers. In this paper we consider one important applications of the corresponding frequentist simulations, namely code validation. That is, we generate a set of 1-year LFI 30 GHz frequentist simulations with known inputs, and use these to validate the core low-level BeyondPlanck algorithms; gain estimation, correlated noise estimation, and mapmaking.

Rosetta is a science platform for resource-intensive, interactive data analysis which runs user tasks as software containers. It is built on top of a novel architecture based on framing user tasks as microservices - independent and self-contained units - which allows to fully support custom and user-defined software packages, libraries and environments. These include complete remote desktop and GUI applications, besides common analysis environments as the Jupyter Notebooks. Rosetta relies on Open Container Initiative containers, which allow for safe, effective and reproducible code execution; can use a number of container engines and runtimes; and seamlessly supports several workload management systems, thus enabling containerized workloads on a wide range of computing resources. Although developed in the astronomy and astrophysics space, Rosetta can virtually support any science and technology domain where resource-intensive, interactive data analysis is required.

We present Planck LFI frequency sky maps derived within the BeyondPlanck framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support - for the first time - full Bayesian error propagation for these effects at full angular resolution. We compare our posterior mean maps with traditional frequency maps delivered by the Planck collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of $\delta g_{0}/g_{0} =5 \cdot 10^{-5}$, which is nominally 40 times smaller than that reported by Planck 2018. However, the original Planck 2018 estimate has a non-trivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced directly from the posterior samples without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modelling and error propagation, and may play an important role for future CMB B-mode experiments. (Abridged.), Comment: 32 pages, 23 figures, data available from https://www.cosmoglobe.uio.no/

We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations derived through global end-to-end Bayesian processing. We use these samples to study correlations between CMB, foreground, and instrumental parameters, and we identify a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales, which is mitigated through model reduction, masking, and resampling. We compare our posterior-based CMB results with previous Planck products, and find generally good agreement, but with higher noise due to exclusion of HFI data. We find a best-fit CMB dipole amplitude of $3362.7\pm1.4{\mu}K$, in excellent agreement with previous Planck results. The quoted uncertainty is derived directly from the sampled posterior distribution, and does not involve any ad hoc contribution for systematic effects. Similarly, we find a temperature quadrupole amplitude of $\sigma^{TT}_2=229\pm97{\mu}K^2$, in good agreement with previous results in terms of the amplitude, but the uncertainty is an order of magnitude larger than the diagonal Fisher uncertainty. Relatedly, we find lower evidence for a possible alignment between $\ell = 2$ and $\ell = 3$ than previously reported due to a much larger scatter in the individual quadrupole coefficients, caused both by marginalizing over a more complete set of systematic effects, and by our more conservative analysis mask. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. This is the first time the sample-based asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to $\ell\le600$, and it now accounts for the majority of the cosmologically important information. Cosmological parameter constraints are presented in a companion paper. (Abriged), Comment: 26 pages, 24 figures. Submitted to A&A. Part of the BeyondPlanck paper suite

The BeyondPlanck and Cosmoglobe collaborations have implemented the first integrated Bayesian end-to-end analysis pipeline for CMB experiments. The primary long-term motivation for this work is to develop a common analysis platform that supports efficient global joint analysis of complementary radio, microwave, and sub-millimeter experiments. A strict prerequisite for this to succeed is broad participation from the CMB community, and two foundational aspects of the program are therefore reproducibility and Open Science. In this paper, we discuss our efforts toward this aim. We also discuss measures toward facilitating easy code and data distribution, community-based code documentation, user-friendly compilation procedures, etc. This work represents the first publicly released end-to-end CMB analysis pipeline that includes raw data, source code, parameter files, and documentation. We argue that such a complete pipeline release should be a requirement for all major future and publicly-funded CMB experiments, noting that a full public release significantly increases data longevity by ensuring that the data quality can be improved whenever better processing techniques, complementary datasets, or more computing power become available, and thereby also taxpayers' value for money; providing only raw data and final products is not sufficient to guarantee full reproducibility in the future.

We present cosmological parameter constraints as estimated using the Bayesian BeyondPlanck (BP) analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data to final cosmological parameters. As a first demonstration of the method, we analyze time-ordered Planck LFI observations, combined with selected external data (WMAP 33-61GHz, Planck HFI DR4 353 and 857GHz, and Haslam 408MHz) in the form of pixelized maps which are used to break critical astrophysical degeneracies. Overall, all results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter of about 1 sigma when considering only temperature multipoles between 29

We describe the correction procedure for Analog-to-Digital Converter (ADC) differential non-linearities (DNL) adopted in the Bayesian end-to-end BeyondPlanck analysis framework. This method is nearly identical to that developed for the official LFI Data Processing Center (DPC) analysis, and relies on the binned rms noise profile of each detector data stream. However, rather than building the correction profile directly from the raw rms profile, we first fit a Gaussian to each significant ADC-induced rms decrement, and then derive the corresponding correction model from this smooth model. The main advange of this approach is that only samples which are significantly affected by ADC DNLs are corrected. The new corrections are only applied to data for which there is a clear detection of the non-linearities, and for which they perform at least comparably with the DPC corrections. Out of a total of 88 LFI data streams (sky and reference load for each of the 44 detectors) we apply the new minimal ADC corrections in 25 cases, and maintain the DPC corrections in 8 cases. All these correctsion are applited to 44 or 70 GHz channels, while, as in previous analyses, none of the 30 GHz ADCs show significant evidence of non-linearity. By comparing the BeyondPlanck and DPC ADC correction methods, we estimate that the residual ADC uncertainty is about two orders of magnitude below the total noise of both the 44 and 70 GHz channels, and their impact on current cosmological parameter estimation is small. However, we also show that non-idealities in the ADC corrections can generate sharp stripes in the final frequency maps, and these could be important for future joint analyses with HFI, WMAP, or other datasets. We therefore conclude that, although the existing corrections are adequate for LFI-based cosmological parameter analysis, further work on LFI ADC corrections is still warranted., Comment: 9 pages, 8 figures, mild language edits

We present the first application of the Cosmoglobe analysis framework by analyzing 9-year $\mathit{WMAP}$ time-ordered observations using similar machinery as BeyondPlanck utilizes for $\mathit{Planck}$ LFI. We analyze only the $\mathit Q$-band (41 GHz) data and report on the low-level analysis process from uncalibrated time-ordered data to calibrated maps. Most of the existing BeyondPlanck pipeline may be reused for $\mathit{WMAP}$ analysis with minimal changes to the existing codebase. The main modification is the implementation of the same preconditioned biconjugate gradient mapmaker used by the $\mathit{WMAP}$ team. Producing a single $\mathit{WMAP}$ $\mathit Q$1-band sample requires 22 CPU-hrs, which is slightly more than the cost of a $\mathit{Planck}$ 44 GHz sample of 17 CPU-hrs; this demonstrates that full end-to-end Bayesian processing of the $\mathit{WMAP}$ data is computationally feasible. In general, our recovered maps are very similar to the maps released by the $\mathit{WMAP}$ team, although with two notable differences. In temperature we find a $\sim2\,\mathrm{\mu K}$ quadrupole difference that most likely is caused by different gain modeling, while in polarization we find a distinct $2.5\,\mathrm{\mu K}$ signal that has been previously called poorly-measured modes by the $\mathit{WMAP}$ team. In the Cosmoglobe processing, this pattern arises from temperature-to-polarization leakage from the coupling between the CMB Solar dipole, transmission imbalance, and sidelobes. No traces of this pattern are found in either the frequency map or TOD residual map, suggesting that the current processing has succeeded in modelling these poorly measured modes within the assumed parametric model by using $\mathit{Planck}$ information to break the sky-synchronous degeneracies inherent in the $\mathit{WMAP}$ scanning strategy., Comment: 11 figures, submitted to A&A. Includes updated instrument model and changes addressing referee comments

Learning from fully-unlabeled data is challenging in Multimedia Forensics problems, such as Person Re-Identification and Text Authorship Attribution. Recent self-supervised learning methods have shown to be effective when dealing with fully-unlabeled data in cases where the underlying classes have significant semantic differences, as intra-class distances are substantially lower than inter-class distances. However, this is not the case for forensic applications in which classes have similar semantics and the training and test sets have disjoint identities. General self-supervised learning methods might fail to learn discriminative features in this scenario, thus requiring more robust strategies. We propose a strategy to tackle Person Re-Identification and Text Authorship Attribution by enabling learning from unlabeled data even when samples from different classes are not prominently diverse. We propose a novel ensemble-based clustering strategy whereby clusters derived from different configurations are combined to generate a better grouping for the data samples in a fully-unsupervised way. This strategy allows clusters with different densities and higher variability to emerge, reducing intra-class discrepancies without requiring the burden of finding an optimal configuration per dataset. We also consider different Convolutional Neural Networks for feature extraction and subsequent distance computations between samples. We refine these distances by incorporating context and grouping them to capture complementary information. Our method is robust across both tasks, with different data modalities, and outperforms state-of-the-art methods with a fully-unsupervised solution without any labeling or human intervention., Comment: This work has been accepted for publication in the IEEE Transactions on Information Forensics and Security

We present the intensity foreground algorithms and model employed within the BeyondPlanck analysis framework. The BeyondPlanck analysis is aimed at integrating component separation and instrumental parameter sampling within a global framework, leading to complete end-to-end error propagation in the $Planck$ Low Frequency Instrument (LFI) data analysis. Given the scope of the BeyondPlanck analysis, a limited set of data is included in the component separation process, leading to foreground parameter degeneracies. In order to properly constrain the Galactic foreground parameters, we improve upon the previous $\texttt{Commander}$ component separation implementation by adding a suite of algorithmic techniques. These algorithms are designed to improve the stability and computational efficiency for weakly constrained posterior distributions. These are: 1) joint foreground spectral parameter and amplitude sampling, building on ideas from Miramare; 2) component-based monopole determination; 3) joint spectral parameter and monopole sampling; and 4) application of informative spatial priors for component amplitude maps. We find that the only spectral parameter with a significant signal-to-noise ratio using the current BeyondPlanck data set is the peak frequency of the anomalous microwave emission component, for which we find $\nu_{\mathrm{p}}=25.3\pm0.5$ GHz; all others must be constrained through external priors. Future works will be aimed at integrating many more data sets into this analysis, both map and time-ordered based, thereby gradually eliminating the currently observed degeneracies in a controlled manner with respect to both instrumental systematic effects and astrophysical degeneracies. When this happens, the simple LFI-oriented data model employed in the current work will need to be generalized to account for both a richer astrophysical model and additional instrumental effects., Comment: 27 pages, 23 figures, 3 tables, part 13 of the BeyondPlanck release. All BeyondPlanck products and software will be released publicly at http://beyondplanck.science. Paper version as accepted by A&A

We constrain the level of polarized anomalous microwave emission (AME) on large angular scales using $\textit{Planck}$ LFI and $\textit{WMAP}$ polarization data within a Bayesian CMB analysis framework. We model synchrotron emission with a power-law spectral energy distribution, and the sum of AME and thermal dust emission through linear regression with the $\textit{Planck}$ HFI 353 GHz data. This template-based dust emission model allows us to constrain the level of polarized AME while making minimal assumptions on its frequency dependence. We neglect cosmic microwave background fluctuations, but show through simulations that these have a minor impact on the results. We find that the resulting AME polarization fraction confidence limit is sensitive to the polarized synchrotron spectral index prior, and for priors steeper than $\beta_{\mathrm{s}} = -3.1\pm0.1$ we find an upper limit of $p_{\mathrm{AME}}^{\rm max}\lesssim 0.6\,\%$ ($95\,\%$ confidence). In contrast, for $\beta_{\mathrm{s}}=-3.0\pm0.1$, we find a nominal detection of $p_{\mathrm{AME}}=2.5\pm1.0\,\%$ ($95\,\%$ confidence). These data are thus not strong enough to simultaneously and robustly constrain both polarized synchrotron emission and AME, and our main result is therefore a constraint on the AME polarization fraction explicitly as a function of $\beta_\mathrm{s}$. Combining the current $\textit{Planck}$ and $\textit{WMAP}$ observations with measurements from high-sensitivity low-frequency experiments such as C-BASS and QUIJOTE will be critical to improve these limits further., Comment: 10 pages, 9 figures, part 15 of the BeyondPlanck release. All BeyondPlanck products and software will be released publicly at http://beyondplanck.science. Refereed, edited, and accepted by A&A. Added references, added arxiv IDs to BeyondPlanck papers. Figure update. Expanded discussion on AME models. Moved title from BeyondPlanck XV to BeyondPlanck XVI due to internal reordering

We describe the computational infrastructure for end-to-end Bayesian CMB analysis implemented by the BeyondPlanck collaboration. This code is called commander3, and provides a statistically consistent framework for global analysis of CMB and microwave observations, and may be useful for a wide range of legacy, current, and future experiments. The paper has three main goals. Firstly, we provide a high-level overview of the existing code base, aiming to guide readers who wish to extend and adapt the code according to their own needs, or to reimplement it from scratch in a different programming language. Secondly, we discuss some critical computational challenges that arise within any global CMB analysis framework, for instance in-memory compression of time-ordered data, FFT optimization, and parallelization and load-balancing. Thirdly, we quantify the CPU and RAM requirements for the current BeyondPlanck analysis, and find that a total of 1.5 TB of RAM is required for efficient analysis, and the total cost of a full Gibbs sample is 170 CPU-hrs, including both low-level processing and high-level component separation, which is well within the capabilities of current low-cost computing facilities. The existing code base is made publicly available under a GNU General Public Library (GPL) license., Comment: 16 Pages, 7 Figures. Part of the BeyondPlanck paper suite

We introduce a new formulation of the Conviqt convolution algorithm in terms of spin harmonics, and apply this to the problem of sidelobe correction for BeyondPlanck, the first end-to-end Bayesian Gibbs sampling framework for CMB analysis. We compare our implementation to the previous Planck LevelS implementation, and find good agreement between the two codes in terms of accuracy, but with a speed-up reaching a factor of 3--10, depending on the frequency bandlimits, $l_{\textrm{max}}$ and $m_{\textrm{max}}$. The new algorithm is significantly simpler to implement and maintain, since all low-level calculations are handled through an external spherical harmonic transform library. We find that our mean sidelobe estimates for Planck LFI agree well with previous efforts. Additionally, we present novel sidelobe rms maps that quantify the uncertainty in the sidelobe corrections due to variations in the sky model., Comment: 9 pages, 8 figures. Part of the BeyondPlanck paper suite

We discuss the treatment of bandpass and beam leakage corrections in the Bayesian BeyondPlanck CMB analysis pipeline as applied to the Planck LFI measurements. As a preparatory step, we first apply three corrections to the nominal LFI bandpass profiles including removal of a known systematic effect in the ground measuring equipment at 61 GHz; smoothing of standing wave ripples; and edge regularization. The main net impact of these modifications is an overall shift in the 70 GHz bandpass of +0.6 GHz; we argue that any analysis of LFI data products, either from Planck or BeyondPlanck, should use these new bandpasses. In addition, we fit a single free bandpass parameter for each radiometer of the form $\Delta_i = \Delta_0 + \delta_i$, where $\Delta_0$ represents an absolute frequency shift per frequency band and $\delta_i$ is a relative shift per detector. The absolute correction is only fitted at 30 GHz with a full $\chi^2$-based likelihood, resulting in a correction of $\Delta_{30}=0.24\pm0.03\,$GHz. The relative corrections are fitted using a spurious map approach, fundamentally similar to the method pioneered by the WMAP team, but without introducing many additional degrees of freedom. All bandpass parameters are sampled using a standard Metropolis sampler within the main BeyondPlanck Gibbs chain, and bandpass uncertainties are thus propagated to all other data products in the analysis. In total, we find that our bandpass model significantly reduces leakage effects. For beam leakage corrections, we adopt the official Planck LFI beam estimates without additional degrees of freedom, and only marginalize over the underlying sky model. We note that this is the first time leakage from beam mismatch has been included for Planck LFI maps., Comment: 14 pages, 11 figures, this is part 10 in the BeyondPlanck release. All BeyondPlanck products and software will be released publicly at http://beyondplanck.science. Submitted to A&A

Interference-fit joints are typically adopted to produce permanent assemblies among mechanical parts. The resulting contact pressure is generally used for element fixing or to allow load transmission. Nevertheless, some special designs take advantage of the contact pressure to induce desiderata deformation or to mitigate the stress field inside the structure. Biased interference fitting between a planar mirror and an external ring could be used to induce the required curvature to realize new adaptive lens for optical aberration correction. Recently, thermally-actuated deformable mirror on this principle based, was proposed and prototyped. Although the feasibility and utility of such innovative lens was demonstrated, no comprehensive theory was developed to describe mirror behaviour and predict their curvature. Nowadays, the use of approximated numerical approach, such as the finite element method, is the only way to study the interaction between biased and interference fitted bodies. The paper aims to give the theoretical background for the correct design of adaptive lens actuated by interference fitting. A new formulation for the curvature prediction is proposed and compared with finite element analysis and available experimental measurements., Comment: 25 pages, 14 figures