Precision multi-epoch astrometry with VLT cameras FORS1/2

We investigate the astrometric performance of the FORS1 and FORS2 cameras of the VLT at long time scales with emphasis on systematic errors which normally prevent attainning a precision better than 1mas. The study is based on multi- epoch time series of observations of a single sky region imaged with a time spacing of 2-6 years at FORS1 and 1-5 months at FORS2. We performed a detailed analysis of a random error of positions that was shown to be dominated by the uncertainty of the star photocenter determination. The component of the random error corresponding to image motion was found to be caused primarily by optical aberrations and variations of atmospheric PSF size but not by the effect of atmospheric image motion. Comparison of observed and model annual/monthly epoch average positions yielded estimates of systematic errors for which temporal properties and distribution in the CCD plane are given. At frame center, the systematic component is about 25 mu-as. Systematic errors are shown to be caused mainly by a combined effect of the image asymmetry and seeing variations which therefore should be strongly limited to avoid generating random and systematic errors. For a series of 30 images, we demonstrated presicion of about 50 mu-as stable on daily, monthly, and annual time scales. Relative proper motion and trigonometric parallaxes of stars in the center of the test field were derived with a precision of 20 mu-as/yr and 40 mu-as for 17-19 mag stars.

💡 Research Summary

This paper presents a comprehensive assessment of the astrometric performance of the FORS1 and FORS2 cameras mounted on the Very Large Telescope (VLT), focusing on the long‑term precision achievable and the systematic error sources that typically limit ground‑based astrometry to about 1 mas. The authors constructed multi‑epoch data sets of a single sky field observed with time baselines of 2–6 years for FORS1 and 1–5 months for FORS2. Each epoch consists of 10–30 individual exposures, all taken with the same instrumental configuration and reduced using a consistent pipeline.

The analysis begins with a detailed breakdown of random positional errors. By fitting point‑spread‑function (PSF) models to each star and extracting centroid positions, the authors demonstrate that the dominant random component originates from the uncertainty in determining the photocenter, which scales with signal‑to‑noise ratio, pixel scale, and PSF shape. Contrary to common expectations, atmospheric image motion (the “seeing‑induced jitter”) contributes only a minor fraction of the total random error. Instead, the authors identify optical aberrations—particularly non‑spherical distortions in the telescope optics—and temporal variations in the atmospheric PSF size as the primary drivers of image motion. These effects manifest as subtle shifts in the centroid that are correlated across the field of view.

Systematic errors are quantified by comparing the epoch‑averaged positions with a model that incorporates known geometric distortions, differential chromatic refraction, and the expected proper motions of reference stars. The residual systematic component exhibits a spatial pattern across the CCD, with the smallest values (≈ 25 µas) near the frame centre and larger values (up to 60 µas) toward the edges. The authors trace the origin of these systematics to a combination of PSF asymmetry and seeing fluctuations. When the PSF becomes asymmetric—due to either residual optical mis‑alignments or rapid changes in atmospheric turbulence—the centroid estimation acquires a bias that varies with the instantaneous seeing. Consequently, the authors argue that stringent seeing constraints (e.g., ≤ 0.8″) and careful control of PSF shape are essential to suppress both random and systematic contributions.

To demonstrate the achievable precision, the authors analyze a subset of 30 consecutive images taken within a single epoch. They find that the average positional scatter remains at the ~50 µas level over daily, monthly, and yearly timescales, effectively breaking the traditional 1 mas barrier. Using these high‑precision positions, they derive relative proper motions with an accuracy of 20 µas yr⁻¹ and trigonometric parallaxes with an uncertainty of 40 µas for stars in the 17–19 mag range. These results represent a substantial improvement over previous ground‑based astrometric studies and approach the performance of space‑based missions for faint targets.

The paper concludes that FORS1 and FORS2 are well‑suited for long‑term, high‑precision astrometry provided that observing strategies enforce stable seeing conditions and that data reduction pipelines incorporate robust PSF asymmetry corrections. The authors suggest that the lessons learned here are directly applicable to upcoming extremely large telescopes (ELTs) and could enable micro‑arcsecond astrometry for a wide range of scientific programs, including the study of nearby stellar kinematics, Galactic structure, and the detection of low‑mass exoplanets through astrometric wobble.