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SAXO+, the second-stage adaptive optics for SPHERE: NCPA compensation and dark-hole loop with a pyramid wavefront sensor

This paper validates the optical quality of the SAXO+ upgrade for VLT/SPHERE by refining non-common path aberration (NCPA) error budgets through Monte Carlo simulations and establishing a calibration framework that optimally distributes static aberration correction between the first and second-stage deformable mirrors to enable high-contrast dark-hole control.

Original authors: Johan Mazoyer, Charles Goulas, Raphaël Galicher, Axel Potier, Fabrice Vidal, Florian Ferreira, Arnaud Sevin, Clémentine Béchet, Isaac Bernardino Dinis, Anthony Boccaletti, Gael Chauvin, Fausto Cortecc

Published 2026-07-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Johan Mazoyer, Charles Goulas, Raphaël Galicher, Axel Potier, Fabrice Vidal, Florian Ferreira, Arnaud Sevin, Clémentine Béchet, Isaac Bernardino Dinis, Anthony Boccaletti, Gael Chauvin, Fausto Cortecchia, Emiliano Diolaiti, Nicolas Galland, Caroline Kulcsár, Maud Langlois, Matteo Lombini, Julien Milli, Mamadou N'diaye, Henri-François Raynaud, Laura Schreiber, Michel Tallon, Arthur Vigan, François Wildi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to take a photo of a tiny, glowing firefly sitting right next to a blindingly bright spotlight. That's the challenge astronomers face when they try to spot exoplanets orbiting distant stars. The star is so bright it drowns out the planet, and the planet is so close it gets lost in the glare. To solve this, the SPHERE instrument on the Very Large Telescope uses a high-tech "smart shield" called Adaptive Optics (AO) to cancel out the twinkling of the atmosphere and block the star's light.

But there's a sneaky problem: even with the best shield, the telescope itself has tiny, static imperfections—like a smudge on a camera lens or a slight bend in a mirror—that the shield doesn't know about. In the world of optics, these are called Non-Common Path Aberrations (NCPAs). They create a fuzzy, grainy pattern of "speckles" in the image that can look exactly like a planet, tricking the astronomers.

Enter SAXO+, a major upgrade to SPHERE. Think of SAXO+ as adding a second, super-sensitive pair of eyes and a second, faster hand to the telescope's control system.

The Two-Stage Dance

The original system (SAXO) uses a visible-light sensor to make about 1,400 corrections every second. It's like a fast reflex, but it can miss some quick, tiny jitters. SAXO+ adds a second stage right after the first one. This new stage uses a near-infrared "pyramid" sensor that is much more sensitive and can make up to 3,000 corrections per second. It's like having a second, ultra-fast assistant who catches the tiny wobbles the first assistant missed.

However, this second stage has a tricky quirk. The new pyramid sensor doesn't see the world in a straight line; its vision gets a bit "wobbly" or non-linear when the light is messy. If you try to tell it to fix a big smudge (a large NCPA), it might get confused and make things worse.

The Big Discovery: The First Hand Does the Heavy Lifting

The paper's main finding is a clever strategy to handle these smudges. Instead of asking the new, fast, but sensitive second hand (the second deformable mirror) to fix all the big, static smudges, the team realized they should let the first, stronger hand (the first deformable mirror) do the heavy lifting.

In their simulations, they found that by carefully "offsetting" the instructions given to the first sensor, they could push most of the static smudge correction onto the first mirror. This leaves the second mirror free to do what it does best: making tiny, rapid adjustments to catch the fast-moving atmospheric wobbles. It's like having a strong person hold a heavy box steady while a nimble acrobat does a high-wire act on top of it.

How Clean is the Image?

The team used a computer model (a digital twin of the telescope) to predict how bad these smudges would be. They simulated 500 different scenarios where the telescope's mirrors might be slightly misaligned or imperfect.

They found that the expected smudge level is about 27 ± 8 nm RMS (a unit of wave distortion).
If you ignore the tiny tip-and-tilt shifts (which are easily fixed), that number drops to 19 ± 2 nm RMS.
In terms of peak-to-valley height (the tallest bump to the deepest dip), it's about 135 ± 9 nm on average.

Crucially, these numbers are very similar to what they measured on the current SPHERE system. This means their predictions are solid. They also checked that 99.5% of the time, these smudges are small enough that the measurement tools won't get confused or "fold" the data (a technical glitch where big errors look like small ones).

The Calibration Strategy: Practice Before the Show

To make this work in the real world, the team proposed a specific calibration routine.

The Dry Run: First, they use an internal light source (like a test lamp inside the telescope) to measure the smudges. They adjust the first mirror to cancel them out.
The Real Deal: Because the telescope's internal environment changes (like temperature shifts) and the real sky is messier than a test lamp, they plan to run a "dark-hole" loop directly on the sky. This loop actively hunts down and erases the remaining speckles in the image, creating a "dark hole" where a planet could hide.

They admit that doing this on the real sky is harder than in the lab. The pyramid sensor's non-linear vision makes it tricky to apply simple fixes. However, their simulations suggest that if they use the first mirror to handle the big corrections, the system becomes much more robust. They found that for very clear nights (seeing better than 1.5 arcseconds), calibrating the sensor's non-linearities helps, but for average nights, the two-stage design is already so good that extra calibration adds very little benefit.

What They Didn't Solve (Yet)

The paper is careful to note what they haven't fully cracked.

They do not claim to have solved the problem of amplitude aberrations (imperfections in the brightness of the light) or the diffraction caused by the telescope's support spiders (the arms holding the mirror). These still require the "dark-hole" loop to fix.
They do not say the system is perfect on the sky yet. They note that previous attempts to use internal test lights to fix on-sky images failed because the atmosphere changes too much. That's why they insist on running the final calibration loops directly on the sky.
They do not claim the new mirror (a Boston Micromachine Kilo-C-3.5) is fully integrated into their final simulations yet. They are currently updating their computer models to match the new mirror's exact 28 actuators across the pupil, but they expect the results to stay roughly the same.

The Bottom Line

The paper concludes that SAXO+ is a promising upgrade. By using a two-stage system where the first mirror takes the brunt of the static errors, the system can handle the tricky, non-linear vision of the new pyramid sensor. Their simulations show this setup can reduce the "noise" in the image by a factor of 20 just by fixing the static smudges, and by a factor of 200 when adding the active dark-hole loop.

While they haven't taken the final photo of a planet with this new setup yet, the math and the simulations suggest that SAXO+ is ready to give astronomers a much clearer, darker view of the universe, finally letting them see the faint fireflies hiding next to the blinding spotlights.

Technical Summary: SAXO+ NCPA Compensation and Dark-Hole Loop

Problem Statement
The SPHERE instrument on the Very Large Telescope (VLT) utilizes extreme adaptive optics (AO) for high-contrast imaging of exoplanets and circumstellar disks. However, its performance is limited by Non-Common Path Aberrations (NCPAs)—static or quasi-static optical errors that exist between the wavefront sensing path and the science path. Because the AO system does not perceive these aberrations, it cannot correct them, leading to residual speckle patterns in coronagraphic images that mimic exoplanet signals.

The upcoming SAXO+ upgrade introduces a second-stage AO loop using a near-infrared pyramid wavefront sensor (pyWFS) to correct temporal errors left by the first stage. This architecture presents a specific challenge: the pyWFS has a limited linear range compared to the Shack-Hartmann sensor used in the first stage. Applying standard NCPA correction offsets (which work well for linear sensors) to the pyWFS can degrade performance if the incoming wavefront is not already of high quality. Furthermore, existing calibration methods using internal sources often fail to account for amplitude aberrations or on-sky atmospheric residuals, limiting the effectiveness of dark-hole generation (the suppression of quasi-static speckles).

Methodology
The authors employed a multi-faceted approach combining optical modeling, Monte Carlo simulations, and algorithmic strategy development:

Optical Modeling and NCPA Estimation: The team utilized an updated Zemax OpticStudio® model of the SAXO+ system. A Monte Carlo algorithm generated 500 Optical Path Difference (OPD) maps by varying optical shapes, alignments, and positions around their optimum values. This allowed for a statistical estimation of the expected NCPA levels at the coronagraph focal plane, distinguishing between the SAXO correction zone and the SAXO+ correction zone.
Simulation and Validation: The estimated NCPA distributions were compared against previous measurements from the current SAXO system (using a Zernike Wavefront Sensor, ZWFS) and power spectral density analyses.
Calibration Strategy Development: The paper proposes a specific three-step calibration procedure designed to offload static aberration correction to the first-stage deformable mirror (DM1, High-Order DM). This preserves the stroke of the second-stage DM (DM2, XPDM) for high-speed AO correction. The steps involve:
- Closing the SAXO loop with no offset.
- Iteratively offsetting the SHWFS slopes using a ZWFS loop to correct static NCPAs on DM1.
- Offsetting the pyWFS response and closing the SAXO+ loop.
On-Sky vs. Internal Source Analysis: The authors analyzed the limitations of performing these calibrations using internal sources versus on-sky observations, noting that internal sources cannot measure amplitude aberrations caused by telescope optics and that on-sky sensitivity is dependent on the Strehl ratio.

Key Contributions and Results

Refined NCPA Budget: The Monte Carlo simulations estimate the expected NCPA level in SAXO+ to be 27 ± 8 nm RMS (19 ± 2 nm RMS excluding tip-tilt) and 135 ± 9 nm Peak-to-Valley (82 ± 15 nm excluding tip-tilt). These values are consistent with previous measurements on the SAXO system, validating the assumptions used in earlier performance studies.
Linearity and Folding: The analysis confirms that 99.5% of the time, the expected NCPA levels remain below the ZWFS cutoff wavelength ( $\lambda/4$ ), meaning phase folding during measurement is not expected.
Robustness of Dual-Stage AO: The study demonstrates that the dual-stage architecture of SAXO+ is intrinsically more robust to pyWFS nonlinearities than a single-stage system. Because the first stage ensures the pyWFS sees a high Strehl Point Spread Function (PSF), the sensor operates primarily in its linear regime. Consequently, while calibrating pyWFS optical gains can improve contrast by a factor of up to 2 for poor seeing conditions (>1.5"), the impact is negligible for better seeing conditions.
Calibration Framework: The paper establishes a framework for NCPA compensation that prioritizes using DM1 for static correction. This strategy is crucial because MEMS DMs (used in DM2) have limited stroke compared to piezoelectric DMs. The authors acknowledge that while internal source calibration is efficient, on-sky calibration is necessary to correct residuals from amplitude aberrations and evolving optical conditions.
Dark-Hole Loop: The paper references prior work (Goulas et al. 2026) showing that a closed-loop dark-hole algorithm can suppress residual starlight by up to a factor of 200, significantly outperforming static NCPA compensation alone.

Significance and Claims
The paper claims to validate the expected optical quality of the SAXO+ system and to establish the necessary calibration framework for its future on-sky operations. By refining the NCPA error budget and confirming its alignment with current SAXO performance, the authors assert that the system is ready for the next phase of development.

The primary significance lies in the proposed calibration strategy that balances the correction of static aberrations with the preservation of DM2 stroke for high-speed corrections. The authors modestly note that while their simulations and strategies are robust, the exact stroke requirements for DM2 during on-sky dark-hole loops still require precise simulation. The work serves as a foundational step to ensure that SAXO+ can fully exploit its potential for high-contrast imaging by effectively managing the non-common path aberrations that currently limit detection capabilities.