Rubin Observatory Active Optics System

• Rubin Observatory AOS is a highly integrated system that uses real-time wavefront sensing and elasticity-based mirror control to maintain optimal image quality.
• The system employs both open-loop and closed-loop paradigms with Zernike polynomial decomposition and TSVD for noise mitigation and robust state estimation.
• Recent integration of deep learning accelerates wavefront coefficient prediction, achieving faster corrections and improved accuracy for high-throughput astronomical surveys.

The Rubin Observatory Active Optics System (AOS) is a highly-integrated suite designed to maintain optimal image quality in the presence of gravitational and thermal deformations of the telescope’s optical train. Leveraging real-time wavefront sensing, advanced control algorithms, and elasticity-based mirror deformation, the system operates across a wide field of view and corrects both alignment and surface figure errors with a large number of degrees of freedom. As such, the AOS represents a critical enabling technology for the deep, time-domain surveys central to the Rubin Observatory scientific mission.

1. Theoretical Foundations and Elasticity Methods

Active optics is grounded in elasticity theory, which models the controlled deformation of optical surfaces—primarily telescope mirrors—using distributed forces. The relevant mathematical framework includes:

• Small Deformation Thin Plate Theory: Applied when mirror curvature is minor, with displacements $z$ governed by the biharmonic equation $\nabla^4 z + \frac{q}{D} = 0$, where $q$ is the force per unit area and $D$ the flexural rigidity.
• Large Deformation Thin Plate Theory: Necessary for substantial mirror deformations as in variable-curvature mirrors (VCMs), accommodating finite amplitude changes.
• Shallow Spherical Shell Theory: For fast mirrors (f/3 or faster), it accounts for membrane stresses induced over the shell, enabling calculation of radial thickness profiles $t(r)$ that yield precise aspheric figures under a uniform load.
• Weakly Conical Shell Theory: Suited for tubular mirrors in X-ray optics, this approach models radial flexure $W(x)$ and correlates thickness $T(x)$ using product laws linked to load and geometry.

Analytical solutions and finite element analysis are used to refine these thickness distributions and the associated actuator force boundaries, enabling the generation of highly aspheric or non-axisymmetric figures required for diffraction-limited imaging (Lemaitre, 2013).

2. Operational Modes and Correction Strategies

The AOS operates in both open- and closed-loop control paradigms:

• Open-Loop Corrections utilize precomputed Look-Up Tables (LUTs) based on forecasted aberrations from temperature gradients, elevation, and telescope state. These provide preliminary actuator settings.
• Closed-Loop Control incorporates real-time wavefront sensing centered on the acquisition of out-of-focus “donut” images via curvature wavefront sensors at the focal plane edges. Zernike polynomial decomposition of these images yields modal coefficients quantifying aberration.

Actuator arrays—ranging from mirror benders to rigid-body hexapods—apply corrections across approximately 50 degrees of freedom, including primary (M1M3) and secondary (M2) mirror modes, tip/tilt, piston, decentering, and camera alignment (Homar et al., 7 Jun 2024).

3. Degeneracy and Noise-Mitigated State Estimation

With high-dimensional adjustment spaces, AOS control involves significant challenges related to mode degeneracies and noise amplification:

• Sensitivity Matrix Analysis: The mapping of actuator states to wavefront coefficients is encoded in a sensitivity matrix $A$. Singular Value Decomposition (SVD) is employed: $A = U \Sigma V^\mathrm{T}$, decomposing the system into orthogonal modes with associated singular values $\sigma_i$.
• Truncated SVD (TSVD): Noise-induced degeneracies—dominant in modes with small $\sigma_i$—are suppressed by truncating SVD to retain only physically meaningful, well-determined modes (typically the top 25 for Rubin). State estimation is then performed as

$$\hat{x}_\mathrm{reduced} = \sum_{i=1}^{K} \frac{\langle y, u_i \rangle}{\sigma_i} v_i$$

where $K$ is set by the noise threshold.

• Rescaling Matrix $\Omega$: Due to heterogeneous units and actuation ranges, corrections are weighted by $\Omega_{ii} = \Delta x_i \Delta \psi_i$, ensuring the optimization prioritizes DOF most impactful to image quality (FWHM).

The transition from previous Optimal Integral Controller (OIC) schemes to a TSVD-guided Proportional-Integral-Derivative (PID) controller yields robust convergence, avoiding unwanted excursions in noise-dominated subspaces (Homar et al., 7 Jun 2024).

4. Wavefront Sensing and Deep Learning Integration

Wavefront estimation is performed using donut images, decomposed into Zernike polynomial modes:

$$\alpha_i = \frac{1}{A} \int d^2\rho\, Z_i(\rho)\, \varphi(\rho)$$

where $\varphi$ is the wavefront map, $Z_i$ are annular Zernike basis functions, and $A$ is the pupil area.

Recent advances have seen the deployment of deep learning (DL) models in this role (Crenshaw et al., 12 Feb 2024):

• Architecture: A convolutional neural network (CNN) extracts features from each donut image, supplemented with metadata (focus flag, position, wavelength). Dense layers predict Zernike coefficients directly.
• Performance: DL approaches outperform classical solvers (e.g., iterative transport of intensity methods), achieving:
  • 40x faster inference (70 ms vs. 3 s per donut pair),
  • 2–14x improved median error (depending on vignetting and blending),
  • Error rates approaching irreducible atmospheric floors,
  • Robustness in crowded fields and variable vignetted conditions.
• Operational Integration: The DL model accommodates rapid cadence (requirement <12 s for full correction), enables scalable (vectorized) processing, and increases usable survey area for precision work by up to 8%.

Domain adaptation techniques (e.g., adversarial training against simulated-vs-real data) are planned to ensure cross-calibration between simulation-based training and real observations.

5. Commissioning, Quality Metrics, and Science Impact

During commissioning, the AOS is benchmarked using challenging astronomical targets, notably quadruply lensed quasars (Smith et al., 2021):

• DIQ Testing: Quad quasars—exhibiting four closely spaced images (0.6–1.5 arcsec)—are exceptionally sensitive to PSF degradation. Observations at multiple focal plane positions enable mapping of field-dependent DIQ and temporal variability.
• Metrics:
  • FWHM extracted from model fits to PSF,
  • Covariance analysis across image and environmental parameters,
  • Residual wavefront error quantified as RMS deviation.
• Feedback: Immediate visual and quantitative assessment informs AOS adjustments, allowing rapid diagnostic closure on delivered image quality.

Precision in DIQ directly impacts strong lensing science, time-delay cosmography, and studies of dark matter substructure, among other high-impact science goals.

6. Applications to Large-Scale Telescopes and Broader Significance

Techniques central to the Rubin Observatory AOS—analytical elasticity modeling, controllable substrate thickness distributions, distributed actuator control, and adaptive optics pipelines—parallel methodologies in other large-scale telescopes:

• Segmented Mirror Control: Parallel active optics approaches support multi-segment figures in telescopes such as Keck and LAMOST (Lemaitre, 2013).
• Variable Curvature Mirrors: Used in interferometric delay lines and adaptive secondary mirrors, both at the European Southern Observatory and analogous survey facilities.
• Extension to Future Facilities: The methodology—SVD-based control, actuator weighting, DL-enabled wavefront sensing—is directly transferrable to instruments with high numbers of adjustment DOFs, including ELT and GMT.

A plausible implication is that as telescopes grow in aperture and control complexity, the outlined AOS paradigms will become increasingly central to maintaining high-fidelity, wide-field imaging under stringent performance constraints.

7. Summary and Outlook

The Rubin Observatory Active Optics System embodies an overview of elasticity-based mirror design, distributed actuator control, noise-mitigated state estimation, and real-time wavefront sensing—with recent integration of deep learning technologies for optimal modal decomposition. Noise suppression via TSVD, physically-informed rescaling, and robust feedback controllers yield improved stability, faster convergence, and maximally prioritized corrections based on image quality impact. This approach not only underpins the operational requirements for the Rubin Observatory survey mission—delivering sub-arcsecond image quality over thousands of square degrees—but provides a template adaptable to other large-scale telescopic systems seeking similar performance in the era of ultra-precise, high-throughput astronomical surveys.