EAGLE-Net: Adaptive Optics Framework

• EAGLE-Net is a suite of simulation, modeling, and algorithmic approaches for multi-object adaptive optics, combining high-fidelity Monte-Carlo methods with hardware-aware compression.
• It employs matrix-based wavefront reconstruction and FPGA-friendly techniques to achieve real-time wavefront correction at update rates around 250 Hz.
• The framework optimizes control performance by reducing memory bandwidth through variable precision matrix compression, critical for next-generation telescope instruments.

EAGLE-Net encompasses a suite of simulation, modeling, and algorithmic approaches that originated from the EAGLE instrument's adaptive optics control system for the European Extremely Large Telescope (E-ELT) (Basden et al., 2010). In its initial context, EAGLE-Net refers to the system-level strategy that tightly couples high-fidelity Monte-Carlo simulations with hardware-aware compressed representations to enable efficient, scalable, multi-object adaptive optics correction. The following sections detail the technical foundations, algorithmic workflow, hardware implications, and broader significance of EAGLE-Net.

1. High-Fidelity Monte-Carlo Adaptive Optics Simulation

At the core, EAGLE-Net leverages a full time-domain Monte-Carlo simulation package tailored for modeling the Multi-Object Adaptive Optics (MOAO) system implemented in the EAGLE instrument.

• Atmospheric Turbulence Modeling: The simulation uses translating phase screens following the frozen-flow turbulence model, with specific parameters such as Fried’s parameter ($r_0 \sim 10.6$ cm at $500$ nm), an outer scale of $50$ m, and a layered turbulence profile. Turbulence may be resolved into as few as two discrete layers or more complex stratified models.
• Instrument Optics: The simulation incorporates the detailed geometry and physics of a 42-m telescope, including the modeling of Shack–Hartmann sensors with realistic noise sources (detector, photon shot, spot elongation from sodium laser guide stars), and deformable mirrors (DMs) operating in open loop.
• Parallel Computing Architecture: Simulation tasks, including generation and application of interaction matrices, are distributed using MPI over compute clusters to enable high-throughput end-to-end runs, which reflect real deployment hardware needs.

2. Wavefront Correction and Matrix-Based Reconstruction

The MOAO system reconstructs the incoming atmospheric wavefront for multiple science fields using matrix–vector operations.

• Sensing: Shack–Hartmann sensors measure slopes via a center-of-gravity calculation.
• Reconstruction: Virtual DMs are placed conjugate to dominant turbulent layers. Their reconstructed shapes are projected along the science field line-of-sight and summed to yield the commands for the physical DMs.
• Numerical Scheme: The DM command vector $d$ is obtained via a truncated least-squares approach:

$d = R \cdot s$

where $R$ is the pseudo-inverse reconstructor matrix and $s$ is the stacked slope vector. The least-squares problem solved,

$\text{minimize}~\|A \cdot d - s\|^2$

yields $d = A^+ s$ with $A^+$ the pseudo-inverse of the system interaction matrix. The update frequency is $\sim$250 Hz with 4 ms latency.

3. Compressed Reconstructor Matrix Representation

The scale of the control matrix in EAGLE-Net is extreme (up to $10^9$ elements, accessed at $250$ Hz), necessitating radical compression strategies for deployment viability, especially in FPGA-based real-time systems.

• Sparse Matrix Representation: Truncating small entries retains $\sim$70% of the matrix and introduces indexing overhead, yielding minimal real gain.
• Fixed-Point and Reduced-Bitwidth Floating-Point: Using 16-bit fixed point or floating point formats with mantissa reduced to 10–12 bits (total $\sim$19–21 bits) preserves performance with moderate bandwidth reduction.
• Variable Precision Floating-Point Scheme: The most efficient scheme achieves as few as 9 bits per element (4-bit exponent, 4-bit mantissa, 1 sign bit) using:

$(-1)^s \cdot b \cdot a^e \cdot (a/2 + m)$

where $s$ is the sign bit, $a$ the base, $b$ scaling, $e$ exponent, and $m$ mantissa.

This approach reduces bandwidth and memory requirements by nearly a factor of four and is hardware-efficient due to small lookup-table-based expansion to standard 32-bit floats in matrix-vector multiplication.

4. Performance Metrics and Field Uniformity

EAGLE-Net’s simulation and control strategy is evaluated by a rigorous set of astronomical AO performance metrics:

Metric	Simulation Description	Typical Reference Value/Stat
Ensquared energy	Fraction of energy in a defined angular box (e.g., $75$ mas) in science band ($1.65\,\mu$m)	Quantified across field positions
Strehl ratio	Ratio of peak corrected PSF intensity to diffraction limit	Uncertainties $<$2%
Field uniformity	Performance map versus pick-off field and off-axis angle	Visual plots across pick-off fields
DM mis-conjugation	Degradation as virtual DM heights offset from turbulent layers	Sensitivity analysis presented

These metrics directly inform hardware and system configuration decisions and expose sensitivity to factors such as DM mis-conjugation and nonuniformity across the field.

5. Hardware and Implementation Implications

The compressed reconstructor matrix representations in EAGLE-Net have direct hardware consequences:

• Bandwidth Reduction: For all science channels, memory bandwidth requirements drop to $\sim$5 TB/s from a previous maximum of 20 TB/s when using variable precision compression.
• FPGA Deployment: The compressed format supports efficient FPGA architectures, where small lookup tables ($\sim$256 elements for 8-bit mantissa) convert compressed values to standard 32-bit floats.
• Real-Time Viability: With compression, real-time control across all science paths at high update rates ($250$ Hz) is achievable with more manageable interconnect and logic complexity.

6. Comparative Analysis with Analytical Methods

Monte-Carlo results from EAGLE-Net are systematically compared with contemporaneous analytical codes:

• Analytical models, which neglect effects such as cone effect and spot elongation, consistently yield performance estimates that are $\sim$10% optimistic relative to detailed simulation.
• Monte-Carlo simulation captures non-linearities (e.g., three-dimensional sodium layer effects), which are essential for realistic system performance prediction.
• The compression results inform and constrain real-time control system engineering, providing a direct feedback loop between simulation and hardware.

7. Impact and Future Directions

The EAGLE-Net paradigm, as instantiated for E-ELT’s EAGLE instrument, sets the standard for:

• End-to-end AO system simulation that integrates atmospheric physics, instrument hardware, and computational platform constraints.
• Algorithms for matrix-based wavefront reconstruction that are robust to multi-layer turbulence and field projection.
• Data compression strategies for real-time control systems that enable next-generation hardware deployment (notably FPGA-based AO controllers).
• Validation approach mixing rigorous statistical metrics with simulation–analytical code cross-checks, driving design optimization.
• Techniques introduced in EAGLE-Net form a basis for future multi-object AO systems on ELTs, highlighting the necessity of compressive representations in high-throughput real-time astronomical instrumentation.

EAGLE-Net’s integrated framework provides a blueprint for simulating, optimizing, and deploying complex adaptive optics control systems at the scale required by upcoming extremely large telescopes.