Atomizer/studies/M1_Mirror/SAT3_Trajectory/README.md

SAT3_Trajectory - Zernike Trajectory Method Optimization

Status: Active Created: 2026-01-29 Method: Zernike Trajectory Analysis Optimizer: TPE (Tree-Parzen Estimator)

---

Executive Summary

First production implementation of the Zernike Trajectory Method for M1 mirror optimization. Instead of optimizing discrete WFE values at fixed angles, this study optimizes integrated RMS metrics across the full 20°-60° operating range with mode-specific aberration tracking.

Key Innovation: Physics-based trajectory model tracks how each Zernike mode (coma, astigmatism, trefoil, spherical) evolves with elevation angle.

---

Study Overview

Primary Objective

• total_filtered_rms_nm - Integrated RMS across full operating range (weight=1.0)

Logged Objectives (Not Optimized, weight=0)

• coma_rms_nm - Coma aberration (Z7, Z8)
• astigmatism_rms_nm - Astigmatism (Z5, Z6)
• trefoil_rms_nm - Trefoil (Z9, Z10)
• spherical_rms_nm - Spherical aberration (Z11)
• linear_fit_r2 - Physics model validation (should be ~1.0)

Design Variables (9 enabled)

Parameter	Min	Max	Baseline	Units	Category
lateral_inner_angle	20.0	30.0	30.18	deg	Lateral Support
lateral_outer_angle	11.0	17.0	15.09	deg	Lateral Support
lateral_outer_pivot	4.0	9.0	6.036	mm	Lateral Support
lateral_inner_pivot	5.0	13.0	12.072	mm	Lateral Support
lateral_middle_pivot	12.0	25.0	14.0	mm	Lateral Support
lateral_closeness	5.0	12.5	7.89	mm	Lateral Support
whiffle_min	30.0	72.0	56.7	mm	Whiffle Tree
whiffle_outer_to_vertical	60.0	80.0	75.67	deg	Whiffle Tree
whiffle_triangle_closeness	50.0	80.0	60.00	mm	Whiffle Tree

Disabled (fixed at baseline):

• blank_backface_angle = 4.00 deg
• inner_circular_rib_dia = 537.86 mm

Optimizer Configuration

• Algorithm: TPE (Tree-Parzen Estimator)
• Budget: 100 trials
• Startup Trials: 15 (random sampling for initial exploration)
• Seed: 42 (for reproducibility)

Constraints

1. Mass: blank_mass <= 120 kg (hard constraint, penalty=1e6)
2. R² fit: linear_fit_r2 >= 0.95 (soft constraint, ensures physics model validity)

---

Trajectory Method Details

Physics Basis

At elevation angle θ, gravity decomposes into:

Axial load:   F_axial ∝ sin(θ)
Lateral load: F_lateral ∝ cos(θ)

Each Zernike coefficient follows:

c_j(θ) = a_j·(sin θ - sin θ_ref) + b_j·(cos θ - cos θ_ref)

The sensitivity matrix [a_j, b_j] reveals which modes respond to axial vs lateral loads.

Elevation Angles Analyzed

• 90° - Manufacturing reference (excluded from trajectory)
• 20° - Measurement/polishing reference
• 30° - New trajectory point
• 40° - Primary operational angle
• 50° - New trajectory point
• 60° - Secondary operational angle

Extractor Configuration

• Method: Zernike Trajectory
• Reference Angle: 20° (polishing/measurement)
• Focal Length: 22000 mm (OPD correction for lateral displacements)
• Inner Radius: 135.75 mm (annular aperture, excludes 271.5mm central hole)
• N Modes: 50 (filtered from mode 5 onward)

---

Expected Performance

Baseline (from test on M1_Tensor model)

• Total Filtered RMS: 4.30 nm
• Coma RMS: 9.16 nm
• Astigmatism RMS: 6.55 nm
• Trefoil RMS: 6.44 nm
• Spherical RMS: 10.51 nm
• R² fit: 1.0000 (perfect)
• Dominant mode: Spherical

Optimization Targets

• Total Filtered RMS: < 4.0 nm
• Coma RMS: < 5.0 nm
• R² fit: > 0.95 (validates physics model)

---

Usage

Start Optimization

cd studies/M1_Mirror/SAT3_Trajectory
python run_optimization.py --start

Resume Optimization

python run_optimization.py --start --resume

Custom Trial Count

python run_optimization.py --start --trials 150

Test Single FEA Run

python run_optimization.py --test

Analyze Results

# View convergence
python -m optimization_engine.reporting.visualizer 3_results/study.db

# Generate report
python -m optimization_engine.reporting.markdown_report 3_results/study.db

---

File Structure

SAT3_Trajectory/
├── README.md                    (This file)
├── STUDY_REPORT.md              (Results report - updated after optimization)
├── run_optimization.py          (Main optimization script)
├── 1_setup/
│   ├── optimization_config.json (Study configuration)
│   └── model/                   (NX model files - copied from M1_Tensor)
│       ├── ASSY_M1.prt
│       ├── ASSY_M1_assyfem1.afm
│       ├── ASSY_M1_assyfem1_sim1.sim
│       ├── M1_Blank.prt
│       ├── M1_Blank_fem1.fem
│       ├── M1_Blank_fem1_i.prt
│       ├── M1_Vertical_Support_Skeleton.prt
│       ├── M1_Vertical_Support_Skeleton_fem1.fem
│       └── M1_Vertical_Support_Skeleton_fem1_i.prt
├── 2_iterations/
│   ├── iter_0001/               (Trial 1 FEA files)
│   ├── iter_0002/               (Trial 2 FEA files)
│   └── ...
└── 3_results/
    ├── study.db                 (Optuna database)
    ├── optimization.log         (Execution log)
    └── trajectory_analysis/     (Mode-specific analysis plots)

---

Key Differences from Previous Studies

vs. Discrete WFE Optimization (V11-V15)

• Old: Optimize 6*wfe_40_20 + 5*wfe_60_20 + 3*mfg_90
• New: Optimize integrated RMS across continuous operating range
• Benefit: Physics-based, mode-specific tracking, better understanding of support behavior

vs. SAT (Surrogate-Assisted Tuning)

• SAT: Builds neural surrogate for fast exploration (100 FEA + 10K surrogate)
• TPE: Direct Bayesian optimization (100 FEA, no surrogate)
• This Study: TPE for initial trajectory exploration, may switch to SAT later

---

Dependencies

• NX 2512 (FEA solver)
• Python 3.9+ (Atomizer environment)
• Optuna (TPE sampler)
• pyNastran (OP2 reading)
• NumPy (trajectory fitting)

---

References

• Physics Documentation: docs/physics/ZERNIKE_TRAJECTORY_METHOD.md
• Implementation: optimization_engine/extractors/extract_zernike_trajectory.py
• Example Config: docs/examples/trajectory_optimization_config.yaml
• Handoff Doc: docs/handoff/SETUP_TRAJECTORY_OPTIMIZATION.md

---

Notes

1. R² Monitoring: If R² drops below 0.95, it indicates nonlinearity (e.g., contact lifting). Designs with poor R² should be investigated.

2. Mode-Specific Insights: After optimization, analyze which modes improved most. Coma improvements indicate lateral support changes were effective.

3. Comparison with V15: After completion, compare trajectory-based results with V15 NSGA-II Pareto front to validate new method.

4. Future Work: If this study succeeds, extend to SAT with trajectory objectives for 10K+ design exploration.

---

Study created by Atomizer, 2026-01-29 First implementation of Zernike Trajectory Method for M1 GigaBIT mirror