Atomizer/studies/m1_mirror_zernike_optimization

M1 Mirror Zernike Optimization

Multi-objective telescope primary mirror support structure optimization using Zernike wavefront error decomposition with neural network acceleration.

Created: 2025-11-28 Protocol: Protocol 12 (Hybrid FEA/Neural with Zernike) Status: Setup Complete - Requires Expression Path Fix

---

1. Engineering Problem

1.1 Objective

Optimize the telescope primary mirror (M1) support structure to minimize wavefront error (WFE) across different gravity orientations (zenith angles), ensuring consistent optical performance from 20° to 90° elevation.

1.2 Physical System

• Component: M1 primary mirror assembly with whiffle tree support
• Material: Borosilicate glass (mirror blank), steel (support structure)
• Loading: Gravity at multiple zenith angles (20°, 40°, 60°, 90°)
• Boundary Conditions: Whiffle tree kinematic mount
• Analysis Type: Linear static multi-subcase (Nastran SOL 101)
• Output: Surface deformation → Zernike polynomial decomposition

---

2. Mathematical Formulation

2.1 Objectives

Objective	Goal	Weight	Formula	Units	Target
rel_filtered_rms_40_vs_20	minimize	5.0	\sigma_{40/20} = \sqrt{\sum_{j=5}^{50} (Z_j^{rel})^2}	nm	4 nm
rel_filtered_rms_60_vs_20	minimize	5.0	\sigma_{60/20} = \sqrt{\sum_{j=5}^{50} (Z_j^{rel})^2}	nm	10 nm
mfg_90_optician_workload	minimize	1.0	\sigma_{90}^{J4+} = \sqrt{\sum_{j=4}^{50} (Z_j^{rel})^2}	nm	20 nm

Where:

• Z_j^{rel} = Relative Zernike coefficient (target subcase minus reference)
• Filtered RMS excludes J1-J4 (piston, tip, tilt, defocus) - correctable by alignment
• Manufacturing workload keeps J4 (defocus) since it represents optician correction effort

2.2 Zernike Decomposition

The wavefront error W(r,\theta) is decomposed into Zernike polynomials:

W(r,\theta) = \sum_{j=1}^{50} Z_j \cdot P_j(r,\theta)

Where P_j are Noll-indexed Zernike polynomials on the unit disk.

WFE from Displacement:

W_{nm} = 2 \cdot \delta_z \cdot 10^6

Where \delta_z is the Z-displacement in mm (factor of 2 for reflection).

2.3 Design Variables

Parameter	Symbol	Bounds	Baseline	Units	Description
whiffle_min	w_{min}	[35, 55]	40.55	mm	Whiffle tree minimum parameter
whiffle_outer_to_vertical	\alpha	[68, 80]	75.67	deg	Outer support angle to vertical
inner_circular_rib_dia	D_{rib}	[480, 620]	534.00	mm	Inner circular rib diameter

Design Space:

\mathbf{x} = [w_{min}, \alpha, D_{rib}]^T \in \mathbb{R}^3

Additional Variables (Disabled):

• lateral_inner_angle, lateral_outer_angle (lateral support angles)
• lateral_outer_pivot, lateral_inner_pivot, lateral_middle_pivot (pivot positions)
• lateral_closeness (lateral support spacing)
• whiffle_triangle_closeness (whiffle tree geometry)
• blank_backface_angle (mirror blank geometry)

2.4 Objective Strategy

Weighted Sum Minimization:

J(\mathbf{x}) = \sum_{i=1}^{3} w_i \cdot \frac{f_i(\mathbf{x})}{t_i}

Where:

• w_i = weight for objective i
• f_i(\mathbf{x}) = objective value
• t_i = target value (normalization)

---

3. Optimization Algorithm

3.1 TPE Configuration

Parameter	Value	Description
Algorithm	TPE	Tree-structured Parzen Estimator
Sampler	TPESampler	Bayesian optimization
n_startup_trials	15	Random exploration before modeling
n_ei_candidates	150	Expected improvement candidates
multivariate	true	Model parameter correlations
Trials	100	40 FEA + neural acceleration
Seed	42	Reproducibility

TPE Properties:

• Models p(x|y<y^*) and p(x|y \geq y^*) separately
• Expected Improvement: EI(x) = \int_{-\infty}^{y^*} (y^* - y) p(y|x) dy
• Handles high-dimensional continuous spaces efficiently

3.2 Return Format

def fea_objective(trial) -> Tuple[float, dict]:
    # ... simulation and Zernike extraction ...
    weighted_obj = compute_weighted_objective(objectives, config)
    return weighted_obj, trial_data

---

4. Simulation Pipeline

4.1 Trial Execution Flow

┌─────────────────────────────────────────────────────────────────────┐
│                         TRIAL n EXECUTION                            │
├─────────────────────────────────────────────────────────────────────┤
│                                                                      │
│  1. OPTUNA SAMPLES (TPE)                                            │
│     whiffle_min = trial.suggest_float("whiffle_min", 35, 55)        │
│     whiffle_outer_to_vertical = trial.suggest_float(..., 68, 80)    │
│     inner_circular_rib_dia = trial.suggest_float(..., 480, 620)     │
│                                                                      │
│  2. NX PARAMETER UPDATE                                             │
│     Module: optimization_engine/solve_simulation.py                  │
│     Target Part: M1_Blank.prt                                        │
│     Action: Update expressions with new design values                │
│                                                                      │
│  3. NX SIMULATION (Nastran SOL 101 - 4 Subcases)                    │
│     Module: optimization_engine/solve_simulation.py                  │
│     Input: ASSY_M1_assyfem1_sim1.sim                                │
│     Subcases: 1=20°, 2=40°, 3=60°, 4=90° zenith                     │
│     Output: .dat, .op2, .f06                                        │
│                                                                      │
│  4. ZERNIKE EXTRACTION (Displacement-Based)                          │
│     a. Read node coordinates from BDF/DAT                           │
│     b. Read Z-displacements from OP2 for each subcase               │
│     c. Compute RELATIVE displacement (subcase - reference)           │
│     d. Convert to WFE: W = 2 * Δδz * 10^6 nm                        │
│     e. Fit 50 Zernike coefficients via least-squares                │
│     f. Compute filtered RMS (exclude J1-J4)                         │
│                                                                      │
│  5. OBJECTIVE COMPUTATION                                           │
│     rel_filtered_rms_40_vs_20 ← Zernike RMS (subcase 2 - 1)        │
│     rel_filtered_rms_60_vs_20 ← Zernike RMS (subcase 3 - 1)        │
│     mfg_90_optician_workload ← Zernike RMS J4+ (subcase 4 - 1)     │
│                                                                      │
│  6. WEIGHTED SUM                                                    │
│     J = Σ (weight × objective / target)                             │
│                                                                      │
│  7. RETURN TO OPTUNA                                                │
│     return weighted_objective                                        │
│                                                                      │
└─────────────────────────────────────────────────────────────────────┘

4.2 Multi-Subcase Structure

Subcase	Zenith Angle	Role	Description
1	20°	Reference	Near-zenith baseline orientation
2	40°	Target	Mid-elevation performance
3	60°	Target	Low-elevation performance
4	90°	Polishing	Horizontal (manufacturing reference)

---

5. Result Extraction Methods

5.1 Zernike Extraction (Displacement-Based Subtraction)

Attribute	Value
Method	extract_zernike_with_relative()
Location	run_optimization.py (inline)
Geometry Source	.dat (BDF format)
Displacement Source	.op2 (OP2 binary)
Output	50 Zernike coefficients per subcase

Algorithm (Correct Approach - Matches Original Script):

1. Load Geometry: Read node coordinates (X_i, Y_i) from BDF
2. Load Displacements: Read \delta_{z,i} from OP2 for each subcase
3. Compute Relative Displacement (node-by-node): \Delta\delta_{z,i} = \delta_{z,i}^{target} - \delta_{z,i}^{reference}
4. Convert to WFE: W_i = 2 \cdot \Delta\delta_{z,i} \cdot 10^6 \text{ nm}
5. Fit Zernike (least-squares on unit disk): \min_{\mathbf{Z}} \| \mathbf{W} - \mathbf{P} \mathbf{Z} \|^2
6. Compute RMS: \sigma_{filtered} = \sqrt{\sum_{j=5}^{50} Z_j^2}

Critical Implementation Note: The relative calculation MUST subtract displacements first, then fit Zernike - NOT subtract Zernike coefficients directly. This matches the original zernike_Post_Script_NX.py implementation.

5.2 Code Pattern

from pyNastran.op2.op2 import OP2
from pyNastran.bdf.bdf import BDF

# Read geometry
bdf = BDF()
bdf.read_bdf(str(bdf_path))
node_geo = {nid: node.get_position() for nid, node in bdf.nodes.items()}

# Read displacements
op2 = OP2()
op2.read_op2(str(op2_path))

# Compute relative displacement (node-by-node)
for i, nid in enumerate(node_ids):
    rel_dz = disp_z_target[i] - disp_z_reference[nid]

# Convert to WFE and fit Zernike
rel_wfe_nm = 2.0 * rel_disp_z * 1e6
coeffs, R_max = compute_zernike_from_wfe(X, Y, rel_wfe_nm, n_modes=50)

---

6. Neural Acceleration (AtomizerField)

6.1 Configuration

Setting	Value	Description
enabled	true	Neural surrogate active
model_type	ParametricZernikePredictor	Predicts Zernike coefficients
hidden_channels	128	MLP width
num_layers	4	MLP depth
learning_rate	0.001	Adam optimizer
epochs	200	Training iterations
batch_size	8	Mini-batch size
train_split	0.8	Training fraction

6.2 Surrogate Model

Input: \mathbf{x} = [w_{min}, \alpha, D_{rib}]^T \in \mathbb{R}^3

Output: \hat{\mathbf{Z}} \in \mathbb{R}^{200} (50 coefficients × 4 subcases)

Architecture: Multi-Layer Perceptron

Input(3) → Linear(128) → ReLU → Linear(128) → ReLU →
Linear(128) → ReLU → Linear(128) → ReLU → Linear(200)

Training Objective:

\mathcal{L} = \frac{1}{N} \sum_{i=1}^{N} \| \mathbf{Z}_i - \hat{\mathbf{Z}}_i \|^2

6.3 Training Data Location

studies/m1_mirror_zernike_optimization/2_results/zernike_surrogate/
├── checkpoint_best.pt          # Best model weights
├── training_history.json       # Loss curves
└── validation_metrics.json     # R², MAE per coefficient

6.4 Expected Performance

Metric	Value
FEA time per trial	10-15 min
Neural time per trial	~10 ms
Speedup	~60,000x
Expected R²	> 0.95 (after 40 samples)

---

7. Study File Structure

m1_mirror_zernike_optimization/
│
├── 1_setup/                              # INPUT CONFIGURATION
│   ├── model/                            # NX Model Files (symlinked/referenced)
│   │   └── → C:\Users\Antoine\CADTOMASTE\Atomizer\M1-Gigabit\Latest\
│   │       ├── ASSY_M1.prt               # Top-level assembly
│   │       ├── M1_Blank.prt              # Mirror blank (EXPRESSIONS HERE)
│   │       ├── ASSY_M1_assyfem1.afm      # Assembly FEM
│   │       ├── ASSY_M1_assyfem1_sim1.sim # Simulation file
│   │       └── assy_m1_assyfem1_sim1-solution_1.op2  # Results
│   │
│   └── optimization_config.json          # Study configuration
│
├── 2_results/                            # OUTPUT (auto-generated)
│   ├── study.db                          # Optuna SQLite database
│   ├── zernike_surrogate/                # Neural model checkpoints
│   └── reports/                          # Generated reports
│
├── run_optimization.py                   # Main entry point
├── DASHBOARD.md                          # Quick reference
└── README.md                             # This blueprint

---

8. Results Location

After optimization completes, results are stored in 2_results/:

File	Description	Format
study.db	Optuna database with all trials	SQLite
zernike_surrogate/checkpoint_best.pt	Trained neural model	PyTorch
reports/optimization_report.md	Full results report	Markdown

8.1 Results Report Contents

The generated report will contain:

1. Optimization Summary - Best WFE configurations found
2. Zernike Analysis - Coefficient distributions per subcase
3. Parameter Sensitivity - Design variable vs WFE relationships
4. Convergence History - Weighted objective over trials
5. Neural Surrogate Performance - R² per Zernike mode
6. Recommended Configurations - Top designs for production

8.2 Zernike-Specific Analysis

Mode	Name	Physical Meaning
J1	Piston	Constant offset (ignored)
J2, J3	Tip/Tilt	Angular misalignment (correctable)
J4	Defocus	Power error (correctable)
J5, J6	Astigmatism	Cylindrical error
J7, J8	Coma	Off-axis aberration
J9-J11	Trefoil, Spherical	Higher-order terms

---

9. Quick Start

Staged Workflow (Recommended)

cd studies/m1_mirror_zernike_optimization

# Check current status
python run_optimization.py --status

# Run FEA trials (builds training data)
python run_optimization.py --run --trials 40

# Train neural surrogate
python run_optimization.py --train-surrogate

# Run neural-accelerated optimization
python run_optimization.py --run --trials 500 --enable-nn

Stage Descriptions

Stage	Command	Purpose	When to Use
STATUS	--status	Check database, trial count	Anytime
RUN	--run --trials N	Run FEA optimization	Initial exploration
TRAIN	--train-surrogate	Train neural model	After ~40 FEA trials
NEURAL	--run --enable-nn	Fast neural trials	After training

Dashboard Access

Dashboard	URL	Purpose
Optuna Dashboard	optuna-dashboard sqlite:///2_results/study.db	Trial history

# Launch Optuna dashboard
cd studies/m1_mirror_zernike_optimization
optuna-dashboard sqlite:///2_results/study.db --port 8081
# Open http://localhost:8081

---

10. Configuration Reference

File: 1_setup/optimization_config.json

Section	Key	Description
design_variables[]	11 parameters	3 enabled, 8 disabled
objectives[]	3 WFE metrics	Relative filtered RMS
zernike_settings.n_modes	50	Zernike polynomial count
zernike_settings.filter_low_orders	4	Exclude J1-J4
zernike_settings.subcases	["1","2","3","4"]	OP2 subcase IDs
zernike_settings.reference_subcase	"1"	20° baseline
optimization_settings.n_trials	100	Total FEA trials
surrogate_settings.model_type	ParametricZernikePredictor	Neural architecture
nx_settings.model_dir	M1-Gigabit/Latest	NX model location
nx_settings.sim_file	ASSY_M1_assyfem1_sim1.sim	Simulation file

---

11. Known Issues & Solutions

11.1 Expression Update Failure

Issue: NX journal cannot find expressions in assembly FEM.

Cause: Expressions are in component part M1_Blank.prt, not in ASSY_M1_assyfem1.

Solution: The solve_simulation.py journal now searches for M1_Blank part to update expressions. If still failing, verify:

1. M1_Blank.prt is loaded in the assembly
2. Expression names match exactly (case-sensitive)
3. Part is not read-only

11.2 Subcase Numbering

Issue: OP2 file uses numeric subcases (1,2,3,4) not angle labels (20,40,60,90).

Solution: Config uses subcases: ["1","2","3","4"] with subcase_labels mapping.

---

12. References

• Noll, R.J. (1976). Zernike polynomials and atmospheric turbulence. JOSA.
• Wilson, R.N. (2004). Reflecting Telescope Optics I. Springer.
• pyNastran Documentation: BDF/OP2 parsing for FEA post-processing
• Optuna Documentation: TPE sampler for black-box optimization