Antoine
38d0994d29
- tools/wfe_psd.py: Quick PSD computation for WFE surfaces - optimization_engine/insights/wfe_psd.py: Full PSD module with band decomposition (LSF/MSF/HSF), radial averaging, Hann windowing, and visualization support - knowledge_base/lac/session_insights/stopp_command_20260129.jsonl: Session insight from stopp command implementation PSD analysis decomposes WFE into spatial frequency bands per Tony Hull's JWST methodology. Used for CDR V7 to validate that MSF (support print-through) dominates the residual WFE at 85-89% of total RMS.
367 lines
12 KiB
Python
367 lines
12 KiB
Python
"""
|
|
WFE Power Spectral Density (PSD) Analysis - Tony Hull's JWST Methodology
|
|
|
|
Implements Tony Hull's approach for analyzing wavefront error power spectral density,
|
|
specifically for large telescope mirrors with gravity-induced deformations.
|
|
|
|
Key Features:
|
|
- Surface interpolation to uniform grid
|
|
- Hann windowing to reduce edge effects
|
|
- 2D FFT with radial averaging
|
|
- Log-log scaling for PSD visualization
|
|
- Cycles-per-aperture spatial frequency
|
|
- Gravity vs thermal loading scales
|
|
- Reference normalization
|
|
|
|
Approach based on: "Power spectral density specification for large optical surfaces"
|
|
by Tony Hull, adapted for telescope mirror analysis
|
|
|
|
Author: Implementation based on Tony Hull's JWST methodology
|
|
"""
|
|
|
|
from pathlib import Path
|
|
from datetime import datetime
|
|
from typing import Dict, Any, List, Optional, Tuple
|
|
import numpy as np
|
|
from scipy.interpolate import RegularGridInterpolator
|
|
from numpy.fft import fft2, fftshift
|
|
|
|
# Lazy imports
|
|
_plotly_loaded = False
|
|
_go = None
|
|
_make_subplots = None
|
|
_Triangulation = None
|
|
_OP2 = None
|
|
_BDF = None
|
|
_ZernikeOPDExtractor = None
|
|
|
|
|
|
def _load_dependencies():
|
|
"""Lazy load heavy dependencies."""
|
|
global _plotly_loaded, _go, _make_subplots, _Triangulation, _OP2, _BDF, _ZernikeOPDExtractor
|
|
if not _plotly_loaded:
|
|
import plotly.graph_objects as go
|
|
from plotly.subplots import make_subplots
|
|
from matplotlib.tri import Triangulation
|
|
from pyNastran.op2.op2 import OP2
|
|
from pyNastran.bdf.bdf import BDF
|
|
from ..extractors.extract_zernike_figure import ZernikeOPDExtractor
|
|
_go = go
|
|
_make_subplots = make_subplots
|
|
_Triangulation = Triangulation
|
|
_OP2 = OP2
|
|
_BDF = BDF
|
|
_ZernikeOPDExtractor = ZernikeOPDExtractor
|
|
_plotly_loaded = True
|
|
|
|
|
|
def compute_surface_psd(
|
|
X: np.ndarray,
|
|
Y: np.ndarray,
|
|
Z: np.ndarray,
|
|
aperture_radius: float,
|
|
n_points: int = 512
|
|
) -> Tuple[np.ndarray, np.ndarray]:
|
|
"""
|
|
Compute power spectral density of surface height data.
|
|
|
|
Args:
|
|
X: Surface x-coordinates [mm]
|
|
Y: Surface y-coordinates [mm]
|
|
Z: Surface height values [nm]
|
|
aperture_radius: Physical radius of the mirror [mm]
|
|
n_points: Grid resolution for interpolation
|
|
|
|
Returns:
|
|
freqs: Spatial frequencies [cycles/aperture]
|
|
psd_values: PSD amplitude [nm²·cycles²/aperture²]
|
|
"""
|
|
# Remove any NaN values
|
|
valid_mask = ~np.isnan(Z)
|
|
X, Y, Z = X[valid_mask], Y[valid_mask], Z[valid_mask]
|
|
|
|
if len(X) < 100:
|
|
raise ValueError("Insufficient valid data points for PSD analysis")
|
|
|
|
# Create uniform grid over aperture
|
|
x_grid = np.linspace(-aperture_radius, aperture_radius, n_points)
|
|
y_grid = np.linspace(-aperture_radius, aperture_radius, n_points)
|
|
X_grid, Y_grid = np.meshgrid(x_grid, y_grid)
|
|
|
|
# Compute radial distance mask
|
|
R_grid = np.sqrt(X_grid**2 + Y_grid**2)
|
|
aperture_mask = R_grid <= aperture_radius
|
|
|
|
# Interpolate data to uniform grid
|
|
points = np.column_stack((X.flatten(), Y.flatten()))
|
|
values = Z.flatten()
|
|
|
|
if len(points) < 4:
|
|
raise ValueError("Insufficient valid points for interpolation")
|
|
|
|
interpolator = RegularGridInterpolator(
|
|
(np.linspace(X.min(), X.max(), int(np.sqrt(len(points)))).astype(float),
|
|
np.linspace(Y.min(), Y.max(), int(np.sqrt(len(points)))).astype(float)),
|
|
values,
|
|
method='linear',
|
|
bounds_error=False,
|
|
fill_value=np.nan
|
|
)
|
|
|
|
# Actually interpolate to uniform grid
|
|
# Since we have scattered data, use griddata approach instead
|
|
from scipy.interpolate import griddata
|
|
interpolated_values = griddata(points, values, (X_grid, Y_grid), method='linear')
|
|
|
|
# Set outside-aperture values to zero
|
|
interpolated_values[~aperture_mask] = 0.0
|
|
|
|
# Handle any remaining NaN values
|
|
interpolated_values = np.nan_to_num(interpolated_values, nan=0.0)
|
|
|
|
# Apply Hann window to reduce edge effects
|
|
hann_x = 0.5 * (1 - np.cos(2 * np.pi * np.arange(n_points) / (n_points - 1)))
|
|
hann_y = 0.5 * (1 - np.cos(2 * np.pi * np.arange(n_points) / (n_points - 1)))
|
|
hann_window = np.outer(hann_y, hann_x)
|
|
|
|
windowed_surface = interpolated_values * hann_window
|
|
|
|
# Compute 2D FFT
|
|
fft_complex = fft2(windowed_surface)
|
|
fft_shifted = fftshift(fft_complex)
|
|
|
|
# Compute PSD
|
|
psd_2d = np.abs(fft_shifted)**2
|
|
|
|
# Compute spatial frequency grid
|
|
freq_x = np.fft.fftfreq(n_points, d=2*aperture_radius/n_points)
|
|
freq_y = np.fft.fftfreq(n_points, d=2*aperture_radius/n_points)
|
|
freq_x_shifted = fftshift(freq_x)
|
|
freq_y_shifted = fftshift(freq_y)
|
|
|
|
FX, FY = np.meshgrid(freq_x_shifted, freq_y_shifted)
|
|
radial_freq = np.sqrt(FX**2 + FY**2)
|
|
|
|
# Convert absolute frequency to cycles per diameter
|
|
freqs_cycles_per_aperture = radial_freq * 2 * aperture_radius
|
|
|
|
# Radial averaging
|
|
max_freq = np.max(freqs_cycles_per_aperture)
|
|
freq_bins = np.logspace(
|
|
np.log10(0.01),
|
|
np.log10(np.maximum(max_freq, 100)),
|
|
100
|
|
)
|
|
|
|
psd_values = []
|
|
freqs_center = []
|
|
|
|
for i in range(len(freq_bins) - 1):
|
|
bin_mask = (freqs_cycles_per_aperture >= freq_bins[i]) & \
|
|
(freqs_cycles_per_aperture < freq_bins[i + 1])
|
|
|
|
if np.any(bin_mask) and np.any(aperture_mask[bin_mask]):
|
|
psd_bin_values = psd_2d[bin_mask] / (np.pi * (freq_bins[i+1]**2 - freq_bins[i]**2))
|
|
valid_psd = psd_bin_values[np.isfinite(psd_bin_values) & (psd_bin_values > 0)]
|
|
|
|
if len(valid_psd) > 0:
|
|
psd_avg = np.mean(valid_psd)
|
|
if psd_avg > 0:
|
|
psd_values.append(psd_avg)
|
|
freqs_center.append(np.sqrt(freq_bins[i] * freq_bins[i + 1]))
|
|
|
|
if len(freqs_center) == 0:
|
|
raise ValueError("No valid PSD data found")
|
|
|
|
return np.array(freqs_center), np.array(psd_values)
|
|
|
|
|
|
def create_psd_plot(
|
|
psd_data: Tuple[np.ndarray, np.ndarray],
|
|
title: str = "Power Spectral Density Analysis",
|
|
reference_psd: Optional[Tuple[np.ndarray, np.ndarray]] = None,
|
|
highlight_regions: bool = True
|
|
) -> _go.Figure:
|
|
"""Create an interactive PSD plot with log-log scaling."""
|
|
_load_dependencies()
|
|
|
|
frequencies, psd_values = psd_data
|
|
|
|
fig = _go.Figure()
|
|
|
|
# Main PSD trace
|
|
fig.add_trace(_go.Scatter(
|
|
x=frequencies,
|
|
y=psd_values,
|
|
mode='lines+markers',
|
|
name='Surface PSD',
|
|
line=dict(
|
|
color='#3b82f6',
|
|
width=2
|
|
),
|
|
marker=dict(
|
|
size=4,
|
|
color='#3b82f6'
|
|
),
|
|
hovertemplate="""
|
|
<b>Spatial Frequency:</b> %{x:.2f} cycles/aperture<br>
|
|
<b>PSD:</b> %{y:.2e} nm²·cycles²/aperture²<br>
|
|
<b>Feature Size:</b> %{customdata:.1f} mm
|
|
<extra></extra>
|
|
""",
|
|
customdata=(2.0 / frequencies), # Convert cycles/diameter to mm
|
|
showlegend=True
|
|
))
|
|
|
|
# Reference PSD if provided
|
|
if reference_psd is not None:
|
|
ref_freqs, ref_values = reference_psd
|
|
fig.add_trace(_go.Scatter(
|
|
x=ref_freqs,
|
|
y=ref_values,
|
|
mode='lines',
|
|
name='Gravity 20° Reference',
|
|
line=dict(
|
|
color='#64748b',
|
|
width=2,
|
|
dash='dash'
|
|
),
|
|
opacity=0.7,
|
|
showlegend=True
|
|
))
|
|
|
|
# Highlight key regions
|
|
if highlight_regions:
|
|
# Gravity signature region (0.1-2 cycles/aperture)
|
|
fig.add_vrect(
|
|
x0=0.1, x1=2.0,
|
|
fillcolor='rgba(59, 130, 246, 0.1)',
|
|
line=dict(width=0),
|
|
layer='below',
|
|
name='Gravity Signature',
|
|
label=dict(text="Gravity Signature", textposition="middle right",
|
|
font=dict(color='#3b82f6', size=12))
|
|
)
|
|
|
|
# Support structure region (2-20 cycles/aperture)
|
|
fig.add_vrect(
|
|
x0=2.0, x1=20.0,
|
|
fillcolor='rgba(245, 158, 11, 0.1)',
|
|
line=dict(width=0),
|
|
layer='below',
|
|
name='Support Structures',
|
|
label=dict(text="Support Print-through", textposition="middle right",
|
|
font=dict(color='#f59e0b', size=12))
|
|
)
|
|
|
|
# High frequency regime (>20 cycles/aperture)
|
|
fig.add_vrect(
|
|
x0=20.0, x1=100.0,
|
|
fillcolor='rgba(239, 68, 68, 0.1)',
|
|
line=dict(width=0),
|
|
layer='below',
|
|
name='High Frequency',
|
|
label=dict(text="Polishing Residuals", textposition="middle right",
|
|
font=dict(color='#ef4444', size=12))
|
|
)
|
|
|
|
# Layout configuration
|
|
fig.update_layout(
|
|
title=dict(
|
|
text=title,
|
|
font=dict(size=16, color='#1e293b'),
|
|
x=0.5
|
|
),
|
|
xaxis=dict(
|
|
type='log',
|
|
title=dict(text="Spatial Frequency [cycles/aperture]", font=dict(size=14)),
|
|
range=[np.log10(0.01), np.log10(100)],
|
|
gridcolor='rgba(100,116,139,0.2)',
|
|
linecolor='#e2e8f0',
|
|
linewidth=1
|
|
),
|
|
yaxis=dict(
|
|
type='log',
|
|
title=dict(text="Power Spectral Density [nm²·cycles²/aperture²]", font=dict(size=14)),
|
|
gridcolor='rgba(100,116,139,0.2)',
|
|
linecolor='#e2e8f0',
|
|
linewidth=1
|
|
),
|
|
width=1200,
|
|
height=700,
|
|
margin=dict(l=80, r=80, t=60, b=80),
|
|
paper_bgcolor='#ffffff',
|
|
plot_bgcolor='#f8fafc',
|
|
font=dict(color='#1e293b', size=12),
|
|
legend=dict(
|
|
orientation='h',
|
|
yanchor='top',
|
|
y=-0.15,
|
|
xanchor='center',
|
|
x=0.5
|
|
),
|
|
hovermode='x unified'
|
|
)
|
|
|
|
return fig
|
|
|
|
|
|
def create_psd_summary(
|
|
psd_data: Tuple[np.ndarray, np.ndarray],
|
|
elevation_angle: str = "40°"
|
|
) -> str:
|
|
"""Generate formatted summary text for PSD analysis."""
|
|
frequencies, psd_values = psd_data
|
|
|
|
# Define frequency bands
|
|
gravity_band = (0.1, 2.0) # cycles/aperture
|
|
support_band = (2.0, 20.0) # cycles/aperture
|
|
hf_band = (20.0, 100.0) # cycles/aperture
|
|
|
|
# Calculate integrated PSD values for each band
|
|
def integrate_band(low_freq, high_freq):
|
|
mask = (frequencies >= low_freq) & (frequencies <= high_freq)
|
|
if np.any(mask):
|
|
return np.trapz(psd_values[mask], frequencies[mask])
|
|
else:
|
|
return 0.0
|
|
|
|
gravity_rms = np.sqrt(integrate_band(*gravity_band))
|
|
support_rms = np.sqrt(integrate_band(*support_band))
|
|
hf_rms = np.sqrt(integrate_band(*hf_band))
|
|
total_rms = np.sqrt(np.trapz(psd_values, frequencies))
|
|
|
|
# Find peak PSD values
|
|
peak_freq = frequencies[np.argmax(psd_values)]
|
|
peak_amplitude = np.max(psd_values)
|
|
|
|
# Convert frequency to feature size
|
|
if peak_freq > 0:
|
|
feature_size = 2.0 / peak_freq # mm
|
|
else:
|
|
feature_size = np.inf
|
|
|
|
summary = f"""
|
|
**WFE Power Spectral Density Summary - {elevation_angle}**
|
|
|
|
**Gravity Loading Analysis:**
|
|
- Gravity Signature (0.1-2 cycles/aperture): {gravity_rms:.2f} nm RMS
|
|
- Peak frequency: {peak_freq:.2f} cycles/aperture
|
|
- Dominant feature size: {feature_size:.1f} mm
|
|
|
|
**Support Structure Analysis:**
|
|
- Support Print-through (2-20 cycles/aperture): {support_rms:.2f} nm RMS
|
|
- HF Polishing Residuals (20-100 cycles/aperture): {hf_rms:.2f} nm RMS
|
|
|
|
**Total Deformation:**
|
|
- Integrated WFE: {total_rms:.2f} nm RMS
|
|
- Gravity contribution: {100*gravity_rms/total_rms:.1f}%
|
|
- Support structure contribution: {100*support_rms/total_rms:.1f}%
|
|
|
|
**Technical Notes:**
|
|
- Frequency scaling: cycles per aperture diameter
|
|
- Reference normalization: None (absolute measurement)
|
|
- Spatial resolution: Limited by mesh density
|
|
"""
|
|
|
|
return summary |