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