#3180 Machine Learning for Correcting a Low-Budget Astronomical Mirror

1 Optical test bench

Item	Why	Tips
Back-illuminated square grid (e.g. an LCD tablet showing a black/white checker or a printed transparency on a light panel)	Provides thousands of precisely known feature points	Use a grid whose cell size is ≤3 mm so that many cells are visible at once. The target must be perfectly flat.
Distance	Makes the rays effectively parallel, mimicking a star	≥50 × focal-length (put it down a hallway or outdoors at night).
Monochrome astrophotography camera at Newtonian focus	Captures distortions introduced by your mirror only (no Bayer artifacts)	Lock focus; record RAW frames.
Stable mount & collimation	Ensures repeatability so ML sees only mirror-induced changes	Re-collimate after each mirror tweak.

2 Data acquisition loop

Collect baseline frames
Capture 50–100 short-exposure images of the grid. Average or median-stack to kill sensor noise.
Introduce controlled perturbations (optional)
If you plan to drive actuators later, deliberately tilt / slightly torque the mirror and collect new stacks.
These become labelled examples of “input → desired output”.
Save metadata
Focal length, grid-to-mirror distance, temperature, any mirror adjustments.
Store it in a CSV/JSON sidecar for supervised learning later.

3 Computer-vision extraction of an “error map”

OpenCV gives you a deterministic pipeline that you’ll reuse inside the ML training script:

import cv2, numpy as np

img   = cv2.imread("stacked_grid.tif", cv2.IMREAD_GRAYSCALE)
# find all black-white crossings
ret, thresh = cv2.threshold(img, 0, 255, cv2.THRESH_OTSU)
corners = cv2.goodFeaturesToTrack(thresh, maxCorners=4000,
                                  qualityLevel=0.01, minDistance=8)

# sort the corners into a rectangular lattice
# … (hierarchical clustering / BFS) …

# fit an ideal square lattice by least squares
ideal_pts = fit_perfect_grid(corners)          # (Nx2 array)
H, _       = cv2.findHomography(corners, ideal_pts)

# residual = actual – ideal  ⇒  vector field of distortions
residuals = corners.squeeze() - (cv2.perspectiveTransform(
               corners, H)).squeeze()

# build dense 2-D distortion map with radial-basis interpolation
dist_map  = interpolate_to_full_frame(residuals, img.shape)
np.save("distortion_map.npy", dist_map)

Interpretation:

The x/y residual vector field is an image-space manifestation of your mirror’s slope errors.
Convert it to wavefront error by multiplying by focal length (small-angle approximation) if you want Zernike coefficients for classical optics analysis.

4 Machine-learning approaches

4.1 Image-space “de-warper” (fast post-processing)

Step	Details
Dataset	Input = distorted raw frame. Target = `cv2.warpPerspective(input, H)` (i.e. corrected grid).
Model	A lightweight U-Net or residual CNN (PyTorch). Acts like an adaptive deconvolution / distortion compensator.
Loss	`L_total = L1(output, target) + λ⋅TV(output)` to preserve edges.
Augmentation	Random brightness, sensor noise, small rotations → robustness to field & seeing changes.
Output	A `.pt` file you call in your astrophotography script: `clean = model(raw_tensor).cpu().numpy()`

Edge benefit: you can train on synthetic stars too—render perfect Airy disks, warp them with the measured distortion_map, and include them in training so the network learns to sharpen point sources, not just grids.

4.2 Wavefront-to-actuator regressor (active optics)

If you retrofit the mirror with a handful of push–pull screws or stepper-driven supports:

Step	Details
Labels	Record the actuator offsets A used for each grid capture.
Features	Zernike coefficients Z or the raw distortion map flattened.
Model	Small fully-connected network: `A = f(Z)` trained by MSE.
Usage loop	① Capture grid → ② Extract Z → ③ Predict actuator deltas → ④ Move mirror → ⑤ Repeat until residual RMS < goal.

Because the mapping is smooth and low-dimensional (~15 Zernike terms ↔ up to 18 screws), you often need <500 labelled samples.

5 Putting it into practice

Prototype quickly: Run the OpenCV extraction once; inspect the heat-map with matplotlib.imshow(dist_map[...,0]) to verify you’re seeing sane patterns (coma, astigmatism, trefoil…).
Decide latency target:
- Photographers: ≤1 s/frame is fine → use GPU inference on a laptop or Raspberry Pi 5 + NPU.
- Real-time active optics: aim for <100 ms → quantize the network with ONNX Runtime.
Automate capture: Small script that slews between grid and sky so every observing session starts with a recalibration stack.
Monitor drift: Append each night’s distortion statistics to a CSV so you can tell whether the mirror is settling, warping with temperature, or the tube is flexing.
Iterate: The more varied examples (temps, focus offsets, mirror tweaks) you feed the model, the better it generalizes to real stars and nebulae.

6 Resources & code starters

Purpose	Library / paper / repo
Grid detection / homography	OpenCV (`goodFeaturesToTrack`, `findHomography`)
Thin‐plate spline warping	SciPy RBF or `torchvision.transforms.TPS`
Fast CNN inference on small devices	ONNX Runtime / PyTorch Mobile
Optical wavefront theory reference	Mahajan, “Optical Imaging & Aberrations, Vol. II”
Example telescope-distortion ML pipeline	GitHub → `AstroAI/distortion-unwarp` (synthetic data + UNet)

What if you skip ML?

A single least-squares fit of Zernike polynomials to the distortion map already tells you which aberrations dominate (e.g., 0.4 λ of third-order coma). You can then:

Refigure the mirror (classical polishing).
Insert a custom 3-D-printed corrector lens optimized in Zemax.
Live-stack with drizzle + deconvolution (e.g., AstroSurface) guided by the measured PSF.

ML doesn’t replace those optics fundamentals; it simply lets you reach parity with a far better mirror today, while you decide whether physical fixes are worthwhile.

7 Next steps checklist

□ Build/print a precise square grid and verify flatness.
□ Capture and stack baseline images through the 16" optics.
□ Run the OpenCV script to compute distortion_map.npy.
□ Choose path 4.1 (post-processing) or 4.2 (active optics) and create a minimal PyTorch training loop.
□ Validate on a real nighttime star field; compare FWHM before/after correction.
□ Iterate with new data whenever temperature, collimation, or mirror support changes.

Good luck turning that budget mirror into a surprisingly sharp reflector!

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