1. Problem statement: You have spectra recorded by multiple cameras that view the same scene from slightly different angles, with some cameras running slower or faster and with different pixel and spectral resolutions, and your goal is to align those spectra so corresponding spectral features match across cameras. 2. Inventory the data and assumptions: list camera intrinsic calibrations (wavelength calibration, pixel scale), known reference peaks or fiducials, approximate angular offsets (few degrees), and timestamps for frames. 3. Preprocessing: perform dark/flat corrections and convert raw counts to radiance or a consistent unit if possible. 4. Spectral calibration: if each camera reports spectra at sample wavelengths $\lambda_i$, resample each spectrum to a common wavelength grid using linear interpolation. $$f(\lambda)=f(\lambda_i)\frac{\lambda_{i+1}-\lambda}{\lambda_{i+1}-\lambda_i}+f(\lambda_{i+1})\frac{\lambda-\lambda_i}{\lambda_{i+1}-\lambda_i}$$ 5. Spatial model choice: for small angular offsets and negligible perspective, use an affine model that accounts for rotation, scale, shear and translation, written component-wise. $$x'=a_{11}x+a_{12}y+t_x,\quad y'=a_{21}x+a_{22}y+t_y$$ 6. Parameter estimation (affine) from matched correspondences: collect matched points $\{(x_k,y_k)\}$ and $\{(x'_k,y'_k)\}$ and stack linear equations to solve by least squares. $$p=(M^TM)^{-1}M^T b$$ Explain: here $p$ is the vector $[a_{11},a_{12},t_x,a_{21},a_{22},t_y]^T$ and $M,b$ are built from the source coordinates and target coordinates respectively, and the solution minimizes squared reprojection error. 7. When perspective matters use a homography and estimate $H$ such that points satisfy projective equivalence. $$x'\sim H x$$ Explain: use 4 or more non-collinear correspondences and solve for $H$ with RANSAC to reject outliers. 8. Subpixel registration with Fourier phase correlation: estimate pure shifts robustly using the Fourier shift theorem if the dominant difference is translation. $$F_2(u)=F_1(u)e^{-2\pi i u \Delta x}$$ Compute the cross-power spectrum $$R(u)=\frac{F_1(u)\overline{F_2(u)}}{|F_1(u)\overline{F_2(u)}|}$$ and inverse Fourier transform; the peak gives $\Delta x$ with subpixel accuracy after parabolic interpolation. 9. Temporal alignment: convert frame indices to a common time axis using timestamps, and interpolate spectra in time when frame rates differ so you compare spectra at matched instants. 10. Handle resolution mismatch: if you need a common spatial/spectral resolution, low-pass filter and downsample the higher-resolution data or upsample the lower-resolution data with a proper interpolation kernel while guarding against aliasing. Express convolution for smoothing: $$g=k*f$$ 11. Combining spectra from multiple cameras: fuse using weights proportional to SNR or inverse variance to favor higher-quality measurements. $$S(\lambda)=\frac{\sum_i w_i(\lambda)S_i(\lambda)}{\sum_i w_i(\lambda)},\quad w_i=1/\sigma_i^2$$ 12. Validation metrics and diagnostics: compute residuals after registration and report RMSE and cross-correlation peak sharpness. $$\mathrm{RMSE}=\sqrt{\frac{1}{N}\sum_{k=1}^N (s_k-\hat s_k)^2}$$ 13. Practical workflow checklist: calibrate radiometrically and spectrally first, resample spectra to a shared wavelength grid, spatially register (affine or homography) using spectral or spatial fiducials, refine with phase-correlation for subpixel shifts, temporally align via timestamps, match resolutions, fuse with SNR weights, and validate with RMSE and visual overlays. 14. Tips: use robust estimators (RANSAC) for geometric fits, prefer phase correlation for pure shifts, use reference lines if available for spectral calibration, and track metadata (intrinsics, timestamps, exposure) to guide weighting and corrections. Final answer: follow the stepwise pipeline above to align spectra spatially, spectrally, and temporally, estimate transforms via least squares or RANSAC for geometry, refine shifts via phase correlation, resample to common wavelength and time grids, and fuse with SNR-based weights.