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Table 1.
Notations used throughout this work.
| Symbol | Meaning |
|---|---|
 |
N × N identity matrix |
| Δ(λ) | Dispersion function |
| ℱ | Fourier operator |
| f(u) | Sampled observational spectrum |
| g(x, σ, μ) | Gaussian with standard deviation σ and mean μ |
| H(ν) | Optical transfer function |
| ℐ | Instrument operator |
| I(u, λ) | Instrument kernel |
| I | Instrument matrix |
| λ | Wavelength |
| Λ(x) | Triangular function |
| L(u, λ) | Sampled line spread function |
| ℒ2(X) | Space of square-integrable functions on X over  |
| N | Dimension of V and W |
| N* | Dimension of V* and W* |
| ν | Frequency variable associated with pupil function |
| Π(x) | Rectangular function |
 |
nth Hermite function |
| R(λ) | Response function |
| s(λ) | Spectral photon distribution |
| Σy | Variance-covariance matrix of a random vector y |
| sinc(x) | Normalised cardinal sine function |
| u | Focal plane variable |
 |
Singular value decomposition of matrix M |
| V | Space spanned by calibration SPDs |
| V* | Finite-dimensional expansion of V |
| vec (M) | Vectorisation of the matrix M |
| W | Space spanned by observed calibration spectra |
| W* | Finite-dimensional expansion of W |
| ▫ | Place holder for variables |
| ⋆ | Correlation operation |
| ⊗ | Kronecker product |
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