Table 1
Summary of the main notations used in this paper.
| Not. | Range | Definition |
|---|---|---|
| Constants | ||
| T | ℕ | Number of epochs |
| Kt | ℕ | Number of frames per epoch t |
| L | ℕ | Number of spectral channels(a) |
| N | ℕ | Number of pixels per frame(a) |
| Indexes | ||
| t | ⟦1, T⟧ | Epoch index |
| k | ⟦1, Kt⟧ | Temporal frame index |
| ℓ | ⟦1, L⟧ | Spectral channel index |
| Physical quantities | ||
| α |  |
Source’s spectral energy distribution |
| αint |  |
Source’s spectrally integrated energy distribution |
| f |  |
Nuisance (stellar leakages and noise) |
| h | ℝNTL | Off-axis PSF |
| r |  |
Observed intensity |
| γ | ℝTL | Source’s prior spectrum |
| Positions | ||
| μ | ℝ7 | Orbital elements(b) |
| θt (μ) | ℝ2 | 2D position on the detector |
| Other quantities and metrics | ||
| C | ℝN×N | Spatial covariance matrix of f(c) |
| Σ | ℝL×L | Spectral covariance matrix of f |
| S/𝒩t | ℝ+ | Mono-epoch S/N at epoch t |
| 𝒮/𝒩 | ℝ+ | Multi-epoch S/N |
| C | ℝ+ | Multi-epoch cost function |
Notes. (a)The number of spectral channels and the number of pixels per frame are constant for a given instrument so that L and N are independent of t. (b)See Sect. 3 and Table 2 for the allowable ranges of each orbital element. (c)As discussed in the text, with PACO, covariance matrices are evaluated locally at a scale of small patches so that the full covariance, C, is never evaluated explicitly.
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