Open Access
Table 1
All variables used in the spatial (PSD) and temporal evolution models of dome-seeing phase screens.
| Symbol | Units | Definition |
|---|---|---|
| k | cycles m−1 | Radial spatial frequency |
| fx, fy | cycles m−1 | Spatial frequencies in the horizontal and vertical directions of the screen |
| α | – | Power-law slope of the baseline turbulence spectrum |
| ß0 | – | Global scaling factor of the quasi-static background PSD |
| ßHF | – | Amplitude of the high-frequency enhancement component |
| ßbump | – | Amplitude of the localized spectral enhancement |
| k0 | cycles m−1 | Central frequency of the Gaussian spectral bump representing intermediate-scale convection |
| σk | cycles m−1 | Spectral width of the Gaussian bump |
| kout | rad m−1 | Cutoff spatial frequency associated with an outer scale L0 |
| kin | rad m−1 | Cutoff spatial frequency associated with an inner scale 10 |
| kNyq | cycles m−1 | Nyquist spatial frequency of the sampling grid |
| T (k) | – | Soft taper near kNyq to avoid spectral ringing |
| n | – | Threshold fraction defining where the high-frequency taper begins |
| PSD(k) | rad2 m2 | Spatial power spectral density before tapering |
| PSDfinal(k) | rad2 m2 | PSD after applying the Nyquist taper |
| F (k, t) | rad | Complex Fourier coefficient of the phase at frequency k and time t |
| Δt | s | Temporal step between successive screen updates |
| τ(k) | s | Correlation timescale for spatial frequency k |
| τ0 | s | Reference correlation time at spatial frequency k0 |
| γ | – | Power-law exponent governing how de-correlation varies with scale |
| a(k) | – | Autoregressive damping coefficient |
| η(k, t) | – | Complex Gaussian noise with zero mean and unit variance |
| ε | – | Noise amplitude factor controlling boiling strength |
| v(t) | m s−1 | Advection velocity vector applied to the phase screen |
| Vx,Vy | m s−1 | Components of the advection velocity |
| θ | rad | Rotation angle per time step used for spiral-like flow modes |
| ωspiral | rad s−1 | Angular drift rate governing slow rotational evolution of v(t) |
| R(θ) | – | 2 × 2 rotation matrix |
| φ(x, t) | rad | Real phase screen in spatial domain after inverse FFT |
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