Table 1
Major parameters.
| Av | Visual extinction |
 |
See Eqs. (6) and (7) |
| Bλ,T | Blackbody function |
| d | Distance to the target |
| Fobs;λ | Observed flux for the central illuminating source at the wavelength λ |
| Fλ(x, y) | Flux that the extended disk or envelope receives from the central source at the wavelength λ |
| fλ | A factor to correct foreground extinction for the wavelength λ (see Eq. (30)) |
| Ia;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (via single scattering) |
| Ib;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (via double scattering) |
| Ic;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (thermal emission from the surface layer) |
| Id;λ(x, y) | Intensity distribution for the extended disk at the wavelength λ (thermal emission from the disk interior) |
| Ia′;λ(x, y) | Intensity distribution for the extended envelope at the wavelength λ (via single scattering) |
| Ic′;λ(x, y) | Intensity distribution for the extended envelope at the wavelength λ (thermal emission) |
| i | Viewing angle of the extended disk or envelope |
| P1(λ,θsca) | Scattering phase function for the scattering angle θsca at the wavelength λ |
| P2(λ,θsca) | Product of the scattering phase function and polarization for the scattering angle θsca at the wavelength λ |
| P2(H) | Representative constant for P2(λ; θsca) for the H band (λ = 1.65 μm) |
| (PI)obs;H (x, y) | Observed PI distribution for the H band |
| r | Distance to the central source projected to the midplane  |
| Td(x, y) | Temperature at the disk interior |
| Te(x, y) | Temperature in the envelope |
| Ts(x, y) | Temperature at the surface layer of the disk |
| x, y | Coordinate in the midplane |
| z | Coordinate perpendicular to the midplane |
| zdisk(x, y) | Location of the disk surface |
| zenv(x, y) | Typical height of the envelope |
| α(x,y) | Sine of the radial gazing angle of the disk surface β(x,y) |
| β(x,y) | Radial grazing angle of the disk surface with respect to the incident light (see Fig. 2) |
 |
Typical grazing angle of the flat compact disk from the disk surface or the envelope |
| δ(x, y) | Radial inclination of the disk surface with respect to the midplane (see Fig. 2) |
| θsca(x, y, i) | Scattering angle of the light from the central illuminating source (see Fig. 2) |
| κext;λ | Dust opacity for the wavelength λ |
| λ | Wavelength |
| ∑env(x, y) | Surface density for the extended envelope |
| τl,λ(x, y) | Optical thickness of the extended envelope at line of sight of the observations |
| τr,λ(x, y) | Optical thickness of the extended envelope from the central source in the radial direction |
| ωλ | Scattering albedo for the wavelength λ |
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