Sources

disk(θx::Matrix{<:RV}, θy::Matrix{<:RV}, θr::RV, β::NTuple{2, RV}; A::RV=1.0) --> Matrix{<:RV}

Creates a disk source profile of radius $θ_r$ on a grid defined by $[θ_x, θ_y]$. The center of the disk is at $\pmb{β} = (β_x, β_y)$. By default, the source profile is constant and every pixel has a value of 1.0 and we can scale it using the amplitude $A$. The corresponding formula is:

\[S(θ_x, θ_y) = \begin{cases} A, & \text{if } (θ_x - β_x)^2 + (θ_y - β_y)^2 ≤ θ_r^2 \\ 0, & \text{otherwise} \end{cases}\]

gaussian(θx::Matrix{<:RV}, θy::Matrix{<:RV}, σx::RV, σy::RV, β::NTuple{2, RV}; A::RV=1.0) --> Matrix{<:RV}

Creates a Gaussian source profile on a grid defined by $[θ_x, θ_y]$. Standard deviations along $(x, y)$ axis are given by $(σ_x, σ_y)$. The center of the Gaussian is at $\pmb{β} = (β_x, β_y)$. The overall normalization is determined by $A$. The corresponding formula is:

\[S(θ_x, θ_y) = \frac{A}{2 π σ_x σ_y} \exp\left[-\frac{1}{2} \left(\frac{(θ_x - β_x)^2}{σ_x^2} + \frac{(θ_y - β_y)^2}{σ_y^2}\right)\right]\]

sersic(θx::Matrix{<:RV}, θy::Matrix{<:RV}, n::RV, θe::RV, β::NTuple{2, RV}; A::RV=1.0) --> Matrix{<:RV}

Creates a Sersic source profile on a grid defined by $[θ_x, θ_y]$. The Sersic index is given by $n$ and the effective radius is given by $θ_e$. The center of the Sersic profile is at $\pmb{β} = (β_x, β_y)$. The overall normalization is determined by $A$. The corresponding formula is:

\[S(θ_x, θ_y) = \frac{A \,b_n^{2n}}{π θ_e^2 \, Γ(2n+1)} \exp\left[-b_n \left(\frac{\sqrt{(θ_x - β_x)^2 + (θ_y - β_y)^2}}{θ_e}\right)^{1/n}\right]\]