Table 2.

Expressions of the three channel functions.

Channel name	Expressions of the channel function
Laguerre-Gauss (LG)	$U_j(r|a)=\frac{\sqrt{2}}{a}{\mathrm{e}}^{-\frac{\pi r^2}{a^2}}{L}_j(\frac{2\pi r^2}{a^2}),$, with the Laguerre polynomial function $L_j(x)={\sum }_{i=0}^j{(-1)}^i\left(\begin{array}{c}j\\ i\end{array}\right)\frac{x^i}{i!}$
Square (SQR)	$C_j(\rho )=\{\begin{array}{cc}0& \text{for}\rho \le {\rho }_0{a}^{j-1}\\ 1& \text{for}{\rho }_0{a}^{j-1}<\rho \le {\rho }_0{a}^j\\ 0& \text{for}\rho >{\rho }_0{a}^j\end{array}$
Sparse difference of Gaussian (sDOG)	$C_j(\rho )={\mathrm{e}}^{-\frac{1}{2}{\left(\frac{\rho }{Q{a}_j}\right)}^2}-{\mathrm{e}}^{-\frac{1}{2}{\left(\frac{\rho }{a_j}\right)}^2}\text{with}{a}_j=a_0{a}^j$