Algorithm 1.

Selection of computation boundaries and β ranges

if $L_r>Z_0^{+}-Z_0^{-}$: # wide receiver slit

if $Z_0^{+}\le \frac{L_r}{2}$ and $Z_0^{-}\ge \frac{L_r}{2}$:

# parabola apexes entirely within slit

rr = 1; ${\epsilon }_a={\epsilon }_1^{+}$; ${\epsilon }_b={\epsilon }_2^{+}$; ${\epsilon }_c={\epsilon }_1^{-}$; ${\epsilon }_d={\epsilon }_2^{-}$

seel if $\left(Z_0^{+}>\frac{L_r}{2}\text{and}{Z}_0^{-}<\frac{L_r}{2}\right)$or $\left(Z_0^{+}>-\frac{L_r}{2}\text{and}{Z}_0^{-}<-\frac{L_r}{2}\right)$:

# one apex outside of slit

rr = 2; ${\epsilon }_a={\epsilon }_2^{+}$; ${\epsilon }_b={\epsilon }_1^{+}$; ${\epsilon }_c={\epsilon }_1^{-}$; ${\epsilon }_d={\epsilon }_2^{-}$

else:

# both apexes outside of slit

rr = 3; ${\epsilon }_a={\epsilon }_2^{+}$; ${\epsilon }_b={\epsilon }_1^{+}$; ${\epsilon }_c={\epsilon }_1^{-}$; ${\epsilon }_d={\epsilon }_2^{-}$

else: # narrow receiver slit

if $Z_0^{+}\ge \frac{L_r}{2}\text{and}{Z}_0^{-}\le -\frac{L_r}{2}$:

# parabola apexes hanging off both ends of slit

rr = 1; ${\epsilon }_a={\epsilon }_1^{-}$; ${\epsilon }_b={\epsilon }_2^{+}$; ${\epsilon }_c={\epsilon }_1^{+}$; ${\epsilon }_d={\epsilon }_2^{-}$

else if $\left(Z_0^{+}>\frac{L_r}{2}\text{and}-\frac{L_r}{2}<Z_0^{-}<\frac{L_r}{2}\right)$ or $\left(-\frac{L_r}{2}<Z_0^{+}<\frac{L_r}{2}\text{and}{Z}_0^{-}<-\frac{L_r}{2}\right)$ :

# one apex of beam within slit

rr = 2; ${\epsilon }_a={\epsilon }_2^{+}$; ${\epsilon }_b={\epsilon }_1^{-}$; ${\epsilon }_c={\epsilon }_1^{+}$; ${\epsilon }_d={\epsilon }_2^{-}$

else:

rr = 3; ${\epsilon }_a={\epsilon }_2^{+}$; ${\epsilon }_b={\epsilon }_1^{-}$; ${\epsilon }_c={\epsilon }_1^{+}$; ${\epsilon }_d={\epsilon }_2^{-}$