Orthogonal polynomial fits to one noise realization of case 3 to demonstrate the BIC selection. For the 3^rd order, the retrieved time delay and differential dust extinction deviate strongly from the input, which is visible from the different shapes of the fits in the range of the data points of image A and image B. Panel a: 6^th order, Panel b: 5^th order, Panel c: ${\displaystyle \underline{4^{\mathrm{th}}\text{order}}}$, Panel d: 3^rd order, Panel e: 2^nd order; The selected order is underlined and highlighted with a red frame of the plot.