Reconstructed radiation field after t = 1500 Myr, at column densities of N_HI = 10¹⁷,  10¹⁸, and 5 × 10¹⁸ cm⁻² (from left to right) from the source, for the pure hydrogen (top) and primordial hydrogen and helium mixture (bottom) case. The black line denotes the CLOUDY reference runs, the red lines show the reconstructed spectrum using the PWPL approximation and the blue line represents the classic three-band PWC approach. For illustrative purposes, we represent the spectral shape of the three-band PWC case as scaled intervals of the initial black-body spectrum, while in practice it is treated as a delta function at the effective frequency of each band.