Left panels present the emergent spectrum (top panel) and the temperature structure (bottom panel) of the fiducial model computed using four different RFs: (a) exact angle-dependent (solid curves), (b) exact angle-averaged (dashed curves), (c) approximate angle-dependent (dot-dashed curves), and (d) approximate angle-averaged (dotted curves). In the top lower sub-panel, the ratios of the spectra (b), (c), and (d) to the spectrum for case (a) are shown. In the bottom lower sub-panel, the ratio of the temperature structures (b), (c), and (d) to that of case (a) are shown. Right panels present the emergent spectrum (top panel) and the temperature structure (bottom panel) of the fiducial model computed using an exact angle-dependent RF (solid curves) and the Kompaneets operator (dashed curves).