Table 1.

Ratios of uncertainties in A and LW for absorption and derivative Lorentzian lines with the same SNR.

Row	Method	Filter	Broadening	SNR	$\frac{{\mathrm{\sigma }}_{\mathrm{A}}^{\text{der}}}{{\mathrm{\sigma }}_{\mathrm{A}}^{\text{abs}}}$	$\frac{{\mathrm{\sigma }}_{\text{Lw}}^{\text{der}}}{{\mathrm{\sigma }}_{\text{Lw}}^{\text{abs}}}$
1	Eq. [19]	-		-	2.60	1.06
2	Monte-Carlo	None	-	5	2.64 (2%)a	1.06 (0%)a
3	Monte-Carlo	None	-	10	2.61 (0%)a	1.07 (1%)a
4	Monte-Carlo	None	-	15	2.62 (1%)a	1.07 (1%)a
5	Monte-Carlo	Butterworth	1%	5	2.58 (-1%)a	0.94 (-11%)a
6	Monte-Carlo	Butterworth	1%	10	2.13 (-18%)a	0.87 (-18%)a
7	Monte-Carlo	Butterworth	1%	15	2.12 (-18%)a	0.87 (-18%)a

^aDeviations from the values predicted by Eq. [19], row R1, are shown in parentheses.