- for line profiles we assume :
\[d\nu = -\frac{c}{\lambda^{2}}d\lambda \approx -\frac{c}{\lambda_{0}^{2}}d\lambda\]
- therefore, we have
\[\frac{d\nu}{\nu_{0}} \approx \frac{d\lambda}{\lambda_{0}}\]
- and for wavelength/frequency mesh conversion, we have
\[d\lambda = - \frac{c}{\nu_{0}^{2}} d\nu\]
- for conversion between intensities in wavelength/frequency units, we have
\[ \begin{align}\begin{aligned}I_{\nu} d\nu = -I_{\lambda} d\lambda\\I_{\lambda} = I_{\nu} \frac{c}{\lambda_{0}^{2}}\end{aligned}\end{align} \]
- for Voigt function, we have
\[\int_{-\infty}^{+\infty} H(a,x) dx = \sqrt{\pi}\]
- where
\[x \equiv \frac{(\nu-\nu_{0})}{\Delta\nu_{D}} \approx \frac{(\lambda-\lambda_{0})}{\Delta\lambda_{D}}\]
- and \(\Delta\nu_{D}\), \(\Delta\lambda_{D}\) are Doppler Width in frequency, wavelength unit, respectly, since
\[\frac{\Delta\lambda_{D}}{\lambda_{0}} = \frac{\Delta\nu_{D}}{\nu_{0}}\]