Hilbert transforms 

of a spectrum
https://doi.org/10.1351/goldbook.08256
Functions that interrelate the real part, f, and imaginary part, f, of the refractive index, n^=n+ik, or relative permittivity, ϵ^=ϵ+iϵ, through f(ν~a)f=1πPf(ν~)ν~ν~adν~ f(ν~a)f=1πPf(ν~a)fν~ν~adν~ where P means that the principal part of the integral is taken at the singularity.
Source:
PAC, 2021, 93, 647. (Glossary of methods and terms used in analytical spectroscopy (IUPAC Recommendations 2019)) on page 661 [Terms] [Paper]