Peak Shape Functions II. Lorentzian (or Cauchy)

Course Material Index  Section Index  Previous Page  Next Page 

Lorentzian (or Cauchy)

The Lorentzian is also a well-used peak function with the form:

where w is equal to half of the peak width (w = 0.5 H). The main features of the Lorentzian function are:

• that it is also easy to calculate
• that, relative to the Gaussian function, it emphasises the tails of the peak
• its integral breadth β = π H / 2
• it has a convenient convolution property (see later)
• it is symmetrical
• instrumental peak shapes are not normally Lorentzian except at high angles where wavelength dispersion is dominant

We note again that since peak intensity is identified with peak area, it is often convenient to also have a form of Lorentz function normalised so that the area is unity; i.e.

Course Material Index  Section Index  Previous Page  Next Page