fwH

FWH, short for Full Width at Half Maximum (often abbreviated FWHM), is a measure used to describe the width of a peak, pulse, or distribution. It is defined as the distance between the two points on the curve where the value is equal to half of the peak’s maximum. FWHM is commonly applied to spectra, imaging point spread functions, and chromatography peaks to characterize resolution and sharpness.

For specific peak shapes, FWHM has useful relationships with fitted parameters. For a Gaussian peak f(x) = A exp(-(x−μ)²/(2σ²)), the FWHM equals 2√(2 ln 2) σ ≈ 2.3548 σ. For a Lorentzian peak f(x) = A/(1 + ((x−μ)²/γ²)), the FWHM is 2γ. In practice, FWHM is determined by locating half-maximum points on the measured or modeled curve and computing their separation, or by fitting a chosen model and extracting the width parameter.

Applications span many fields. In spectroscopy and astronomy, FWHM describes spectral line widths and instrumental resolution. In imaging, it quantifies the point spread function and camera sharpness. In chromatography and mass spectrometry, FWHM reflects peak resolution and separation efficiency. The metric is also used in laser optics and signal processing to compare pulse or signal quality.

Measurement can be affected by noise, baseline drift, or peak asymmetry, so FWHM is often estimated via curve fitting with Gaussian, Lorentzian, or mixed models, or by deconvolution when multiple overlapping peaks are present.