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Measurement under real operating conditions

Standardisation according to DIN and ISO provides the formal framework for the reproducible measurement of laser beams according to internationally recognised rules. Around the turn of the millennium, the foundations for this were laid by the CHOCLAB project, among others. PRIMES and others were involved in this project. Results from the project fed into the following standards: 11145, 11146, 11670 and 11554.

Central formulae for beam measurement

Beam parameter product BPP

The beam parameter product is a physical parameter which describes the beam quality, and hence the focusability, of a laser beam.

Θ = full beam divergence angle
w0 = radius of the beam waist
dF = focal diameter
rF= wF= focal radius
k= 1/M2= beam propagation factor
M2 = diffraction index

Diffraction index M²

The diffraction index  M² is an absolute parameter that characterises a laser beam: the greater M² is, the worse the beam is to focus, i.e., the larger the smallest possible focal diameter is.

diffraction index M² = 1/k

F= F-number - focal length/ raw beam diameter   
λ= wavelength
dF= focal diameter


Rayleigh length zR (colloquial term: depth of focus)

The Rayleigh length is the distance along the optical axis that a laser beam requires until the area of its cross-section doubles, starting from the beam waist.

zR= Rayleigh length
λ= wavelength

Formulae for pulse applications:

PP= pulse power 
EP= pulse energy
tp= pulse duration
fp= pulse frequency
P= average power
I= power density
A= beam area


Formula for fibre applications:

NA= numerical aperture
n= refractive index in front of the fibre
α= full angular aperture of the fibre