Technical Guide: Laser Optics - Formulary


1. Focussing lenses

1.1 Calculation of the minimum focal diameter

dF:      focal spot diameter
dEP:    entrance pupil of the scanner
dL:      entrance beam diameter (1/e²)
f':        focal length
λ:       wavelength
APO:  apodisation factor
M²:     diffraction value of the laser
T:        trunctation ratio


1.2 Calculation of the rayleigh length

zR:   rayleigh length


1.3 Calculation of the focal diameter for fiber imaging

fC:          fiber core diameter
NAfiber:  numerical aperture of the fiber
α:           half beam cone angle
M:          magnification by NA calculation
dF:         focal spot diameter
f1:          focal length of the collimating lens
f2:          focal length of the focussing lens


2. Laser Induced Damage Threshold (LIDT)

2.1 Energy- and power density

F:          energy density / fluence
E:          pulse energy
F:          focal spot diameter
I:           power density / irradiance
Ppeak:   peak power of the laser


2.2 Estimate of the LIDT

E:               pulse energy
dF:             focal spot diameter
λ:               used wavelength
λspec:        specified wavelength
τ:               pulse duration of the used laser
τspec:        specified pulse duration
LIDT:         real LIDT
LIDTspec:  specified LIDT


3. Beam expanders

3.1 Calculation of the magnification

β':             magnification
β'max:       maximum magnification
din:           entrance beam diameter
dout:         outgoing beam diameter
dscanner:  aperture of the scanner


The outgoing beam diameter dout is limited by the beam expander or by the aperture of the scanner.


3.2 Divergence angle

Θ0:  divergence angle
λ:     wavelength
ω0:  beam diameter at the waist


The higher the beam diameter the lower is the divergence!