Technical Guide: Laser Optics - Formulary
Overview
> 1. Fokussing lenses
> 1.1 Calculation of the minimum focal diameter
> 1.2 Calculation of the rayleigh length
> 1.3 Calculation of the focal diameter for fiber imaging
> 2. Laser Induced Damage Threshold (LIDT)
> 2.1 Energy- and power density
> 2.2 Estimate of the LIDT
> 3. Beam expanders
> 3.1 Calculation of the magnification
> 3.2 Divergence angle
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!