Technicon: 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

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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

 
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1.2 Calculation of the rayleigh length

zR:   rayleigh length

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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

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2. Laser Induced Damage Threshold (LIDT)

2.1 Energy- and power density

F:         energy density / fluence

E:         pulse energy

dF:        focal spot diameter

I:           power density / irradiance

Ppeak: peak power of the laser

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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

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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.

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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!

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