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Wavelength
Let’s look at the lasers first. They have the following wavelengths Alexandrite - 755nm
Diode - 808 or 810nm Nd:YAG - 1064nm.
These are all in the infra-red part of the spectrum - they are invisible to the naked eye.
From the melanin absorption graph above, we can see that melanin absorbs the alexandrite wavelength more than the diode or Nd:YAG wavelengths - in fact, the alexandrite wavelength is absorbed more than 3 times more readily than the YAG 1064nm wavelength (see 'Absorption' figure in the table below).
What this means is that, if we were to fire, say, 10 Joules of each wavelength at the same hair, more of the alexandrite light will be absorbed than the diode or YAG wavelengths. Likewise, more diode energy will be absorbed compared with the YAG, since it is better absorbed by melanin.
If we wanted to achieve the same amount of energy absorbed in the hair, we would need to compensate for the lower absorption by the diode and YAG wavelengths, by increasing their energies.
Hence, 30 Joules of the YAG energy would be equivalent to 11.5 Joules of the diode and 9 Joules of the alexandrite energy (assuming all else is the same).
IPL is different - it emits energy over a wide range of wavelengths (lasers can’t do that!). We use filters in IPLs to block the wavelengths we don’t want - the blues and greens and yellows. So a 640nm filter will only allow through the wavelengths above 640nm (up to 1200
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