The assumption is that you have combined the beams into a single path and you have telescopes on the beams before the beam combiners so you can control their diameters. As we will see you don't want all of the beams to be the same diameter!
From Edmund:
1.0 Beam Spot Diameter (microns) = (1.27 * l * f) / D
where, l = wavelength of laser (microns)
f = focal length of objective lens (mm)
D = input beam diameter (mm)
2.0 Pinhole size is then determined for the table (see note):
Pinhole Diameter (microns) = 1.5 * Beam Spot Size Diameter (microns)
So we notice that wavelength makes a difference.
For this example we will use the wavelengths of:
650nm
532nm
473nm
Because I like them. :-,
In order to make white we need the beem spot diameters of all three beams to be equal. If we miss, the balance of white will be uneven radially from the center out.
dspot=(1.27*.650*f)/D
dspot=(1.27*.532*f)/D
dspot=(1.27*.473*f)/D
We will choose 8mm as the focal length of our objective in the spatial filter.
dspot=(1.27*.650*8)/D
dspot=(1.27*.532*8)/D
dspot=(1.27*.473*8)/D
dspot=6.604/D
dspot=5.405/D
dspot=4.806/D
In order to allow more light through we multipuly a correction factor of 1.5 to the calculated values.
Pinhole=9.906/D
Pinhole=8.108/D
Pinhole=7.209/D
Now we are using only one pinhole and we need three beam diameters to make three equal spot sizes.
If our red laser is 10mm then we use a 10 micron pinhole.
For green the beam needs to be 8.1 mm in diameter.
The blue beam needs to be 7.2 mm.
Now the last equation we need is a way to change the diameter of our laser beams.
In order to make a beam larger (or smaller really) we need to understand a very simple equation.
InputD/OutputD=fl1/fl2 when the lenses are at fl1+fl2 distance apart.
So if our red laser is 10mm dia. And our Green laser is 5mm then we need a telescope in the path of the green laser in the ratio of 5 to 8. If the lenses we have access to are 50mm and 80mm focal length then we place them 130mm apart and in the path of the green beam before the beam combiner. Now for example if the blue laser is 2.5mm we need to be 2.5 to 7.2 ratio and we could choose 25mm and 75mm focal length lenses placed 100mm apart. Now when we combine the beam we get a true guasian white beam. When we pass them through the spatial filter we have a white guasian spot with no color variation across the beam diameter.
Note these same equations can be used to circularize a elliptical laser beam using cylindrical lenses.
For reference:
http://www.edmundoptics.com/techsupport ... icleid=272
Thank you to Hanz for pointing out this very significant problem in color holography. (The solution is mine especially if I have a math error
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