Re: [CAD_CAM_EDM_DRO] Re: added laser cutter to my mill (pics)

Hello Rick,

Here are the equations for a pair of airspaced thin lenses.

I am not at home so scratched a lot of this out on paper. I tried to be consistent in naming and using variables. Let me know if any of this does not work out to values that are similar to your experience. I can correct it when I get home tonight or Tuesday.

Tom Hubin
thubin@...

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f1 = focal length of first lens (nearer to laser).

f2 = focal length of second lens (nearer to target).

f = focal length of system.

a = distance between first lens and first focal plane. Positive if focal plane is before first lens. Negative is valid but means the focal plane is virtual and not real.

b = distance between first and second lenses. Must be positive or zero to be meaningful.

c = distance between second lens and second focal plane. Positive if focal plane is after the second lens. Negative is valid but means the focal plane is virtual and not real.

D0 = laser Gaussian waist diameter. For Synrad 10 watt this is 3.5mm.

theta = laser divergence in radians. For Synrad 10 watt this is 0.004rad.

M2 = M squared = fudge factor for deviation from perfect Gaussian. For Synrad 10 watt this is 1.2.

FSD = focused spot diameter.

FStheta = focused spot divergence.

CDOF = classical depth of focus.

PDOF = practical depth of focus.

lambda = laser wavelength. For CO2 this is 10.6 microns.

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1) Start by deciding on focused spot diameter. Then compute the necessary system focal length. This can be a positive or negative value. Both are acceptable so be sure to evaluate for both possibilities.

f = +/- FSD/theta

2) Choose a pair of lenses from a catalog or from your inventory. Assign one focal length as f1 and the other focal length as f2. Compute the distance between the lenses. The separation can be zero or positive but a negative number means this is not a usable combination.

b = f1 + f2 - f1 * f2 / f

Note: If you have a pair of lenses with known seperation you can compute the equivalent focal length. An easy combination is to stack lenses close together (b=0). Then the calculation of the combined focal length f is similar to resistors in parallel.

1/f = 1/f1 + 1/f2 - b/(f1*f2)

3) Compute the distance from the second lens to the second focal plane where the spot will hit the target. A negative value is valid but not useful for machining. You need to have c positive so that you can focus on the target and large enough so that you do not damage your lens when burning.

c = f2 * ( b - f1 ) / ( b - f1 - f2 )

4) Compute the distance from the first lens to the first focal plane. This is where the laser waist should be located so it should be a positive value. However, you can generally ignore this and put the laser in a convenient location with little concern.

a = f1 * ( b - f2 ) / ( b - f1 - f2 )

5) Compute divergence of focused spot.

FStheta = M2 * (4/pi) * (lambda/FSD)

6) Compute classical depth of focus. This is where the beam diameter has spread by the square root of two so the energy is spread over twice the area. This is equivalent to the engineering term of "half power point". A variation in power density of a factor of two may be excessive for machining.

CDOF = 2 * FSD / FStheta

7) Compute practical depth of focus. I choose this arbitrarily to be where the power density is down by 10% from the peak in the focal plane. This is a small range but probably more useful than the classical definition of depth of focus. I would machine something this thickness. Any thicker and I would be be concerned about power variation as I machine through depth.

PDOF = CDOF * sqrt(0.1)