Lens Selection
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The most important relationships that we will use in the process of lens
selection for Gaussian beam optical systems are as follows: |
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Focused Spot Radius |
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where wF is the spot radius at the focal point, and
wL is the radius of the collimated
beam at the lens. M 2 is the
quality factor (1.0 for a theoretical Gaussian beam). |
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Beam Propagation |
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and |
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where w0 is the radius of a real
(non-Gaussian) beam at the waist, and w
(z) is the radius of the beam at a distance
z from the waist. For
M 2 = 1, the formulae reduce to
that for a Gaussian beam. w0(optimum) is the beam waist radius that minimizes the beam radius at
distance z. Finally, |
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where zR is the Raleigh range. We can also utilize the equation for the approximate on-axis spot size caused by spherical aberration for a plano-convex lens at the infinite conjugate: |
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This formula is for uniform illumination, not a Gaussian intensity
profile. However, since it yields a larger value for spot size than
actually occurs, its use will provide us with conservative lens choices.
Keep in mind that this formula is for spot diameter whereas the Gaussian
beam formulas are all stated in terms of spot radius. |
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| Optics Guide Copyright 2002 Melles Griot Inc. |