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 © 2004 Melles Griot Inc. |