dr (mm) (Diameter of the Ring): --
t (mm) (Line Thickness of the Ring): --
β (°) (Half Fan Angle): --
$$ d_r = 2L \cdot \tan{\left[ \left( n - 1 \right) \alpha \right]} $$ |
$$ \beta = \sin^{-1}{\left( n \, \sin{\alpha} \right)} - \alpha $$ |
$$ t = \frac{1}{2} d_b $$ |
dr: | Outer diameter of the ring that the beam forms |
db: | Diameter of the beam that enters the lens |
t: | Thickness of the line that the beam forms |
β: | Half fan angle that beam forms |
L: | Length from Axicon to image formed |
n: | Refractive index of the Axicon |
α: | Axicon angle |
Axicons are conical prisms that are defined by the alpha and apex angle. As the distance from the Axicon to the image increases, the diameter of the ring increases, while the line thickness remains constant.
Given the input is a collimated beam, you can calculate the outer ring diameter and the line thickness an Axicon will produce. The half fan angle calculation will be an approximation.
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