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Zooming in on the focal point one can see that the dimensions of the focal region is measurable in micrometers (μm = 10-6 meters).
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The hyperbola's formula, x(y), assumes that the it passes through the origin so one needs to add or subtract a constant to shift it slightly left or right. I was able to eliminate the scale factor, a, for the x axis by solving for a value which gives the curvature, κ0, at the origin of the function. The remaining scale factor, b, for the y axis was then available to adjust the focusing properties of the lens.
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