8/19/23, 2:34 PM
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`Beam Shaping with Cylindrical Lenses
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`Resources / Technical Notes / Optics / Beam Shaping with Cylindrical Lenses
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`Beam Shaping with Cylindrical Lenses
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`Cylindrical Lenses focus or expandlight in one axis only. They can be usedto focuslight into
`a thin line in optical metrology, laser scanning, spectroscopic, laser diode, acousto-optic, and
`optical processor applications. They can also be used to expandthe outputof a laser diode
`into a symmetrical beam.
`
`Generating a Line of Light from a Collimated Laser
`Acommonapplication of cylindrical lenses is shownin Figure 1. A collimated laser beam of
`radius rp is incident upona cylindrical plano-concavelens of focal length -f. In this figure, the
`radius of the laser beam is exaggerated for clarity. The laser beam will expand with a half-
`angle 6 of ro/f. The laser beam will appear to be expanding from a virtual source placed a
`distance f behind the lens. At a distance z after the lens, there will be a line with thickness 2r)
`(ignoring expansion of the Gaussian beam) and length
`
`L = 2 (ro/f)(z+f)
`If z is large comparedto f, then we have an expansion ratio thatis very close to z/f. This is
`not an imaging problem; weare projecting the laser beam intoa line at a particular distance.
`The length of the line is simply proportional to z,
`
`
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`Figure 1. Diagram of line oflight generation with a plano-concavecylindrical lens.
`
`If the thinnest possibleline is required, then a secondlens, this one a cylindrical plano-
`convex lensof focal length ~ z, can be inserted into the system just before or after the plano-
`concavelens. When oriented on the orthogonal axis,it will focus the laser at the screen onto
`which theline is projected
`
`In somecasesa sheetof light is required for an application. The projected beam of Figure 1
`can be thoughtofas a sheetoflight, but note that the sheet is not square or rectangular.
`The sheetthatis available for use is the isosceles triangle formed by the projected line at the
`screen and the maximum rays formedat the angles given by @.
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`Circularizing the Beam from a Laser Diode
`The outputof a laser diode diverges in an asymmetrical pattern, making collimating the
`beam a challenge. Cylindrical lenses can be used to circularize the beam. Considera laser
`diode with beam divergenceof 6, x 82 = 10°x 40°. Any attemptto collimate this beam with
`spherical optics would result in collimation in one direction only, with a diverging or
`converging beam in the otherdirection. With cylindrical optics the problem can be
`approachedas two one dimensional problems. The simplest solution would be to collimate
`the beam in one dimension with a single cylindrical lens, then collimate the orthogonal
`dimension with a second cylindrical lens (see Figure 2).
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`8/19/23, 2:34 PM
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`Beam Shaping with Cylindrical Lenses
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`Figure 2, Diagram ofcircularizing the beam from a laser diode using two cylindrical
`lenses.
`
`A few observationswill guide the selection and placementof the lenses:
`
`1) To achieve a symmetrical beam shape,the ratio of the focal length of the two lenses
`should be approximately equivalent to the ratio of the beam divergences:
`
`9,/0, = 10°/40° = f,/f,
`
`2) First, to order, the laser diode is approximated by a point source, so the lenses should be
`placed at a distance equal to their respective focal lengths from the source to create a
`collimated output.
`
`3) The principal planes of the two lenses should be spaced at a distance apart equal to the
`difference of their focal lengthsf2 - f;. The actual spacing between plano surfaces of the
`lenses is BFL, - BFL,. As with spherical lenses the convex surfaces should face the collimated
`rays to minimize aberrations.
`
`4) Becauseof the rapid divergence of the laser diode beam, care must be taken to make sure
`the beam width at each lens does not exceed the lens clear aperture. Since eachlensis
`placed one focal distance from the laser diode, the maximum beam width at each lens(d,
`and d,) can be determined from the following equations:
`
`d, = 2f,(tan (82/2)), and do = 2f2(tan (8,/2))
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`For this example a convenient choice of lenses is Newport CKX012 (f; = 12.7 mm, BFL, = 7.49
`mm) and CKX050(f2 = 50.2 mm, BFL, = 46.03 mm). The nominal spacing between plano
`surfaces of the lenses is BFL, - BFL, = 38.54 mm, The beam diameter at the first lens is
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`d, = 2x 12.7 mm x tan(20°) = 9.2 mm
`The beam diameterat the second lens is
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`dz = 2 x 50.2 mm x tan(5°) = 8.8 mm
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`so a slight asymmetry remains, but a substantial improvement has been achieved with a
`simple arrangementof standard lenses.
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