# What are Cylinder Lenses?

Cylinder lenses are a type of lens that have differing radii in the X and Y axes, causing the lens to have a cylindrical or semi-cylindrical shape, and image magnification in only a single axis. Cylinder lenses are commonly used as laser line generators, or to adjust image height size or correct for astigmatism in imaging systems.

## Creating a Laser Line Generator

When using a cylinder lens as a laser line generator, it is important to calculate the required Effective Focal Length $\small{\left( \text{EFL} \right)}$ for the application. To do so, first calculate the fan angle $\small{ \left( \theta \right)}$ using the needed line length $\small{\left( x \right)}$ at the given working distance $\small{\left( L \right)}$ in centimeters:

(1)$$\theta = 2 \cdot \tan^{-1}{\left( \frac{x}{2 \, L} \right)}$$

The fan angle can also be used to determine the line length at a given working distance:

(2)$$x = 2 \cdot L \cdot \tan{\left( \frac{\theta}{2} \right)}$$

##### Figure 4: Visual Illustration of Equations 1 – 2 for Creating a Laser Line Generator

The $\small{\left( \text{EFL} \right)}$can then be calculated using the input beam radius $\small{ \left( \frac{d}{2} \right) }$ and the following equation:

(3)$$\frac{d}{2} = \text{EFL} \cdot \tan{\left( \frac{\theta}{2} \right)}$$

## Creating Circular Beams

Typically, laser diodes emit elliptical-shaped beams that may be unsuitable for applications that require a collimated, circular laser source. Using two cylinder lenses is a common method to circularize an elliptical beam - the first lens magnifies the minor axis of the laser diode, and the second lens collimates the beam. The curved side of the lenses and the minor axis of the laser diode should be oriented so that the minor axis is magnified.

For example, to modify an elliptical beam with a 4.0mm major axis and a 1.0mm minor axis to a circular beam with a 4.0mm diameter, the minor axis needs to be magnified by 4X. The magnification power (Mag) of a two-lens setup can be calculated by dividing the focal length of the second lens $\small{\left( f_2 \right)}$ by the focal length of the first $\small{\left( f_1 \right)}$.

(4)$$\text{Mag} = \frac{f_2}{f_1}$$

One way to achieve the required magnification is to use a 25mm diameter x -25mm EFL PCV Cylinder Lens (#46-196) with a 25mm diameter x 100mm EFL PCX Cylinder Lens (#46-018). Two PCX cylinder lenses can also be used, but add additional length to the system. The use of cylinder lenses also decreases beam divergence, increasing the beam’s collimation, which is ideal for long-distance projection applications. To help in selecting the right cylinder lens for any application, refer to Table 1.

## Cylinder Lens Selection Guide

Table 1: Cylinder Lens Selection Guide
TypeWavelengthIdeal Application
Fast Axis Collimators 0.8 – 1.0μm Collimating high power laser diode bars
Illunimation PCX Cylinder Lenses 0.4 - 1.6μm Focusing a laser to a line or circularizing a laser beam
UV Fused Silica PCX Cylinder Lenses 0.2 - 2.2μm Operating in harsh or rugged environments
Achromatic Cylinder Lenses 0.4 - 1.0μm Creating line profiles of broadband light sources
Plastic Hybrid Acylinder Lenses 0.4 - 1.6μm Creating line profiles of broadband light sources
Illumination PCV Cylinder Lenses 0.4 - 1.6μm Beam expansion
Cylindrical Microlens Arrays 0.2 - 2.2μm Beam homogenization
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Offered uncoated or with multiple anti-reflection coating options for the UV, visible, or IR spectrum. Achromatic, acylinder, plano-convex, plano-concave, or rod versions available.

Zu den Vorteilen der achromatischen Zylinderlinsen gehören u.a. die Verringerung der sphärischen und chromatischen Aberration in der Bildebene.

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