Cylindrical lens : a complete guide

Cylindrical lenses are less common than spherical lenses, but are still wide spread in many Photonics applications, below you’ll find a complete guide to let you learn more about it:

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What is a cylindrical lens ?

A cylindrical lens is a lens with at least one optical surface has the shape of a section of a cylinder. While spherical lenses surfaces are defined from a fix center of curvature and a radius, cylinder lens shape are made along a central axis with a fix radius of curvature.

Illustration of a convex and a concave cylindrical lens.

What are the types of cylindrical lens ?

Like other lenses a cylindrical lens is defined from the shape of it’s optical surfaces :

Cylindrical lens type Detail PCV – Plano-concave  lens one flat surface and a concave cylindrical surface.  Focus light on one line. PCX – Plano-convex cy one flat surface and a concave cylindrical surface. Expend the light in one direction. Biconvex both sides with convex cylindrical shape (can be of different radius of curvature) Biconcave both sides with concave cylindrical shape (can be of different radius of curvature) Doublet Achromatic cylindrical lens.

Lenses outer shape may be cut in round shape of square shape.

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What are the material used to make cylindrical lens ?

Most of the optical raw materials may be used are :

• Optical glass : BK7, H-K9L, B270 from Schott, Corning, Ohara or CDGM
• Fused silica : JGS1, JGS2, Corning
• IR materials : Ge, Si, MgF2, CaF2
• Other materials : Sapphire, Optical plastics

What are the usage of cylindrical lens ?

Cylindrical lenses are mainly used to focus a incident light signal into a one dimension line, below are the most commun applications :

• Laser scanning (when the scan signal should form a line)
• Vision quality control (concentrate the lighting on one dimension)
• Metrology
• Ophtalmology
• Defense
• Sensors
• Lighting

How is polished a cylindrical lens ?

Cylindrical polishing of a lens doesn’t require rotational polishing machines, but specific polishing  equipment working way and forth in one direction.

To guaranty a good surface aspect, polishing cylindrical lens use specific polishing toolings and polishing pads. See above an example of such a tool, you’ll notice that for cost saving, several cylindrical glass lenses are polish at the same time.

What is the the difference between a spherical lens and a cylindrical lens ?

The main difference stands in the way the light rays are deviated through it. Spherical lens tends to focus on a point whereas cylindrical ones focus on a one dimension line.

Whereas a spherical lens is perfectly symmetric along a central rotational axis, it is not the case for the cylindrical ones.  Which means while the rotation angle by which the lens is used has no impact for the first one but will impact the optical system for the former one. Assembly of cylindrical lenses are therefore subject to one more constraint.

The plano-concave lens is a staple in many optical setups and is an optical lens with one surface being concave and one side being flat. The “concave” refers to the lens curving inward, which diverges parallel rays as opposed to the plano-convex lens, which converges parallel rays into a single point. Often used in imaging instruments, light collimators, telescopes and magnifiers, this is an essential optical component in most systems.

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The inward bowing produces what’s commonly referred to as a negative focal length. This means that the focal point (or the point at which the light converges) is on the same side of the lens as the origin of the light rays.

Various Applications for Plano-Concave Lenses

Eyeglasses

One of the first recorded uses of corrective eyeglasses was in Pliny the Elder’s account of the Roman Emperor Nero using a modified emerald to view gladiatorial matches. The emerald was hollowed out at the back forming the world’s first recorded plano-concave lens, which would have assisted his sight in seeing the battle in the arena.

This principle survives into the modern age with corrective optics being used to treat the condition of nearsightedness, also known as myopia. This is a condition in which close objects appear clearly but objects that are far away appear as blurry. This condition comes from the distance between the eye’s lens and retina being longer than it should be.

Placing a concave lens in front of a nearsighted eye reduces light refraction and lengthens the focal length so that the image is formed on the retina, bringing far away objects back into focus.

Peepholes in Doors

The peephole enables viewers to peek outside of their doors to determine whether they will answer the door or pretend to be not home. The lenses are configured in such a a way in that viewing is only possible in one direction with the opening typically being smaller than a dime.

The peephole’s optics consists of one convex lens and three plano-concave lenses. Rays of light from a wide angle are funneled through an array of plano-concave lenses to form an image with a convex lens serving as the eyepiece. If someone attempts to see from the outside in, their eye can only see a small range of angles and a tiny bit of light. You are now safe to hide from the door-to-door encyclopedia salesmen.

Telescopes

First constructed in by famed Italian astronomer Galileo Galilei, the Galilean telescope was able to see spots on the sun, phases of Venus and even hills on the surface of the moon! Not bad for the 17th century. A Galilean consists of one convex lens and one plano-concave lens set a given distance away from each other.

The plano-concave lens in this configuration functions as the eyepiece with the flat (plano) side facing the eye, while the convex lens is the objective lens. The eyepiece is situated in front of the focal point of the objective at a distance from the focal point equal to the focal length of the eyepiece. This simple refracting telescope generates a smaller, upright “virtual image”.

The largest known version of this telescope made it to a length of just over 3 feet and produced a 30x magnification. Unfortunately, this design left much to be improved as there was a narrow field of view and a blurry image.

Flashlights

In its role as a beam expander, the most illuminating (see what we did there?) example of this is the standard flashlight. As the rays from the light source pass through the plano-concave lens inside, the light beams slow down and refract causing the light to be cast on a wide field of vision. This light-diverging property of the lens can be adjusted in many flashlights by adjusting the distance between the light source and the plano-concave lens.

Use in Laser Systems- Beam Expander

Up until this point we have mostly discussed low-cost, basic BK7 versions of the plano-concave lens.

When it comes to high power laser applications, we will need to up the specs on our lenses. These types of laser grade lenses can be made from fused silica or a range of IR materials that have high damage thresholds and low thermal expansion coefficients. Optical coatings such as AR (anti-reflective) coatings are common with laser systems.

As in the other applications, this type of plano-concave lens is used to diverge collimated laser beams and expand the beam similar to a flashlight. In this type of setup, also known as a beam-expander, a plano-concave lens is often used with other lenses such as biconvex lenses to make the beam larger. The concave lens should be facing the light source in order to reduce spherical aberration.

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