How to Select a Spherical Lens

March 29, 2017
This selection guide will review the singlet spherical lens shapes offered by CVI Laser Optics and offer some practical guidance on determining the best material type and lens quality for your application. Read More...

How to Select a Spherical Lens

Lenses are an integral component in most optical systems, where they are used to focus, collimate, expand, collect and image light. Many optical tasks require several lenses in order to achieve an acceptable level of performance. This selection guide will review the singlet spherical lens shapes offered by CVI Laser Optics and offer some practical guidance on determining the best material type and lens quality for your application. For a complete discussion of lens theory, use, and aberrations please refer to the Fundamental Optics and Gaussian Beam Optics sections of the Technical Guide found online.

Lens Shape

CVI Laser Optics offers four lens types for converging or focusing light. A biconvex lens is the classic symmetric lens, possessing two convex surfaces of equal radii. Biconvex lenses have positive focal lengths and form both real and virtual images. It is the best singlet lens for imaging at unit magnification; spherical aberration is minimized, and coma, distortion, and transverse chromatic aberration exactly cancel each other out for a perfectly made lens (longitudinal chromatic aberration is not corrected). This is true regardless of the material used or wavelength, although use of a remote stop can reduce the degree of cancellation. Aberrations increase as conjugate ratios (object distance/image distance) depart from unity. Bi-convex lenses can also be used for focusing applications, in particular when a lower f-number (ƒ /CA) is required, even if they do not have the best shape for this conjugation. They are recommended for virtual imaging of real objects and for positive conjugate image ratios from approximately 0.2 to 5 (note that these values are wavelength sensitive).

Away from unity, the singlet lens shape that best minimizes spherical aberration at a given conjugate ratio is called a bestform lens, in which the two convex sides are of different radii. The marginal rays are equally refracted at each of the lens/air interfaces for this shape, and surface-reflection loss is minimized. Another benefit is that absolute coma is nearly minimized for bestform shape, at both infinite and unit conjugate ratios. It does not, however, perform well in wide-field applications, except in very specific configurations (with a meniscus for instance). At infinite conjugate ratio, the best form lens is not the optimum singlet shape, since it results in high field curvature. Positive bestform lenses are of exceptional performance and provide the smallest spot size available in a singlet lens.

When working at infinite or near-infinite conjugate ratio, plano-convex lenses with the convex side toward the infinite conjugate perform nearly as well as the best-form lens. Convex on one side and flat on the other, these positive focal length lenses cost much less to manufacture than a bestform lens. This lens shape also exhibits near minimum transverse spherical aberration and near-zero coma when used off-axis. Longitudinal aberration is low, but is only minimized when using a bestform lens.

If bulk light collection is required at minimal cost, an aspheric glass condenser lens may be the solution. Aspheric lenses provide better performance by reducing aberrations when used in low f-number, high-throughput applications. One surface is aspheric; the second surface is flat, or spherical-convex. A flat second surface minimizes aberration, while a spherical-convex second surface provides the lowest f-number and highest transmission. Only single-layer MgF2 antireflection coatings are recommended for these lenses due to the steep curvature of the surface. The molding and felt-polishing processes used to manufacture these lenses economically, together with the use of optical crown glass, makes these lenses best suited to less demanding light collection applications. They are not recommended for imaging, precise focusing, or high power applications, but are ideal for gathering low-power light with minimal aberration.

CVI Laser Optics offers two lens types for diverging or expanding light. A bi-concave lens is a symmetric lens, possessing two concave surfaces of equal radii. Biconcave lenses have negative focal lengths and form only virtual images which can be seen through a lens. They are used in laser beam expanders, optical character readers, viewers, and projection systems to diverge collimated incident light.

Like their convex counterparts, plano-concave lenses can reduce aberrations as compared to bi-concave lenses, depending on the configuration. They have a negative focal length and are often used to expand light or to increase focal lengths in optical systems, as they diverge collimated incident light. When working at infinite or nearinfinite conjugate ratio, plano-concave lenses with concave side toward the infinite conjugate reduce spherical aberration, and coma. Additionally, the negative spherical and chromatic aberration that plano-concave lenses exhibit can be used to balance the aberrations resulting from other lenses within a system.

Lens Materials

Aside from lens shape, the material a lens is made from has the greatest impact on its performance. Not only does it determine the transmission properties, refractive index, laser damage threshold, thermal coefficient, durability and weight, but it also impacts cost. It even imposes practical limits on manufacturing tolerances, especially surface cosmetic quality. CVI Laser Optics utilizes five different materials to manufacture our catalog singlet lenses, but other materials such as magnesium fluoride, sapphire, Infrasil, Suprasil, or different grades of the materials listed below are available on a custom basis. We can also manufacture many of our lenses with custom dimensions and focal lengths.

N-BK7 is a lead- and arsenic-free borosilicate crown glass that is used widely in the optics industry. It has excellent transmission from 350 nm – 2.0 μm, good thermal expansion coefficient, moderate laser damage threshold, and is relatively low in cost. It is a hard glass that stands up well to handling, with good chemical resistance.

Our fused silica is Standard Grade Corning 7980, a synthetic form of fused silica manufactured by flame hydrolysis to extremely high standards. Its ultra-low impurity content is evident in the wide transmission range of 180 nm – 2 μm and its high laser damage threshold. It does not fluoresce in response to wavelengths longer than 290 nm, and in general exhibits good resistance to radiation darkening from ultraviolet, x-rays, gamma rays, and neutrons. It also boasts excellent thermal properties, including a wide operating temperature range, low thermal coefficient, and resistance to thermal shock. Fused silica lenses from CVI Laser Optics have increased hardness and resistance to scratching, resulting in better surface quality than their N-BK7 equivalents.

KrF and ArF grade fused silica is fused silica that has been manufactured with near-zero defects for use with either KrF lasers at 248 nm or ArF lasers at 193nm. This material has very low levels of inclusions, bubbles, striation and striae, and minimal variations in index of refraction. Its exhibits the lowest level of laser induced fluorescence of compared to most glasses, strong resistance to radiation-induced defect generation, and higher UV laser damage threshold than CaF2. Internal transmittance is also guaranteed at high levels at their respective wavelength of use. It is one of the more expensive UV material options, particularly at larger diameters and available as a custom option.

N-SF11 is a type of lead- and arsenic-free Schott glass with much higher refractive index than N-BK7, resulting in greater focusing power and reduced spherical aberration. Its transmission is best in the visible and near-infrared, from 500 nm – 2.5 μm. Its thermal and hardness characteristics are comparable to N-BK7.

CaF2 is a cubic single-crystal material with transmission spanning the deep UV through infrared, 150 nm – 8 μm. It can be mined or manufactured synthetically, but is higher in cost than other lens materials, particularly in the high purity forms used for deep-UV applications. That being said, its excellent transmission and high laser damage threshold in the deep UV makes it the material of choice for many excimer laser applications. Lenses manufactured with CaF2 tend to have slightly lower surface quality than their N-BK7 or fused silica equivalents per its soft nature.

Optical crown glass is a low-index, commercial-grade glass. Its index of refraction, transmittance, and homogeneity are not controlled as carefully as in optical grade glasses like N-BK7. It transmits from 200 nm – 2 μm, with best performance from 400 nm – 1.5 μm. Though its thermal expansion coefficient is reasonable and its hardness makes it robust to handling, its laser damage threshold is low.

Lens Quality

Once the lens shape and material has been selected, the next step is to determine the lens quality required. This will depend on the application and performance needed, but factors to consider include laser damage threshold, degree of scatter, surface figure, and focal length tolerance.

Standard lenses possess a surface irregularity of λ/4 to λ/2 before coating, and are manufactured to a minimum surface quality of 60-40 to 40-20 scratch and dig, depending on material. They are an economical solution for many applications, but lower surface accuracy impacts resolution, and laser damage threshold is not as high. CVI Laser Optics offers standard singlet lenses in both N-BK7 and fused silica. These lenses are available uncoated, or with a selection of antireflection coating options from the UV to near-infrared.

Our laser quality lenses differ from standard lenses in two key aspects. First, high cosmetic surface quality (10-5 scratch and dig for fused silica, 20-10 for CaF2 and N-SF11) reduces scatter, making them more suitable for high energy laser applications. Second, careful polishing to λ/10 surface figure and tighter paraxial focal length tolerance yields the low wavefront distortion and accuracy required for use in ultra-violet and performance critical applications. The term “laser quality” therefore refers to both high laser damage threshold and to high performance specifications. CVI Laser Optics manufactures CaF2 , N-SF11, and excimer grade UV fused silica spherical lenses only in laser quality grade. All of our laser quality lenses are available with a wide range of broadband, dual band 1064/532, and narrowband V-coat antireflection coatings at wavelengths from the UV through near infrared. These AR coatings offer high durability and damage threshold, low loss, and peak performance when applied to laser quality optics. For best laser damage threshold performance, we recommend V-coat antireflection coatings on laser quality 10-5 fused silica substrates.

Our aspheric glass condenser lenses, in contrast, are fabricated to light collection quality standards. This involves a low-cost process in which the aspheric side is precision molded and the second surface is felt polished to achieve 80-50 scratch and dig surface quality. Light collection quality is more than adequate for many low f-number, high throughput applications in the visible wavelength region, and provides an economical alternative to standard N-BK7 lenses. These lenses are available with an optional single-layer MgF2 coating for 400 – 700 nm.

Making the Final Decision

Choosing the right singlet lens or combination of lenses for your application involves much more than identifying the required lens material and quality. Detailed performance analysis of an optical system is accomplished by using computerized ray-tracing software, and CVI Laser Optics applications engineers are available to provide a ray-tracing analysis of simple catalog-component systems. If you need assistance in determining the performance of your optical system, or in selecting optimum components for your particular application, please contact us.

Numerous other factors, such as lens manufacturing tolerances and component alignment, impact the performance of an optical system. It should be kept in mind that if calculations indicate that a lens system only just meets the desired performance criteria; in practice, it may fall short of this performance as a result of other factors. In critical applications, it is generally better to select a lens whose calculated performance is significantly better than needed.

In addition to the array of singlet lenses described, CVI Laser Optics also offers many cylindrical lenses, as well as multi-element lenses that can simplify your optical design. No singlet lens can correct for chromatic aberration, an important consideration when working with multiple wavelengths. Achromatic lenses may be needed to improve performance in this case. Additionally, a multielement lens system is often required at low focal ratios when the aberrations of a singlet lens are too large to satisfy performance requirements. Regardless of your needs, we can work with you to find the right solution by combining products from our catalog with lenses manufactured to your exact specifications using custom coatings.

At CVI Laser Optics, we specialize in the design and manufacture of high performance optical components for use in lasers, laser beam conditioning, and laser beam delivery from the UV to the near-IR. We create optical assemblies and subsystems for volume OEM applications in science and industry, including spherical components, flats, polarization control, prisms and waveplates. We also provide a range of low dispersion and dispersion compensated optical components for ultrafast laser applications.

Our global network of applications and technical support staff, is ready to assist with your custom optical component needs.

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