# Spherical Lenses Information

Image credit: Thorlabs, Inc. | Indiamart | Qioptiq

Spherical lenses are optical lenses with curved surfaces which converge or diverge light rays, thus forming a real or virtual image of an object. They are also known as singlets.

## Spherical Lens Fundamentals

Before selecting a specific type of spherical lens, buyers must consider several important optical specifications and apply them to their intended application.

### Focal Length

The image below illustrates several important optical parameters related to an optical lens. The focal point, which is unlabeled, is the point on the optical axis where light converges. The lens's focal length is the distance from the lens to this point, as indicated in the image. A positive lens (to be discussed in the Type section below) has a positive focal length, while a negative lens has a focal length less than zero.

Image credit: Australian Customs and Border Protection

### Conjugate Ratio

The conjugate ratio is defined as the ratio between two distances: the distance from the object (light source) to the lens, and the distance from the lens to the projected image. The endpoints of these two lengths are known as the object and image points. These two points lie on the lens's optical axis and are positioned so that light emitted from the object point will be focused at the image point. An object placed at the focal point of a lens results in an infinite conjugate ratio, while an object placed at twice the focal length results in an image formed at twice the focal length, giving a conjugate ratio of 1.

The images below illustrate the important optical points.

Image credit: Florida State University

An application's conjugate ratio largely determines the ideal type of spherical lens.

## Lens Type

The table below details common lens types, along with their ideal conjugate ratios and polarity specifications. By taking these specifications into account, users can minimize aberrations in their specialty or application. In terms of polarity, lenses can be described as either positive or negative:

• Positive, or convergent, lenses focus light to a set point on an axis.
• Negative, or divergent, lenses spread (or diverge) light, effectively performing in an opposite manner when compared to positive lenses.

Meniscus lenses, which effectively combine convex and concave lenses, can be positive or negative, depending on which side of the lens is convex or concave. The meniscus lens image below shows a negative meniscus lens.

 Type Polarity Ideal conjugate ratio Image Biconvex Positive < 5:1 Plano-convex Positive All Plano-concave Negative Infinite, larger finite (ie 10:1) Biconcave Negative < 5:1 Meniscus Either; dependent upon lens

Image credit: Freewebs | Standa | Direct Industry | Play Hookey

## Specifications

### Wavelength Range

Spherical lenses can be designed to operate within specific ranges of the electromagnetic spectrum.  Wavelength range is largely determined by a lens's material of construction. Manufacturers may specify lenses as:

• Infrared - used within the 750 to 2500 nm range.
• Visible - used within the 380 to 750 nm range.
• Ultraviolet - used within the 4 to 380 nm range.

### Optical Surface Quality

A spherical lens's surface quality rating is based on the MIL-0-131830A(1963) standard. The standard specifies two different types of surface defects:

• Scratches are defects with lengths many times their widths.
• Digs are defects with nearly equal lengths and width.

Surface quality ratings consist of two numbers separated by a hyphen, as in x-y. The x in this formula refers to the maximum allowable width of a scratch — expressed in tenths of a micron — while the y refers to the maximum width of a dig, expressed in hundredths of a millimeter. For example, a lens with a 20-10 scratch/dig rating specifies that any scratches have a maximum width of .002 millimeters (2 microns), while any digs must not exceed .10 mm in width. For both scratch and dig specifications, smaller numbers are desirable.

### Flatness

Optics manufacturers often specify optical surface flatness using a "peak to valley" (P-V) measurement. This value is the difference between the relative highest and lowest points of the optical surface. P-V is expressed as a ratio of a set wavelength, as shown in the table below. When expressed as a fraction, a higher denominator indicates better quality.

 Surface flatness Relative quality Description λ/2 Very low Lowest quality; suitable for noncritical applications. λ/4 Low Typically used for beam splitters; not suited to high power applications. λ/10 Good Suitable for many laser and scientific applications. λ/20 Very good Most precise quality; suitable for critical wavefront control applications.

### Surface Geometry

Other geometric lens specifications — such as radius of curvature, surface height, optical center, and lens thickness — are important to consider when researching or selecting a spherical lens. More information about these parameters and their relationship to other specs such as focal power and surface power can be found here.

## References

Opticampus - High-powered lenses

The Optics Institute - Lens design (pdf)