# Lens Geometry Performance Comparison

Authors: Ian Schwartz, Amy Frantz

The ideal: each point on an object being imaged maps perfectly to a point on the image. The reality: aberrations blur perfect image points to larger spots. Though manufacturing tolerances also contribute to performance degradation, these aberrations occur even for a perfectly manufactured lens.

Spherical aberrations occur when rays at the aperture’s edge focus at a different axial position compared to rays at the aperture’s center (Figure 1a). These aberrations increase with pupil size, so smaller f/# lenses are affected more than larger f/# lenses. Aspheric lenses can be designed with a different curvature at the lens edge instead of the center to correct for spherical aberrations.

Due to the glass property of dispersion, different wavelengths of light experience unique indices of refraction thus are bent by different amounts. Chromatic focal shift (CFS) describes the change in the axial position of focal wavelength. The resulting chromatic aberrations lead to larger spot sizes (Figure 1b). Achromatic lenses use multiple materials with opposed dispersions to improve performance with multichromatic light.

Since these aberrations can drastically affect spot size and image quality, deciding which lens is the best for a given task is not always straightforward. Does it always make sense to use the highest-precision asphere? Is a spherical plano-convex (PCX) lens ever sufficient? Zemax OpticStudio was used to answer these questions.

### Simulation One: Single Wavelength Focusing

Consider a single wavelength beam that needs to be focused to the smallest spot size possible. Aspheres are designed for this purpose, so it is unsurprising that they outperformed each of the other lenses in the simulation (Figure 2). In practice, however, one must consider factors such as diffraction limit, a physical limit to the resolution of light which is discussed in detail in our Airy Disk and Diffraction Limit application note. The smallest spot size for aspheres will be limited by the diffraction limit, which is smaller for lower f/# lenses. Aspheres have better real-world performance at lower f/#'s due to the diffraction limit.

##### Figure 2: Performance of various PCX, achromatic, and aspheric lenses for a single wavelength source (diffraction-limited performance from aspheres 89434, 37431, and 37428 as well as achromat 32327).

While PCX and achromatic lenses have worse performance at lower f/#'s, at a large enough f/#, singlets and achromats can also achieve diffraction limited performance, indicating they would perform just as well as an asphere. In fact, for f/# > 7, spherical lenses can theoretically meet the diffraction limit, meaning the benefits of using an asphere may not justify the additional cost (Figure 3). Achromats usually have better performance than PCX lenses because the additional spherical surfaces lead to more degrees of freedom to optimize performance.

### Simulation Two: Multiple Wavelength Focusing

Which lens would have the best performance for a beam consisting of multiple wavelengths? Achromats are designed to reduce chromatic focal shift, but they are not always the best choice (Figure 4). For small f/#'s, the spherical aberration in lenses dominates other factors that determine performance, but for larger f/#'s chromatic aberration is more significant (in either case, the spot size is not diffraction limited). Because of this, aspheres still demonstrate the best performance for small f/# applications, even when using multiple wavelengths. Consider the wavelength range and f/# when choosing an asphere or achromat for the best, multiple wavelength performance. Single material lens elements exhibit chromatic focal shift dependent on thickness and the dispersion properties of the material, but they should not be ruled out until f/# is considered.

While none of the selected lenses meet the diffraction limit, it is certainly possible to achieve such performance for multiple wavelengths. For applications where diffraction-limited performance is required, see Edmund Optics’ best form aspheric lenses, aspherized achromatic lenses, or contact us for custom options!

### Simulation Three: Relay with 5mm Half Field

Finally, consider a relay consisting of two identical lenses. In this case, the same general principles for single element system apply and performance with field will decrease compared to only on-axis systems (Figure 5). Larger f/#'s play a significant role in decreasing the spot size of both single and multiple wavelength light, causing an f/4 PCX lens relay to outperform an f/2 asphere system. For low f/#'s, multiple spherical surfaces minimize spherical and other monochromatic aberrations while multiple materials minimize chromatic aberrations.

### Lens Comparison

Given the tests shown above, there are several important considerations to keep in mind when selecting a lens. To help find the best lens for a given application for both performance and cost, please contact us to receive complimentary engineering support.

Plano-ConvexAchromatAsphere
Description Single material with one convex spherical surface and one planar surface Two cemented materials, generally convex on both outer surfaces, and a cemented inner spherical surface Single material, typically one side is a convex asphere and other side is planar
Advantages Many available off-the-shelf, simple designs for focusing light Better performance for using multiple wavelengths High performance even at high numerical apertures
Disadvantages Lower performance Adhesive layer not ideal for high power lasers Specialized design typically optimized for single wavelength, longer lead time for custom designs
Cost Low Medium High
Comments Flexible, useful for many applications Improved chromatic aberrations Improved monochromatic aberrations (particularly spherical)

### Test Case Lenses

 45097 PCX Material: N-SF5 25mm Diameter 25mm Focal Length 32477 PCX Material: N-BK7 25mm Diameter 50mm Focal Length 32481 PCX Material: N-BK7 25mm Diameter 100mm Focal Length 65553 Achromat Material: N-BASF64/N-SF66 25mm Diameter 25mm Focal Length 32323 Achromat Material: N-BAF10/N-SF10 25mm Diameter 50mm Focal Length 32327 Achromat Material: N-BK7/N-SF5 25mm Diameter 100mm Focal Length 37428 Asphere Material: N-SF6 25mm Diameter 25mm Focal Length 37431 Asphere Material: N-BK7 25mm Diameter 50mm Focal Length 89434 Asphere Material: N-BK7/N-SF5 25mm Diameter 100mm Focal Length

### The Right Lens from Edmund Optics®

Edmund Optics® offers a wide range of PCX, achromatic, and aspheric lenses in many different sizes, focal lengths, materials, and coatings in-stock and available for immediate shipping. Additionally, Edmund Optics manufacturing engineers are available to make custom lenses tailored for any application.

### Plano-Convex (PCX) Lenses

• Precision Diameter and Centration Tolerances Allow for Easy OEM Integration
• Wide Variety of Diameters, Focal Lengths, and Coatings
• Anti-Reflection Coating Options: MgF2, VIS 0°, VIS-NIR, NIR I, NIR II, VIS-EXT, and YAG-BBAR