## Need Help?

Our team is ready to assist you!

# Comparison of Optical Aberrations

Optical aberrations are deviations from a perfect, mathematical model. It is important to note that they are not caused by any physical, optical, or mechanical flaws. Rather, they can be caused by the lens shape itself, or placement of optical elements within a system, due to the wave nature of light. Optical systems are typically designed using first order or paraxial optics in order to calculate image size and location. Paraxial optics does not take into account aberrations; it treats light as a ray, and therefore omits the wave phenomena that cause aberrations. For an introduction on optical aberrations, view Chromatic and Monochromatic Optical Aberrations.

After defining the different groups and types of chromatic and monochromatic optical aberrations, the difficult part becomes recognizing them in a system, either through computer analysis or real-world observation, and then correcting the system to reduce the aberrations. Typically, optical designers first put a system into optical system design software, such as Zemax® or Code V®, to check the performance and aberrations of the system. It is important to note that after an optical component is made, aberrations can be recognized by observing the output of the system.

## OPTICALLY IDENTIFYING ABERRATIONS

Determining what aberrations are present in an optical system is not always an easy task, even when in the computer analysis stage, as commonly two or more aberrations are present in any given system. Optical designers use a variety of tools to recognize aberrations and try to correct for them, often including computer generated spot diagrams, wave fan diagrams, and ray fan diagrams. Spot diagrams illustrate how a single point of light would appear after being imaged through the system. Wave fan diagrams are plots of the wavefront relative to the flattened wavefront where a perfect wave would be flat along the x direction. Ray fan diagrams are plots of points of the ray fan versus pupil coordinates. The following menu illustrates representative wave fan and ray fan diagrams for tangential (vertical, y direction) and sagittal (horizontal, z direction) planes where H = 1 for each of the following aberrations: tilt (W111), defocus (W020), spherical (W040), coma (W131), astigmatism (W222), field curvature (W220), and distortion (W311). Simply select the aberration of interest to see each illustration.

### Aberration Name (Wavefront Coefficient): Tilt (W111) Defocus (W020) Spherical (W040) Coma (W131) Astigmatism (W222) Field Curvature (W220) Distortion (W311)

Figure 1: Airy Disk Pattern

Recognizing aberrations, especially in the design stage, is the first step in correcting for them. Why does an optical designer want to correct for aberrations? The answer is to create a system that is diffraction limited, which is the best possible performance. Diffraction-limited systems have all aberrations contained within the Airy disk spot size, or the size of the diffraction pattern caused by a circular aperture (Figure 1).

Equation 1 can be used to calculate the Airy disk spot size (d) where λ is the wavelength used in the system and f/# is the f-number of the system.

(1)

Optics Application Examples – Read our most popular Optics app note. Learn about detector systems, selecting the right lens, and building a projection system.

Laser Spot Size Calculator – Use our featured EO Tech Tool to determine spot size from user-supplied working distances.

Spotlight on EO – What's new in the tech library? With new content every month, check back often for the latest updates.