As optical engineers, we use different tools and techniques to evaluate the performance of an optical design when simulating the system in a ray tracing program. One of those tools are spot diagrams. They may be a little bit confusing to use at first but are an excellent way to communicate the quality of an optical system.
Let’s say we have an imaging optical system. We want that system to reproduce an image as close as possible to the real object. A spot diagram shows the image produced by an optical system assuming that the object was a spot of light. It provides a quick visual evaluation of the optical system quality. Deformations of the image caused by different aberrations such as astigmatism, coma, spherical aberration, chromatic aberration, and more can be instantly viewed.
Below are some spot diagrams for some typical aberrations.
Let’s compare these spot diagrams with a non-aberrated one (shown in the first row in Figure 1). The non-aberrated spot diagram keeps the same distribution of rays regardless of the viewing plane. Compare this, for example, with spherical aberration where there is a higher concentration either at the edges or the center of the spot diagram. Coma deforms the shape of the spot diagram to give it the comet-like shape that is expected, and astigmatism shows the change from sagittal to transverse focal points.
Spot diagrams may not however be enough to describe the quality of an optical system by itself. It is possible to have a good spot diagram but with more wavefront error than desired. It is necessary to look at other kinds of analyses to double check the spot diagram. For example, the Strehl ratio is another good tool used for further qualification of an optical system.
It is common that spot diagrams are shown in a matrix like the one shown in Figure 2. The matrix has two axes; the horizontal axes are distances to the left and to the right of the focal point. This is useful to see the changes in spot shape at different planes (it can be used to define depth of focus, or circle of least confusion in astigmatic systems). The vertical displacement evaluates how the system behaves when the object is placed above the optical axis. In the case of our figure, the top row shows the spot diagram for an object that is placed 0.253 degrees off-axis.
If you look carefully at the spot diagram above, you may see a small black circle. That’s the Airy disk, which represents the diffraction limit for an optical system. That’s the smallest spot size assuming a perfect lens. If your spot diagram is within that black circle, you may assume that final spot will be that of the airy disk.
Spot diagrams are a fast and easy way to evaluate the image quality of an optical system. They should however be used in combination with other tools to provide a complete image analysis.