Get to know the Optical Aberrations present in
your Image

Simply viewing a modulation transfer function (MTF) plot does not provide all the information necessary to choose a lens or to diagnose problems with an image. While the MTF plot/data does take into account the cumulative effect of all optical aberrations present, the end user cannot distinguish individual aberrations using only the MTF plot. To maximize optical performance, it is critical to understand how those aberrations may or may not influence the imagery the lens is attempting to capture.

The table right lists primary optical aberrations that optical engineers attempt to minimize when creating a high-performing lens. The list depicts how the magnitude of each aberration is affected by changing the lens aperture (f/#) and/or field size (AKA image height). Note that a number of higher order aberrations also exist; this table simply represents the most commonly encountered issues. As an example, assume you haveba lens with known aberrations and you wish to determine the impact on the aberrations if the aperture diameter is increased by 50% (1.5x original parameter) and the field height is reduced by 50% (0.5x original parameter). The longitudinal spherical aberration is shown to vary with y², so a 50% increase in aperture will cause the longitudinal spherical aberration to be (1.5)², or 2.25 times as large. Notably, coma varies as y² and h; thus, under the changes described, the coma will be (1.5)² x 0.5, or 1.125 times as large.

Below are some examples of aberrations, viewed individually, that can be present in final imagery. Each example depicts a diffraction-limited airy disk (the perfect image of a pinhole in image space), an airy disk containing the named aberration, and a photograph example containing the aberration. Geometric distortion, an unwanted “warping” that distorts the spatial relationship among objects in an image, also can change the apparent size and shape of objects. Geometic distortion plays a vital role in optical measurement, and its value can manifest as negative or positive. Negative distortion is called barrel distortion, and positive distortion is called pincushion distortion, so named because of how they stretch or compress the image (Figs. 2 and 3).

Fig. 2 — Depictions of geometric distortion: (R-L) No distortion, barrel (-) distortion, and pincushion (+) distortion.

Fig. 3: Distorted picture

Table 1 — Primary optical aberrations, plus variance by aperture and field. y = semi aperture, h = image height

Ray Aberration Plots Fill The Knowledge Gap

Again, it is not possible to understand which aberrations might be present or to gauge the magnitude of aberrations in the final image using an MTF plot. The MTF plot merely provides an indication of how well a lens works overall. So, a lens desinger is trained to interpret ray aberration plots (Fig. 4), which are generated by the optical design software as the lens is being created.

Ray plots indicate which aberrations are present and their magnitude. Any lens manufacturer has a complete data package for every lens it has produced, which includes lens design values, curvature, glass types, distortion values, and ray plots. All optical tolerances (e.g., thickness of each glass element) are listed in that package, too, to help ensure mechanical engineers are able to design mechanical components that mimic the same tolerances.

So, a customer might request, from a lens manufacturer, the MTF plot as well as more information about a lens relevant to issues they believe may arise in their imaging system. The only way to obtain that information is by requesting information about different potential aberrations (e.g., a coma aberration plot, a spherical aberration plot, etc.). Ideally, this information is presented in part as ray plots, and an optical engineer/lens designer is available to explain the plots’ significance as well as potential solutions to the aberrations. Armed with this data and appropriate context, the customer can help their technicians understand what to expect from the lens’ performance.

To better understand potential aberrations, provide the lens manufacturer as much relevant information as possible to generate MTF and ray plot data, including the lens of interest, the f/#, magnification, and the wavelength region in which the lens will be used. The lens manufacturer should then be able to provide plots of different aberrations and their respective magnitudes. By obtaining/ understanding these individual plots, you can determine if aberrations present will impact optical imaging goals within your system. Fig. 5 depicts individual aberration plots for the same lens data shown in Fig. 4:

Fig. 4 — A ray aberration plot

Lateral Chromatic

Is the Lens Manufacturer Transparent?

When optical engineers complete their work — when they are satisfied with the lens’ MTF plot and the glass’ fabrication tolerances and understand the impact of each aberration — the lens proceeds to mechanical engineering and then on to production. Every manufacturer maintains a record of this process. The problem is, most lens manufacturers do not provide specific data characterizing a lens to their customers.

A key reason is the majority of the lenses now sold in the United States come from Asia, but they are purchased through the lens manufacturer’s U.S. office, where an optical engineer may not be available to help you. Therefore, any time a customer requests data such as specific ray plots, the company must contact its overseas experts to request that information. Does the lens manufacturer value your business enough to invest the time and effort to obtain that data? Will that cost extra or only be provided if you buy a certain number of lenses?

It is important to understand what information lens manufacturers are willing to provide. The standard answer is “all of the test/performance data we can share is published to our website.” But all data posted on websites is generic. It is not lab tested and it does not include lens tolerances. It comes from the optical engineer prior to fabrication, and every lens will exhibit slightly different aberrations after fabrication. This is why 10 of the same lenses from the same company can be sent to an independent testing house and every lens can slightly differ in performance — not just the MTF but also the aberrations from lens to lens.

The website information is the bare minimum to help start your search. How much the lens manufacturer decides to engage with a potential customer ahead of time is really up to the manufacturer. Schneider Optics, though, provides the MTF plot and lens tolerances upfront. Rather than limit customers to theoretical knowledge, we are eager to discuss real-life data and to help our customers understand ray aberration plots and how the findings will impact their lens(es).

Curvature (Petzval) Geometric Distortion

Axial (Longitudinal) aberration (focal shift)

Clear Data Keeps the Focus on Quality

As we noted in a previous article, the International Organization for Standardization (ISO) and Deutsche Industrial Normen (DIN) standards associated with lens specification allow a significant margin of error. That article used lens focal length (f’) as an example: According to DIN standard 4522, section 11,[i] the standard for engraving a lens for focal length is ±6%. So, when you buy a dozen 100-mm lenses, some could be 106 mm, others 94 mm, and anything in between. The same is true for aberrations. In practical terms, this means every single lens and camera would need to be set up at a slightly different distance for each to provide the same magnification and field of view.

How do you determine how well a lens will perform after fabrication? What is the quality threshold where a lens manufacturer decides a lens is no good? You usually do not know any of this. Schneider Optics eliminates this huge variable by testing every lens produced — every single one — whether the customer has ordered one lens or hundreds of lenses. Contact us to learn more about the aberrations impacting your lenses as well as how to secure in-depth data about them that the other guys simply are not sharing.