Abstract

For students using optical design software for the first time (or even the hundredth time), understanding how the software handles apertures and vignetting in lens systems is a common challenge. This article discusses these concepts within CODE V.

What are Aperture and Vignetting?

Aperture (strictly speaking, clear aperture, also referred to as light-passing aperture) is relatively straightforward to understand. A clear aperture is the opening associated with each surface through which light rays can pass. Rays within the clear aperture continue onward to the next surface, while rays outside the clear aperture are blocked. In all standard imaging optical systems, there is one special clear aperture, usually the only one that restricts on-axis field rays passing through the optical system. This surface is defined as the Aperture Stop, or simply the stop. For some systems, it is also the only aperture limiting off-axis field beams.

In many systems, however, off-axis rays are blocked by other clear apertures besides the stop. Consider the scenario shown in Figure 1: the stop is the sole clear aperture that clips the on-axis beam (shown in black). For off-axis beams, nevertheless, part of the rays passing through the stop will be blocked by the clear aperture on the front surface of the first lens, and another portion will be blocked by the clear aperture on the rear surface of the third lens. Only the beam represented by the blue rays reaches the image plane; all red rays are blocked.

This phenomenon, where light rays are blocked by clear apertures other than the aperture stop, is known as vignetting. Vignetting is sometimes undesirable because it reduces the amount of light reaching the image plane (sensor position). Yet it is often intentionally employed to improve the off-axis performance of a lens by blocking aberration-affected rays or reducing the overall diameter of the lens system.

In CODE V, four vignetting factors are associated with each field point (found under the menu: Lens > System Data, Fields/Vignetting tab; +Y or VUY; -Y or VLY; +X or VUX; and -X or VLX). Figure 2 shows the Fields/Vignetting window containing the vignetting factor table in CODE V.

These factors, together with the pupil settings (Lens > System Data, Pupil tab), define the constraints for the beam entering the optical system. It is important to understand that these vignetting factors are used not only to simulate beam clipping by clear apertures but also to model pupil aberrations.

In CODE V, vignetting factors are applied at a special location called the Entrance Pupil (the apparent position of the aperture stop when viewed through any lenses in front of it). Since lenses introduce aberrations, an unvignetted entrance pupil definition may not fully fill the physical aperture stop (or may overfill it). When an aperture stop is defined inside the optical system in CODE V, vignetting factors adjust the beam at the entrance pupil to account for clear-aperture clipping and pupil aberrations. Figure 3 illustrates the changing appearance of the entrance pupil of a fisheye lens.

When importing lens prescription data into CODE V, sometimes you know the clear apertures, but more often you only know (or can estimate) off-axis vignetting. It is particularly common for patent lens documents to contain only limited information about clear apertures and/or vignetting factors. Regardless of what information you have or can deduce, CODE V provides tools to set vignetting factors from clear apertures and vice versa. Consistency between vignetting factors and clear aperture specifications is critical. Most analysis functions use clear apertures to limit beams (while vignetting factors are used to determine reasonable default clear apertures). Other CODE V functions, especially optimization, use pupil and vignetting factor definitions to define the size of the incident beam. This serves as a useful default setting because the clear apertures required to maintain a specific pupil specification and vignetting will change during system optimization.

Patent Lens Example

To illustrate these concepts, we will use a lens from the CODE V patent lens database. US 1,987,878 (or 02448) is an f/4.5 triplet with a 28° half field of view. Its effective focal length (EFL) is set to 1 (common in patents), though it can be easily scaled to 50 mm. The patent document does not include clear aperture or vignetting information. It only defines an f/4.5 pupil and specifies the surface location of the aperture stop.

When you load this patent lens from the CODE V database, you will see non-zero vignetting values defined for off-axis fields (Figure 4). Where do these values come from?

The answer is that these values are estimates of the off-axis vignetting needed to reduce aberrations and maintain reasonable edge thickness for the lens. This determination is typically made by the optical designer.

Figure 5 shows the lens layout, transverse ray aberration plots, and spot sizes for the original patent lens prescription with vignetting factors set to zero.

You can see that the front lens element is too thin to allow the full off-axis beams to pass through. From the transverse ray aberration curves, the -Y side of the pupil exhibits significant aberrations for both off-axis fields. Furthermore, if you zoom into the aperture stop region (Figure 6), you will observe that with vignetting factors set to zero, off-axis rays do not fill the stop for the third field, while rays at the bottom of the pupil slightly overfill the stop for the second field. In CODE V, zero vignetting factors mean the paraxial entrance pupil is perfectly filled; therefore, underfilling or overfilling of the stop indicates the system suffers from pupil aberration.

If we reapply the estimated design vignetting factors shown in Figure 4, we can see in Figure 7 that off-axis rays no longer extend beyond the edge of the first lens. The most prominent aberration components in the off-axis beam are eliminated or reduced, and RMS and 100% spot sizes decrease substantially. On-axis performance remains unchanged, as there is no vignetting on the axis.

CODE V automatically calculates implicit (default) clear apertures based on pupil and vignetting factors. These are displayed in the Y Semi-Aperture column of the Lens Data Manager (LDM) spreadsheet, marked with a grey background and a circle symbol.

If the lens undergoes optimization, these default clear apertures may change, yet they remain consistent with the pupil specification and vignetting factors. This is the benefit of CODE V’s default behaviour of using vignetting factors to control beam size during optimization, even before the final required clear aperture dimensions are known.

It is important to understand that approximate vignetting factors may not be precisely realizable using the default apertures calculated for that lens, especially when multiple off-axis fields are involved. As shown in Figure 7, vignetting caused by aperture clipping arises from the apertures on Surface 1 and Surface 7 in the lens prescription. In Figure 9, we can convert these into explicit, centered circular clear apertures by right-clicking the semi-aperture cell, selecting change to circular aperture, then choosing the menu Lens > Calculate > Set Vignetting Data. This resets the vignetting factors to be consistent with these two explicit clear apertures (and the stop clear aperture based on the default beam size for Field 1).

You can verify that the actual vignetting resulting from the physical apertures defined on Surface 1 and Surface 7 matches the approximate vignetting factors from the patent. The actual values are, however, slightly different. Small negative vignetting factors are another indication that certain pupil aberrations exist in this lens. For a system free of pupil aberration where the aperture stop only limits on-axis beams, off-axis vignetting factors will always be positive.

Even so, the original approximate vignetting factors are very close to the “real” vignetting values. The difference for each factor is less than 0.005, which means that despite using estimated values, the aberration and imaging performance of the system will remain roughly unchanged (or in any case, within most manufacturing tolerances).

Conclusion

By defining approximate vignetting factors, designers can quickly determine the general aberration and imaging performance of a lens system. When actual aperture and vignetting values are specified, CODE V can automatically optimize and adjust the lens system to achieve optimal performance. This approach helps designers rapidly evaluate systems in the early design phase and carry out more precise adjustments in later stages.