Cooke Triplet Tutorial (Part C): Modifying and Improving the Design

Introduction

In Part C we will do something closer to real optical design. We will introduce field angle, add an aperture stop, and then make small, controlled edits in the S-plane editor to see how the aberrations redistribute.

Introducing field angle with tilted parallel rays

Up to now, all rays have travelled parallel to the optical axis. That corresponds to an on-axis object at infinity. An off-axis object at infinity is represented by rays that are still parallel to each other, but tilted by a small angle relative to the optical axis. This is the simplest way to introduce field angle without changing the rest of the setup. The goal in this section is to introduce a small, repeatable tilt that clearly changes the spot diagram. Once you can do that, you can explore coma, astigmatism, and lateral colour in a controlled way.

Open the light source editor and locate the control that sets the beam direction. Set a small tilt in one direction (for example, a small positive tilt in y), and keep the beam collimated. Your setup should look similar to ?? and ??.

Run the simulation and open detector0/RAY_image.csv. Compare the tilted-beam spot diagram to the on-axis reference. You should see a lateral shift of the spot and a more asymmetric footprint. This is where coma and astigmatism start to become obvious. You may also see increased colour separation across the spot, which is a simple visual signature of lateral chromatic behaviour.

Adding an aperture stop and understanding the trade-off

Real lenses are not used wide open by default. An aperture stop limits which rays pass through the system. Stopping down usually improves image quality because it removes marginal rays, which are often the most aberrated. The trade-off is reduced throughput and reduced brightness at the detector.

Add an aperture stop to the scene and set a moderate diameter. Use your on-axis reference first, then repeat for the tilted-beam case from Section ??.

Compare the stopped-down and wide-open cases. The stopped-down spot is usually smaller and cleaner, especially for the tilted-beam case. That improvement is the reason aperture stops exist. The cost is throughput: fewer rays reach the detector, so the image becomes dimmer unless you compensate with longer exposure or higher source intensity.

Change the air gap between elements and observe the effect

Spacing changes are one of the simplest ways to redistribute aberrations within a multi-element lens. In a Cooke Triplet, small air-gap changes can noticeably affect coma and astigmatism, and they can shift the detector position for best focus. Open the S-plane editor and locate the air gap between Lens 1 and Lens 2. Record the baseline value, then apply a small change such as +0.5 mm. Re-run both the on-axis case and the tilted-beam case, keeping the same detector position for a fair comparison.

After the spacing change, do a quick best-focus check using the three-position method from Part B. This keeps the workflow simple and makes it obvious when the lens has moved its best-focus plane.

C4: Adjust one surface curvature and observe spherical aberration and focal shift

Curvature changes mainly affect focal length and the balance of on-axis aberrations. For this reason, curvature is best explored first using the on-axis case. Keep the edit small. A 2–5 percent change is enough to see a difference without destroying the design.

Re-run the on-axis case and re-find best focus using the three-position method. If the lens has changed focal length, the smallest spot will move to a new detector position. If residual spherical aberration has changed, the spot shape will change even when you are at best focus.

Swap glass types and observe chromatic effects

Glass changes affect dispersion, which changes chromatic aberration. Use the RGB wavelength mesh for this section so the colour behaviour is visible in the spot diagram. Make one glass change at a time, and re-run both on-axis and tilted-beam cases.

On-axis, the main effect is usually axial chromatic behaviour: the three colours prefer slightly different best-focus planes. With field angle, you may also see changes in lateral colour, where the RGB components separate more across the image plane.

C6: Form an image of a resolution chart

Spot diagrams are a compact diagnostic, but an image is easier to interpret. In this section you will form a simple test-chart image and connect the spot-diagram changes to perceived sharpness, smearing, and colour fringing.

When you compare images, look for three practical signatures. First: fine line pairs merge or blur when the spot diagram grows. Second: edges smear more in one direction when astigmatism dominates. Third: coloured fringes appear when the RGB components do not overlap in the image plane. These are the image-level consequences of the spot-diagram behaviour you have been analysing.

Conclusion and next steps

You now have a complete, practical workflow for exploring a real lens design in OghmaNano. You can introduce field angle using tilted parallel rays, improve performance using an aperture stop, and study how spacing, curvature, and glass choices redistribute aberrations. Most importantly, you can connect spot-diagram diagnostics to real image quality using a test chart.

Links to related tutorials

• Telephoto lens example.
• S-plane editor documentation.
• Pictures database (test charts and scenes).
• CAD / Mesh-based optical components.