# How to place dummy surfaces at the front and rear principal planes

This article demonstrates how to insert dummy surfaces at the front and rear principal planes of system, using a Cooke Triplet as an example. The surfaces will then appear in the layout plots and can be used for various analyses.

Authored By Erin Elliott

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## Introduction

For a complex lens, it can be convenient to add dummy surfaces at various locations including the entrance and exit pupils, the nodal points, or the principal planes. This article demonstrates how to insert dummy surfaces at the front and rear principal planes of a Cooke Triplet.

## The system

Displayed below is a layout drawing of the system we are hoping to achieve by the end of this article. The fully-finished system is attached to this article. The system is a Cooke Triplet with dummy surfaces at the front and rear principal planes.

A "dummy" surface is a surface without material which means it is a surface that will not affect the tracing of rays. In Configuration 1 shown in the Lens Data Editor below, surfaces two and three are used to reach the principle plane, and represent it. Similarly, surfaces 11 and 12 are used to reach the rear principal plane and to represent it.

To set up the dummy surfaces, only a few steps need to be followed:

• Insert pairs of dummy surfaces after the object and before the image plane.
• Create a configuration with the object at infinity to find the rear principal plane.
• Create a configuration with the object at the front focal plane to find the front principal plane.
• Set up the Merit Function using the separate configurations to optimize for the locations of the dummy surfaces.

The attached lens file contains three configurations. The first configuration is the lens as it will be operated. This is the configuration one would use to analyze and/or optimize the lens performance in the usual way. The second configuration is used to find the location of the rear principal plane. The third configuration is used to find the location of the front principal plane.

## Finding the rear principal plane

The rear principal plane is at the plane located at the point where a ray in object space, traced from an object at infinity, intersects the same ray in image space. Configuration 2 will be used to locate the rear principal plane. Using this configuration, the distance needed to travel to the rear of the principal plane can be found. This corresponds to the thickenss of surface 11. The thickness of surface 12 contains a pickup solve with respect to surface 11, allowing us to return from the principal plane to the image plane.

In order to obtain these values, we start by setting the object distance to infinity in Configuration 2 using the Multi-Configuration Editor, as shown below.

This gives the Layout plot below for Configuration 2. With the object at infinity, the image plane is out of focus. That’s okay, because we’re using this configuration just to locate the principal plane, and not for any other purpose.

In the Merit Function, we can use Configuration 2 to optimize for the thickness of surface 11. In order to optimize, we first set the thickness of surface 11 to variable. Then, in the Merit Function, we measure the Y-height of a paraxial ray in object space using the PARY operand in line 34. And we measure the Y-height of a paraxial ray in image space (line 35). In line 36, we ask that the difference between the two measurements is zero.

After optimizing this, the location of the rear principal plane is correctly captured in the thickness of surface 11, and is found to be -97.3 mm before the image plane.

## Finding the front principal plane

Configuration 3 is used to locate the front principal plane. The front principal plane, by definition, is at the location where a ray in collimated image space intersects the same ray in object space. The first step is to place the object at a location that produces a collimated beam in image space. To do that, we set the thickness of surface 1 to be a variable, and the thickness of surface 0 to zero. The Lens Data Editor for Configuration 3 and the Multi-Configuration Editor are shown below.

Back in the Merit Function Editor, we trace a few paraxial rays to check the collimation of the beam in image space. This is done using the paraxial ray angle operands, PARB, in lines 43-47.

After optimizing, Configuration 3 now contains a system with the object at the front focal plane and a collimated beam in image space.

The second step in locating the front principal plane is to optimize to find the thickness of surface 2, which is set to variable (see Figure 7). In the Merit Function, working in Configuration 3, we measure the height of a paraxial ray in object space and another in image space. We then use the DIFF operand to require that the difference in the two measurements goes to 0. This is shown in lines 52-54 of the Merit Function Editor.

After optimizing to find the thickness of surface 2, then, surface 3 will be correctly located at the front principal plane of the lens. For this system, the front principal plane is about 12.6 mm to the right of the first lens surface.

## Checking the results

We can confirm the locations of the principal planes by looking at Analyze...Reports...Prescription Data and selecting “Cardinal Points” in the settings.

In the Lens Data Editor, the front principal plane location is +102.6 mm from the object. And the rear principal plane is -97.3 mm from the image plane. The Prescription Data lists the same values, confirming our results.

KA-01627