Image space telecentric lenses are useful for a variety of applications, e.g. for radiometric measurements. Image space telecentric lenses have their exit pupil located at infinity. In this article, we discuss three different methods of making a lens that is telecentric in image space in OpticStudio.

**Authored By Tawnya Martin**

## Introduction

The size of images produced with image space telecentric lenses are independent of the back focal length of the optical system. In addition, image space telecentric systems force incident rays on the detector to be at normal incidence, providing a uniformly illuminated image, which is useful for radiometric applications. A lens which is telecentric in image space has its exit pupil at infinity, so the chief ray has zero angle with respect to the optical axis as it passes through the exit pupil and arrives at the image plane.

There are three different methods to enforce the exit pupil of an optical system to be at infinity in OpticStudio as shown:

- Using a Chief Ray Angle curvature solve
- Using EXPP operand
- Using RANG operand

## Using a curvature solve to target chief ray angle

If the chief ray angle, with respect to the optical axis, on the last surface with optical power is forced to be zero, then this will make the exit pupil be at infinity. A curvature solve may be placed on the last surface with optical power and the targeted angle set to zero:

## Using EXPP operand to target exit pupil position

Use the EXPP operand to compute the exit pupil position and target it to some large number. NOTE: it is numerically more stable to target the reciprocal of a large number to zero, so this form of merit function construction is advised:

The EXPP operand (operand #1) has a weight of zero, so its value is computed but does not affect the merit function value. Then the RECI operand takes the reciprocal of operand 1, targets it to zero and uses a weight of 1. This pushes the value of EXPP to become very large.

## Using RANG operand to target chief ray angle

Use the RANG operand on the last surface with optical power to target the angle of the chief ray to zero:

Note that to make a system telecentric in **object**** **space, simply specify this requirement in the **System Explorer... Aperture tab:**

If this is selected, OpticStudio will assume the entrance pupil is at infinity irrespective of the location of the stop surface. All chief rays leaving the object surface will be parallel to the local Z axis. Ray aiming and field points defined using angles may not be used when this option is selected. For best performance, set the stop surface to surface 1 when using Telecentric Object Space mode.

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