Object Distance Calculation for Collimators

Collimators are designed for a target at infinity. However, in practical applications, the object distance that produces the sharpest image on the DUT may be finite. According to the principles of lens imaging, when the target is located outside or inside the focal plane of the collimating objective Lcol, it forms an image at a finite positive or negative distance, respectively. A collimator with an adjustable target position is called a variable object distance collimator, adjustable-focus collimator, or finite-conjugate collimator, as shown in Figure 1. This type of collimator is compatible with a wider range of DUTs and supports defocus testing, which can be used to indirectly measure the actual back focal shift of DUTs with a fixed back focus.

Figure 1. Principle of a collimator with an adjustable object distance

The object–image relationship for the target imaged by the collimating objective is as follows:

Lcol manufacturers typically provide a table correlating the target position with the corresponding simulated object distance for use by collimator manufacturers and end users. However, most Lcol designs are generic, and the designer cannot anticipate the parameters of the imaging objective Ldut. Therefore, the simulated object distances listed in the table are referenced to a specific plane, which is often the plane where the exit pupil (ExP) is located. For the DUT, however, the object distance should be calculated with respect to the first principal plane of Ldut, which is located in object space, as shown in Figure 2. Neglecting the position of the principal plane can affect the accuracy of the measurement results. In practical applications, if the ExP and EnP are coplanar, the user can correct the simulated object distance provided by the Lcol supplier using the distance between the EnP and the first principal plane to obtain the accurate object distance.
Figure 2 The position of the first principal plane of the DUT imaging lens is the reference plane for object distance calculation and measurement