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Object Distance Calculation for Collimators

Collimators are designed with infinity as the target object distance, but in practical applications, the object distance that yields the sharpest image of 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 can form an image at a positive or negative finite distance, respectively. A collimator with an adjustable target position is called a variable object distance collimator (or adjustable focus collimator, finite conjugate collimator), as shown in Figure 1. This type of collimator is compatible with a wider range of DUTs and supports defocus testing to indirectly measure the actual back focal shift of DUTs with a fixed back focus.
Figure 1 Principle of a variable object distance collimator

The object-image relationship of the target imaged through the collimating objective is as follows:

Lcol manufacturers typically provide a table that correlates the target position with the corresponding simulated object distance for the convenience of collimator manufacturers or end users. However, most Lcol designs are generic, and the designer cannot foresee the parameters of the imaging objective Ldut. Therefore, the simulated object distances given in the table are relative to a specific reference plane, which is often the plane where the ExP is located. However, for the DUT, the object distance calculation should be referenced to the first principal plane of Ldut (located in the object space), as shown in Figure 2. Ignoring the position of the principal plane will 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