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==== Pupil Matching Between Collimator and DUT ====
The image of the aperture stop formed by the optical system between it and the image is called the exit pupil, or **exit pupil** for short. The exit pupil is the common exit for all rays emerging from the optical system, and the **center of the exit pupil** is the intersection of the image-space chief rays (or their extensions).\\

When we use a collimator to test a DUT, the collimating objective Lcol of the collimator and the imaging objective Ldut of the DUT form an optical imaging system, and the image of the target formed by Lcol serves as the object for Ldut. At this point, the two should be strictly coaxial (otherwise aberrations may be introduced), and the exit pupil ExP of Lcol should be efficiently coupled with the entrance pupil EnP of Ldut, which is referred to as **pupil matching**.\\
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Figure 1 Exit pupil of the collimator's collimating objective and entrance pupil of the DUT's imaging objective\\

Pupil matching is a fundamental requirement in optical system design. For a collimator, the ExP is the common exit for the emergent rays. Since the target inside the collimator has a finite size and is not an ideal point object, the emergent beam across the full field of view is divergent.\\

In this case, if there is a pupil mismatch, it may cause the following issues:\\

First, if the EnP is located behind the ExP, some of the marginal rays emerging from the ExP will be blocked by the EnP and fail to enter Ldut, resulting in additional energy loss. Even if the beam in the central field of view can fully fill the EnP, it may still fail to fill it at the edge of the field, causing vignetting and making the illuminance on the image plane of the DUT even more non-uniform. It is easy to see that making the ExP and EnP coplanar can minimize energy loss, as shown in Figure 2;\\

Second, the aberrations of the DUT objective typically degrade as the aperture area increases. If the diameter of the EnP is larger than that of the ExP, the incident beam will not fully fill the EnP, causing the DUT to actually operate at a higher F-number than its design value. This will artificially reduce lens aberrations, resulting in artificially high spatial frequency response measurements that are inconsistent with the DUT's performance in practical applications. Therefore, the diameter of the ExP should be no less than that of the EnP.\\

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Figure 2 The exit pupil diameter of the collimator's collimating objective should be larger than the entrance pupil diameter of the DUT's imaging objective, and the two should be coplanar\\

In summary, when selecting a collimator, we should try to make the diameter of the ExP larger than that of the EnP, so that the incident light completely fills the EnP with a certain margin, and the ExP and EnP should be as coplanar as possible.\\