When testing a DUT using a collimator, the collimating objective Lcol of the collimator and the imaging objective Ldut of the DUT form an optical imaging system. The image of the target formed by Lcol serves as the object for Ldut. Focal length is one of the primary parameters of Lcol. In collimator selection, the choice of focal length reflects a trade-off between test accuracy and equipment size.

First, consider Lcol and Ldut as a single optical system. Given a fixed focal length of Ldut and a fixed target size, a longer focal length of Lcol results in a lower lateral magnification of the target, producing a smaller image on the DUT and thus a higher spatial frequency in the resulting image. If the focal length of Lcol is N times that of Ldut, the spatial frequency requirement for the target can be reduced to 1/N of the required test spatial frequency. This reduces the difficulty of target fabrication and minimizes the impact of target tolerances and defects on measurement results, as shown in Figure 1.

Second, the focal length of Lcol is inversely proportional to the angle generated by the lateral displacement of the target (for small angles). If the focal length of Lcol is N times that of Ldut, the angular error caused by lateral positional deviations of the target can be reduced to 1/N, thereby decreasing the angular sensitivity of the measurement, as shown in Figure 2.

From a metrological perspective, the measurement standard should have a lower measurement uncertainty than the DUT. A widely accepted measurement uncertainty ratio in industrial practice is 1:4, meaning the instrument error should be less than 1/4 of the DUT tolerance. As mentioned above, if the focal length of Lcol is 4 times that of Ldut, the target fabrication error and angular error of the test system can be reduced to 1/4, meeting the requirement for the measurement uncertainty ratio.

Furthermore, the F-number of Lcol is the ratio of the focal length to the exit pupil diameter. For a fixed F-number, a longer focal length means a larger aperture for the ExP, making it easier to cover the EnP.

However, focal length is also one of the factors determining the field of view that the collimator can cover. With a constant target size, a longer focal length results in a smaller coverable field of view. Therefore, while using a long focal length is beneficial for improving accuracy, a sufficiently large target must be used to cover the field of view required by wide-angle lenses. Increasing the size of the target and light source causes a sharp rise in the volume, weight, and cost of the collimator, thereby constraining the upper limit of the selectable focal length.