When testing a DUT using a collimator, the collimator objective \(L_{\mathrm{col}}\) and the DUT’s imaging objective \(L_{\mathrm{DUT}}\) together form an optical imaging system. The image of the target formed by \(L_{\mathrm{col}}\) serves as the object for \(L_{\mathrm{DUT}}\). The focal length is one of the key parameters of \(L_{\mathrm{col}}\). In selecting a collimator, the choice of focal length represents a trade-off between measurement accuracy and system size.

First, consider \(L_{\mathrm{col}}\) and \(L_{\mathrm{DUT}}\) as a single optical system. For a fixed focal length of \(L_{\mathrm{DUT}}\) and a fixed target size, increasing the focal length of \(L_{\mathrm{col}}\) reduces the lateral magnification of the system. Consequently, the target forms a smaller image at the DUT’s image plane, corresponding to a higher spatial frequency at that plane. If the focal length of \(L_{\mathrm{col}}\) is \(N\) times that of \(L_{\mathrm{DUT}}\), the spatial-frequency requirement for the target can be reduced to \(1/N\) of the spatial frequency required at the DUT image plane. This reduces the difficulty of fabricating the target and decreases the influence of target-manufacturing tolerances and imperfections on the measurement results, as shown in Figure 1.

Second, for a given lateral displacement of the target, the angular deviation it produces is inversely proportional to the focal length of \(L_{\mathrm{col}}\), provided that the angle is small. If the focal length of \(L_{\mathrm{col}}\) is \(N\) times that of \(L_{\mathrm{DUT}}\), the angular error caused by the target’s lateral positional deviation can be reduced to \(1/N\). This reduces 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 used uncertainty ratio in industrial practice is 1:4, meaning that the measurement-system error should be less than one quarter of the DUT tolerance. As discussed above, if the focal length of \(L_{\mathrm{col}}\) is four times that of \(L_{\mathrm{DUT}}\), the target-fabrication error and the angular error of the test system can each be reduced to one quarter of their original values, thereby satisfying the 1:4 uncertainty-ratio requirement.

Furthermore, the F-number of \(L_{\mathrm{col}}\) is the ratio of its focal length to the diameter of its entrance pupil. For a fixed F-number, a longer focal length requires a larger entrance-pupil diameter, making it easier for the collimator to fully illuminate the DUT’s entrance pupil.

However, focal length is also one of the factors that determine the field of view covered by the collimator. For a fixed target size, a longer focal length results in a smaller achievable field of view. Therefore, although a long focal length is beneficial for improving measurement accuracy, a sufficiently large target is required to cover the field of view needed by wide-angle lenses. Increasing the sizes of the target and the light source causes the volume, weight, and cost of the collimator to increase sharply, thereby limiting the upper end of the practical focal-length range.