Inaccurate Positioning: A Pitfall Where You Can Easily Suffer in silence. Let's consider a real-world scenario. You're inspecting a concave aspherical mirror. The CGH is designed, the optical path is set up, and interference fringes have appeared. Based on experience, you adjust the mirror slightly; the fringes look good, the PV value is nice, and you breathe a sigh of relief. But three months later, the mirror is installed in the system, and the image quality is substandard. After investigation, you find that the radius of curvature differs from the design value by more than ten micrometers. Where did the problem lie? During inspection, the mirror wasn't in its theoretical pose. You thought you had adjusted it to the "optimal fringes," but in reality, you used pose deviation to compensate for the manufacturing error in the radius of curvature—two errors cancel each other out, creating a self-consistent but deviating-from-true illusion. Even more insidious is that if the mirror's radius of curvature itself is problematic, and you haven't precisely controlled the pose to the theoretical value, the measured surface data becomes a mess: it's impossible to determine how much is a surface shape problem and how much is a pose problem. How do you avoid this pitfall? A peephole. How does a peephole guarantee its theoretical pose? In a CGH (Concave Aspherical Mirror) inspection system, the core task of the cat's eye structure is clear: to ensure that the mirror under test (DUT) and the CGH maintain the theoretical pose. What is the theoretical pose? It is the spatial relationship rigorously calculated during the design phase—the axial distance, tilt, and eccentricity are all clearly defined design values. The entire job of the cat's eye is to ensure that the actual assembled pose matches these design values. How does it work in practice? Let's break it down using a common inspection scenario. Scenario: The CGH is inspected and has an alignment holographic area. The light projected from this area, after being reflected by the DUT, forms a cat's eye image—usually a clear, focused spot of light.
Figure 1. Optical path for cat's eye detection
The operating procedure is as follows: 1. Coarse adjustment: Mount the test mirror and CGH in place, and adjust the axial distance, tilt, and eccentricity to be close to the theoretical values. 2. Cat's eye fine adjustment: Observe the cat's eye image projected onto the holographic display. As the position and pose of the test mirror gradually approach the theoretical value, the cat's eye image will tend towards a preset optimal shape.
Figure 2. Cat's eye image when the pose is correct.
Figure 3. Cat's eye image with incorrect pose (axial distance error and tilt).
3. Position Locking: Once the cat's eye image reaches the preset standard, it indicates that the mirror under test is in its theoretical position. At this point, all adjustment mechanisms are locked, and surface shape detection begins. The cat's eye here essentially acts as a highly sensitive "position indicator." It tells you when the mirror's position is "in place." The surface shape data measured after it's in place is the true performance of the mirror in its theoretical position. A Real-World Case: Where Does Spherical Aberration Come From? Simulation Provides the Answer. Now that the principle is clear, let's look at a real engineering scenario. Many field engineers may resonate with the troubleshooting process in this case. There is an aspherical lens, and its surface shape is first detected using a DUI non-contact profilometer. The profilometer scans the mirror's contour through an optical probe, directly acquiring surface topography data. The measured results are fine; the surface shape looks quite clean.
Figure 4 DUI Test Results
The same lens was tested again on the CGH testing system. The cat's eye was aligned correctly, and the pose was locked at the theoretical value. The result came out—a large spherical aberration was clearly visible on the face.
Figure 5 CGH test results
Two reports lay on the table. DUI said the surface shape was fine, while CGH said there was a large spherical aberration. Which to believe? To find the source of this spherical aberration, the radius of curvature of the lens was measured using DUI. A non-contact profilometer can directly scan the generatrix to fit the radius of curvature, without relying on an external reference wavefront. The measurement results came back—the measured radius of curvature differed from the theoretical value by 112 μm. Next, this radius of curvature deviation was substituted into the optical simulation model of the CGH detection system. After the simulation results were obtained, they were compared with the measured surface shape data from CGH—the two matched remarkably well. This large spherical aberration was precisely the behavior that the radius of curvature deviation should exhibit under the theoretical pose.
Figure 6 Simulation results
The chain is now closed: Curvature radius deviation → Spherical aberration should appear under the theoretical pose → CGH measured spherical aberration matches the simulation → CGH measurement is the real one. Why didn't DUI show obvious spherical aberration in the surface shape results before? Because when a non-contact profilometer scans a surface, the correspondence between the measurement coordinate system and the mechanical reference of the mirror depends on the clamping posture. If the mirror is not strictly locked under the theoretical pose, the surface shape component caused by the curvature radius deviation may be diluted by the change in measurement posture, and further smoothed in data processing, ultimately appearing "not noticeable" in the surface shape report. But the measurement of the curvature radius does not lie—the curvature radius value measured by DUI deviates from the theoretical value, and this deviation, after being put into simulation, is exactly equal to the spherical aberration measured by CGH. What's so powerful about the CGH + cat's eye combination? It separates the surface shape error and the curvature radius error. With the pose fixed, a deviation in the curvature radius is spherical aberration, nowhere to hide. Moreover, this spherical aberration can be reproduced by simulation—it doesn't appear out of nowhere, but is an inevitable manifestation of the curvature radius deviation under the theoretical pose. What does this mean for frontline operators? The cat's eye's guarantee of theoretical pose brings tangible changes to on-site testing:
◆ Possession is now based on evidence: The accuracy of mirror placement is no longer judged by the "look of the stripes." The cat's eye image is a quantitative pose judgment standard independent of the stripes.
◆ Surface shape data is reliable: With the pose fixed, the measured surface shape is the true surface shape of the mirror itself. If the radius of curvature is incorrect, the surface shape will accurately reflect the out-of-focus state, not be obscured by the incorrect pose.
◆ Reproducible: The standard of the cat's eye image remains unchanged regardless of the operator. The pose adjusted by Zhang San and Li Si is the same pose.
◆ When data from different instruments conflict, there's a clear way to resolve the issue: CGH has a cat's eye that locks the pose, measuring the true surface shape under the theoretical pose. With other methods, if the pose is not strictly locked, "good-looking" data may not be correct—in this case, measuring the radius of curvature separately often provides the answer. Finally, in the CGH testing system, wavefront compensation is most frequently mentioned—it guarantees surface shape accuracy. However, wavefront compensation relies on the assumption that the pose between the tested mirror and the CGH (Curve Front Gauge) is in the theoretically designed state. The cat's eye acts as the "stabilizing force" that locks in the pose. By fixing the pose, the true shape of the mirror is revealed. The radius of curvature is either correct or incorrect. Nothing is hidden. And this is precisely what precision testing requires most: authenticity.
