Swing-arm optical coordinate measuring machine for aspheric optics

For several hundred years optics were made by polishing spherical surfaces, for which many simple testing methods exist. In recent decades, optical instruments from astronomical telescopes to cell-phone cameras have increasingly sought to incorporate aspheric surfaces, which make it possible to achieve better performance while using fewer lens elements. Yet aspheric surfaces are much harder to test than their spherical counterparts, a drawback that has prevented widespread use of the newer technology.

At least two commercial instruments have tackled aspheric surface testing: the Zygo Verifire Asphere and the QED Aspheric Stitching Interferometer. But both are limited in the diameter of the surfaces they can measure, and one is largely limited to aspheres that are rotationally symmetric. Another method, called deflectometry, measures the slopes of surfaces and can be applied to nonrotationally symmetric aspheres. However, it is still in its infancy, and slope errors must be integrated to recover the surface shape. We developed the swing-arm optical coordinate measuring machine (SOC), or profilometer, to overcome these problems. It represents a high-precision metrology approach to full-aperture testing of highly aspheric surfaces.^1–4

The SOC is easily configured for measuring concave, convex, and plane surfaces. Moreover, it can be used in situ on the polishing machine so the optic does not have to be removed to a separate test instrument. Adding a second probe makes the machine self-calibrating, and using a triangulation sensor enables measurement of aspheres while they are being ground prior to polishing. Precise control of the aspheric shape at this stage speeds up fabrication because material removal is more efficient than in the polishing stage.

Figure 1 shows the basic geometry of the SOC. A probe is mounted at the end of an arm that swings across the optic under test such that the axis of rotation of the arm intersects the center of curvature of the optic. For a constant probe reading, the arc defined by the probe tip trajectory lies on a spherical surface defined by this center of curvature. For measuring aspheric surfaces, the probe is aligned parallel to the normal at the vertex of the optical surface and reads only the departure from spherical. The SOC employs this simple geometry together with an interferometric probe that measures continuously as it moves across the polished optic. The optic, or test, part is rotated in azimuth after each profile is measured. Figure 2 shows an example of the profiling pattern we generally use during a test. Since the arcs cross each other while the sensor scans the part edge to edge, we know that the surface heights must be the same at these scan crossings. We use the crossing height information to stitch the profiles into a continuous surface using a maximum likelihood reconstruction method.⁵

Figure 1. Geometry of the swing-arm optical coordinate measuring machine (SOC).

Figure 2. An example of the SOC profiling pattern showing how the sensor trajectories cross each other.

Figure 3 shows the results of applying the SOC and a full-aperture interferometric null test to measure a 1.4m-diameter, off-axis, convex surface with an aspheric departure of 300μm. The test shows excellent agreement with the interferometric test. The direct subtraction of the maps from the two methods after alignment terms have been removed shows a mere 9nm rms difference, much of which appears to originate with the interferometric test.

Figure 3. Comparison of interferometric Fizeau null test data (top) and SOC data (middle) with tilt, power, coma, astigmatism, and trefoil removed. Fizeau test data rms=0 .0357μm. SOC data rms=0 .0356μm. Direct subtraction shows a 9nm rms difference (bottom).

The geometry of the SOC has the advantage that only one precision continuous scan motion—the arm bearing—is required. A high-quality rotary table for the optic under test is not needed because the effects of reasonable table wobble and runout are corrected during the maximum likelihood stitching. The SOC systematic errors stem mainly from errors in the arm bearing, and the odd component of those errors cancels due to reversal of the part during a complete measurement cycle. Previously, we used an independent test method to calibrate the even SOC arm bearing errors.³

We recently added a second probe to the setup: see Figure 4(a). When the two probes are aligned to swing across the same trajectory on the part, both see the same bearing errors while measuring different positions of the test surface along the trajectory. This shear between the probes allows us to reconstruct the test surface without using an external reference, which makes the SOC self-calibrating. Figure 4(b) shows the raw data (forward and reverse scans) from each of the two probes. The data becomes random when the probes move beyond the edge of the test surface. Data from measuring a 350mm-diameter, convex aspheric surface shows a calibration precision of ∼2nm rms.⁶

Figure 4. (a) The setup for using the dual-probe SOC to measure a 350mm-diameter convex aspheric surface. (b) Raw data (forward and reverse scans) from the two probes.

Visible light interferometric tests provide high-accuracy measurements once the test surface is polished. But during polishing, the surface shape, or figure, correction is slow. It is desirable to measure the surface accurately during grinding to minimize figure errors and speed up fabrication. We enhanced the SOC with an optical laser triangulation sensor for measuring ground surfaces before polishing. We calibrated the triangulation sensor with a distance-measuring interferometer, a laser tracker, and both ground and polished optical surfaces of known shapes. Once calibrated, the sensor had good linearity and was robust to the angular variations in the surface under test within the sensor's 2mm working range.

We incorporated the sensor's working parameters—sensor tip location, angle of the projected beam, measurement axis, and so forth—into the SOC data reduction software to correctly relate the sensor readout to the test surface sag.⁷ We attached the calibrated sensor to the SOC to guide the grinding of the aspheric mirrors for the Hobby Eberly Telescope wide-field correctors.⁸ Figure 5 shows a comparison of the measurements from both the SOC and an interferometric null test on a polished, 1m-diameter mirror with 80μm peak-to-valley aspheric departure. The SOC and interferometer data agree within 100nm rms or better. This result shows that the triangulation sensor is reliable for measuring both ground and polished surfaces.

Figure 5. Measurement of a highly aspheric surface using (a) the SOC with an optical laser triangulation sensor (surface map with power, astigmatism, coma, and trefoil removed), rms=0 .41μm, and (b) the null interferometric test, rms=0 .44μm.

In summary, the SOC is an effective metrology technique for testing highly aspheric surfaces with a precision that rivals full-aperture, interferometric tests. Using dual probes, the SOC can be self-calibrated to ∼2nm rms, as demonstrated by measurement of a 350mm-diameter convex asphere. We also showed how the measurement range of the SOC can be extended to ground surfaces using a calibrated laser triangulation sensor. The experimental data show that, equipped with this sensor, the SOC can measure a test surface to a precision of better than 100nm rms. At present the amount of asphericity we can measure with the SOC is limited by the interferometric probe's dynamic range of about 5mm and its angular acceptance from normal. We plan to investigate probes with greater versatility to extend the range of aspheric surfaces that the SOC can measure.