Surface accuracy measurement methods for aspherical optical mirror

Aspherical optical elements are cold-processed, from milling, precision grinding, rough polishing to precision polishing and finishing, each process corresponds to the measurement of the surface accuracy. This article mainly introduces the surface accuracy measurement method of cold processing in each process.

 

Aspherical optical elements are cold-processed, from milling, precision grinding, rough polishing to precision polishing and finishing, each process corresponds to the measurement of the surface accuracy. This article mainly introduces the surface accuracy measurement method of cold processing in each process.

I. Surface accuracy measurement at the aspherical milling stage

Coordinate Measuring Machine(CMM)

CMM has been widely used in various measurement fields. The current CMM software generally supports the import of CAD models, so by importing the CAD model of the aspherical surface to be tested into the software and conducting automatic testing, the distribution of surface accuracy errors of the aspherical surface to be tested can be obtained. The common Zeiss CMM is shown in the figure below:

The measurement accuracy of high-precision CMM has reached within 0.5μm, so the use of CMM to test the surface accuracy of aspherical elements can also obtain the PV value of micron magnitude, which is very helpful for measuring off-axis aspherical and freeform surfaces.

 

II.Surface accuracy measurement at the precision grinding & rough polishing stage

During the precision grinding and rough polishing stages, the PV value of the aspherical surface is at the micrometer and submicron level. At this time, combined with commercial testing equipment, accurate testing of the element can be achieved. Commonly used testing equipment includes the Luphoscan series equipment produced by Taylor Hobson, the Nanomefos equipment produced by Dutch DUI, and the UA3P equipment produced by Japanese Panasonic.

The Luphoscan equipment is based on laser multi-wavelength interferometry (MWLI) technology, which can use a non-contact method to test the sagittal height variation of the aspherical surface, thereby evaluating the distribution of surface errors of the entire aspherical surface. The surface measurement accuracy is about ±50nm (PV). This series of equipment includes Luphoscan 260 HD, Luphoscan 420 HD, Luphoscan 600 HD, and customized large-diameter models, corresponding to maximum measurable diameters of 260mm, 420mm, 600mm, and larger sizes respectively.

For large-diameter aspherical elements, such as aspherical reflectors with diameters exceeding 1m, the above-mentioned commercial equipment is no longer applicable due to measurement diameter limitations. Scientists have invented a swing arm profilometer, which uses a rotating measuring arm to test and obtain the surface shape error distribution of large-diameter aspherical surfaces. The principle is shown in the figure below:

In the above figure, a measuring arm is suspended above the large-diameter aspherical surface. For each rotation of the tested mirror, the measuring arm rotates one full circle to collect data. By combining multiple rounds of measurement tracks, data collection is completed. Processing the data allows for obtaining the surface shape distribution of large-diameter aspherical elements. Currently, this method has been successfully applied in the surface shape testing of large-diameter aspherical surfaces used in aerospace and astronomy. The knife-edge shadow method, with its advantages of low cost and high measurement sensitivity, can still be seen in its application scenarios. By observing the size of the scattered spot reflected back by the tested aspherical surface with a knife-edge instrument, the boundaries of contour variations on the aspherical surface can be sensitively determined. This enables targeted grinding of the aspherical surface. Although this method is only qualitative analysis, it can still effectively guide the convergence of surface shape errors. Additionally, by complementing it with pitch polishing techniques, it is possible to effectively reduce the numerical values of mid-frequency errors while improving the surface shape, ensuring that the final surface shape error converges with sufficient accuracy. This method has remained vigorous after more than a century of application, demonstrating its significant value as a detection tool.

 

III. Surface accuracy measurement at the precision polishing stage

Quadratic surfaces, with their special surface forms, can be tested using the null test method with the help of an auxiliary mirror. For example, for a parabolic surface, its focal point and infinity are conjugate to each other, so testing can be achieved using a flat mirror or a reflection sphere. The common testing optical path is shown below:

In the above diagram, one method is to place a reflection sphere at the focal point where parallel light is incident on the concave parabolic surface to reflect the light beam back along the original path, achieving self-collimation testing. Another method is to use a flat mirror with a central aperture to reflect the light beam back to the focal point for testing.

For an ellipsoidal surface, its front and back focal points are conjugate to each other. A spherical wave emitted from one focal point, after reflecting off the ellipsoidal surface, will converge at the other focal point, forming an ideal spherical wave. Therefore, it can also be used for null test method, and the optical path is shown as follows:

 

For hyperbolic surfaces, which have two focal points distributed on both sides, the null test method for hyperbolic surfaces is typically achieved using a spherical mirror. The common Hindle sphere method for testing hyperbolic surfaces is shown in the following optical path:

Zero-position compensation method

For large-diameter aspherical surfaces or higher-order aspherical surfaces, it is inconvenient to use the null test method. Therefore, people have invented the zero-position compensation method to test the surface accuracy of aspherical surfaces. The zero-position compensation method utilizes a compensator that can compensate for spherical aberration to convert the plane wave or spherical wave emitted by the interferometer into a aspherical wavefront that matches the aspherical surface to be tested, thereby achieving zero-position testing. There are typically two common types of compensators. One type is achieved through a lens group composed of two or three spherical lenses, assembled into a compensation lens, known as a Null lens. The other type involves using computer-generated holograms (CGH), which are diffraction elements that utilize the principles of diffraction to modulate the wavefront by adjusting the +1-order light emitted by the interferometer, to achieve the wavefront conversion. The common zero-position compensation optical path is shown in the following figure:

CGH test accuracy can achieve RMS 1/100 λ.

In addition, the American company QED has developed the ASI (Asphere Stitching Interferometer) interferometric measurement device, which can achieve stitching testing of shallow aspherical surface shapes through sub-aperture stitching. Zygo company has developed the VFA (Verifire Asphere) interferometric measurement device, which can achieve axisymmetric aspherical surface shape stitching testing through annular band stitching and provide the resulting surface shape distribution. Stitching methods used in the surface shape measurement of aspherical surfaces are also a valuable innovation.