Instrumentation and measurement

Hexapod Performs Precision Positioning: Fast and Flexible Analysis of Aspherical Lenses

September 27, 2018

Aspherical lenses have rotationally symmetrical optics around the optical axis, whose radius of curvature changes radially with the distance from the center. This allows optical systems to achieve high image quality, whereby the number of elements required decreases and that saves on both costs and weight. However, testing the aspheric shape accuracy, what means the quality of this type of lenses is a considerable challenge to the manufacturer: This requires measuring the tiniest deviations in shape in the nanometer range and at the same time, making short measuring and setup times possible. The solution is to use a new type of interferometer multiple tilted wavefronts. As part of the overall system, the hexapod takes over several positioning functions.

Several methods have been established for checking the shape of aspherical lenses for accuracy (image 1): For example, interferometers with computer-generated holograms (CGHs) generate an aspherical wavefront in the desired shape and therefore make it possible to determine the deviation of the lens. The CGHs need to be created individually for each test object shape and are therefore only economical for series production. Interferometric measuring of aspheres in circular subsections is another possibility. Finally, each partial measurement is combined to a full-surface interferogram. The process is very flexible compared to CGHs and is also suitable for the production of prototypes and smaller series. However, “stitching” the circular rings is often very time consuming, as in the case of steeper optics, only smaller circular interference pattern rings can be captured and therefore many interference patterns have to be stitched together. In addition to this noncontact measuring method, tactile and “quasi-tactile” measuring is possible (similar to a scanning probe microscope). In this case, the surface is only scanned “point-to-point! and with gaps instead of homogeneous coverage. However, the use of tactile measuring methods for polished surfaces is not the best choice because of to the risk of scratching.

A New Approach: Tilted Wavefront Technology

For this reason, Mahr, the measuring technology specialists, rely on a new instrument for precise, fast, flexible measuring of different aspheres directly on the production line, without CGH, classical stitching or tactile contacting. In contrast to existing systems that need several minutes to do the measuring, the MarOpto TWI 60 (image 2) needs only 20 to 30 seconds to measure the entire surface. The next test object can be measured while the previous one is being evaluated, which typically takes around 2 minutes. In addition to the short measuring and evaluation times, the system distinguishes itself by its flexibility. It’s not only possible to measure aspheres, but also other optics that have geometries deviating from standard shapes, so-called freeforms (image 3). The system is so robust that it is possible to set it up directly in production area.

The new measuring system works in a similar was to a “normal” interferometer, but does not immediately acquire the entire test object optically in one single image, but in several subapertures that are active at different times. In the case of optics with steep surfaces, such as aspheres and freeforms, acquiring the test object “at once” would cause the interference patterns to converge and it would not be possible to resolve them afterwards. If the individual geometrically distributed subapertures are actively switched and different tilted wavefronts hit the inspection optics without overlapping interference patterns. An undisturbed interference pattern of a local part of the test object surface is obtained from each subaperture and the entire surface of the test object can be measured within a short time (image 4).

Finally, the individual interference patterns are combined to form a topography of the test object’s surface. This represents the surface of the (aspherical) test object and can then be evaluated accordingly (image 5a/b). The deviation of the test object’s actual shape from the nominal shape is important for the user. The design of the TWI also makes it very flexible with respect to the surface geometry of the test object. This means that each test object can have an individual surface shape without the need to change the setup of the TWI or even interrupt the production process at all. Even segmented and off-axis aspheres, toroid, and freeform optics can be measured quickly with high lateral resolution and measuring uncertainties under 50 nm.

The Referencing Process

The TWI needs to be referenced and calibrated just like every other measuring device. For this purpose, a highly accurate sphere with known geometrical specifications is moved for each subaperture to a specific position and then measured by this subaperture. Due to the complex optical beam path and in contrast to conventional systems, these types of interferograms are more sophisticated (image 6a/b).

The wavefronts generated from the individual subapertures are combined to an overall wavefront. Finally, all measurements are evaluated and an algorithm is used to correct the systematic measurement deviations across all subapertures.

As all kind of positioning errors of the calibration sphere affect the correction algorithm of the respective subaperture, the calibration sphere needs to be positioned very exactly. A maximum lateral position error of 5 µm with a repeatability of less than 0.5 µm is required.

In order to meet the high demands on the positioning mechanism in the TWI and after careful testing, Mahr finally made the decision to use the H-824 hexapod from PI (Physik Instrumente). This hexapod also positions the test object in five degrees of freedom before the actual measuring process starts (image 7). Also, both the nominal and actual position need to be matched exactly. For example, deviations in tilt may not exceed 60 µrad.

Advantages of the Parallel-Kinematic Positioning System

Of course, hexapods, otherwise known as parallel-kinematic positioning systems, are predestined for this, because they are able to position in all degrees of freedom with high accuracy and travel along trajectories with high precision. In the case of hexapods and in contrast to serial kinematics, all six actuators act directly on the same platform (image 8). This allows a more compact design than stacked systems. Because hexapods move only one platform, the overall mass is also less, which results in high dynamics in all motion axes.

In contrast to a stacked system, hexapods are also distinguished by their improved path accuracy, higher repeatability, and flatness. Another essential characteristic of hexapods is the freely definable rotation or pivot point, which means it is possible to define various coordinate systems that for example, refer to the position of the workpiece or tool.

The high-performance C-887 digital controller (image 9) takes care of controlling the hexapod that, thanks to the user-friendly software, enables easy commanding. The positions are specified in Cartesian coordinates, and all transformations to the individual drives are done inside the controller. In the meantime, the innovative measuring system has proven itself in practice. TWI 60 systems are currently being used at the PTB (Physikalisch-Technische Bundesanstalt Braunschweig, Germany) as well as by a number of well-known manufacturers of aspheric precision optics.

Testing the shape accuracy and therefore the quality of the aspheric lenses is a considerable challenge to the optics manufacturer. It is necessary to measure the tiniest deviation in shape in the nanometer range and at the same time, also work as efficiently as possible. (Source: Yakobschuk Vasy/

In contrast to existing systems that need several minutes to do the measuring, the MarOpto TWI 60 needs only 20 to 30 seconds to measure the entire surface. (Source: Mahr)

It’s not only possible to measure aspheres, but also so-called freeforms. (Source: Docter Optics SE

The individual subapertures are spread out and actively switched. This allows the various tilted wavefronts to hit the inspection optics so that the resulting interference patterns do not overlap. (Source: Mahr)

Image 5a/b: The individual interference patterns are combined to a single pattern (5a). This represents the surface of an (aspheric) test object (5b) and can then be evaluated accordingly. (Source: Mahr)

Image 6a/b: Interferograms of a subaperture from the calibration sphere. (Source: Mahr)


Image 7: The H-824 hexapod positions the calibration sphere and also the test object before the measuring process starts. Both the nominal and actual position need to be matched exactly. (Source: PI)


Image 8: In contrast to serial kinematics, the actuators in parallel-kinematic systems act directly on the same platform. This makes it possible for hexapods to provide improved path accuracy, higher repeatability, and flatness. (Source: PI)


Image 9: The high-performance C-887 digital controller takes care of controlling the hexapod that, thanks to the user-friendly software, enables easy commanding. (Source: PI)



Dr.-Ing. Jürgen Schweizer (image 10), Product Management Marketing at Mahr GmbH and Dipl. Geogr. Doris Knauer (image 11), Global Campaign Manager Industrial Automation at Physik Instrumente (PI) GmbH & Co. KG.


Mahr in Brief

Mahr is a globally operating group of companies with headquarters in Göttingen, whose name is traditionally linked to production measuring technology, quality, and innovation. The Mahr Group employs 1,900 people and is one of the largest family-own companies in the field of measuring technology. Whether the lens in a mobile phone camera, the camshaft of an engine or an artificial hip joint – measuring devices from Mahr document the quality of a variety of products and verify results in research and development. The companies of the Mahr group have pioneered the technical and economic progress in virtually every field in the industry of dimensional measuring technology.


PI (Physik Instrumente) in Brief

Well known for the high quality of its products, PI (Physik Instrumente) has been one of the leading players in the global market for precision positioning technology for many years. PI has been developing and manufacturing standard and OEM products with piezo or motor drives for 40 years. Continuous development of innovative drive concepts, products, and system solutions and more than 200 technology patents distinguish the company history today. PI develops, manufactures, and qualifies all core technology itself: From piezo components, -actuators, and motors as well as magnetic direct drives through air bearings, magnetic and flexure guides to nanometrological sensors, control technology, and software.

PI is therefore not dependent on components available on the market to offer its customers the most advanced solutions. The high vertical range of manufacturing allows complete control over processes and this allows flexible reaction to market developments and new requirements.

By acquiring the majority shares in ACS Motion Control, a worldwide leading developer and manufacturer of modular motion controllers for multi-axis drive systems, PI can also supply customized complete systems for industrial applications that make the highest demand on precision and dynamics. In addition to four locations in Germany, the PI Group is represented internationally by fifteen sales and service subsidiaries.