Logo of the Physikalisch-Technische Bundesanstalt
symbolic picture: "magazines"

AI for the form measurement of optical surfaces

Deep neural networks for topography measurements with tilted-wave interferometers

PTB-News 2.2022
Especially interesting for

optical form measurement

machine learning in optics

The highly accurate form measurement of optical aspheres and free-form surfaces represents a great challenge in metrology. A new method uses artificial intelligence (AI) – i.e., deep neural networks – to reconstruct optical surfaces from the measurement data of a tilted-wave interferometer. In addition, this method quantifies the uncertainty of the prediction.

Asphere being measured by means of the tilted-wave interferometer. The screen in the background displays the difference between the measured SUT and the expected design topography.

Optical aspheres and free-form surfaces are widespread in industry. PTB, in cooperation with a partner from industry, has been doing research on how to enhance the tilted-wave interferometer – an interferometric measurement system used for the optical measurement of such surfaces – and perform traceable form measurement with the device. This device’s reconstruction procedure is based on the comparison of the measurement data of the surface under test (SUT) with the simulated data of a design topography, i.e., with the expected form of the SUT. The deviation of the SUT from the design is then determined from the difference between the measurement data and the simulated data.

The new method exploits deep neural networks to determine this deviation. Using a set of several trained neural networks, the model uncertainty can also be reconstructed. In numerical experiments, it has been demonstrated that the method also provides reliable results even in the presence of calibration errors or noise.

The method was first applied to the measurement data of an aspherical SUT whose design topography has a base area diameter of approx. 25 mm and a maximum peak-to-valley value of approx. 4 mm. The reconstructed surface form is in agreement with the form reconstruction provided by a modern comparison method used in industry – their differences lie within the limits of the model uncertainties.

As soon as the neural networks have been trained, it is possible to assess new data at the push of a button. The method is thus fast and includes an uncertainty quantification of the prediction, making it potentially very interesting for use in mass production quality control and other future applications.


Lara Hoffmann
Departments 8.4
Mathematical Modelling and Data Analysis
and 4.2 Imaging and Wave Optics
Phone: +49 30 3481-7807
Opens local program for sending emaillara.hoffmann(at)ptb.de

Scientific publication

L. Hoffmann, I. Fortmeier, C. Elster: Uncertainty quantification by ensemble learning for computational optical form measurements. Machine Learning: Science and Technology 2, 035030 (2021)