Tilted-wave interferometry is a promising measurement technique for the highly accurate measurement of aspheres and freeform surfaces. However, the interferometric fringe evaluation of the sub-apertures causes unknown patch offsets, which currently prevent this measurement technique from providing absolute measurements. Simple strategies, such as constructing differences of optical path length differences (OPDs) or ignoring the piston parameter, can diminish the accuracy resulting from the absolute form measurement. Additional information is needed instead; in this paper, the required accuracy of such information is explored in virtual experiments. Our simulation study reveals that, when one absolute OPD is known within a range of 500 nm, the accuracy of the final measurement result is significantly enhanced.

A round robin comparison of freeform form measurements was carried out by the project partners and stakeholders of a European metrology research project. Altogether six measuring instruments were considered: five different (pointwise and areal) optical devices and one tactile device. Three optical freeform surfaces were used for the comparison measurements, where two specimens were measured by five instruments and one specimen by four instruments. In this paper, the evaluation methods and results of this round robin are presented for the three freeform surfaces made from a temperature-stable material, Super Invar^®. The freeforms had diameters of 40 mm, 50 mm and 100 mm and best-fit radii of 39.75 mm (convex), 40.9 mm (convex) and 423.5 mm (concave). For comparison, the bilateral pointwise differences between the available measurements were calculated. The root-mean-square values of these differences ranged from 15 nm to 110 nm (neglecting spherical contributions) and provided an insight into the status of typical freeform measurement capabilities for optical surfaces.

Tilted-wave interferometry (TWI) is a novel optical measurement principle for the measurement of aspherical surfaces. For the reconstruction of the wavefront and the surface under test, respectively, perturbation methods are applied, which require the calculation of the Jacobian matrix. For the practical use of the instrument, a fast and exact calculation of the Jacobian matrices is crucial, since this strongly influences the calculation times of the TWI. By applying appropriate approaches in optical perturbation methods we are able to calculate the required Jacobian matrices analytically when the nominal optical path through the system is given. As a result, calculation times for the TWI can be considerably reduced. We finally illustrate the improved TWI procedure and apply methods of optimal design to determine optimal positions of the surface under test. For such applications the fast calculation of the Jacobian matrices is essential.

The tilted-wave interferometer (TWI) is a recent and promising technique for optically measuring aspheres and freeform surfaces and combines an elaborate experimental setup with sophisticated data analysis algorithms. There are, however, many parameters that influence its performance, and greater knowledge about the behavior of the TWI is needed before it can be established as a measurement standard. Virtual experiments are an appropriate tool for this purpose, and in this paper we present a digital twin of the TWI that was carefully designed for such experiments. The expensive numerical calculations involved combined with the existence of multiple influencing parameters limit the number of virtual experiments that are feasible, which poses a challenge to researchers. Experimental design is a statistical technique that allows virtual experiments to be planned such as to maximize information gain. We applied experimental design to virtual TWI experiments with the goal of identifying the main sources of uncertainty. The results from this work are presented here.

Aspheres and freeform surfaces play an important role in today’s optics industry. However, the measurement of such complex surfaces is still challenging even with state-of-the-art manufacturing technology, and there is an urgent need in industry for a non-contact, highly accurate reference measurement technique. To meet this demand, at Physikalisch-Technische Bundesanstalt (PTB), a metrological reference system for the contact-free form measurement of aspheres and freeform surfaces is under development. The measurement system is based on a tilted-wave interferometer. Advances in computational capabilities have made it possible to solve the complex inverse problems associated with this measurement system and to develop sophisticated analysis procedures for reconstructing the surface under test from the measured interferogram data. In this paper, we will present the status of the tilted-wave interferometer-based measurement system at PTB, describe the analysis procedures we have designed and show initial measurement results. The benefit of the implementation presented here is that it allows insight to be gained into the performance of the measurement system and enables traceable measurements to be established with low uncertainty.

Asphere and freeform surfaces play a central role in modern optical systems of all kinds.^1,2 Nevertheless, accurate manufacturing is still a challenging task that depends on how well such forms can be measured. Currently, no primary reference measuring instrument with sufficiently low uncertainty of well below 50 nm exists.³ [Here and in the following, the term uncertainty refers to the expanded uncertainty ($k=2$)⁴.] Therefore, evaluating the performance of asphere and freeform measurement systems still represents a bottleneck situation in the highly accurate manufacturing of these forms.