Tilted Wave Interferometer Research Articles

Concept for improving the form measurement results of aspheres and freeform surfaces in a tilted-wave interferometer

Abstract. Accurate and flexible form measurements for aspherical and freeform surfaces are in high demand, and non-null-test interferometric methods such as tilted-wave interferometry have gained attention as a promising response to this need. Interferometric methods, however, display ambiguities between the measurement of certain form errors and the misalignment of the measured specimen. Therefore, improved knowledge of the absolute measurement position of the specimen in relation to the interferometer setup may improve the form measurement result. In this work, we propose a concept that uses a white light interferometer to measure the absolute distance between a transparent specimen's surface and the interferometer's objective and present preparatory data to qualify the white light interferometer for the improvement of tilted-wave interferometer measurements.

Bayesian uncertainty evaluation applied to the tilted-wave interferometer

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements, acquired with a special setup, and sophisticated mathematical evaluation procedures. To determine the form of the surface under test, a computational model is required that closely mimics the measurement process of the physical measurement instruments. The parameters of the computational model, comprising the surface under test sought, are then tuned by solving an inverse problem. Due to this embedded structure of the real experiment and computational model and the overall complexity, a thorough uncertainty evaluation is challenging. In this work, a Bayesian approach is proposed to tackle the inverse problem, based on a statistical model derived from the computational model of the tilted-wave interferometer. Such a procedure naturally allows for uncertainty quantification to be made. We present an approximate inference scheme to efficiently sample quantities of the posterior using Monte Carlo sampling involving the statistical model. In particular, the methodology derived is applied to the tilted-wave interferometer to obtain an estimate and corresponding uncertainty of the pixel-by-pixel form of the surface under test for two typical surfaces taking into account a number of key influencing factors. A statistical analysis using experimental design is employed to identify main influencing factors and a subsequent analysis confirms the efficacy of the method derived.

Complex illumination system for fast interferometric measurements

Freeform metrology is an enabling technology for today’s research and advanced manufacturing. The Tilted Wave Interferometer is a full field measurement system for fast and flexible measurements. It is based on an off-axis illumination scheme based on a microlens array. In this contribution, we present a novel illumination system for the tilted wave interferometer, that allows to reduce the measurement time by a factor of four using parallelization based on wavelength multiplexing. Here we present a design solution that utilizes the flexibility of 3D-printing. The microlenses are realized as multi-order diffractive optical elements, providing a high efficiency compared to colorfilter based realizations. To boost the light efficiency of the novel illumination system further, a field lens functionality is added to the system by adding individual micro-prisms to each microlens. The system is manufactured by the use of grayscale two-photon polymerisation.

Experimental Design for Virtual Experiments in Tilted-Wave Interferometry

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.

Development of a metrological reference system for the form measurement of aspheres and freeform surfaces based on a tilted-wave interferometer

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.

Investigation of dynamic influences in tilted-wave interferometry

Aspherical and freeform lenses allow for compact optical systems and have therefore gained high interest in optics. The interferometric measurement of these forms is a challenge, for which the tilted-wave interferometer (TWI) has been developed. To evaluate the measurement uncertainty of the TWI, both the static and the dynamic influence parameters have to be investigated. In this work, we focus on the dynamic influences on the measurement data of the interferometer. To this end, the individual influences as well as their point of insertion into the process chain are identified. Then the measurement of the interferogram data is modelled as a Monte Carlo simulation. The propagation of different influences through the data process chain to the optical path length differences (OPDs) is also simulated, and the resulting variation of the OPDs is estimated. Furthermore, the variation of the OPDs resulting from measured interferogram data is investigated for comparison. The analysis and quantification of variation of the OPDs along with its contributing influence sources are important steps on the way towards a full uncertainty estimation of optical form measurement with the TWI.

Deep learning for tilted-wave interferometry

Abstract The tilted-wave interferometer is an interferometrical measurement system for the accurate optical form measurement of optical aspheres and freeform surfaces. Its evaluation procedure comprises a high-dimensional inverse problem to reconstruct the form of the surface under test from measured data. Recent work has used a deep learning hybrid approach to solve the inverse problem successfully in a simulation environment. A quantification of the model uncertainty was incorporated using ensemble techniques. In this paper, we expand the application of the deep learning approach from simulations to measured data and show that it produces results similar to those of a state-of-the-art method in a real-world environment.

Simultaneous removal of nonrotationally symmetric errors in tilted wave interferometry

The tilted wave interferometer has been developed as a fast and accurate instrument for the measurement of aspheric and freeform surfaces. We present a method for increasing its robustness and flexibility. Tilted wave interferometry crucially depends on accurate calibration and any changes to a calibrated setup require, in general, a recalibration. Therefore, we propose a method for simultaneous topography reconstruction and elimination of errors arising from such changes. An approach to identify trends in systematic errors for the complex non-null setup with a large number of blackbox model parameters is worked out. The procedure allows deriving an error removal scheme for nonrotationally symmetric components based on measurements in different rotational positions. The feasibility and benefit of the error elimination method are shown both by simulation methods and dedicated experiments. A significant reduction of systematic errors even in a miscalibrated state is achieved. Hence, recalibrations are avoided and measurement time and flexibility are improved.

Traceability of form measurements of freeform surfaces: metrological reference surfaces

Due to the complexity of measurement systems for asphere and freeform surfaces, well-known artifacts are required to characterize the accuracy of the results of their form measurements. We present advancements in manufacturing and characterization of metrological multispherical freeform artifacts. The strong cooperation between the manufacturing and measurement units of Physikalisch–Technische Bundesanstalt (PTB) allows the form of the artifacts to be manufactured very accurately and the root-mean-square deviation from the desired design form to be improved by a factor of >20 compared to former results (e.g., from a value >500 nm to about 20 nm). Furthermore, a nickel/phosphorous coating is added to the copper surface, resulting in greater hardness and allowing the coated surface to be used as a reference for low-force tactile measurement systems. Four Gaussian peak fiducial marker structures are added to the design to improve the evaluation of comparison measurements. In addition to characterizing the radii in the spherical segments using PTB’s radius measurement bench, we also characterize the sphericity of the spherical segments using a Fizeau interferometer. We show form measurement results for a full-field measuring tilted-wave interferometer and compare the form measurement results in the spherical segments with measurement results obtained with the Fizeau interferometer.

Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm

The precision of the measurements of aspheric and freeform surfaces remains the primary factor restrict their manufacture and application. One effective means of measuring such surfaces involves using reference or probe beams with angle modulation, such as tilted-wave-interferometer (TWI). It is necessary to improve the measurement efficiency by obtaining the optimum point source array for different pieces before TWI measurements. For purpose of forming a point source array based on the gradients of different surfaces under test, we established a mathematical model describing the relationship between the point source array and the test surface. However, the optimal point sources are irregularly distributed. In order to achieve a flexible point source array according to the gradient of test surface, a novel interference setup using fiber array is proposed in which every point source can be independently controlled on and off. Simulations and the actual measurement examples of two different surfaces are given in this paper to verify the mathematical model. Finally, we performed an experiment of testing an off-axis ellipsoidal surface that proved the validity of the proposed interference system.

Tilted wave interferometer measures aspheres and freeform optics

Tilted wave interferometer measures aspheres and freeform optics

Metrological multispherical freeform artifact

Precisely known artifacts are required to characterize the accuracy of asphere and freeform measuring instruments. To this end the best knowledge of the surface characteristics in conjunction with a low measurement uncertainty are necessary. Because this is a challenging task for typical freeform surfaces used in optical systems, the concept of “metrological” artifacts is introduced. We have developed a multispherical freeform artifact for performance tests of tactile touch probe and contact-free optical measuring systems. The measurement accuracy of the complete form and the deviation from calibrated spherical sections can thus be determined. The radius calibration of multiple spherical sections is performed with an extended radius measuring procedure by interferometry. Evaluated surface forms of different measuring methods and the radii determined can be compared to each other. In this study, a multispherical freeform specimen made of copper, with two differing radii, has been measured by two optical measuring methods, a full field measuring tilted-wave interferometer and a high accuracy cylinder coordinate measuring machine with an optical probe. The surface form measurements are evaluated and compared, and the radii determined are compared to the results of a radius measurement bench.

Evaluation of absolute form measurements using a tilted-wave interferometer.

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.

Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm

As is well-known, optical testing has begun to emerge as a limiting factor in the application of freeform surfaces. In all kinds of published freeform optical metrology, the tilted-wave-interferometer (TWI) is the precise and flexible method for testing a freeform surface as it can compensate the local surface’s deviation from its best fit sphere by using a set of tilted waves. In the process of measurement with TWI, accurate assessment of the test surface error from the fringes plays a key role. We present a method for evaluation and characterization of surface aberrations in TWI by combining computer-generated wave technology and a retrace errors elimination algorithm. The feasibility of the method is proved by the simulation and experimental results.

Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces.

The measurement of aspheric and free-form surfaces in a non-null test configuration has the advantage that no compensation optics is required. However, if a surface is measured in a non-null test configuration, retrace errors are introduced to the measurement. We describe a method to calibrate the test space of an interferometer, enabling to compensate retrace errors. The method is effective even for strong deviations from null test configuration up to several 100 waves, enabling the fast and flexible measurement of aspheres and free-form surfaces. In this paper we present the application of the method to the calibration of the Tilted Wave Interferometer. Furthermore, the method can be generalized to the calibration of other setups.

Fast and Flexible Non-Null Testing of Aspheres and Free-Form Surfaces with the Tilted-Wave-Interferometer

The Tilted-Wave-Interferometer (TWI) is a non-null, full-field interferometric measuring technique for aspheric and free-form surfaces with a new degree of flexibility. The interferometer uses a set of tilted wavefronts to locally compensate the deviation of the surface under test from its spherical form. Since it is a non-null technique, there is no need for costly compensation optics. The measurement data acquisition is highly parallelized, leading to a short measurement time in the region of few seconds, by simultaneously achieving a high lateral resolution. The unique combination of these characteristics makes the TWI a perfect candidate for the integration into the process chain of aspheric and free-form surface manufacturing.

Flexible and Rapid Measurement

AbstractOnly what you can measure, you can produce. This often quoted statement aptly describes the area of aspheric lenses production in its interplay of progress in fabrication technology and metrology. Nowadays not only the pure feasibility is in focus, but also economical factors: higher flexibility, high measurement speed and high lateral resolution, ideally all combined with a low measurement uncertainty. In this context, we discuss the recently proposed tilted wave interferometer (TWI, Fig. 1), an approach to interferometrically measure steep aspheres and freeforms within a few seconds.