Goran Baer

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.

Automated surface positioning for a non-null test interferometer

An automatic method for the positioning of the test surface in a non-null interferometer is presented. A major task in the interferometric testing of surfaces is to avoid the introduction of surface aberrations due to an incorrect placement of the test object in the interferometer cavity. In the case of plane and spherical surfaces, adjustment errors can usually be distinguished from surface figure errors and therefore removed, but in the case of aspherical surfaces this task becomes nontrivial. In this work, the effect on the measured phase due to lateral and axial displacements of the aspherical surface is calculated, and an adjustment method for the positioning of the surface at a predefined measurement location presented. Experimental results showing the feasibility of the proposed procedure are shown.

Measurement of aspheres and free-form surfaces in a non-null test interferometer: reconstruction of high-frequency errors

The tilted wave interferometer is a non-null test interferometer for the measurement of aspheres and freeform surfaces without dedicated null-optics that uses an array of tilted waves to locally compensate the deviation of the surface from the spherical form. The concept allows for short measurement times of only a few minutes and high lateral resolutions at the same time. The calculation of the surface error is performed by perturbation of a polynomial representation of the surface. Since we are also interested in higher frequency errors of the surface which cannot be described by a polynomial of finite order these errors are evaluated in an additional step. Since every wavefront only covers a small area of the surface the challenge here is to reconstruct the surface from the information that is distributed over the different patches. We will present the method that was developed for the reconstruction of these high frequency errors as well as measurement results of aspheres and freeform surfaces without rotational symmetry that were obtained by this method.

Measuring aspheres quickly: tilted wave interferometry

Abstract. Functional surfaces with a rising degree of complexity are becoming increasingly important for modern industrial products. It is common knowledge that one cannot produce surfaces better than it is possible to measure them. Consequently, the demand for their effective and precise measurement has increased to the same extent as their production capabilities have grown. Important classes of optical functional surfaces are aspheres and freeforms. Both types of surfaces have become essential parts of modern optical systems such as laser focusing heads, sensors, telescopes, glasses, head-mounted displays, cameras, lithography steppers, and pickup heads. For all of them, the systematic quality control in the process of their fabrication is essential. We review the challenges of asphere and freeform testing and how available metrology systems cope with it. A special focus is on tilted wave interferometry and how it compares to other methods.

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.

Sensitivity analysis of tilted-wave interferometer asphere measurements using virtual experiments

The tilted-wave interferometer (TWI) was recently developed by the University of Stuttgart for the high-accuracy measurement of aspheres and freeform surfaces. The system works in a non-null measurement fashion and si multaneously uses several test beams with different tilts. Reconstruction of the specimen under test from TWI measurements is challenging and in order to correctly separate the real surface topography from systematic aberrations, the employed interferometer needs to be characterized. This characterization, as well as the recon struction of the specimen from TWI measurements, requires sophisticated data analysis procedures including ray tracing and the solution of an inverse problem. A simulation environment was developed at the Physikalisch-Technische Bundesanstalt (PTB) in order to inves tigate the accuracy and stability of TWI systems, and to explore possibilities and limitations of this promising measurement technique. Virtual experiments were carried out to quantify the sensitivity of the results with respect to the assumed linearity in the reconstruction procedure, positioning errors, and measurement noise. Our first results suggest that the mathematical TWI reconstruction technique basically allows highly accurate measurements with uncertainties down to a few nanometers, provided that calibration errors of the optical sys tems are kept small. The stability of the results and their accuracy can, however, depend significantly on the particular surface of the specimen and on the choice of experimental settings.

Measurement of Aspheres and Free-Form Surfaces with the Tilted-Wave-Interferometer

In the area of high performance optics aspherical surfaces have become the solution of choice over the past years [1] [2]. The advantage of aspherical, compared to spherical elements, is the highly increased degree of freedom for the optics design. This allows better correction of aberrations, by simultaneously reducing the number of elements needed to fulfill a given design target, enabling the construction of more compact optical systems, with higher optical performance at the same time. As a result of these convincing advantages aspherical optics are widely used in state of the art optical systems, starting from mass products like imaging systems for micro cameras in smartphones, reaching to high end optical systems used in lithography or space applications. Even more degrees of freedom in the design can be reached, if the rotational symmetry of the aspheric surface is broken. Such free-form surfaces that do not have to show any symmetry at all can be used to further improve the performance of an optical system. One possibility is the construction of systems where the elements are no longer arranged along a straight line, but where the optical axis is folded. By taking advantage of this design option it is possible to develop very compact systems, which also are less sensitive to mechanical and thermal influences. Another advantage of off-axis systems that can be realized with free-form elements is the avoidance of reflexes that often occur at the center of the lens in a classical system. This is especially important for applications with coherent sources. Further, certain wavelengths demand the usage of mirror optics instead of lenses, if there aren’t any optical refractive materials with tolerable absorption available. To avoid central obscurations, here again the easiest way is to use free-from mirrors. One example for this kind of optical systems is the EUV lithography that will be used in the next generation of semiconductor fabrication.

Advanced studies on the measurement of aspheres and freeform surfaces with the tilted-wave interferometer

This work presents further insight into the working principles of the tilted-wave interferometer regarding the system characterization for the measurement of aspheres and freeform surfaces. A method to characterize an optical system for the measurement of aspheric and freeform surfaces without dedicated null optics in a non-null measurement fashion is presented. Even though non-null test arrangements allow for increased measurement flexibility the evaluation of the measurement results becomes much more complex than in the null test variant. The problem becomes then the identification of small phase deviations caused by the test surface in the presence of systematic system aberrations several orders of magnitude larger. The characterization of the interferometer aberrations plays hereby a central role in the measurement process for an accurate assessment of the test surface. In this work, a novel method for the characterization of the interferometer setup is described and measurement results in a non-null test configuration for an aspheric element with several hundred waves departure from its best-fit sphere presented.

Model-based calibration of an interferometric setup with a diffractive zoom-lens

The fabrication of aspheres and freeform surfaces requires a high-precision shape measurement of these elements. In terms of accuracy, interferometric systems provide the best performance for specular surfaces. To test aspherical lenses, it is necessary to adapt or partially adapt the test wavefront to the surface under test. Recently, we have proposed an interferometric setup with a diffractive zoom-lens that includes two computer generated holograms for this purpose.1 Their surface phases are a combination of a cubic function for the adaption of aberrations and correction terms necessary to compensate substrate-induced errors. With this system based on Alvarez design a variable defocus and astigmatism controlled by a lateral shift of the second element is achieved. One of the main challenges is the calibration of the system. We use a black-box model2 recently introduced for a non-null test interferometer, the so called tilted wave interferometer3 (TWI). With it, the calibration data are calculated by solving an inverse problem. The system is divided in the two parts of illumination and imaging optics. By the solution of an inverse problem, we get a set of data, which describes separately the wavefronts of the illumination and imaging optics. The main difference to the TWI is the flexible diffractive element, which can be used in continuous positions. To combine the calibration data of a couple of positions with the exact placement, we designed alignment structures on the hologram. We will show the general functionality of this calibration and first simulation results.

The tilted-wave-interferometer: freeform surface reconstruction in a non-null setup

The measurement of aspheres and freeforms poses several challenges to interferometric and other optical testing methods which are well established for spherical surfaces. Accuracy, measurement time and flexibility are requirements encountered in a production environment. The approach of tilted-wave-interferometry is to illuminate the specimen with a whole ensemble of wavefronts. Each of these wavefronts has a different amount of tilt with respect to the optical axis. The surface under test is completely covered by interferogram patches where rays from one source hit the surface such that resolvable fringe densities result. Yet, one still deviates from the null setup which requires that the interferometer is calibrated precisely. This is obtained by recording interferograms of a known reference object placed in the test space. The aberrations of the interferometer are described within a black box model. A sophisticated set of algorithms is used to reconstruct these coefficients with high accuracy. The non-null configuration prohibits a direct evaluation of the measurement from the interferograms. Instead, the surface is reconstructed by the solution of an inverse problem. A second step gives access to the remaining high-frequency errors. The key ideas and implementations in the process of measurement and calibration are explained and the differences to other common concepts in optical testing are elaborated. As an example, results of a freeform measurement, including both form and high-frequent deviations from design, are discussed.