Johannes Schindler

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.

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.

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.

Resolving the depth of fluorescent light by structured illumination and shearing interferometry

A method for the depth-sensitive detection of fluorescent light is presented. It relies on a structured illumination restricting the excitation volume and on an interferometric detection of the wave front curvature. The illumination with two intersecting beams of a white-light laser separated in a Sagnac interferometer coupled to the microscope provides a coarse confinement in lateral and axial direction. The depth reconstruction is carried out by evaluating shearing interferograms produced with a Michelson interferometer. This setup can also be used with spatially and temporally incoherent light as emitted by fluorophores. A simulation workflow of the method was developed using a combination of a solution of Maxwells equations with the Monte Carlo method. These simulations showed the principal feasibility of the method. The method is validated by measurements at reference samples with characterized material properties, locations and sizes of fluorescent regions. It is demonstrated that sufficient signal quality can be obtained for materials with scattering properties comparable to dental enamel while maintaining moderate illumination powers in the milliwatt range. The depth reconstruction is demonstrated for a range of distances and penetration depths of several hundred micrometers.

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.

Comparison of alignment errors in asphere metrology between an interferometric null-test measurement and a non-null measurement with the tilted-wave-interferometer

In interferometric testing of surfaces a major task is to avoid the introduction of aberrations due to misalignment of the surface under test (SUT). An automated method for the positioning of aspheric and free-form surfaces in a non-null test interferometer, as well as a method for the distinction between alignment introduced aberrations and surface errors is presented. A combination of both methods allows for a fully automated alignment with low accuracy requirements concerning the positioning stage. In this work the method for the alignment as well as the alignment error correction is presented and the misalignment introduced measurement uncertainties are estimated. Simulation results as well as experimental results showing the feasibility of the method are presented.

Shaping the light for the investigation of depth-extended scattering media

Scattering media are an ongoing challenge for all kind of imaging technologies including coherent and incoherent principles. Inspired by new approaches of computational imaging and supported by the availability of powerful computers, spatial light modulators, light sources and detectors, a variety of new methods ranging from holography to time-of-flight imaging, phase conjugation, phase recovery using iterative algorithms and correlation techniques have been introduced and applied to different types of objects. However, considering the obvious progress in this field, several problems are still matter of investigation and their solution could open new doors for the inspection and application of scattering media as well. In particular, these open questions include the possibility of extending the 2d-approach to the inspection of depth-extended objects, the direct use of a scattering media as a simple tool for imaging of complex objects and the improvement of coherent inspection techniques for the dimensional characterization of incoherently radiating spots embedded in scattering media. In this paper we show our recent findings in coping with these challenges. First we describe how to explore depth-extended objects by means of a scattering media. Afterwards, we extend this approach by implementing a new type of microscope making use of a simple scatter plate as a kind of flat and unconventional imaging lens. Finally, we introduce our shearing interferometer in combination with structured illumination for retrieving the axial position of fluorescent light emitting spots embedded in scattering media.

Increasing the accuracy of tilted-wave-interferometry by elimination of systematic errors

This work investigates methods to eliminate calibration errors as one of the limiting factors to reduce measurement uncertainty in Tilted-Wave-Interferometry. The correlations between errors in the model parameters and in the measurement result are investigated, taking into account the symmetry of the surface under test. Two schemes for the elimination of such errors are introduced: Rotations around the z-axis allow the removal on non-rotationally symmetric error components. Measurements in lateral shears allow the elimination of calibration errors with higher spatial frequency. The corresponding algorithms and underlying models are explained for both approaches and examples for their application are presented.