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.
Two techniques for the measurement of aspheres as well as freeforms are presented. The first method, the tilted wave interferometer, is a full aperture interferometric measurement method without any moving parts during the measurement. The second method applies an optical single point sensor in conjunction with two translational and one rotational axes. Both techniques are compared by measuring a selected asphere and a special freeform surface. Differences between both measurement principles are discussed.
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 techniques to determine the aberration of an optical system, by obtaining through-focus intensity
images that are produced when the object is a point source at infinity, are shown. The analysis of the aberrations
is made using the extended version of the Nijboer-Zernike diffraction theory. This theory provides a semi
analytical solution of the Debye diffraction integral and thus a direct relation between the intensity distribution
of the field at the focal region and the exit pupil of the optical system.
Interferometry is often used to measure the form of optical surfaces. While interferometry is generally expected to give
high accuracy results, a variety of error influences exist which have to be considered. Some typical error influences
which are often underestimated will be discussed in this paper. In flatness metrology, the main error influences are
imperfections of the reference surfaces, specimen support or cavity influences. For non-flat surfaces like aspheres or free
form surfaces, in particular the influence of errors from the determination of the lateral coordinates becomes very
important. Sub-aperture interferometry copes with stitching errors, which can be reduced by Traceable Multi Sensor subaperture
methods where the influence of the imaging system of the interferometer may dominate the error budget. This
can be similar for other types of interferometers.
In dimensional nano- and micrometrology, single sensors are often combined into an array of sensors to enable faster
measurements by utilizing parallel data acquisition. If combined with appropriate scanning techniques, the use of sensor
arrays additionally facilitates the estimation and correction of systematic sensor errors and, thus, enables more accurate
measurements. To exploit these options, the arrays have to be aligned carefully with respect to the scanning direction,
and, in addition, the lateral distances between the sensors have to be determined with sufficient accuracy.
This presentation describes a method to align an optical distance sensor array parallel to the direction of a linear translation
stage, which is used to scan the specimen under test, and it describes a method to evaluate and determine the sensor
distances with high accuracy.
Alignment is a multi step procedure: The first step is to orientate a step edge profile perpendicular to the scanning direction
of the sensor using an M-array and an auxiliary CCD camera. In a second step, the line sensor array is scanned
across the edge using different rotation angles of the sensor. The positions where the different sensors cross the edge are
evaluated to obtain the sensor orientation relative to the scanning direction, the distances between the sensors, and their
We will show experimental data obtained with an optical line sensor array of three single sensors. The measurements
will be compared to simulated data carried out with a virtual experiment programmed at PTB. Relevant error sources are
assessed and the limitation of the method is discussed.
The Nanometer Comparator is the PTB reference length measuring machine for high precision calibrations of line scales
and encoder systems. Up to now the Nanometer Comparator allows to measure the position of line structures in one
dimension only. For high precision characterisations of masks, scales and incremental encoders, the measurement of the
straightness of graduations is a requirement from emerging lithography techniques. Therefore the Nanometer
Comparator will be equipped with an additional short range measurement system in the Y-direction, realized as a single
path plane mirror interferometer and supposed to achieve sub-nm uncertainties.
To compensate the topography of the Y-mirror, the Traceable Multi Sensor (TMS) method will be implemented to
achieve a reference-free straightness measurement. Virtual experiments are used to estimate the lower accuracy limit and
to determine the sensitive parameters. The virtual experiments contain the influence of the positioning devices,
interferometer errors as well as non-perfect adjustment and fabrication of the machine geometry. The whole dynamic
measurement process of the Nanometer Comparator including its influence on the TMS analysis, e.g. non-equally spaced
measurement points, is simulated.
We will present the results of these virtual experiments as well as the most relevant error sources for straightness
measurement, incorporating the low uncertainties of the existing and planned measurement systems.
To minimize the measurement uncertainty of one dimensional length measurements on line scales, linear encoders and
interferometers the PTB in cooperation with the Dr. Johannes Heidenhain GmbH had built up a new length comparator.
The Nanometer Comparator [1,2] has already proven its performance during the measurements of incremental encoders
and line scales with an expanded measurement uncertainty of below 5 nm [3,4,5]. Due to the introduction of double and
multiple exposure in advanced lithography techniques the overlay and registration metrology requirements will
drastically increase so that reference metrology tools need to be developed further to be able to follow the resulting
decrease of the specifications. Therefore, the PTB further develops the new 1D vacuum comparator to add a
measurement possibility for straightness and to reach a measurement accuracy in the sub nanometer range . One key
development will be the interferometric measurement of all six degrees of freedom of the measurement slide of the
comparator. A new multi axis heterodyne interferometer electronics and optical interferometer designs minimizing
nonlinearities by spatially separated beams are under development.
The so-called Nanometer Comparator is the PTB vacuum length comparator which has been developed for high precision
length metrology on measurement objects with micro- and nanostructured graduations, like e.g. line scales, incremental
encoders or photomasks. The Nanometer Comparator allows to achieve smallest measurement uncertainties in the
nm-range by use of vacuum laser interferometry for the displacement measurement. We will report on the achieved
measurement performance of this high precision vacuum length comparator and the already started developments to substantially
enhance its measurement capabilities by additional straightness measurement capabilities. The enhanced
Nanometer Comparator will provide traceability for photomask pattern placement measurements in industry, also facing
the challenges due to the increased requirements on registration metrology as set by the introduction of new lithography
techniques like double patterning methods.
The Traceable Multi Sensor (TMS) system is a scanning system for the measurement of the topography of large
optical surfaces. The system uses a compact interferometer with an aperture of some millimetres to realize
multiple distance sensors and an autocollimator for the angle measurement. In contrast to common stitching
techniques, the systematic sensor errors are calculated in addition to the entire topography by the TMS algorithm.
Additionally, piston and tilt at each position of the interferometer are determined by the algorithm. An essential
requirement for the algorithm is the exact lateral positioning of the sensor at given locations.
The goal of this paper is to investigate the influence of a class of error sources on the resulting topography
estimation using computer simulations. The errors of this class result in inexact measurement positions of the
distance sensors. Especially the lateral positioning errors of the scanning stage lead to increasing errors for short
wavelengths. For topography wavelengths below 3mm with an amplitude of 100nm the resulting topography
error increases to 3nm and more. For longer wavelengths the positioning errors are no longer the dominant
error source and the root mean square error of the resulting topography is approximately 1 nm for positioning
errors with a standard deviation of 5 &mgr;m. The pixel distance error and distortion of the interferometer strongly
influence the topography measurement of specimens with large deviations from a plane. The simulations show
that for a topography with a peak to valley of 50 &mgr;m the root mean square error of the reconstructed topography
is below 10 nm.
Furthermore, a possibility to compensate the lateral positioning error of the scanning stage is presented which
makes the TMS method nearly independent of positioning errors of the scanning stage. As a consequence, it
is possible to use systems of non equidistant distance sensors whose lateral distances are independent of the
The following article describes a stereophotogrammetry based technique for 3D measurement of human faces. The method was developed for function orientated diagnostics and therapy in dentistry to provide prognoses for jaw-growth or surgical procedures. The main aim of our activities was to realize both -- a rapid measurement and a dense point cloud.
The setup consists of two digital cameras in a convergent arrangement and a digital projector. During the measurement a rapid sequence of about 20 statistical generated patterns were projected onto the face and synchronously captured by the two cameras. Therefore, every single pixel of the two cameras is encoded by a characteristically stack of intensity values. To find corresponding points into the image sequences a correlation technique is used. At least, the 3D
reconstruction is done by triangulation.
The advantages of the shown method are the possible short measurement time (< 1 second) and - in comparison to gray code and phase shift techniques - the low quality requirements of the projection unit. At present the reached accuracy is +/- 0.1mm (rms), which is sufficient for medical applications. But the demonstrated method is not restricted to evaluate the shape of human faces. Also technical objects could be measured.
At present several methods are adapted for the optical characterization of 3D surface profiles and forms, which are based on fringe projection, moire techniques, gray-code projection or photogrammetry [1-5]. According to principle and application the methods differ in accuracy of measurement as well as computation time or their technical complexity.
Photogrammetry is a well-adapted method for the measurement of 3D objects. The basic idea of the method is to get the whole 3D matrix of real objects by capturing a number of 2D images. In this work we show a possibility for a rapid measurement (< 1 second) of the shape of a human face for medical applications (e. g. jaw-measurement).
The surface structure of the human face is too homogenous to find homologous points by an ordinary illumination; therefore about 20 special statistical patterns are projected on the face and taken by cameras of a convergent stereo system. At present a digital projector is used but it is also possible to generate the statistical patterns by a classical one.
To find the corresponding points in the pictures we use an enhanced correlation technique, which takes into account the characteristic intensity sequence of every single sensor element - unlike other correlation techniques, which avail a pixel area as a template. The influence of distortion - caused by the surface profile - is kept to a minimum. Therefore at higher profile gradients a denser point cloud is generated.
At present the reachable accuracy is +/- 0.1mm (rms), which is sufficient for medical and other applications. But the demonstrated method is not restricted to evaluate the shape of human faces. Also technical objects could be measured.