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Some widely used optical measurement systems require a scan in wavelength or in one spatial dimension to measure the topography in all three dimensions. Novel hyperspectral sensors based on an extended Bayer pattern have a high potential to solve this issue as they can measure three dimensions in a single shot. This paper presents a detailed examination of a hyperspectral sensor including a description of the measurement setup. The evaluated sensor (Ximea MQ022HG-IM-SM5X5-NIR) offers 25 channels based on Fabry–Perot filters. The setup illuminates the sensor with discrete wavelengths under a specified angle of incidence. This allows characterization of the spatial and angular response of every channel of each macropixel of the tested sensor on the illumination. The results of the characterization form the basis for a spectral reconstruction of the signal, which is essential to obtain an accurate spectral image. It turned out that irregularities of the signal response for the individual filters are present across the whole sensor.

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.

We present an improved iteration algorithm for speckle-correlation imaging through scattering media. We employ an approximate solution obtained from a bispectrum-analysis method as the initial condition of the iterative process. This method avoids several different runs performed with different random initial conditions in the traditional iteration algorithm and reduces the execution time in comparison with the conventional bispectrum-analysis method. Therefore, we obtain a balance between image quality and reconstruction speed. The feasibility of the proposed method is proved by the experimental results.

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.

We present the design of a compact zoom-lens for the realization of a space-limited interferometer objective with a large range of possible sphere radii. Based on the idea of Alvarez to change the lens-power by shifting two glass plates with cubic surface functions along their lateral axis and the implementation with diffractive optical elements by Lohmann, we realized a focal shift between 200 and 360 mm with two elements in a single shift setup. Additionally, astigmatism can be compensated by moving the plates in the related orthogonal direction as required for the measurement of anamorphic, aspheric, or freeform lenses.

An absolute testing method for cylindrical surfaces is presented in a null test setup with a computer-generated hologram. The absolute test exploits the symmetry of cylinders, which allows us to introduce a certain shift of the test surface both parallel to and rotated about the centerline while the null test condition is still maintained. With two shifts of the cylindrical surface, four measurements belonging to two groups in conjugate positions can be accomplished to obtain the absolute differential map with the interferometer and null optics errors removed. The absolute surface can be obtained by wavefront reconstruction from local differential data. A simulation of the method is presented to estimate the error propagation. Experimental absolute test results of a concave cylindrical surface with 100-mm radius are given. The measured profiles are compared with those obtained from a commercial profiler, showing a difference of less than 15 nm (root-mean-square).

Different methods for the measurement of in-plane and out-of-plane nanodisplacements of microscopic samples are discussed and compared. It is shown that correlation methods are suited for in-plane displacement measurements and can achieve accuracies of a few nanometers. The method based on vortices tracking can be used for in-plane displacement measurements, but its accuracy is lower compared with the intensity correlation method. The holographic methods allow the measurement of in-plane and out-of-plane displacements at the same time; but in this case, a quite complex setup is required. A combination of correlation methods for in-plane measurement and digital holography for out-of-plane plane measurements is also discussed. The accuracy of the different methods was determined by comparison with a calibrated reference.

In order to expand the field of view in spatial light modulator-based phase contrast microscopy, we employ a two-image recording method with digital postprocessing. Using this approach, we suppress the superimposed unwanted diffraction orders on the image sensor, thus eliminating the necessity to assure a strict separation of the diffraction orders. These methods allow for a significantly smaller microscope setup and an increased effective spatial bandwidth product. We apply this method for a number of phase contrast methods to show its capabilities and limitations. Mainly, the signal-to-noise ratio is decreased by η/2. Furthermore, we employ a simple field-dependent aberration correction scheme to improve the image quality.

Ray tracing still is the workhorse in optical design and simula- tion. Its basic principle, propagating light as a set of mutually independent rays, implies a linear dependency of the computational effort and the num- ber of rays involved in the problem. At the same time, the mutual independ- ence of the light rays bears a huge potential for parallelization of the computational load. This potential has recently been recognized in the visualization community, where graphics processing unit (GPU)-acceler- ated ray tracing is used to render photorealistic images. However, preci- sion requirements in optical simulation are substantially higher than in visualization, and therefore performance results known from visualization cannot be expected to transfer to optical simulation one-to-one. In this contribution, we present an open-source implementation of a GPU-accel- erated ray tracer, based on nVidias acceleration engine OptiX, that traces in double precision and exploits the massively parallel architecture of modern graphics cards. We compare its performance to a CPU-based tracer that has been developed in parallel. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. (DOI: 10.1117/1.OE.52.5.053004) Subject terms: ray tracing; graphics processing unit-accelerated computing; optical simulation.

We present the development of a speckle interferometer based on a CO 2 laser and using a thermal infrared camera based on an uncooled microbolometer array. It is intended to be used for monitoring deformations as well as detecting flaws in aeronautical composites, with a smaller sensitivity to displacement compared to an equivalent system using visible (VIS) lasers. Moreover the long wavelength allows working with such interferometers outside the laboratory. A mobile system has been developed on the basis of previous laboratory developments. Then it is validated in a variety of industrial nondestructive testing applications in field working conditions.

Testing with lateral and radial shears is becoming standard in optical shops. Of late, holographic optical elements have proven to be easy and simple to set up, and can be used in both a collimated and convergent beam. However, there is very little work on making quantitative measurements using a symmetric radial shear. We demonstrate a simple method of obtaining both asymmetric and symmetric radial shears, and use the inherent tilt in the wavefronts to perform spatial Fourier transformation to extract phase maps. This radial shear interferometer is also suitable for static and dynamic situations.

Testing with a single holographic lens or grating in a collimated beam is normally not possible because of the inherent tilt caused in the wavefront. The tilt between the two beams in shearing creates a large number of linear fringes which overshadow the information about the wavefront. However, here, we show that we can use this tilt to make quantitative measurements which was otherwise not possible. In the novel method, we obtain shear in a relatively simple way, and at the same time we extract phase information using spatial Fourier transform technique. This technique is suitable for making quantitative measurement of wavefront and disturbances in turbulent conditions. Here, we demonstrated the real-time phase measurement capacity of the interferometer, a result of one such application is shown.

In recent years image-processing has become a central part of optical inspection and measurement systems. Typically, after measuring the given specimen by utilizing a suitable sensor, image-processing algorithms are used to detect dedicated features such as surface defects. These algorithms are usually designed, optimized, and tested by an image-processing expert according to the task specifications. A methodology (based on genetic programming) is presented to automatically generate, optimize, and test such algorithms without the necessity of an image-processing expert. We also present several examples of inspection tasks to support the concept. For efficiency, an automated multi-scale multi-sensor inspection strategy is employed.

We propose a new phase contrast filtering technique based on a combination of a focused and a defocused point-spread-function. This way, an axial shear is introduced in the imaging system. Compared to conventional differential interference contrast, an isotropic behavior is achieved. The lateral resolution is improved compared to conventional defocusing. Furthermore, the digital combination of multiple images leads to strongly enhanced visualization of small structures. We show simulated results as well as experimental results using a spatial-light modulator-based microscope.

Optical techniques are well suited for the measurement of microcomponents but give accurate results only when calibrated systems are used. We present a strategy for the calibration of setups to be used for the measurements of microsystems. We develop, at first, standard reference devices whose out-of-plane and in-plane displacements are precisely reproducible when submitted to standard loadings. These reference devices have been manufactured and tested by optical techniques and may be used for the calibration of optical measuring systems. Furthermore, a detailed discussion of the measurement uncertainty, according to the ISO's "Guide of Expression of Uncertainty in Measurement," is given.

Computer-generated holograms (CGHs) allow to transfer the high 2D-positioning accuracy of modern lithography equipment into high precision 3D-shape measurements, e.g. in CGH asphere metrology. In this contribution, we give a detailed look into the characterization of steep topologies with CGHs on the example of a 90 deg axicon surface, requiring rather high line densities in the hologram. Several aspects gain importance with increasing CGH line densities when measuring dimensional quantities such as the cone angle of the surface: misalignment of the setup, fabrication effects of the CGH rigorous effects of the high density grating, and effects due to wavelength variations of the interferometer. This paper presents the experimental approach for the cone angle measurement and a systematic analysis of its measurement uncertainty, focusing on the specifics of this null test CGH measurement.

Efficient inspection of an object for deformations and defects requires comparison with an existing real or simulated reference model. Fourier descriptor (FDs) based shape analysis is an effective method for describing a shape using the Fourier transform. This shape representation can be easily modified to achieve shift, rotation, and scale invariance. We propose two new methods, namely the ring sampling and the spiral sampling methods, which enable the usage of FDs in order to detect defects on micro-optical elements like microlens arrays. As an example the measurement data obtained from a confocal microscope has been used to show the effectiveness of the two approaches for both indicating and detecting surface defects. Microlens arrays with different types of defects including global (deformed lenses causing aberrations) and local defects (scratches) were simulated using a confocal microscopy simulation tool to test the reliability of the methods. A classifier differentiates between global and local defective lenses. In order to represent other kinds of objects using FDs, the methods can be easily modified or extended. The whole process has been implemented into an automated multiscale multisensor measurement system, which focuses on fast detection of defects on micro-optical and microelectromechanical systems.

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.

We present a method for measuring all eight parameters in- cluding the signs of the Jones matrices of liquid-crystal displays. The method can be applied to measure the Jones matrices for all address- able gray levels thus delivering the specifications needed for calculating characteristic curves for arbitrary input and output polarizations. Unlike other approaches, we do not rely on a physical model of the LCD. Thus, it is possible to measure the Jones matrices of a more complex optical system in one step e.g., when a reflective LCD is used in combination with a beamsplitter. Though the method presented is, in principle, appli- cable for transmissive and reflective LCDs, calculations and experiments are only shown using the example of a reflective liquid-crystal-on-silicon

With surface-relief structures, optical functions that are required for radiation power management such as antireflection, light trapping, or light distribution and redirection can be obtained for new applications in solar energy systems and in displays. There, structures with submicrometer features must be distributed over large areas homogeneously. We address the design and the whole experimental process chain from the microstructure origination on large areas to the replication and the system integration in the specific application. Topics are antireflective surfaces for solar systems and displays, light trapping in polymer solar cells, sun protection systems for facades, and diffusers for projection displays and in glazing. For the microstructure origination we investigate the suitability of holographic recording in photoresist using a large-scale interferometer. We use an argon ion laser as a coherent light source at a wavelength of 364 nm. Periodic and stochastic interference patterns are recorded in positive photoresist with the interferometer setup. In the case of periodic structures, grating periods between 200 nm and 20 µm are realized. By carefully modeling the resulting resist profiles it is possible to originate even prismatic surface-relief profiles. Structures with good homogeneity are originated on areas of up to 4800 cm2 by optimizing the interferometer setup and the photoresist processing.

Reliable real-time surface inspection of extended surfaces with high resolution is needed in several industrial applications. With respect to an efficient application to extended technical components such as aircraft or automotive parts, the inspection system has to perform a robust measurement with a ratio between depth resolution and lateral extension of less than 10–6. This ratio is at least 1 order beyond the solutions that are offered by existing technologies. The concept of scaled topometry consists of a systematic combination of different optical measurement techniques with overlapping ranges of resolution systematically to receive characteristic surface information with the required accuracy. In such a surface inspection system, an active algorithm combines measurements on several scales of resolution and distinguishes between local fault-indicating structures with different extensions and global geometric properties. The first part of this active algorithm finds indications of critical surface areas in the data of every measurement and separates them into different categories. The second part analyzes the detected structures in the data with respect to their resolution, and decides whether a further local measurement with a higher resolution has to be performed. The third part positions the sensors and starts the refined measurements. The fourth part finally integrates the measured local dataset into the overall data mesh. We have constructed a laboratory setup capable of measuring surfaces with extensions up to 1500×1000×500 mm3 (in x, y, and z directions, respectively). Using this measurement system we are able to separate the fault-indicating structures on the surface from the global shape, and to classify the detected structures according to their extensions and characteristic shapes simultaneously. The level of fault-detection probability is applicable by input parameter control.

Shearography is an approved and powerful tool for the nondestructive investigation of technical components with respect to material faults and structural imperfections. An application field of high interest is the inspection of aircraft and automotive components. Both material and structural imperfections can be recognized as typical fringe patterns in the shearogram. However, a reliable fault detection requires a detectable fault response to the applied load at the surface and a sufficient quality of the fringe pattern as well. Therefore, the testing of large-scale technical objects having in general noncooperative surfaces needs a careful design of the following system components: the shearography sensor, the illumination unit, the loading system, and the evaluation software. We report a mobile shearography system that was especially designed for the inspection of aircraft and automotive parts under industrial boundary conditions. Several examples illustrate the efficiency of the system.

Holographic interferometry makes it possible to measure high-precision displacement data in the range of the wavelength of the laser light used. However, for a precise determination of 3-D displacement vectors of complex objects the 3-D shape of the surface is required. Modern optical shape measurement technologies enable a very effective approach to finding the Cartesian coordinates of complex surfaces. These data are used to calculate the spatially variable sensitivity vectors for the displacement measurement. The shape data are measured with white-light fringe projection using a multiwavelength technique to acquire absolute phase values. To make the shape data available for 3-D displacement measurement they have to be transferred into a reference coordinate system of the interferometric setup, where the deformation of the object caused by operational load is measured precisely. For this purpose a registration procedure is applied. For engineering applications it is useful to make the data available for computer-aided engineering systems. The object surface has to be approximated analytically from the measured point cloud to generate a surface mesh. The displacement vectors can be assigned to the nodes of this surface mesh for visualization of the deformation of the object under test. They also can be compared with the results of finite-element calculations or can be used as boundary conditions for further numerical investigations. The described procedure is demonstrated on an automotive component. Thus more accurate and effective measurement techniques make it possible to bring experimental and numerical displacement analysis closer together.

In an interferogram, the variation of intensity background and fringe amplitude displaces the fringe centerlines and gives rise to some systematic phase error if fringe tracking techniques are used. The behavior of this systematic phase error is analyzed in detail. This phase error oscillates from zero in the middle between bright and dark fringes to its extrema in both bright and dark fringe centerlines, but it is not accumulated over the whole image. A 2-D envelope transform with correct envelopes is proposed to remove the systematic phase error. To illustrate, some simulated fringe patterns are processed and analyzed.