Extended-Aperture Shape Measurements Using Spatially Partially Coherent Illumination (ExASPICE).

We have recently demonstrated that the 3D shape of micro-parts can be measured using LED illumination based on speckle contrast evaluation in the recently developed SPICE profilometry (shape measurements based on imaging with spatially partially coherent illumination). The main advantage of SPICE is its improved robustness and measurement speed compared to confocal or white light interferometry. The limited spatial coherence of the LED illumination is used for depth discrimination. An electrically tunable lens in a 4f-configuration is used for fast depth scanning without mechanically moving parts. The approach is efficient, takes less than a second to capture required images, is eye-safe and offers a depth of focus of a few millimeters. However, SPICE's main limitation is its assumption of a small illumination aperture. Such a small illumination aperture affects the axial scan resolution, which dominates the measurement uncertainty. In this paper, we propose a novel method to overcome the aperture angle limitation of SPICE by illuminating the object from different directions with several independent LED sources. This approach reduces the full width at half maximum of the contrast envelope to one-eighth, resulting in a twofold improvement in measurement accuracy. As a proof of concept, shape measurements of various metal objects are presented.

Flash-profilometry: fullfield lensless acquisition of spectral holograms for coherence scanning profilometry.

Flash-profilometry is a novel measurement approach based on the fullfield lensless acquisition of spectral holograms. It is based on spectral sampling of the mutual coherence function and the subsequent calculation of its propagation along the optical axis several times the depth-of-field. Numerical propagation of the entire coherence function, rather than solely the complex amplitude, allows to digitally reproduce a complete scanning white-light interferometric (WLI) measurement. Hence, the corresponding 3D surface profiling system presented here achieves precision in the low nanometer range along an axial measurement range of several hundred micrometers. Due to the lensless setup, it is compact, immune against dispersion effects and lightweight. Additionally, because of the spectral sampling approach, it is faster than conventional coherence scanning WLI and robust against mechanical distortions, such as vibrations and rigid body movements. Flash-profilometry is therefore suitable for a wide range of applications, such as surface metrology, optical inspection, and material science and appears to be particularly suitable for a direct integration into production environments.

Functional pixels: a pathway towards true holographic displays using today's display technology.

Today's 3D dynamic holographic display techniques suffer from severe limitations due to an available number of pixels that is several orders of magnitude lower than required by conventional approaches. We introduce a solution to this problem by introducing the concept of functional pixels. This concept is based on pixels that individually spatially modulate the amplitude and phase of incident light with a polynomial function, rather than just a constant phase or amplitude. We show that even in the simple case of a linear modulation of the phase, the pixel count can be drastically reduced up to 3 orders of magnitude while preserving most of the image details. This scheme can be easily implemented with already existing technology, such as micro mirror arrays that provide tip, tilt and piston movement. Even though the individual pixels need to be technologically more advanced, the comparably small number of such pixels required to form a display may pave the way towards true holographic dynamic 3D displays.

Extending vision ray calibration by determination of focus distances.

The application of cameras as sensors in optical metrology techniques for three-dimensional topography measurement, such as fringe projection profilometry and deflectometry, presumes knowledge regarding the metric relationship between image space and object space. This relation is established by camera calibration and a variety of techniques are available. Vision ray calibration achieves highly precise camera calibration by employing a display as calibration target, enabling the use of active patterns in the form of series of phase-shifted sinusoidal fringes. Besides the required spatial coding of the display surface, this procedure yields additional full-field contrast information. Exploiting the relation between full-field contrast and defocus, we present an extension of vision ray calibration providing the additional information of the focus distances of the calibrated camera. In our experiments we achieve a reproducibility of the focus distances in the order of mm. Using a modified Laplacian based focus determination method, we confirm our focus distance results within a few mm.

Chocolate inspection by means of phase-contrast imaging using multiple-plane terahertz phase retrieval.

Terahertz (THz) radiation has shown enormous potential for non-destructive inspection in many contexts. Here, we present a method for imaging defects in chocolate bars that can be extended to many other materials. Our method requires only a continuous wave (CW) monochromatic source and detector at relatively low frequencies (280 GHz) corresponding to a relatively long wavelength of 1.1 mm. These components are used to construct a common-path configuration enabling the capturing of several images of THz radiation diffracted by the test object at different axial depths. The captured diffraction-rich images are used to constrain the associated phase retrieval problem enabling full access to the wave field, i.e., real amplitude and phase distributions. This allows full-field diffraction-limited phase-contrast imaging. Thus, we experimentally demonstrate the possibility of identifying contaminant particles with dimensions comparable to the wavelength.

Terahertz referenceless wavefront sensing by means of computational shear-interferometry.

In this contribution, we demonstrate the first referenceless measurement of a THz wavefront by means of shear-interferometry. The technique makes use of a transmissive Ronchi phase grating to generate the shear. We fabricated the grating by mechanical machining of high-density polyethylene. At the camera plane, the +1 and -1 diffraction orders are coherently superimposed, generating an interferogram. We can adjust the shear by selecting the period of the grating and the focal length of the imaging system. We can also alter the direction of the shear by rotating the grating. A gradient-based iterative algorithm is used to reconstruct the wavefront from a set of shear interferograms. The results presented in this study demonstrate the first step towards wavefield sensing in the terahertz band without using a reference wave.

Γ-profilometry: a new paradigm for precise optical metrology.

We show that the shape of a surface can be unambiguously determined from investigating the coherence function of a wave-field reflected by the surface and without the requirement of a reference wave. Spatio-temporal sampling facilitates the identification of temporal shifts of the coherence function that correspond to finite height differences of the surface. Evaluating these finite differences allows for the reconstruction of the surface using a numerical integration procedure. Spatial sampling of the coherence function is provided by a shear interferometer whereas temporal sampling is achieved by means of a Soleil-Babinet compensator. This low coherence profiling method allows to determine the shape of an object with sub-micrometer resolution and over a large unambiguity range, although it does not require any isolation against mechanical vibration. The approach therefore opens up a new avenue for precise, rugged optical metrology suitable for industrial in-line applications.

Efficient vision ray calibration of multi-camera systems.

Vision ray calibration provides imaging properties of cameras for application in optical metrology by identifying an independent vision ray for each sensor pixel. Due to this generic description of imaging properties, setups of multiple cameras can be considered as one imaging device. This enables holistic calibration of such setups with the same algorithm that is used for the calibration of a single camera. Obtaining reference points for the calculation of independent vision rays requires knowledge of the parameters of the calibration setup. This is achieved by numerical optimization which comes with high computational effort due to the large amount of calibration data. Using the collinearity of reference points corresponding to individual sensor pixels as the measure of accuracy of system parameters, we derived a cost function that does not require explicit calculation of vision rays. We analytically derived formulae for gradient and Hessian matrix of this cost function to improve computational efficiency of vision ray calibration. Fringe projection measurements using a holistically vision ray calibrated system of two cameras demonstrate the effectiveness of our approach. To the best of our knowledge, neither any explicit description of vision ray calibration calculations nor the application of vision ray calibration in holistic camera system calibration can be found in literature.

Fast 3D form measurement using a tunable lens profiler based on imaging with LED illumination.

We present a fast shape measurement of micro-parts based on depth discrimination in imaging with LED illumination. It is based on a 4f-setup with an electrically adjusted tunable lens at the common Fourier plane. Using such a configuration, the opportunity to implement a fast depth scan by means of a tunable lens without the requirement of mechanically moving parts and depth discrimination using the limited spatial coherence of LED illumination is investigated. The technique allows the use of limited spatially partially coherent illumination which can be easily adapted to the test object by selecting the geometrical parameters of the system accordingly. Using this approach, we demonstrate the approach by measuring the 3D form of a tilted optically rough surface and a cold-formed micro-cup. The approach is robust, fast since required images are captured in less than a second, and eye-safe and offers an extended depth of focus in the range of few millimetres. Using a step height standard, we determine a height error of ±1.75 µm (1σ). This value may be further decreased by lowering the spatial coherence length of the illumination or by increasing the numerical aperture of the imaging system.

Multiple Aperture Shear-Interferometry (MArS): a solution to the aperture problem for the form measurement of aspheric surfaces.

Multiple Aperture Shear-Interferometry (MArS) is a shape measurement technique that uses multi-spot illumination to overcome the problem of a limited observation aperture of conventional interferometric techniques and thus considerably simplifies the measurement of optical aspheres and freeform surfaces. Using a shear interferometry setup, MArS measures the coherence function in order to obtain wave vector distributions created from multi-spot LED illumination reflected by the specimen. Based on the wave vectors we reconstruct the surface topography of aspheric lenses using an inverse ray tracing approach and prior knowledge about the individual source locations. We present the topographic measurement of two aspheric lenses with different global curvature radii measured with the same identical reflection setup. In addition, we examine the achievable accuracy of the wave vector measurement using a single light source to find physical limits of MArS.

Fast form measurements using a digital micro-mirror device in imaging with partially coherent illumination.

We present a new technique for fast form measurement based on imaging with partially coherent illumination. It consists of a 4f-imaging system with a digital micro-mirror device (DMD) located in the Fourier plane of its two lenses. The setup benefits from spatially partially coherent illumination that allows for depth discrimination and a DMD that enables a fast depth scan. Evaluating the intensity contrast, the 3D form of an object is reconstructed. We show that the technique additionally offers extended depth of focus imaging in microscopy and short measurement times of less than a second.

Form determination of optical surfaces by measuring the spatial coherence function using shearing interferometry.

We present a new method for the form measurement of optical surfaces using the spatial coherence function, which enables a shearing interferometer in combination with an LED multispot illumination to function as a measurement device. A new evaluation approach connects the measured data with the surface form by inverse raytracing. First measurement results with the inverse evaluation procedures are shown. We present the whole measurement in combination with the evaluation procedure. In addition, the convergence and stability of the implemented optimization task is investigated.

Spatial multiplexing and autofocus in holographic contouring for inspection of micro-parts.

We present a method for fast geometrical inspection of micro deep drawing parts. It is based on single-shot two-wavelength contouring digital holographic microscopy (DHM). Within the capturing process, spatial multiplexing is utilized in order to record the two required holograms in a single-shot. For fast evaluation, determining the locations where the object is in focus and stitching all focus object's areas together is achieved digitally without the need for any external intervention using an autofocus algorithm. Thus, the limited depth of focus of the microscope objective is improved. The autofocus algorithm is based on minimizing the total variation (TV) of phase difference residuals of the two-wavelength measurements. In contrast to standard DHM, an object side telecentric microscope objective is used for overcoming the image scaling distortions caused by a conventional microscope objective. The method is used to reconstruct the 3D geometrical shape of a cold drawing micro cup. Experimental results verify the improvement of DHM's depth of focus.

Sparse light fields in coherent optical metrology [Invited].

In this publication, we demonstrate that recording the mutual intensity, instead of a wavefront, enables interferometric measurements with multiple independent light sources at the same time. This scheme can, for example, be used to overcome the problem of a limited acceptance angle of imaging systems in interferometry. We further show that, for a finite number of light sources, measuring a subspace of the mutual intensity equals the recording of the corresponding light field, which is sparse in phase space. This recording modality offers more flexibility with respect to the trade-off between angular multiplexing and spatial resolution than the state of the art, because it is not restricted by the geometric properties of a microlens array, but rather allows arbitrary sampling of the light field.

Holographic display system for dynamic synthesis of 3D light fields with increased space bandwidth product.

We present a new method for the generation of a dynamic wave field with high space bandwidth product (SBP). The dynamic wave field is generated from several wave fields diffracted by a display which comprises multiple spatial light modulators (SLMs) each having a comparably low SBP. In contrast to similar approaches in stereoscopy, we describe how the independently generated wave fields can be coherently superposed. A major benefit of the scheme is that the display system may be extended to provide an even larger display. A compact experimental configuration which is composed of four phase-only SLMs to realize the coherent combination of independent wave fields is presented. Effects of important technical parameters of the display system on the wave field generated across the observation plane are investigated. These effects include, e.g., the tilt of the individual SLM and the gap between the active areas of multiple SLMs. As an example of application, holographic reconstruction of a 3D object with parallax effects is demonstrated.

1 kHz 3.3 µm Nd:YAG KTiOAsO4 optical parametric oscillator system for laser ultrasound excitation of carbon-fiber-reinforced plastics.

We present a new laser prototype for laser ultrasonics excitation. The fundamental wavelength of a Q-switched Nd:YAG laser with a repetition rate of 1 kHz is converted to 3.3 µm with a KTiOAsO4 optical parametric oscillator. The achieved pulse energy at 3.3 µm is 1.7 mJ, and the pulse duration at the fundamental wavelength of 1.06 µm has been measured to be 21 ns. The ultrasonic excitation efficiency is about 3.5 times better compared to the application of state-of-the-art CO2 lasers.

Dynamic wave field synthesis: enabling the generation of field distributions with a large space-bandwidth product.

We present a novel approach for the design and fabrication of multiplexed computer generated volume holograms (CGVH) which allow for a dynamic synthesis of arbitrary wave field distributions. To achieve this goal, we developed a hybrid system that consists of a CGVH as a static element and an electronically addressed spatial light modulator as the dynamic element. We thereby derived a new model for describing the scattering process within the inhomogeneous dielectric material of the hologram. This model is based on the linearization of the scattering process within the Rytov approximation and incorporates physical constraints that account for voxel based laser-lithography using micro-fabrication of the holograms in a nonlinear optical material. In this article we demonstrate that this system basically facilitates a high angular Bragg selectivity on the order of 1°. Additionally, it allows for a qualitatively low cross-talk dynamic synthesis of predefined wave fields with a much larger space-bandwidth product (SBWP ≥ 8.7 × 10(6)) as compared to the current state of the art in computer generated holography.

Efficient laser generation of Lamb waves.

We report about the efficient generation of Lamb waves for nondestructive testing (NDT) of carbon fiber reinforced plastics (CFRP) with spatially formed laser beams. Therefore we describe the successful introduction of a liquid crystal on silicon (LCoS)-based spatial light modulator (SLM) to create predetermined spatial laser light distributions for a flexible Lamb wave excitation. We investigate the influence of the formed beam profiles of the generation laser to the resulting Lamb wave. The further objective of the study is the close adaptation of the laser-generated guided waves to a specific testing situation and an optimized defect evaluation.

Axially distributed sensing with a monoscopic imaging lens for single-shot distance measurements.

Using the image-based optical measurement method known as axially distributed sensing (ADS), the depth information of a scene is retrieved by evaluating images recorded with a camera positioned on multiple points along a common optical axis. We describe the design of a monoscopic lens that images the scene from two different on-axis points of perspective simultaneously onto a single camera. Designed for use in a territorial surveillance video system, this lens allows for capturing 3D scene information based on ADS with a single shot. We present the physical foundations of this approach and its implementation as a compact lens system and show the usability of the system prototype, supported by performance tests.

Wave field sensing by means of computational shear interferometry.

In this paper, we present a method to recover the complex amplitude of speckle fields from measurements performed by a shear interferometer. It is based on the optimization of an objective function using the steepest descent gradient technique in combination with a heuristic initial guess. In contrast to already existing methods, the algorithm finds a local minimum least-squares solution even in the presence of Poissonian and Gaussian noise.