Jan Burke

Reverse engineering by fringe projection

We report on the development of a versatile and portable optical profilometer and show its applicability for quick and accurate digitization of 3-D objects. The profilometer is an advanced fringe-projection system that uses a calibrated LCD matrix for fringe-pattern generation, a hierarchical sequence of fringe patterns to demodulate the measured phase, and a photogrammetric calibration technique to obtain accurate 3-D data in the measurement volume. The setup in itself is mechanically stable and allows for a measurement volume of about 1x1x0.5 m3. We discuss the calibration of the sensor and demonstrate the process of recording phase data for several sub-views, generating 3-D point clouds from them, and synthesizing the CAD representation of an entire 3-D object by merging the data sets.

Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors

The advantages of spatial phase shifting (SPS) compared with temporal phase shifting in the field of electronic speckle pattern interferometry are described. Some periodic phase reconstruction errors occurring in SPS are discussed. It is shown that these errors become minimal for a spatial phase-shift angle of 2pi/3. Furthermore, a modified phase reconstruction formula is presented by which the noise in the reconstructed phase map is reduced.

Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms

Phase retrieval techniques are widely used in optics, imaging and electronics. Originating in signal theory, they were introduced to interferometry around 1970. Over the years, many robust phase-stepping techniques have been developed that minimize specific experimental influence quantities such as phase step errors or higher harmonic components of the signal. However, optimizing a technique for a specific influence quantity can compromise its performance with regard to others. We present a consistent quantitative analysis of phase measurement uncertainty for the generalized linear phase stepping algorithm with nominally equal phase stepping angles thereby reviewing and generalizing several results that have been reported in literature. All influence quantities are treated on equal footing, and correlations between them are described in a consistent way. For the special case of classical N-bucket algorithms, we present analytical formulae that describe the combined variance as a function of the phase angle values. For the general Arctan algorithms, we derive expressions for the measurement uncertainty averaged over the full 2π-range of phase angles. We also give an upper bound for the measurement uncertainty which can be expressed as being proportional to an algorithm specific factor. Tabular compilations help the reader to quickly assess the uncertainties that are involved with his or her technique.

Spatial versus temporal phase shifting in electronic speckle-pattern interferometry: noise comparison in phase maps

Temporal and spatial phase shifting in electronic speckle-pattern interferometry are compared quantitatively with respect to the quality of the resultant deformation phase maps. On the basis of an analysis of the noise in sawtooth fringes a figure of merit is defined and measured for various in-plane and out-of-plane sensitive electronic speckle-pattern interferometry configurations. Varying quantities like the object-illuminating intensity, the beam ratio, the speckle size and shape, and the fringe density allows characteristic behaviors of both phase-shifting methods to be explored.

Tunable phase-extraction formulae for simultaneous shape measurement of multiple surfaces with wavelength-shifting interferometry

The interferometric surface measurement of single or stacked parallel plates presents considerable technical difficulties due to multiple-beam interference. To apply phase-shifting methods, it is necessary to use a pathlength-dependent technique such as wavelength scanning, which separates interference signals from various surfaces in frequency space. The detection window for frequency analysis has to be optimized for maximum tolerance against frequency detuning due to material dispersion and scanning nonlinearities, as well as for suppression of noise from other frequencies. We introduce a new class of phase-shifting algorithms that fulfill these requirements and allow continuous tuning of phase detection to any frequency of interest. We show results for a four-surface stack of nearparallel plates, measured in a Fizeau interferometer.

Calibration of spherical reference surfaces for Fizeau interferometry: a comparative study of methods

We present an experimental study of three calibration methods for spherical reference surfaces in Fizeau interferometry. The ball average, which relies on averaging measurements of a test ball surface over sufficiently many random rotations of the ball, is theoretically an absolute technique but can be very laborious. On the other hand, a recently introduced double-pass technique, comparing the two halves of the reference surface, is able to determine the point-symmetric contribution in as few as three measurements but does not detect the point-antisymmetric portion. Finally, the point-symmetric errors of the reference surface can be captured in a single, so-called “cat’s-eye” measurement. Our study tries to answer the question of which of the techniques is preferable in practice. We find that the answer depends on the required uncertainty, and it appears that the new double-pass technique represents a practical and reasonable trade-off between expediency and accuracy.

Fabrication and testing of a high-precision concave spherical mirror

CSIROs Australian Centre for Precision Optics has recently finished the production of a high-precision concave spherical mirror. The specifications were very ambitious: numerical aperture 0.75; asphericity below 5.5 nm rms and 27.3 nm P-V. The available reference transmission sphere had to be calibrated to enable adequate accuracy. Due to the high numerical aperture of the mirror, sub-aperture measurements had to be stitched together to form a complete surface map of the mirror. Phase-shifting interferometry at high numerical aperture suffers from phase-step non-uniformity because of the large off-axis angles. We present what we believe to be a new interpretation of this phenomenon as a focus error, which clarifies where in the interferometer the phase-shift error occurs. We discuss the ball-averaging method for calibrating the reference transmission sphere and present results from the averaging process to ensure an uncertainty commensurate with the certification requirement. For carrying out the sub-aperture measurements, we constructed a two-axis gimbal mount to swivel the mirror around the focus of the test wavefront. If the centers of curvature of the transmission sphere and the mirror coincide, the mirror can be tilted without losing the interferogram. We present a simple and effective alignment method, which can be generally applied to optical tests where the wavefront comes to a focus. The mirror was coated with protected aluminum and tested in its mount. No effect on the sphericity error from the coating was found, and the specifications were exceeded by approximately 30%. We discuss subtleties of the stitching process on curved surfaces and report final results.

Chemical bonding for precision optical assemblies

We report on the optimization of precision optical component assemblies for space application with respect to mechanical resilience and retention of optical tolerances such as flatness and angles. Optimized parameters include: the cleaning method of the surfaces to be joined; type, concentration, and quantity of the chemical bonding agent; and post-bonding and curing conditions. Experimental studies and quality assurance are complicated by the large statistical spread in breaking stress, which requires the preparation of a large number of samples. The results previously reported in literature have focused primarily on fused silica, rather than space-qualifiable materials such as Zerodur® and ULE®, and have typically addressed only one or two of the parameters. This study provides a comprehensive picture and a better general understanding of what makes a bond reliably strong.

Performance of spatial vs. temporal phase shifting in ESPI

We compare quantitative phase-measuring techniques in ESPI, using temporal and spatial phase shifting (TPS and SPS). The latter is less susceptible to time-dependent disturbances but inherently yields higher noise in the results due to the spatial intensity and phase variations of the object speckle field. Moreover, the necessity of larger speckles limits the light efficiency in SPS. Based on an evaluation of phase errors in sawtooth images, we compare both of the methods quantitatively in various ESPI configurations. By varying quantities like speckle size and shape and sawtooth fringe density, we find out characteristic behaviors of the methods. Some strategies to optimize the accuracy of the SPS method are explored to estimate how competitive SPS can be in ESPI systems.

Absolute optical surface measurement with deflectometry

Deflectometry utilises the deformation and displacement of a sample pattern after reflection from a test surface to infer the surface slopes. Differentiation of the measurement data leads to a curvature map, which is very useful for surface quality checks with sensitivity down to the nanometre range. Integration of the data allows reconstruction of the absolute surface shape, but the procedure is very error-prone because systematic errors may add up to large shape deviations. In addition, there are infinitely many combinations for slope and object distance that satisfy a given observation. One solution for this ambiguity is to include information on the object’s distance. It must be known very accurately. Two laser pointers can be used for positioning the object, and we also show how a confocal chromatic distance sensor can be used to define a reference point on a smooth surface from which the integration can be started. The used integration algorithm works without symmetry constraints and is therefore suitable for free-form surfaces as well. Unlike null testing, deflectometry also determines radius of curvature (ROC) or focal lengths as a direct result of the 3D surface reconstruction. This is shown by the example of a 200 mm diameter telescope mirror, whose ROC measurements by coordinate measurement machine and deflectometry coincide to within 0.27 mm (or a sag error of 1.3μm). By the example of a diamond-turned off-axis parabolic mirror, we demonstrate that the figure measurement uncertainty comes close to a well-calibrated Fizeau interferometer.