Surface Topography Measurement Research Articles

Linear systems characterization of the topographical spatial resolution of optical instruments

Lateral resolving power is a key performance attribute of Fizeau interferometers, confocal microscopes, interference microscopes, and other instruments measuring surface form and texture. Within a well-defined scope of applicability, limited by surface slope, texture, and continuity, a linear response model provides a starting point for characterizing spatial resolution under ideal conditions. Presently, the instrument transfer function (ITF) is a standardized way to quantify linear response to surface height variations as a function of spatial frequency. In this paper, we build on the ITF idea and introduce terms, mathematical definitions, and appropriate physical units for applying a linear systems model to surface topography measurement. These new terms include topographical equivalents of the point-, line-, and edge-spread functions, as well as a complex-valued transfer function that extends the ITF concept to systems with spatial-frequency-dependent topography distortions. As an example, we consider the experimental determination of lateral resolving power of a coherence scanning interference microscope using a step-height surface feature to measure the ITF directly. The experiment illustrates the proposed mathematical definitions and provides a direct comparison to theoretical calculations performed using a scalar diffraction model.

In-fiber illumination-detection-synchronized confocal microscopy for high-precision fast axial scanning

Confocal microscopy remains a major workhorse in the 3D surface topography measurement owing to its reliability and compatibility for workpieces with various reflectance, which, however, suffers from slow scanning speed and limited axial resolution. Commercial confocal microscopy primarily relies on the axial movement of a sample or objective lens to create a series of 2D image stacks, and then reconstruct 3D map. Nevertheless, most samples and objective lens are too bulky to scan rapidly, let alone that multiple scans are required to increase the signal-to-noise ratio (SNR). To address this issue, an original approach named illumination-detection-synchronized confocal microscopy was developed, which enabled high-precision fast axial scanning via a compact fiber-multiplexed port with the high-speed synchronous motion of point source and point detection. The approach can effectively improve the peak localization precision while not requiring a high-precision motion stage. Theoretically, via controlling the magnification of the optical system M > 1, the total peak localization precision of axial light intensity response curve can be improved by M3 times. Experiments show that the single-point repeat measurement precision by this approach is improved by 4 times, and the profile measurement precision is enhanced by 2.3 times. Moreover, this approach can effectively avoid collisions between the sample and objective, and has the potential to design a low-cost single-point confocal sensor or confocal profilometer.

Linearizing the vertical scale of an interferometric microscope and its effect on step-height measurement

Abstract The vertical scale calibration of an interferometric microscope is important for establishing traceability of surface topography measurements to the International System of Units (SI) unit of length, the meter. Building on the calibration procedure for the amplification coefficient developed by de Groot and Beverage [Proc. SPIE 9526, 952610 (2015)], this paper describes a calibration procedure that yields the response curve for the entire vertical scan motion of a coherent scanning interferometric microscope. The method requires only a flat mirror as an artifact, a narrow band spectral filter, an aperture to reduce the effective numerical aperture, and the ability to raise and lower the microscope head so that the center of the interferogram can be varied within the scan range. The local frequency of the interferogram is determined by fitting sections of the interferogram to a sinusoidal function. The nonlinearity determined from the local frequency data can be used to estimate the uncertainty in uncorrected vertical height measurements. We describe how optical profile data can be corrected for nonlinearity due to dynamic effects in the scan motion and show that the correction improves the reproducibility of step height measurements by at least a factor of three and close to that of the repeatability.

Extracting focus variation data from coherence scanning interferometric measurements

Coherence scanning interferometry (CSI), based on the principle of interference, can achieve sub-nanometer precision for height measurements. On the other hand, focus variation microscopy (FVM), combining the small depth of field of the objective, is a widely used surface topography measurement method suited to surface topography that is mostly optically rough. In this paper, we propose a method to simultaneously obtain the interferometric fringe data and focus variation FVM image stack, from a single vertical scanning process, using a CSI instrument without any hardware modifications. Using a 3D Fourier transform, the FVM signal, looks takes the form of a “bowtie” and the CSI signal resembles two “umbrellas” that are separated in 3D K-space. The signal is recovered using a 3D inverse Fourier transform and the surface topography can be determined by fusing the CSI and FVM signals. Since both signals come from the same instrument and scanning process, there is no need for coordinate registration and data interpolation during the data fusion process. Our method combines the features of CSI and FVM measurement, thereby improving the robustness and data coverage of the measurement. An all-in-focus surface topography map can also be generated using this method. This focusing feature has the potential to significantly improve the defect detection and quality control ability of CSI instruments.

Evaluation of High-Frequency Measurement Errors from Turned Surface Topography Data Using Machine Learning Methods.

Manufacturing processes in industry applications are often controlled by the evaluation of surface topography. Topography, in its overall performance, includes form, waviness, and roughness. Methods of measurement of surface roughness can be roughly divided into tactile and contactless techniques. The latter ones are much faster but sensitive to external disturbances from the environment. One type of external source error, while the measurement of surface topography occurs, is a high-frequency noise. This noise originates from the vibration of the measuring system. In this study, the methods for reducing high-frequency errors from the results of contactless roughness measurements of turned surfaces were supported by machine learning methods. This research delves into optimizing filtration methods for surface topography measurements through the application of machine learning models, focusing on enhancing the accuracy of surface roughness assessments. By examining turned surfaces under specific machining conditions and employing a variety of digital filters, the study identifies the Gaussian regression filter and spline filter as the most effective methods at a 22.5 µm cut-off. Utilizing neural networks, support vector machines, and decision trees, the research demonstrates the superior performance of SVMs, achieving remarkable accuracy and sensitivity in predicting optimal filtration methods.

Optical path optimization of chromatic line confocal displacement sensor for high resolution and wide range.

This study introduces the optical path-optimized dual-grating chromatic line confocal imaging (DG-LCI) technique for high-resolution and wide-range surface topography measurements. Chromatic line confocal imaging (LCI) finds extensive applications in high-speed 3D imaging of surface morphology, roughness analysis in industrial production, and quality inspection. A key advantage of LCI is its ability to achieve a large depth of focus, enabling the imaging system to measure a wide range in the Z direction. However, the challenge lies in the trade-off between the measurement range and resolution. Increasing the measurement range reduces the resolution, making it unsuitable for precise measurements required in industrial processing. Conversely, enhancing the resolution limits the measurement range, thereby sacrificing the advantage of LCI systems' broad measurement capabilities. Addressing this limitation, we propose a dual optical path dual-grating structure using a simplified and ingenious optical path optimization design. This design overcomes the challenge of sacrificing the millimeter-level measurement range while simultaneously improving the resolution. Rigorous simulations and experiments validate the effectiveness and validity of our proposed method.

Correlation of transverse rotation of the spine using surface topography and 3D reconstructive radiography in children with idiopathic scoliosis.

The relationship between axial surface rotation (ASR) measured by surface topography (ST) and axial vertebral rotation (AVR) measured by radiography in the transverse plane is not well defined. This study aimed to: (1) quantify ASR and AVR patterns and their magnitudes from T1 to L5; (2) determine the correlation or agreement between the ASR and AVR; and (3) investigate the relationship between axial rotation differences (ASR-AVR) and major Cobb angle. This is a retrospective study evaluating patients (age 8-18) with IS or spinal asymmetry with both radiographic and ST measurements. Demographics, descriptive analysis, and correlations and agreements between ASR and AVR were evaluated. A piecewise linear regression model was further created to relate rotational differences to Cobb angle. Fifty-two subjects met inclusion criteria. Mean age was 14.1 ± 1.7 and 39 (75%) were female. Looking at patterns, AVR had maximal rotation at T8, while ASR had maximal rotation at T11 (r = 0.35, P = .006). Cobb angle was 24.1° ± 13.3° with AVR of - 1° ± 4.6° and scoliotic angle was 20.9° ± 11.5° with ASR of -2.3° ± 6.6°. (ASR-AVR) vs Cobb angle was found to be very weakly correlated with a curve of less than 38.8° (r = 0.15, P = .001). Our preliminary findings support that ASR measured by ST has a weak correlation with estimation of AVR by 3D radiographic reconstruction. This correlation may further help us to understand the application of transverse rotation in some clinical scenarios such as specific casting manipulation, padding mechanism in brace, and surgical correction of rib deformity.

Measurement Studies Utilizing Similarity Evaluation between 3D Surface Topography Measurements

In the realm of quality assurance, the significance of statistical measurement studies cannot be overstated, particularly when it comes to quantifying the diverse sources of variation in measurement processes. However, the complexity intensifies when addressing 3D topography data. This research introduces an intuitive similarity-based framework tailored for conducting measurement studies on 3D topography data, aiming to precisely quantify distinct sources of variation through the astute application of similarity evaluation techniques. In the proposed framework, we investigate the mean and variance of the similarity between 3D surface topography measurements to reveal the uniformity of the surface topography measurements and statistical reproducibility of the similarity evaluation procedure, respectively. The efficacy of our framework is vividly demonstrated through its application to measurements derived from additive-fabricated specimens. We considered four metal specimens with 20 segmented windows in total. The topography measurements were obtained by three operators using two scanning systems. We find that the repeatability variation of the topography measurements and the reproducibility variation in the measurements induced by operators are relatively smaller compared with the variation in the measurements induced by optical scanners. We also notice that the variation in the surface geometry of different surfaces is much larger in magnitude compared with the repeatability variation in the topography measurements. Our findings are consistent with the physical intuition and previous research. The ensuing experimental studies yield compelling evidence, affirming that our devised methods are adept at providing profound insights into the multifaceted sources of variation inherent in processes utilizing 3D surface topography data. This innovative framework not only showcases its applicability but also underlines its potential to significantly contribute to the field of quality assurance. By offering a systematic approach to measuring and comprehending variation in 3D topography data, it stands poised to become an indispensable tool in diverse quality assurance contexts.

3D Back Contour Metrics in Predicting Idiopathic Scoliosis Progression: Retrospective Cohort Analysis, Case Series Report and Proof of Concept.

Adolescent Idiopathic Scoliosis is a 3D spinal deformity commonly characterized by serial radiographs. Patients with AIS may have increased average radiation exposure compared to unaffected patients and thus may be implicated with a modest increase in cancer risk. To minimize lifetime radiation exposure, alternative imaging modalities such as surface topography are being explored. Surface topography (ST) uses a camera to map anatomic landmarks of the spine and contours of the back to create software-generated spine models. ST has previously shown good correlation to radiographic measures. In this study, we sought to use ST in the creation of a risk stratification model. A total of 38 patients met the inclusion criteria for curve progression prediction. Scoliotic curves were classified as progressing, stabilized, or improving, and a predictive model was created using the proportional odds logistic modeling. The results showed that surface topography was able to moderately appraise scoliosis curvatures when compared to radiographs. The predictive model, using demographic and surface topography measurements, was able to account for 86.9% of the variability in the future Cobb angle. Additionally, attempts at classification of curve progression, stabilization, or improvement were accurately predicted 27/38 times, 71%. These results provide a basis for the creation of a clinical tool in the tracking and prediction of scoliosis progression in order to reduce the number of X-rays required.

High-precision and high-speed surface topography measurement method of microstructures based on laser scanning transverse differential confocal

The manufacturing of microstructured devices requires higher performance regarding the increasing development of finer structures and more complex structural shapes, which poses a challenge for existing measurement techniques in terms of anti-scattering, high-precision and high-speed. Accordingly, this study proposes a new technology for surface topography measurement of microstructures based on laser scanning transverse differential confocal (LSTDCM), which inserts a D-shaped aperture into the existing confocal system, and performs split-focal spot detection on the focal plane. This method exhibits improved axial resolution by performing differential phase subtraction of the front- and back-focal signals to obtain a highly sensitive axial response signal. Further normalization of the transverse differential confocal signal eliminates the multiplicative noise of the system, avoids the impact of changes in roughness on the measurement results, and achieves an anti-scattering measurement. The linear region of the axial response signal around the zero-crossing point were used to achieve a “non-axial scanning” height measurement, which was combined with high-speed beam lateral scanning to achieve a high-speed areal topography measurement. Theoretical analysis and experimental results indicate that, for samples with height changes within the linear region of axial response, the method can complete areal topography measurement in 1.7 s with the axial resolution of 1 nm and the measurement range of 128 × 128 μm. A microstructured device processed using a nanoform single-point diamond machine tool and a semiconductor wafer were employed in the application validation experiment. And achieve a wide range stitching measurement of 1 mm × 1 mm under a 100 × objective along with the transverse scanning stage. The measurement efficiency is about three times higher than that of Olympus OLS4100 confocal microscope. The method provides a new and effective technical approach that is not limited by the surface roughness and complex structure of the tested devices, and can achieve high-precision as well as high-speed optical nondestructive measurement without moving the tested device. Thus, this work is expected to has important practical applications in the field of ultra-precision measurement.

Phase Retrieval Algorithm for Surface Topography Measurement Using Multi-Wavelength Scattering Spectroscopy

We are currently developing a high-precision and wide-range in-process surface topography measurement system using the laser inverse scattering method. In the laser inverse scattering method, a monochromatic plane wave is illuminated perpendicular to the target surface and the surface topography is measured by retrieving the phase distribution of the reflected light. However, the dynamic range of this method is limited to the sub-micrometer range because of phase wrapping during phase retrieval. In this paper, we propose a laser inverse scattering method using a multi-wavelength light source based on the fact that the phase of light is inversely proportional to the wavelength with the propagation distance as a coefficient. We also constructed a surface profilometer based on the proposed method and measured the profile of a single rectangular groove with a width of 50 µm and a depth of 2 µm. The dimensions of the measured profiles agree well with the nominal dimensions of the rectangular groove.

Discontinuous Dissolution Mechanism of Olivine Deduced from a Topography Observation Method.

Olivine dissolution plays an important role in environmental science and technology, from controlling global element circulation to carbon capture for climate change mitigation. Most studies have been focused on investigating its dissolution rates by monitoring chemical effluent changes under various conditions. However, only by observation of surface reactivity can we unravel the actual mechanism (s) of dissolution. Here, we studied the dissolution of an olivine (010) plane in a flow-through reaction cell with an acidic solution, a surface-controlled regime, and far-from-equilibrium conditions. Direct mineral surface topography measurements using vertical scanning interferometry and atomic force microscopy allowed for quantitative analyses of the spatial and temporal changes in the dissolution rate. The (010) plane dissolved discontinuously in time for different surface sites, resulting in a heterogeneously distributed rate map. Pits with different depths showed opposite dissolution rate distributions from the dislocation center to further out from the etch pit. Based on the step-wave model, we propose a mechanism of dissolution that is governed by the competition between Gibbs free energy of the dissolution process, ΔG, and the critical free energy of the opening of etch pits, i.e., ΔGcrit. The migration of step waves, the distribution of surface defects, the strain field of etch pits, and other dynamic elements, resulting in the instantaneous change of ΔGcrit on the surface, are important factors leading to the discontinuous dissolution of crystal materials. This discontinuous dissolution provides new insight into the guidance of crystalline mineral applications and the prediction of material properties regarding mineral dissolution variation.

Generating synthetic as-built additive manufacturing surface topography using progressive growing generative adversarial networks

Numerically generating synthetic surface topography that closely resembles the features and characteristics of experimental surface topography measurements reduces the need to perform these intricate and costly measurements. However, existing algorithms to numerically generated surface topography are not well-suited to create the specific characteristics and geometric features of as-built surfaces that result from laser powder bed fusion (LPBF), such as partially melted metal particles, porosity, laser scan lines, and balling. Thus, we present a method to generate synthetic as-built LPBF surface topography maps using a progressively growing generative adversarial network. We qualitatively and quantitatively demonstrate good agreement between synthetic and experimental as-built LPBF surface topography maps using areal and deterministic surface topography parameters, radially averaged power spectral density, and material ratio curves. The ability to accurately generate synthetic as-built LPBF surface topography maps reduces the experimental burden of performing a large number of surface topography measurements. Furthermore, it facilitates combining experimental measurements with synthetic surface topography maps to create large data-sets that facilitate, e.g. relating as-built surface topography to LPBF process parameters, or implementing digital surface twins to monitor complex end-use LPBF parts, amongst other applications.

Estimation of Sea Surface Topography Using Jason-3 Satellite Altimetry Across the Eastern Indonesian Seas in a period of 2016 to 2021

The measurement of sea level height relative to a fixed reference point, such as the geoid or mean sea level, is known as sea surface topography. There are a number of factors that affect it, such as undulation, sea surface height, and tides. Measurement of sea surface topography is very important to understand ocean dynamics. One of the factors that influences the dynamics of the sea is the flow across Indonesia. The Indonesian traffic flow is the mass flow of water from the Pacific Ocean to the Indian Ocean. The difference in pressure between the two oceans is what causes the flow. The purpose of this study is to provide precise information about the sea surface topography in the East Indonesian Sea region during the 2016–2021 period, which is required for various marine applications. This approach involves processing and analysing Jason-3 altimetry satellite data, which provides precise sea level elevation measurements. The data is then used to determine the value of the sea surface topography, which shows the spatial and temporal variations in sea level height in the region. The average sea surface topography value every month from 2016 to 2021 ranges from 1.05m to 1.30m, with the highest value occurring in January 2021 at 1.2542m and the lowest value occurring in February 2016 at 1.0498m. For the accuracy of processing results, data for 2016–2021 is used as training data for model estimation and 2021 as test data. The root mean square error value is 0.0762m. Changes in sea surface topography values tend to increase every year, except for 2019. The decline that occurred in 2019 was caused by the ENSO phenomenon, which had an effect of -0.807 on sea surface topography with an inverse correlation. The findings of this study provide important details about sea surface topography in Eastern Indonesian waters, which can be applied to enhance our understanding of ocean dynamics.

MDP-salts as an adhesion promoter with MDP-primers and self-adhesive resin cement for zirconia cementation

PurposeTo evaluate the effect of zirconia priming with MDP-Salt before MDP containing primers and self-adhesive cement on the shear bond strength.Materials and methodsFully sintered high translucent zirconia specimens (n = 120) were assigned into 2 groups (n = 60 each): Control (No Pretreatment) and Methacryloyloxydecyl dihydrogen phosphate salt (MDP-Salt) pretreated. Each group was divided into 3 subgroups (n = 20) according to cementation protocol: 1) MDP + Silane primer and conventional resin cement, 2) MDP+ Bisphenyl dimethacrylate (BPDM) primer and conventional resin cement, and 3) MDP containing self-adhesive resin cement. Shear bond strength (SBS) was measured after 10,000 thermocycling. Contact angle was measured for tested groups. Surface topography was assessed using a 3D confocal laser scanning microscope (CLSM). Weibull analysis was performed for SBS and one-way ANOVA for contact angle and surface topography measurements (α = 0.05).ResultsThe use of MDP-Salt significantly improved the SBS (p < .05) for all tested subgroups. Self-adhesive cement showed an insignificant difference with MDP + Silane group for both groups (p > .05). MDP + BPDM showed a significantly lower characteristic strength compared to self-adhesive resin cement when both were pretreated with MDP-Salt. No difference between all tested groups in the surface topographic measurements while MDP-Salt showed the highest contact angle.ConclusionMDP-Salt pretreatment can improve bonding performance between zirconia and MDP containing products.

4D hyperspectral surface topography measurement system based on the Scheimpflug principle and hyperspectral imaging.

A four-dimensional (4D) hyperspectral surface topography measurement (HSTM) system that can acquire uniform inelastic signals [three-dimensional (3D) spatial data] and reflection/fluorescence spectra of an object is proposed. The key components of the system are a light-sheet profilometer based on the Scheimpflug principle and a hyperspectral imager. Based on the mapping relationships among the image coordinate systems of the two imaging subsystems and the coordinate system of the real space, the spectral data can be assigned to the corresponding 3D point cloud, forming a 4D model. The spectral resolution is better than 4nm. 700nm, 546nm, and 436nm are selected as the three primary colors of red, green, and blue to restore the color. The 4D hyperspectral surface reconstruction experiments of philodendron and chlorophytum have shown the good performance of the proposed HSTM system and the great application potential for plant phenotype and growth analysis in agriculture.

Topography measurement methods evaluation for entire bending-fatigued fracture surfaces of specimens obtained by explosive welding

In this paper, the methods of compensation of differences in the results of entire bending-fatigued fracture surface topographies were presented. The roughness evaluation was performed with a focus variation microscope and confocal surface topography measurement techniques. The differences in the ISO 25178 roughness parameters were investigated and procedures for their compensation were studied. It was found that various types of optical measurements can cause differences in the errors occurring in the measurement process, such as outliers, and noise. The reduction of differences in the various optical roughness measurements can be attained when measurement errors are compensated. For this study, the applications of general procedures available in commercial software can be suitable for improvements of the roughness measurement results, such as raw data thresholding technique, digital filtering (S-filter), power spectral density, and autocorrelation function analyses. The validation of measurement techniques was proposed for areal and profile studies, including analysis of differences in the calculation areal ISO 25178 roughness parameters.

Characterization of the Maximum Height of a Surface Texture.

Average surface height and maximum amplitude can affect surface functions. In the industry, these parameters can be obtained based on profile measurements. However, variability in maximum profile height is high. A more stable parameter can be obtained from the results of the areal surface topography measurements as the average value of the parallel profiles. The aim of this study is to establish this parameter directly from the result of the areal surface texture by correcting the maximum surface height to material ratios in the range of 0.13-99.87%. This method was tested by measuring 100 surface topographies with a stylus profilometer and a white light interferometer. It can be utilized correctly for deterministic textures and random one- and two-process surfaces for which the correlation between neighboring profile ordinates is not very high. In other cases, the method should be modified. Employing this method, the maximum profile amplitude Pt and parameters characterizing the average profile height Pq, Pa, and the ratios Pq/Pa and Pp/Pt describing the shape of the profile ordinate distribution can be correctly estimated. Pq/Pa and Pp/Pt were more stable than the kurtosis Pku and skewness Psk. The corrected maximum height S±3σ can be adopted as a parameter that characterizes the areal surface texture as more stable than the maximum surface height St. Pq/Pa and Pp/Pt were more steady than kurtosis Pku and skewness Psk.

Laser stripe center extraction method base on Hessian matrix improved by stripe width precise calculation

The line laser measurement technology based on triangulation is widely used in the field of complex surface topography measurement. The key technology of line laser measurement is laser stripe center extraction. For high reflective surfaces, due to the low surface roughness, some areas of the laser stripe image are overexposed, resulting in uneven stripe width distribution, asymmetric light intensity distribution of the stripe cross section, and difficulty in extracting the center of the stripe. In this paper, Laser stripe center extraction method based on Hessian matrix method improved by stripe width is proposed. Firstly, the laser stripe image is preprocessed, the influence of noise in the image is alleviated by image filtering and adaptive threshold segmentation, and the region of interest of the image is extracted to reduce the amount of subsequent calculation. The laser stripe width is calculated based on BPNN and divided into different width intervals. The Gaussian kernel is calculated according to the light stripe width and the Hessian matrix is constructed. The Hessian matrix method is used to roughly extract the center coordinates of the light stripe. Based on the continuity of the light stripe, the center coordinates of the light stripe are weighted and corrected to realize the smooth optimization of the center coordinates of the light stripe. The experimental results show that the proposed light stripe center extraction method is superior to the traditional method under different surface roughness and exposure time conditions, which can effectively improve the measurement accuracy of the sensor.

Measurements of Complex Free Water Surface Topography Using a Photogrammetric Method

This paper presents a photogrammetry-based system for capturing turbulent aerated flow topography in a laboratory environment, especially for complex hydraulic phenomena character-ised by turbulent, non-stationary, and non-homogeneous aerated flows. It consists of ten high-resolution cameras equipped with monochromatic sensors and custom-built LED lights, all synchronised for accurate data acquisition. Post processing involves Structure-from-Motion and Multi-View Stereo techniques to calculate exterior and interior orientation parameters that ensure accurate alignment within a desired coordinate system, and conversion to point clouds. The proposed method showed great potential for capturing free water surface topography of turbulent aerated flows with high spatial and temporal resolution over the entire field of view of the cameras. Due to the unique capabilities of this system, direct comparisons with existing benchmarks were not possible. Instead, average free water surface profiles were derived from selected control cross sections, using 2D LIDAR measurements for verification. Both the LIDAR and photogrammetry averaged profiles showed remarkably good agreement, with deviations within ±20 mm. Validation showed that photogrammetry can be used to measure the complex aerated turbulent free water surface. In this way, this approach, involving consecutive image dataset acquisition at predefined intervals, is proving to be a valuable tool for observing, visualising, analysing, investigating, and gaining a comprehensive understanding of the dynamics of the free water surface.