Orthogonal Path Research Articles

Fiber Fabry-Perot accelerometer with extended dynamic range and low noise floor.

Optical interferometric accelerometers are widely used in seismic monitoring, petroleum resources exploration, and structural health monitoring due to their low noise floor and resistance to electromagnetic interference (EMI). However, their small working range limits further applications. To broaden the working range of the sensor while ensuring the inherent anti-electromagnetic interference capability of the optical sensor, this paper proposes an orthogonal optical path (OP) range broadening scheme (OORBS). The linear working range is widened by splicing the linear intervals in the two interferometric signals. Subsequently, a platform based on a nano-displacement unit was built to validate the feasibility of the OORBS under static and AC cavity length variations. The experimental results show that the OORBS can recover the cavity length completely. Finally, the OORBS was combined with an accelerometer to realize the range broadening. The OORBS extends the accelerometer's working range from 0.42 mg to 68 mg while maintaining the high sensitivity, which is about a 162-time improvement. The accelerometer's noise floor reaches 4.8 ng/Hz1/2 at 15 Hz and accordingly, the dynamic range of the accelerometer increases from 98.8 dB to 143 dB. The proposed method is general to address the Fabry-Perot-based dynamic range limitation and can be adapted for various interferometric sensors, such as Fabry-Perot, grating, and Mach-Zehnder.

Complete four-dimensional Bell state measurement using weak cross-Kerr nonlinearity

In this paper, we present an efficient scheme for the complete analysis of the four-dimensional Bell state of the photon system in the path degree of freedom, resorting to the weak cross-Kerr nonlinearity and linear optics. In our scheme, the measurements on two probe coherent states are used for obtaining the bit information of high-dimensional entanglement, and the linear optical elements and single-photon detectors are used for obtaining the relative phase information of high-dimensional entanglement. With these two independent processes, the 16 orthogonal four-dimensional path Bell states can be completely distinguished from each other. This simple and realizable scheme may have useful applications in the quantum information technology based on high-dimensional entanglement.

Comparison of homogeneous anisotropic hardening models in the case of the direct redrawing of a DP600 steel

The use of DP600, an advanced high strength steel, has gained significant attention in automotive industry, especially for complex structures that require multi-step forming operations, leading to non-linear strain path changes. From a numerical modelling perspective, the use of advanced constitutive equations has enabled a precise representation of a large range of behaviors, encompassing reverse and orthogonal strain path changes. Within this context, this study is dedicated to the numerical simulation of a two-step deep drawing process based on distortional plasticity. Two models developed within the Homogeneous Anisotropic Hardening (HAH) framework are considered. This study presents a comparison of the model predictions, calibrated over the same experimental database, in terms of their ability to predict the strain path changes and mechanical behavior of the material during the forming process. Several outputs like the punch load evolution and the strain field are compared with experimental data.

Abstract 4901: High-resolution spatial transcriptomics identifies candidate genes facilitating perineural invasion

Abstract Perineural invasion (PNI), or the invasion of cancer to the space surrounding nerves, is associated with poor prognosis, but the underlying molecular factors that drive its initiation and progression are poorly understood. To explore this systematically, we applied a 6000-plex spatial transcriptomic panel with subcellular resolution to curated microarrays from 5 pancreatic ductal adenocarcinoma (PDAC) patients spanning different stages of tumor-nerve involvement. With this preliminary cohort, we explored malignant cell signatures associated with invasion and adaptation to the intraneural environment. Strikingly, we observed enrichment of a classical-like malignant transcriptional program marked by genes involved in glucose and lipid metabolism in nerve-invading malignant cells. Despite the known association of chemoresistance with serine dependence, these cells also exhibited upregulation of genes involved in serine biosynthesis, suggesting that intraneural invasion may offer an orthogonal path of treatment evasion. Overall, our findings indicate that nerve-invasive cancer cells adopt a unique transcriptomic signature within the neuronal microenvironment. Further studies will aim to uncover the relevance of these signatures to survival within the nerve environment and treatment resistance. Citation Format: Deniz Guney Olgun, Peter L. Wang, Ryan Zhao, Dennis H. Gong, William L. Hwang. High-resolution spatial transcriptomics identifies candidate genes facilitating perineural invasion [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 4901.

In-situ residual deformation field analysis of laser repaired metal components by coherent gradient sensing method

Directed Energy Deposition (DED) technology plays an important role in metal additive manufacturing and remanufacturing. However, the quality and repeatability of DED products are still regarded as a challenge that hinders their widespread applications, especially in cutting-edge sectors. As a promising approach to meet that challenge, the in-situ monitoring of mechanical quantities during DED process, such as deformation and stress, has attracted extensive attention in both academic and engineering fields. In this study, a coherent gradient sensing (CGS) system that matches DED equipment is developed and used for in-situ monitoring the residual deformation of DED repaired metal components. The accuracy of the CGS system has been verified by measuring the curvature of a spherical mirror, and the relative error of the curvature is within 2.5% as a whole. Then, through single-layer/double-layers repair experiments, the influence of dwell time between adjacent tracks, cooling process between adjacent layers, and scanning path of the second layer on the residual deformation are analyzed. In single-layer repair experiment, the value of residual deformation increases with the dwell time, while its distribution characteristic almost keeps the same. In double-layers repair experiment, the anisotropy of residual deformation field is mainly influenced by the deposition direction of the second layer. Compared with parallel deposition path in double-layer repair experiment, the orthogonal deposition path results in a reduction of both the anisotropy and the maximum value of residual deformation field. Moreover, in the cooling process of orthogonal deposition, the residual deformation increases while the distribution characteristic remains unchanged. In conclusion, the feasibility of residual deformation measurement by CGS method in DED repairing process is verified, which provides both data support and tool for the future industrial application.

Three-Channel Metasurfaces for Multi-Wavelength Holography and Nanoprinting.

Metasurfaces, employed to simultaneously generate nanoprinting and holographic images, have been extensively explored recently. Among them, multi-wavelength multiplexing in a single metasurface is often accompanied by dispersion and crosstalk, which hinder the display of multicolor patterns. Here, we propose an efficient phase method to decouple the wavelength and realize a three-channel display operating at different wavelengths. Holographic images appear in the far field with the illumination of two different circularly polarized lights while a nanoprinting image is reconstructed by inserting an orthogonal optical path with the illumination of linear polarization light. The proposed metasurface is only composed of four types of unit cells, which significantly decreases the complexity of fabrication and improves the information capacity. Benefiting from its different decoding strategies and capability of multi-wavelength control, this approach may develop broad applications in information encryption, security, and color display.

Tight globally simple nonzero sum Heffter arrays and biembeddings

AbstractSquare relative nonzero sum Heffter arrays, denoted by , have been introduced as a variant of the classical concept of Heffter array. An is an partially filled array with elements in , where , whose rows and whose columns contain filled cells, such that the sum of the elements in every row and column is different from 0 (modulo ) and, for every not belonging to the subgroup of order , either or appears in the array. In this paper we give direct constructions of square nonzero sum Heffter arrays with no empty cells, , for every odd, when is a divisor of and when . The constructed arrays have also the very restrictive property of being “globally simple”; this allows us to get new orthogonal path decompositions and new biembeddings of complete multipartite graphs.

Study on magnetic interference characteristics and optimization design of magneto-optic current transducer

The paper aims at the phenomenon of the magnetic field between phases of magneto-optical current transducer, studies the magnetic field interference distribution characteristics and proposes the orthogonal optical path optimization scheme to improve the ability of the magneto-optic current transducer to resist the external magnetic field interference. The mathematical model of magnetic field interference degree of magneto-optic current transducer is established, and the distribution characteristics of magnetic field interference degree of magneto-optical current transducer under the effect of interfering current are studied. The research shows that the position of interfering current has a specific law on the magnetic field interference degree of the magneto-optic current transducer, and the interfering current at a specific position has no interference effect on magneto-optic current transducer. It is pointed out that magnetic field interference degree is larger when the magneto-optic current transducer is arranged in the conventional way, and the error caused by the magnetic field interference between phases cannot be ignored. The orthogonal optical path optimization scheme of magneto-optic current transducer is put forward, which can improve the anti-interference ability from external magnetic field of magneto-optic current transducer without changing its body structure and installation condition. The experimental results show that the relative error of magneto-optic current transducer caused by the interfering current is less than 0. 1% when the orthogonal optical path optimization scheme is adopted, which proves the correctness and practicability of the orthogonal optical path optimization scheme.

A novel methodology to manufacture complex metallic sudden overhangs in weld-deposition based additive manufacturing

PurposeAmongst various additive manufacturing (AM) techniques for realizing the complex metallic objects, weld-deposition (arc)-based directed energy AM technique is attaining more focus over commercially available powder bed fusion techniques. This is because of the capability of high deposition rates, high power and material utilization, simpler setup and less initial investment of arc-based AM. Nevertheless, realization of sudden overhanging features through arc-based weld-deposition techniques is still a challenging task because of the necessity of support structures. This paper aims to describe a novel methodology for producing complex metallic objects with sudden overhangs without using supports.Design/methodology/approachThe realization of complex metallic objects with sudden overhangs (without using supports) is possible by reorienting the workpiece and/or deposition head at every instance using higher order kinematics (5-axis setup) to make sure the overhanging feature is in line to the deposition direction.FindingsIn the absence of universally applicable support mechanism, deposition of overhanging features remains one of the main challenges in AM. A separate support structure is often necessary for depositing the overhanging features. Small overhang features are usually possible by a little overextension from the previous layer. Nevertheless, deposition of large gradually varying overhangs and sudden overhangs with complex features without support structures is a challenging task in any AM process. This demands higher order kinematics which calls for inclined and/or orthogonal slicing and area filling.Originality/valueThe unique aspect of this paper is the identification of sudden overhang feature from a tessellated computer-aided design (.stl) file and generates an orthogonal tool path for deposition for sudden overhangs. An in-house MATLAB routine has been developed and presented for performing the same. This methodology helps in realization of sudden overhangs without use of supports. To validate proposed technique, various illustrative case studies have been taken up for deposition.

Michelson’s analysis of errors in his 1881/87 experiments of the two swimmers contest; Necessity of correcting college textbooks

The Paper highlights discovery from 2000 of two Errors (ERM81/87) by Michelson in analysis of his experiments ME81/87. ERM81/87 has also been addressed in series of previous articles by the authors. ERM81/87 consisted of assuming the transverse path of light ray 2 or of SW2 swimmer, to be an isosceles triangle (Error 1) inclined with angle β’ in referential frame (RF) ether/water (E/W), or a double orthogonal path (in RF device/bank (D/B)), thus calculating the wrong result, t2 < t1, or Δt = t1-t2 > 0, (Error 2), states SW2 wins the contest. In ERM81/87 it is proven firstly, by Demonstration 1, based on logic, starting from the non-observance in Michelson’s analysis, of rules of correctness and fair play, in development of the two swimmers contest (TSC). Rresulted in correct transversal path as a right triangle, with t2 = t1 (in RF, E/W), the correct contest result is a draw. Demonstration 2 consists, in correction of SW2 route, resulting under fair play conditions, for transversal path, a right triangle with hypotenuse inclined at angle 2β (in RF, E/W) and t2 = t1 or Δt = 0, with the contest result in a tie. Demonstration 3 is based on a new Generalised Case (GC) of the TSC where the orientation of the starting path of SW1 can be inclined at any angle α, always one obtains, t1 = t2, the correct result. Evidence provided shows Michelson designed his interferometer by analogy with TSC, Michelson considered SW2 the winner. Evidence provided in 1892 by Lorenz expressed doubts about the correctness of Michelson’s analysis of ME81/87, without finding errors. We show, an initial error (ERM81) was committed by Michelson in ME81analysis, erroneously superposing paths for SW2 (in RF, D/B), and in incorrect calculations of t2 and Δt obtaining t2 < t1, an error communicated to him by Potier, which also mentioned the correct result Δt = 0, without any demonstration. In analysis of ME87, Michelson acknowledged the error, modified the path of SW2 to isosceles triangle (in RF, E/W), and made new t2 calculation. But he reduced by only half, the Δt compared to Δt in ME81, meaning the basic error in Δt (ERM87) has persisted, until today. We emphasize that errors ERM81/87 in TSC are repeatedly printed, and appear in all college physics textbooks around the world, exemplifying by presenting four such excerpts from college textbooks from the US and Canada. Thus, a correction of ERM81/87 is required, starting with the correction of the TSC, by admitting the correct result of equality of SW1 and SW2, in all college physics textbooks. As result the ether can be reintroduced into physics with multiple consequences including re-evaluation of the Special Relativity Theory.

Recreational fishers contribute to path formation in subalpine vegetation

SummaryThe role of recreational fishers forming paths (routes of concentrated passage characterised by short vegetation or ground indentation) as they gain access to wilderness waterbodies has not been well documented in Australia. Recreational use for trout and tournament fly fishing has increased in the Central Plateau of Tasmania; therefore, it is important to determine the human contribution to path formation and its potential consequences for biodiversity conservation in this area of high conservation value. We predicted that paths parallel to waterbodies experienced more human traffic than orthogonal paths. Across 36 sites at different distances from roads, a parallel and orthogonal path to lakeshore were sampled using eight, 1 × 1 m quadrats randomly located along each path within a 10 × 10‐m plot. Recorded for each quadrat were the path widths, height difference between centre of paths and adjacent vegetation (path depth), vegetation types on and adjacent to paths, Bennetts Wallaby (Notamacropus rufogriseus) and Wombat (Vombatus ursinus) faecal numbers. General linear models indicated that path width was greater on parallel than orthogonal paths and declined with distance from roads. Path depth, however, was not affected by distance from roads but was shallower than orthogonal paths. Separate models used to test the potential effects of edge vegetation type, or the covariates Wallaby and Wombat scats did not have significant effects on‐path variables. Paths encircling or orthogonal to Central Plateau lakes appear different floristically to adjacent vegetation communities, nonetheless. Heath and tussock grassland were largely absent from paths, whereas grassland and herbfield communities were infrequently observed off paths. Herbfield and grassland are rarer communities than heath and tussock grassland, which, in the context of a lack of exposure to erosion, suggests a conservation benefit of paths at present usage levels. The human contribution to parallel path conditions is likely to be high, given the results from the study, so monitoring of change is desirable, especially if predicted increasing human activity eventuates in this area.

Fully Implicit Stress Update Algorithm for Distortion-Based Anisotropic Hardening with Cross-Loading Effect: Comparative Algorithmic Study and Application to Large-Size Forming Problem

A fully implicit stress integration algorithm is developed for the distortional hardening model, namely the e−HAH model, capable of simulating cross−hardening/softening under orthogonal loading path changes. The implicit algorithm solves a complete set of residuals as nonlinear functions of stress, a microstructure deviator, and plastic state variables of the constitutive model, and provides a consistent tangent modulus. The number of residuals is set to be 20 or 14 for the continuum or shell elements, respectively. Comprehensive comparison programs are presented regarding the predictive accuracy and stability with different numerical algorithms, strain increments, material properties, and loading conditions. The flow stress and r−value evolutions under reverse/cross−loading conditions prove that the algorithm is robust and accurate, even with large strain increments. By contrast, the cutting−plane method and partially implicit Euler backward method, which are characterized by a reduced number of residuals, result in unstable responses under abrupt loading path changes. Finally, the algorithm is implemented into the finite element modeling of large−size, S−rail forming and the springback for two automotive steel sheets, which is often solved by a hybrid dynamic explicit–implicit scheme. The fully implicit algorithm performs well for the whole simulation with the solely static implicit scheme.

Oriented structure of short fiber reinforced polymer composites processed by selective laser sintering: The role of powder-spreading process

Short fiber reinforced polymer composites processed by selective laser sintering (SLS) generally show an oriented fiber structure, which leads to anisotropic properties of fabricated components. However, the formation mechanism of fiber orientation is barely investigated. In this study, the oriented structure of the carbon fiber/polyamide12 composites processed by SLS is characterized using the X-ray computed tomography, and the role of powder-spreading in formation of the fiber orientation is investigated by simulation using the discrete element method. The short fibers in the fabricated sample show preferred alignment along the spreading direction (X direction) and perpendicular to the building direction (Z direction), even with the orthogonal scanning path. The formation of fiber orientation is attributed to the powder-spreading process. During the powder-spreading process, the particle pile experiences a shearing flow along the building direction, where the higher the Z position, the faster the X-direction speed of the particle flow. Consequently, short fibers driven by the torque caused by the shearing flow gradually rotate and align to the spreading direction, leading to the anisotropy in the final products. The strength of the shearing flow can be tailored by adjusting the spreading parameters such as layer thickness, spreading speed and rotating speed of the roller. Potential approaches to tailor the fiber orientation during the powder-spreading procedure of SLS are discussed.

Distribution reconstruction of non-uniform combustion field based on improved simulated annealing algorithm

In this paper, a method of selecting the optimal transition lines’ combination is analyzed to measure the absorption spectrum of the non-uniform combustion flow field, which is used to solve the basic two-region distribution, and an improved simulated annealing algorithm (ISA) is proposed for reconstructing the field distribution of the combustion flow field, in order to solve the problems of slow convergence speed and low efficiency of the traditional simulated annealing algorithm. By modifying the model perturbation mode and annealing strategy, the efficiency of the algorithm and the chance to jump out of the local optimal space are further improved. According to the numerical simulation results, more transitions are helpful in improving the accuracy of combustion field reconstruction and making the reconstruction less sensitive to noise. It is worth noting that the optimal transitions’ combination is better than the non-optimal transitions’ combination with more transitions included. In this paper, three different combustion models are constructed to verify the effectiveness of the improved algorithm. A comparison between the reconstruction results of the traditional simulated annealing algorithm and the improved simulated annealing algorithm shows that both algorithms have the same precision but the latter algorithm has a higher operating efficiency, and a faster running time (nearly 40 times faster than the former algorithm). At the same time, the simulation results also show that the reconstruction accuracy will decrease slightly with the complication of combustion flow field. By building the TDLAS-HT measurement system in the laboratory and using 8 × 8 orthogonal optical path arrangement, the two different combustion states formed before and after placing the steel rod in the flat flame furnace are reconstructed, the results show that the reconstruction distribution is basically consistent with the original distribution, and the reconstructed distribution well shows the combustion characteristics of the original distribution of the flame field. The effectiveness of the proposed method is verified by numerical simulation and verification tests. Under the condition of the same reconstruction accuracy as the reconstruction accuracy of the traditional simulated annealing algorithm, the higher operating efficiency is helpful in reconstructing the rapidly changing turbulent field, which has some guiding significance for the hyperspectral reconstruction of temperature and concentration distribution in the combustion flow field.

On Orthogonally Guarding Orthogonal Polygons with Bounded Treewidth

There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see within a rectangle, along a staircase, or along an orthogonal path with at most k bends. In this paper, we study all these guarding models for the special case of orthogonal polygons that have bounded treewidth in some sense. As our main result, we show that the problem of finding the minimum number of guards in all these models becomes linear-time solvable on polygons with bounded treewidth. We complement our main result by giving some hardness results.

Pressure vector sensor based on an orthogonal optical path Sagnac interferometer.

A novel pressure vector sensor based on a short section of PANDA fiber with an orthogonal optical path Sagnac interferometer structure is proposed and experimentally demonstrated. The sensor structure was realized using a gold film, coated on the end of the fiber tip through the magnetron sputtering method. The birefringence-dependent interference dip is sensitive to external force. Therefore, pressure can be monitored by this sensor. The relationship between the force direction and the pressure sensitivity was studied. We embedded the sensor in aluminum, using ultrasonic consolidation technology, to investigate the application of its sensing properties in metal. Based on this, the influence of the embedding direction on the polarization characteristics of the fiber was analyzed. The experimental results showed that the sensor offered a high sensitivity of 2330 pm/(N·m) in its freeform and 780 pm/(N·m) after being embedded in aluminum. Due to its simple fabrication process, low cost, and high sensitivity, the pressure sensor described in this paper could be a competitive candidate in several pressure sensing applications.

First-principles investigation on ideal strength of B2 NiAl and NiTi alloys**Project supported by the Science Challenge Project, China (Grant No. TZ2018002) and the Fundamental Research Funds for the Central Universities, China (Grant No. FRF-TP-18-013A3).

For B2 NiAl and NiTi intermetallic compounds, the ideal stress–strain image is lack from the perspective of elastic constants. We use first-principles calculation to investigate the ideal strength and elastic behavior under the tensile and shear loads. The relation between the ideal strength and elastic constants is found. The uniaxial tension of NiAl and NiTi along crystal direction leads to the change from tetragonal path to orthogonal path, which is driven by the vanishing of the shear constant C66. The shear failure under {110} shear deformation occurring in process of tension may result in a small ideal tensile strength (∼2 GPa) for NiTi. The unlikeness in the ideal strength of NiAl and NiTi alloys is discussed based on the charge density difference.

Path planning method based on discontinuous grid partition algorithm of point cloud for in situ printing

PurposePath planning is an important part of three-dimensional (3D) printing data processing technology. This study aims to propose a new path planning method based on a discontinuous grid partition algorithm of point cloud for in situ printing.Design/methodology/approachThree types of parameters (i.e. structural, process and path interruption parameters) were designed to establish the algorithm model with the path error and the computation amount as the dependent variables. The path error (i.e. boundary error and internal error) was further studied and the influence of each parameter on the path point density was analyzed quantitatively. The feasibility of this method was verified by skin in situ printing experiments.FindingsPath point density was positively correlated with Grid_size and negatively related to other parameters. Point_space, Sparsity and Line_space had greater influence on path point density than Indentation and Grid_size. In skin in situ printing experiment, two layers of orthogonal printing path were generated, and the material was printed accurately in the defect, which proved the feasibility of this method.Originality/valueThis study proposed a new path planning method that converted 3D point cloud data to a printing path directly, providing a new path planning solution for in situ printing. The discontinuous grid partition algorithm achieved controllability of the path planning accuracy and computation amount that could be applied to different processes.

Online Parallel Accumulation–Serial Fragmentation (PASEF) with a Novel Trapped Ion Mobility Mass Spectrometer

In bottom-up proteomics, peptides are separated by liquid chromatography with elution peak widths in the range of seconds, whereas mass spectra are acquired in about 100 microseconds with time-of-flight (TOF) instruments. This allows adding ion mobility as a third dimension of separation. Among several formats, trapped ion mobility spectrometry (TIMS) is attractive because of its small size, low voltage requirements and high efficiency of ion utilization. We have recently demonstrated a scan mode termed parallel accumulation - serial fragmentation (PASEF), which multiplies the sequencing speed without any loss in sensitivity (Meier et al., PMID: 26538118). Here we introduce the timsTOF Pro instrument, which optimally implements online PASEF. It features an orthogonal ion path into the ion mobility device, limiting the amount of debris entering the instrument and making it very robust in daily operation. We investigate different precursor selection schemes for shotgun proteomics to optimally allocate in excess of 100 fragmentation events per second. More than 600,000 fragmentation spectra in standard 120 min LC runs are achievable, which can be used for near exhaustive precursor selection in complex mixtures or accumulating the signal of weak precursors. In 120 min single runs of HeLa digest, MaxQuant identified more than 6,000 proteins without matching to a library and with high quantitative reproducibility (R > 0.97). Online PASEF achieves a remarkable sensitivity with more than 2,500 proteins identified in 30 min runs of only 10 ng HeLa digest. We also show that highly reproducible collisional cross sections can be acquired on a large scale (R > 0.99). PASEF on the timsTOF Pro is a valuable addition to the technological toolbox in proteomics, with a number of unique operating modes that are only beginning to be explored.

Square Layout Four-Point Method for Two-Dimensional Profile Measurement and Self-Calibration Method of Zero-Adjustment Error

An on-machine measurement method, called the square-layout four-point (SLFP) method with angle compensation, for evaluating two-dimensional (2-D) profiles of flat machined surfaces is proposed. In this method, four displacement sensors are arranged in a square and mounted to the scanning table of a 2-D stage. For measuring the 2-D profile of a target plane, height data corresponding to all measuring points are acquired by means of the raster scanning motion. At the same time, pitching data of the first primary scan line and rolling data of the first subsidiary scan line are monitored by means of two auto-collimators to compensate for major profile errors that arise out of the posture error. Use of the SLFP method facilitates connection of the results of straightness-measurements results obtained for each scanning line by using two additional sensors and rolling data of the first subsidiary scan line. Specifically, the height of a measuring point is calculated by means of a recurrence equation using three predetermined height data for adjacent points in conjunction with data acquired by the four displacement sensors. Results of the numerical simulation performed in this study demonstrate higher efficiency of the SLFP method with angle compensation. During actual measurement, however, it is difficult to perfectly align inline the origin height of each displacement sensor. With regard to the SLFP method, zero-adjustment error is defined as the relative height of a sensor’s origin with respect to the plane comprising origins of the other three sensors. This error accumulates in proportion to number of times the recurrence equation is applied. Simulation results containing the zero-adjustment error demonstrate that accumulation of the said error results in unignorable distortion of measurement results. Therefore, a new self-calibration method for the zero-adjustment error has been proposed. During 2-D profile measurement, two different calculation paths – the raster scan path and orthogonal path – can be used to determine the height of a measurement point. Although heights determined through use of the two paths must ideally be equal, they are observed to be different because accumulated zero-adjustment errors for the two paths are different. In view of this result, the zero-adjustment error can be calculated backwards and calibrated. Validity of the calibration method has been confirmed via simulations and experiments.