Microdisplacement Measurement Based on F-P Etalon: Processing Method and Experiments

Herein, a processing method is proposed for accurate microdisplacement measurements from a 2D Fabry–Perot (F-P) fringe pattern. The core of the processing algorithm uses the F-P interference imaging concentric ring pattern to accurately calculate the centre coordinates of the concentric ring. The influencing factors of measurement were analysed, and the basic idea of data processing was provided. In particular, the coordinate rotation by the 45-degree method (CR) was improved; consequently, the virtual pixel interval was reduced by half, and the calculation accuracy of the circle centre coordinate was improved. Experiments were conducted to analyse the influence of the subdivision and circle fitting methods. The results show that the proposed secondary coordinate rotation (SCR) by 45 degrees method can obtain higher accuracy of the centre coordinate than the CR method, and that the multichord averaging method (MCAM) is more suitable for calculation of the centre coordinate than the circular regression method (CRM). Displacement measurement experiments were performed. The results show that the standard experimental deviation of the centre of the circle is approximately 0.009 µm, and the extended uncertainty of the displacement measurement in the range of 5 mm is approximately 0.03 μm. The data processing method studied in this study can be widely used in the field of F-P interferometry.

Eccentricity in Images of Circular and Spherical Targets and its Impact to 3D Object Reconstruction

This paper discusses a feature of projective geometry which causes eccentricity in the image measurement of circular and spherical targets. While it is commonly known that flat circular targets can have a significant displacement of the elliptical image centre with respect to the true imaged circle centre, it can also be shown that the a similar effect exists for spherical targets. Both types of targets are imaged with an elliptical contour. As a result, if measurement methods based on ellipses are used to detect the target (e.g. best-fit ellipses), the calculated ellipse centre does not correspond to the desired target centre in 3D space. This paper firstly discusses the use and measurement of circular and spherical targets. It then describes the geometrical projection model in order to demonstrate the eccentricity in image space. Based on numerical simulations, the eccentricity in the image is further quantified and investigated. Finally, the resulting effect in 3D space is estimated for stereo and multi-image intersections. It can be stated that the eccentricity is larger than usually assumed, and must be compensated for high-accuracy applications. Spherical targets do not show better results than circular targets. The paper is an updated version of Luhmann (2014) new experimental investigations on the effect of length measurement errors.

Camera Calibration Method Based on Circle Plane Board

We present a camera calibration method based on circle plane board. The centres of circles on plane are regarded as the characteristic points, which are used to implement camera calibration. The proposed calibration is more accurate than many previous calibration algorithm because of the merit of the coordinate of circle centre being obtained from thousand of of edge pionts of ellipse, which is very reliable to image noise caused by edge extraction algorithm. Experiments shows the proposed algorithm can obtain high precise inner parameters, and lens distortion parameters.

Significant points on circles centre the circumcentre

In Figure 1, triangle ABC has circumcentre O and X, Y, Z are the midpoints of the sides BC, CA, AB respectively. P is a point in the plane of ABC not lying on any of its sides. Σ is the circumcircle and S is the circle centre O passing through P.Points on S are defined as follows. Points U, V, W are the points of intersection of AP, BP, CP with S. Points L, M, N are the reflections of P in the lines XO, YO, ZO respectively.

Research on Inner Circle of Micro Plastic Gear Based on Sub-Pixel Location

Due to the situation that gears’ defects are uncertain, the paper achieved the rough location of micro plastic gears’ inner circular contour by the method of determining-circle-with- three-points. The experiments showed that the running time by the new method is greatly reduced than that by the traditional Hough transform, and it can provide the primary dates for the sub-pixel location. Colligating the dimensionality reduction gray moment operator and the least square circle, the sub-pixel location of the inner circle centre was realized and the sub-pixel location precision was improved by applying the 3σ iteration algorithm. The results indicate that it can meet request on the automatic inspection of micro plastic gears.

A Trigonometrical Ratio to Replace the Dimensionless Angle in Radians

Equations for use with SI radian units have the option of showing the radian unit or not. When the radian is not shown, identical purely numerical values for angles (θ) are produced in each equation. This is the common procedure. When the radian is shown, not all the θ values can show a radian unit: some must remain as pure numbers. This procedure is used whenever convenient, usually for extra clarity. The article proposes that the constantly numerical values of θ be treated as trigonometrical ratios, currently recognised as the ‘radian measure’ or the ‘circular measure’ (abbreviated: circ) of angles, and replaced by ‘circ θ’. This measure equals the length ratio (subtended arc/radius) for an angle θ at the circle centre. By this means the need for the dimensionless version of ‘angle in radians’ vanishes. In fact even dimensional angles in radians need not be used, because ‘circ θ’ allows any angle units to be used for θ.