## 1 Introduction  
In order to maintain the optimal distribution of airflow in the cascade passage, avoid the separation of airflow and reduce the blade loss, the aeroengine blade must be twisted and stacked by profiles along the airfoil height direction [1]. The twist of the blade plays an important role in optimizing and improving the aerodynamic performance of an aeroengine, and its measurement and evaluation are of great significance. [PERSON] et al. [2, 3] studied the influence law of blade machining error on the aerodynamic performance of a compressor and pointed out that the torsional error of the blade is an important factor affecting the loss of the blade profile. [PERSON] et al. [4] analyzed the influence of blade profile deviation on turbine performance by numerical simulation, and concluded that the deviation of blade profile changes the field structure and the acceleration law of the airflow in the turbine passage, thus affecting the aerodynamic performance of the turbine. [PERSON] et al. [5] researched the effects of six typical blade parameters on compressor performance and drew a conclusion that blade torsion error has an important influence on overall pressure ratio, efficiency, flow rate, etc. At present, the measuring technologies of two-dimensional profile parameters such as the maximum thickness of the profile and the radius of the leading and trailing edges are relatively perfect,and the extraction algorithms of parameters are more mature [6; 7; 8]. However, the measurement and evaluation of blade twist, which characterizes the torsion law of a blade in three-dimensional space, remains a challenge. Difficulties in the measurement of the blade twist are mainly manifested in the following aspects: (1) The twist is a three-dimensional geometric parameter of the blade. The measuring model is complex and the characterization and evaluation are difficult. (2) The parameter of twist angular position is defined by the angle between the profile chord and the axial line of engine. It is another difficult problem to locate the axial line of the engine fast and accurately, and to establish the measurement datum. (3) It is hard to achieve a high-precision measurement of blade twist. Many error factors such as the coordinate acquisition accuracy of the leading and trailing edges and the extraction algorithms of the profile chord line have a great influence on the accuracy of blade twist measurement. At present, some progress has been made in blade twist measurement, and some mature commercial products in the market can be found to meet the basic requirements of blade twist measurement, such as CMM (Coordinate Measuring Machine) of the Global Series from HEAXGON and CORE DS from WENZEL. The existing measuring methods of blade twist mainly involve two categories: the contact measurement method of CMM and the non-contact optical measurement method [9]. Contact measurement technology is the first applied blade twist measurement technology. [PERSON] et al. [10] proposed a two-point measurement method for blade torsional deformation. This method can be used to estimate the rough deformation state of the blade, but measurements with just two points may lose important information and cannot evaluate the blade twist angle with high accuracy. [PERSON] et al. [11] studied a contact measuring method for blades based on CMM and proposed a variable-speed scanning method based on curvature recognition. The method improves the accuracy of measurement by optimizing the measurement path, but has a poor efficiency. [PERSON] et al. [12] analyzed the influence of CMM sampling points on the measurement accuracy of characteristic parameters for turbine blades, and improved the measurement accuracy of parameters such as twist angle by optimizing the sampling strategy. There are disadvantages and constraints in the measurement of blade twist based on contact measurement technology: (1) The theoretical model of the measured blade is necessary for path planning and result analysis, which limits measurement adaptability greatly.