## 1 Introduction  
Phase measuring deflectometry (PMD) is a surface measurement technique for specular or transmitted objects that are commonly used in the processing and manufacturing of optical components, such as wafers, automobile window glass, and other products. PMD has shown the advantages of incoherence, large dynamic range, simple device, low cost, and comparable accuracy to interferometer [1; 2; 3; 4], etc. Currently, it is attracting extensive interest in the field of surface measurement [5; 6; 7] of optics. In PMD, the phase-shifted sinusoidal fringe patterns are projected and reflected of the specular surface to obtain the slope of the surface under test. Although co-axis PMD can reduce the influence of systematic errors, the complexity of the measuring device is increased, and more importantly, there are scenarios where off-axis configuration is required, such as transparent element measurement with a binary pattern [8]. Generally, the off-axis configuration is widely adopted [9] when the sampling points on the measured surface are spaced on distorted quadrilateral grids instead of regular rectangular grids. This leads to a decrease in the accuracy of some slope-based reconstruction algorithms [10]. Modal methods [11; 12], as a member of the broad family of slope-based surface reconstruction algorithms, can integrate the shape with the points as a whole using standard orthogonal polynomial fit. While zonal methods [13; 14] integrate the positions of the points one by one at the location of the sampling points, they still cannot handle a case with irregular sampling points. In 2017, [PERSON] et al. [15] proposed an improved zonal algorithm to address the issue of the aperture of the test optics that are not rectangular due to keystone distortion and occlusion, and even with an arbitrary sampling point distribution, the measurement accuracy still needs to be improved to meet higher requirements. In 2008, [PERSON] et al. [16] introduced the radial basis function, which combines Hermite interpolation for discrete data and allows irregularly shaped sampling ranges or sampling points to be taken at irregular intervals. After that, in 2015, [PERSON] et al. [17] compared the RBF with other slope-based surface reconstruction algorithms in dealing with quadrilateral geometry. During their simulation, a rectangular mesh was mathematically deformed to generate a quadrilateral grid, and the comparison results showed the advantages of RBF in handling quadrilateral geometry. Meanwhile, [PERSON] et al. [18; 19] also simulated the quadrilateral geometry by setting distortion coefficients for the camera, and [PERSON] et al. [20] combined three distorted meshes (random error, distortion, and trapezoid) to generate a new quadrilateral grid. However, both the actual position of the camera or the components and the surface shape of the optics to be measured can change the shape of the area of the CCD acquisition. The interval of points in the actual optical layout was not considered; however, they can cause the distribution of sampling points to be more complex and cannot be described using a mathematical formula, so these approaches are unable to accurately represent the perspective effect in the off-axis PMD. Instead, a method that can reflect the case of the off-axis PMD needs to be investigated, and experiments about RBF in wavefront reconstruction also should be carried out except for their simulation calculation mentioned above. Since the ray tracing can properly describe the actual sampling points distribution, and based on the reconstruction of the RBF interpolation algorithm is more applicable and accurate, a strategy to address the shortages of them is proposed. In this paper, the quadrilateral geometry is generated by a camera simulating multiple poses (the camera's optical axis is at a different angle from the normal of the surface to be measured) using ray tracing, and the surface is reconstructed using the improved Southwest algorithm and RBF interpolation algorithm for comparison.