The accuracy of spatial calibration in Stereo Particle Image Velocimetry (SPIV) has a considerable influence on the accuracy of velocity measurement. To study the ability of various calibration models to handle input errors, we define a dimensionless parameter, namely, the error attenuation coefficient, to evaluate the response of spatial calibration models to input errors. Based on this error attenuation coefficient, the error propagation characteristics of conventional spatial calibration models, including the polynomial model and the camera pinhole model, can be quantitatively evaluated. A neural network-based space calibration model is then developed. Unlike conventional calibration models, this new model is naturally adaptive to multiple-camera joint calibration, thus suitable for SPIV. Synthetic experiments demonstrate the ability of this neural network model to suppress the propagation of the input error in a large measurement parameter space, which is not possessed by the polynomial model or the pinhole model. Additionally, it outperforms traditional models in the scenario of high optical distortion. Therefore, this neural network model might be an ideal candidate for the spatial calibration of SPIV. Finally, it is confirmed in the experiment that the error of neural network calibration model is only a quarter of that of traditional models.
[1] LECERF A, RENOU B, ALLANO D, et al. Stereoscopic PIV:Validation and application to an isotropic turbulent flow[J]. Experiments in Fluids, 1999, 26(1-2):107-115.
[2] BERESH S J, WAGNER J L, SMITH B L. Self-calibration performance in stereoscopic PIV acquired in a transonic wind tunnel[J]. Experiments in Fluids, 2016, 57:48.
[3] 陈钊,郭永彩,高潮.三维PIV原理及其实现方法[J]. 实验流体力学, 2006, 20(4):77-82. CHEN Z, GUO Y C, GAO C. Principle and implementation of 3D PIV[J]. Journal of Experiments in Fluid Mechanics, 2006, 20(4):77-82(in Chinese).
[4] WIENEKE B. Stereo-PIV using self-calibration on particle images[J]. Experiments in Fluids, 2005, 39(2):267-280.
[5] SOLOFF S M, ADRIAN R J, LIU Z C. Distortion compensation for generalized stereoscopic particle image velocimetry[J]. Measurement Science and Technology, 1997, 8(12):1441-1454.
[6] 周凡桂, 王晓光, 高忠信,等. 双目视觉绳系支撑飞行器模型位姿动态测量[J]. 航空学报, 2019, 40(12):123059. ZHOU F G, WANG X G, GAO Z X, et al. Binocular vision-based measurement of dynamic motion for aircraft model suspended by wire system[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(12):123059(in Chinese).
[7] FEI R, MERZKIRCH W. Investigations of the measurement accuracy of stereo particle image velocimetry[J]. Experiments in Fluids, 2004, 37(4):559-565.
[8] 张烁, 燕丹晨, 甄莹, 等.利用线性变换和后方交会的月球车相机标定[J]. 测绘科学, 2015, 40(11):29-33. ZHANG S, YAN D C, ZHEN Y, et al. Calibration of lunar rover's stereo-camera based on 3DDLT and multi-image resection[J]. Science of Surveying and Mapping, 2015, 40(11):29-33(in Chinese).
[9] 陈启刚, 钟强. 体视粒子图像测速技术研究进展[J]. 水力发电学报, 2018, 37(8):38-54. CHEN Q G, ZHONG Q. Advances in stereoscopic particle image velocimetry[J]. Journal of Hydroelectric Engineering, 2018, 37(8):38-54(in Chinese).
[10] YOO S H, LEE D S. Direct calibration methodology for stereo cameras[C]//SPIE Conference on Machine Vision Systems for Inspection and Metrology Ⅶ. Bellingham:SPIE, 1998.
[11] ZHANG C F, NIU Y X, ZHANG H, et al. Optimized star sensors laboratory calibration method using a regularization neural network[J]. Applied Optics, 2018, 57(5):1067-1074.
[12] STANISLAS M, OKAMOTO K, KHLER C J, et al. Main results of the third international PIV Challenge[J]. Experiments in Fluids, 2008, 45(1):27-71.
[13] CALLUAUD D, DAVID L. Backward projection algorithm and stereoscopic particle image velocimetry measurements of the flow around a square section cylinder[C]//11th International Symposium on Applications of Laser Techniques to Fluid Mechanics, 2002.
[14] CALLUAUD D, DAVID L. Stereoscopic particle image velocimetry measurements of the flow around a surface-mounted block[J]. Experiments in Fluids, 2004, 36(1):53-61.
[15] SCARANO F, DAVID L, BSIBSI M, et al. S-PIV comparative assessment:Image dewarping+misalignment correction and pinhole+geometric back projection[J]. Experiments in Fluids, 2005, 39(2):257-266.
[16] WESTERWEEL J. Theoretical analysis of the measurement precision in particle image velocimetry[J]. Experiments in Fluids, 2000, 29(S1):S003-S012.
[17] PRASAD A K. Stereoscopic particle image velocimetry[J]. Experiments in Fluids, 2000, 29(2):103-116.
[18] LAWSON N J, WU J. Three-dimensional particle image velocimetry:Error analysis of stereoscopic techniques[J]. Measurement Science and Technology, 1997, 8(8):894.
[19] 邱思逸, 程泽鹏, 向阳, 等. 基于线性稳定性分析的翼尖涡摇摆机制[J].航空学报, 2019, 40(8):122712. QIU S Y, CHENG Z P, XIANG Y, et al. Mechanism of wingtip vortex wandering based on linear stability analysis[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(8):122712(in Chinese).
[20] COUDERT S J M, SCHON J P. Back-projection algorithm with misalignment corrections for 2D3C stereoscopic PIV[J]. Measurement Science and Technology, 2001, 12(9):1371.
[21] GIORDANO R, ASTARITA T. Spatial resolution of the stereo PIV technique[J]. Experiments in Fluids, 2009, 46(4):643-658.
[22] PRASAD A K, ADRIAN R J. Stereoscopic particle image velocimetry applied to liquid flows[J]. Experiments in Fluids, 1993, 15(1):49-60.
[23] 史泽林, 康娇, 孙锐. 基于BP神经网络的大视场成像畸变校正方法[J]. 光学精密工程, 2005, 13(3):348-353. SHI Z L, KANG J, SUN R. BP NN-based method for lens distortion correction of large-field imaging[J]. Optics and Precision Engineering, 2005, 13(3):348-353(in Chinese).
[24] 田立坤, 刘晓宏, 李洁. BP神经网络用于大视场显示设备的畸变校正[J]. 电光与控制, 2012, 19(12):43-46,57. TIAN L K, LIU X H, LI J. Application of BP neural network in distortion correction of large FOV display[J]. Electronics Optics & Control, 2012, 19(12):43-46,57(in Chinese).
[25] 高涵, 白照广, 范东栋. 基于BP神经网络的GNSS-R海面风速反演[J]. 航空学报, 2019, 40(12):323261. GAO H, BAI Z G, FAN D D. GNSS-R sea surface wind speed inversion based on BP neural network[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(12):323261(in Chinese).
[26] PRASAD A K, JENSEN K. Scheimpflug stereocamera for particle image velocimetry in liquid flows[J]. Applied Optics, 1995, 34(30):7092-7099.