Note: Microbubble experimente by Versluis et al, you will find his video attached to his paper Link
Regading Model 2
We used Matlab 2015a-MathWorks in all numerical process especially the calibration toolbox cameraCalibrator. This toolbox is used to detect and locate the checkerboard calibration pattern including corner detection with subpixel accuracy. We Estimate all intrinsic and extrinsic parameters including axis skew, calculate radial and tangential lens distortion coefficients, correct the optical distortion. This toolbox also support single camera and stereo calibration.To start the calibrationwe have to prepare checkerboardwith specific dimensions. We recorded 50 videos 100fps in different positions for the checkerboard with resolution 1920x1080. This resolution is enough to track all pendulums (which are very small) without loosing any information.From cameraCalibrator one can load all the calibration images. Notice that at some point in the process are asked about the width of one square of the board and you can choose it in mm. After processing each image, it will show the overlapping detected corners on the concrete image. If all went well, you should observe all corners; otherwise, it may happen that you have not indicated the end corners with sufficient precision or because there is too much distortion in the image or the number of image is not enough to cover all the areaof interest. Once you extract all corners, now Matlab is ready to calibrate the camera. After a series of calculations, the result of the calibration parameters should appear with value of Focal Length, Distortion, Errors in pixel....etc.