Particle Image Velocimetry (PIV) Data ProcessingEach student is expected to submit a report on the final project. A complete submissionshould include the following elements:- A written summary that reports the determined 2D velocity distribution of the targetflow field. The write-up should also answer all the questions posed by the projectdescription.- A well commented source code with all subroutines attachedStudents are encouraged to program in Matlab, Python, or C/C++. Other languagesare also acceptable. However, students who choose to program in other languagesare expected to schedule a one-on-one appointment with the instructor to demonstratethe successful compilation of the source code and successful computation of thevelocity field using the complied executable to process the raw images and todetermine the velocity field.- Executable file for Windows 32bit system if the language of your choice requirescompilation of the source code and a short description so that the program can betested.How PIV works:The basic principle of the PIV is that a laser light sheet is used to illuminate the flow fieldwhich is seeded with small particles to visualize a flow to be measured. A double pulseYAG laser and a double shutter camera are synchronized to record two particle imageswith very short time separation, typically less than 100 us.MCG5138 Final ProjectA laser is chosen as the illuminating light source in PIV because laser can deliver highlight intensity for very short pulses, which freeze the motion of seeding particle in effect.The particles that are seeded to flow are typically fine TiO2 powers. It is can be assumedthat the seeding particles follow the motion of fluid parcels that the seeding particlesreside in exactly due to the very small size of the seeding particles.Displacement and velocity evaluationOnce the images are successfully recorded, the next step is the PIV analysis. The imagesare divided into small search areas. These small search areas are called interrogationwindows. The cross correlation is applied to these interrogation windows for both twoimages to obtain the correlation plane for each interrogation window. The location of theinterrogation windows in both images are same in the standard cross correlation algorithm(the interrogation windows are shifted in the advanced algorithms).Then the peak detection and displacement evaluation are applied to obtain the dominantdisplacement in each interrogation window. As the size of a pixel in flow and the timeseparation between two images are known, the velocity can be calculated. The size of apixel in flow is determined by the simple velocity calibration.Your mission:Develop a computer code that completes the following tasks and report your findings inthe written report:1. Confirm the code can read a frame of PIV image and properly display it. Pleasefind and report the highest light intensity scattering off from a seeding particle. Alsotry to find the mean particle size (in terms of number of pixels per particle) byassuming a light intensity threshold for identifying seeding particles.2. Determine the size of a square interrogation window. An optimal interrogationwindow should contain approximately 10 particles. The trade-off here is spatialresolution and the accuracy of each velocity determination. Specifically, biginterrogation windows result in sparse velocity data points. At the same time, toosmall an interrogation window doesn’t contain sufficient number of seedingparticles and results in large uncertainty in velocity.(a) Report the optimal interrogation window size returned by your code. Aninterrogation window size that’s often used is 32 pixel x 32 pixel. How does theoptimal window size that you found compare to the convention?(b) For the interrogation window size of your choice, report the range of particlenumbers contained in each and every window.MCG5138 Final Project(c) If the original PIV frame is too big for your computer or you have difficulties inprocessing pixels near the edge of the image, you may choose to analyze onlya subset of the original image pixels. Please specifically report the size andthe coordinates of the four corners of your subset and display the subset w.r.t.the original frame. When you choose the subset for image processing, bemindful of the size of the interrogation window that you chose in step 2.3. Choose any two consecutive PIV frames and calculate cross-correlations of allinterrogation window pairs between the two frames. You will get a correlation planeas shown below. Report the correlation plane for the center interrogation windowof the original frame or of the subset of your choice. For students choose Matlabas the language for programming, the 2D correlation can be calculated using aMatlab function xcorr2.MCG5138 Final Project4. Find the maximum in the correlation plane for each interrogation window pair.Depending on how the correlation plane is defined, find the displacement of theparticles appear in the interrogation windows of both frames. Display thedisplacement vector at the center of each interrogation window for the area youchose.5. (Optional) advanced algorithm: iteration with decreasing size multi pass asdescribed in LaVision FlowMaster Product Manual page 59 – 62.