PIV Programming. Today s Contents: 1. Matlab Programming 2. An example of PIV in Matlab code 3. EDPIV 4. PIV plugin for ImageJ 5.

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1 PIV Programming Last Class: 1. Introduction of μpiv 2. Considerations of Microscopy in μpiv 3. Depth of Correlation 4. Physics of Particles in Micro PIV 5. Measurement Errors 6. Special Processing Methods Today s Contents: 1. Matlab Programming 2. An example of PIV in Matlab code 3. EDPIV 4. PIV plugin for ImageJ 5. JPIV 1

2 Matlab R2011b MATLAB is a package that has been purpose designed to make computations easy, fast and reliable. Now you re ready to start entering commands. Some basic facts: Matlab is case sensitive. Every command given to Matlab is followed by output from Matlab. Type a semicolon after the command to suppress output. The standard arithmetic expressions are used, +,, *, /, ^. The standard functions are used sin, cos, tan, log, exp, etc. Matlab can be used in two different modes, interactive or script. 2

3 Library Functions Trigonometric sin Sine. sinh Hyperbolic sine. asin Inverse sine. cos Cosine. acos Inverse cosine. tan Tangent. atan Inverse tangent. Rounding floor Round towards minus infinity. ceil Round towards plus infinity. round Round towards nearest integer. Exponential exp Exponential. log Natural logarithm. log10 Common (base 10) logarithm. log2 Base 2 logarithm. sqrt Square root. Complex abs Absolute value. conj Complex conjugate. imag Complex imaginary part. real Complex real part. Functions are incredibly useful and need considerable care when they are implemented. You can create your own functions as well. A function file always begins with a function definition line of the form function [output variables] = functionname(input variables) 3

4 Boolean Operators Operator Name help == is equal to eq ~= is not equal to ne < is less than lt <= is less than or equal to le > is greater than gt >= is greater than or equal to ge & and and or or ~ not (unary) not Example: If x >= 0 & x <= 10 4

5 Conditional Statement (1) A simple form of the if statement is if (condition) statements The if else statement allows us to choose between two courses of action. x = input(' Type x : ') if (x<0) disp('x is negative') elseif (x>0) disp('x is positive') else disp('x is non negative') 5

6 Conditional Statement (2) A switch block conditionally executes one set of statements from several choices. Each choice is a case. switch switch_expr case case_expr, statement,..., statement case {case_expr1, case_expr2, case_expr3,...} statement,..., statement... otherwise statement,..., statement 6

7 Do Loops A simple form of the for loop is for index = beginning : statements The general form of the while loop is while (condition) statements or for index = beginning : increment : statements Example: for i = 1:n for j = 1:n H(i,j) = 1/(i+j 1); Example: i=1; while i <=n j=1; while j <= n H(i,j) = 1/(i+j 1); 1 1/ 1 1/ 1 1/ 2 1 7

8 Vectors and Matrices Suppose you want to enter a column vector b Then you would type Suppose you want to enter a matrix >> b = [ 2; 3; 13] n m A(m,n) Then you would type >> A = [ 3 0 1; 1 2 6; 8 1 3] If you want to see a particular entry in A, say 23 A, type >> A(2,3) 8

9 Matrix Operations in Matlab Addition Subtraction Multiplication Division \ / / /3 1/3 0 1/5 9

10 Implementation of Digital PIV Evaluation If the PIV recording system allows the employment of the double frame/ single exposure recording technique (see figure 4.2) the evaluation of the PIVcrecordings is performed by cross correlation. 10

11 Step by Step Example of Matlab Code 4 roll mill flow with background noise 400 particle in a 256x256 image Amplitude is 4 pixels in both directions (x & y) Particle image sizes range from 2 to 5 pixels 3 image pairs t t+δt 11

12 Procedure : Read Image Files clear; %clear memory clc; %clear screen int_x=32; %interrogation window size in x direction int_y=32; %interrogation window size in y direction overlap_x=0.5; %overlap ratio in x direction overlap_y=0.5; %overlap ratio in y direction upper_limit=1; %the number of image pair [filename,pathname]=uigetfile('*.bmp'); file=strcat(pathname,filename); [X,map]=imread(file); [width,height]=size(x); [tok1,rem1]=strtok(filename,'00'); image_num=num2str(i,'%06d'); new_filename1=strcat(tok1,image_num,'_1.bmp'); file1=strcat(pathname,new_filename1); new_filename2=strcat(tok1,image_num,'_2.bmp'); file2=strcat(pathname,new_filename2); [X1,map]=imread(file1); [X2,map]=imread(file2); 12

13 Procedure : Ensemble FFT CC for m=1:int_x*overlap_x:width j=1+j; k=0; for n=1:int_y*overlap_y:height k=k+1; if ((m+int_x 1)<=width) & ((n+int_y 1)<=height) fftx1=fft2(double(x1(n:n+int_y 1,m:m+int_x 1))); fftx2=conj(fft2(double(x2(n:n+int_y 1,m:m+int_x 1)))); R{i,k,j}=real(ifftshift(ifft2(fftX1.*fftX2))); jj=j; kk=k; R_sum=0; for i=1:upper_limit R_buffer=R{i,n,m}; R_sum=R_sum+R_buffer; 13

14 Procedure : Peak Detection for m=1:jj for n=1:kk count=count+1; [Ix,dx]=max(max(R_sum)); [Iy,dy]=max(max(transpose(R_sum))); dx= (dx int_x/2 1); dy= (dy int_y/2 1); data_x(count)=m*int_x*overlap_x; data_y(count)=n*int_y*overlap_y; data_dx(count)=dx; data_dy(count)=dy; 14

15 Procedure : Plot of Vector Map HQ=quiver(data_x, data_y,data_dx,data_dy,1,'k');

16 PIV Software : EDPIV 16

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24 PIV Software : ImageJ with PIV plugin 24

25 PIV Software : JPIV online.de/ 25