Introduction to IgorPro

Transcription

1 Introduction to IgorPro These notes provide an introduction to the software package IgorPro. For more details, see the Help section or the IgorPro online manual. [ 1. Entering Data Start Igor by double-clicking the icon or choose from Windows Start Menu. An empty grid will appear. As you type each number, press Enter, Return or Down Arrow to move to the next cell. Move to the next column by clicking the mouse in the first cell of the next blank column. The column headings are, by default, 'wave0', 'wave1', etc. You can change these by selecting Data > Rename. Click on `wave0' and the arrow icon and rename as desired. (for example x-value, but you can use any name except "time" because it is the name of a built-in function). Similarly, for "wave1". Then Do It. 1

2 Editing Data: You can change points by simply typing over the numbers in each cell. To add or delete points, use Data > Insert Points... or Data > Delete Points... The data table can be edited just like numbers in a spreadsheet. You can add, multiply, divide, etc., to generate a new column of numbers. For example, you might want to plot the resistance of a component from voltage and current data. This can be achieved using the Command window at the bottom of the screen. Below, we generate a new column of numbers called 'ohms', created by dividing the 'y- value' column by 'x-value'. Make /N =7 ohms ohms = 'y-value'/'x-value' AppendToTable ohms The table becomes: The /N flag ensures that the length of the new column is the same as the others (7, here). The single quotes are requires to prevent the hyphen being interpreted as a minus sign. Quote marks are not required if the column name does not contain non-alphanumeric characters. Most mathematical functions are included, such as sin(), cos() and exp(). Note that ln() is the natural logarithm, while log() is log (base 10). 2. Display the Graph Choose the Windows > New Graph. Highlight the items corresponding to the x and y axes (Xwave and Ywave) and click Do It. A simple graph will appear: 2

3 The graph can be modified by positioning the cursor directly over the trace and doubleclicking (or select Graph> Modify Trace Appearance). Adjust the Mode, Color, marker size, etc as desired. Then click Do It. It is recommended that you use solid black circular markers because you will usually be adding the line of best fit as part of your data analysis 3

4 To modify the axes, position the cursor over the bottom axis line. The cursor changes to this shape:. Double-click and the Modify Axis dialog box appears. Note the Live Update checkbox in the top/right corner. When checked, changes that you make are immediately reflected in the graph. When it is unchecked, the changes appear only when you click Do It. 4

5 Click the Axis tab. Choose On from the Mirror Axis pop-up. This will complete a frame around your graph. Click the Auto/Man Ticks tab to display the following: Click the Minor Ticks checkbox so it is checked. Click the Ticks and Grids tab: Choose Inside from the Location pop-up. Select left axis from the Axis pop-up menu in the top-left corner of the dialog and then repeat the above steps for the bottom axis. Then click Do It. [You can also adjust both axes together by choosing `Select All Axes ]. Your graph will now look like this: 5

6 You can adjust the positions of the markers by choosing Round to nice values from the pop-up menu that initially reads Use data limits. If it is important to include the origin as well, choose "Autoscale from Zero 6

7 Finally click on the Axis Label tab to add labels to your graph: You can add legends and other text to your graph, See the users manual for further details. 2. Regression When fitting data to a straight line, y=mx+b, we need to know the error in the slope and intercept in order to determine the overall uncertainty in the result from a laboratory experiment. Select Analysis> Quick Fit > line. 7

8 Igor will draw the best straight line to the points and generate some statistical information at the bottom of the screen. This says that the slope is 1.71 ± 0.31, while the intercept is 1.02 ± 1.14 (units will be determined from your experiment). To display the result of the fit on the graph itself, select Analysis> Quick Fit > Textbox Preferences. Check the appropriate boxes. 8

9 When you select Analysis > Quick Fit > line, the result will appear on the graph, which you can then move to any location on the plot. 9

10 Extrapolating a Fit to the edge of the frame In order to make the appearance of the graph more pleasing you may want to extrapolate the calculated straight line to the edge of the frame. When you used the Quick Fit menu, Igor created a wave named fit_y-values. This is called the "fit destination wave." It is just an ordinary wave whose X scaling is set to the extent of the X values used in the fit. To extrapolate, we simply change the X scaling of fit_y-values and re-execute the fit destination wave assignment statement which the CurveFit operation put in the history area. Choose the Data Change Wave Scaling menu item. From the SetScale Mode pop-up menu, choose Start and End. Double-click fit_yvalues in the list. This reads in the current X scaling values. The starting X value will be about 2.3 and the ending X will be about 4.8. In the Start box enter 0. In the End box enter 5. Click Do It. The fit_y-values trace is stretched out and now runs between 0 and 5. Now we need to calculate new Y values for fit_y-values using its new X values. In the history, find the line that starts fit_y-values= and click it. 10

11 The entire line is selected. Press Return or Enter once to copy the selection from the history to the command line and a second time to execute it. The fit_y_values wave now contains data between 1 and Error Bars: Unweighted and weighted Fit Consider the following data: 11

12 Tick the Error Bars box in the Modify Trace window. The errors are contained in the err_y column: 12

13 You can fit a straight line to this data using the Analysis > Quick fit > line menu as before. Alternately, you can use the Analysis > Curve Fitting menu item which gives more flexibility. Select the function and the names of the x and y columns. 13

14 Under Data Options set Weighting to _none_, (unweighted fit). Under Output Options check X Range Full Width of Graph. Add Textbox to Graph will display the fit on your graph as well as the command window. 14

15 Weighted Fit: When you include error bars, you expect data points with small errors to be more believable than data points with large errors. Thus you should expect the fit to follow the small error bars more closely than the larger ones. This is known as a weighted fit. The weight depends on the error associated with each data point and is proportional to 1/(error 2 ). Thus points with small error bars have a larger weight than points with large error bars. Choose err_y from the Weighting drop-down menu: 15

16 The weighted plot is shown below. Note that points with the largest error bars are almost ignored by the straight line. 4. Fitting Other Mathematical Functions Both Quick Fit and Curve Fitting allow you to fit other common mathematical functions to your data. These include: Polynomial: One of the most common functions you will use in the laboratory is a 2 quadratic function, of the form ax + bx +c. This is a second order polynomial, and you will be determining the three values of a, b and c. So to fit this function, select Analysis > Quick Fit > poly > 3 Consider the following data: 16

17 The resulting graph is shown below. The equation of the line of best fit is y = x 0.17 x 2 (where x represents time and y represents position). The errors in these coefficients are also calculated by IgorPro. Other functions include: Power Law Fit: Data which obeys a simple power law can be described by a function of the form y = yo+ax n. Analysis > Quick Fit > Power will give values for A and n. Alternately, taking the logarithm of each side gives log(y) = log(a) + n log(x) and a plot of log(y) versus log(x) will give a straight line of slope n. Exponential Functions: Exponential functions occur commonly in physics. Use exp or exp_xoffset You can define your own functions too. Use Analysis > Curve Fitting > New Fit Function. Consider the following data: 17

18 You can define your own function. Use Analysis > Curve Fitting > New Fit Function. Suppose you want to fit your data to the function Asin(Bx)+C, where A, B and C are to be determined. 1. Give the function a name (e.g., myfunc) 2. Enter A, B and C in the Fit Coefficients boxes and x as the independent variable. 3. Type the function in the Fit Expression box. 18

19 Select the columns corresponding to x and y data, and save the function. Enter initial guesses for the coefficients A, B and C. Often using "1" for each will do. Some functions may require more fine-tuning. 19

20 Click Do It to obtain the line of best fit. 20

21 5. Plotting Functions 1. Decide how many points you want to plot. 2. Make a wave with that many points. 3. Use the SetScale operation to set the wave s X scaling. This defines the domain over which you are going to plot the function. 4. Display the wave in a graph. 5. Execute a waveform assignment statement to set the data values of the wave. Example: Type these lines in the Command window. Make/O/N=500 wave0 SetScale/I x, 0, 4*PI, wave0 // plot function from x=0 to x=4π Display wave0 wave0 = 3*sin(x) + 1.5*sin(2*x + PI/6) To see the data generated by the function, choose Data > Data Browser. Clicking on wave0 (the default name of the data set) will display all 500 data points 21

22 6. Plotting Multiple Curves on the same Axes Consider the following data with common x-values, but two different y-values. Select Windows > New Graph as before and highlight the x and y columns. Click Do It and adjust the markers as desired, for example: 22

23 The data sets do not need to contain the same number of points. Select Windows > New Graph to plot the first set of data: 23

24 Tidy the graph as desired. The text "Plotting two graphs together" was created using the Graph > Add Annotation menu. 24

25 The same technique can be used to plot functions and data on the same axes. For example, here is a plot of the function y = 4 x 2 3x + 8 and some data: 25

26 Plotting Different Functions on the same Axes The procedure is the same as for one function, except you need to associate a wave with each function. For example; Make/O/N=500 wave0 wave1 // make space for 2 functions (500 points each) SetScale/I x, 0, 200, wave0 // plot function from x=0 to x=200 wave0=sqrt(x) wave1=x/10 Display wave0 wave1 26

27 7. Fitting a function to selected data points. Consider the following data: Rather than trying to fit this data to a single function, we shall fit the first eight points to a straight line, and the last seven points to a different straight line function. Press Ctrl-I to bring up the plot information window. A small frame will appear just below the graph: 27

28 Use the mouse to drag the cursor labeled 'A' to the first point of your chosen region and drag the cursor labeled 'B' to the second point To fit the points between the cursors, select Analysis-Quick Fit. 28

29 Note the check mark at 'Fit Between Cursors'. For this straight line fit the result is displayed in the Command window: And the line of best fit is drawn between the points. Likewise for the second set of points, we obtain the result: with the corresponding plot: 29

30 You can, of course, use the Curve Fitting menu to control the fit. Here, both fits are displayed on the same axes. 30

31 8. Importing Data from an Experiment Often you will need to load data from a file created by another program. The process of loading a file creates new waves which contain this data. Text files generated by scientific instruments or custom programs often have header information at the start of the file. The header is not part of the block of data but contains information associated with it. Igor s text loading routines are designed to load the block of data, but not the header. Consider the following data file: (which we will call Test_Data_Import.txt) Start IgorPro and select Data - Load Waves - Load General Text: 31

32 The You will be prompted for the name of the file, and the following window will appear: 32

33 33 Note that the header has been skipped, and the data columns have been labelled wave0 and wave1, which you are free to change. Check the Make Table box and ensure that the Column Format drop-down box is set to Number. Clicking Load produces the familiar data window. Sometimes you may need to use the Load Delimited Text routine. This needs to be told where the block of data starts if it is not at the start of the file. Columns may be equal or unequal in length. Using the Command Line Simply type `LoadWave /J' into the command line. The flag '/J' forces the data to be numeric.