Introduction to IgorPro

Transcription

1 Introduction to IgorPro These notes provide an introduction to the software package IgorPro. The software includes an extensive Help section. For more details, see 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. Enter each number and 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 and enter the numbers in the same way. The column headings are, by default, 'wave0', 'wave1', etc. You can change these by choosing Data > Rename. Click on `wave0' and then click the arrow icon. Replace `wave0' with anything else. (Here, we use x-values and y-values. You use any name you wish, except "time" because it is the name of a built-in function). Similarly, select "wave1", click the arrow icon and change its name. Then click Do It. 1

2 Table showing the renamed data columns. Editing Data: You can change points by simply typing over the numbers in each cell. To add or delete points, use the Data > Insert Points... or Data > Delete Points... menu. The data table can be edited just like columns of 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 when your raw data is voltage and current. This can be done using the Command window at the bottom of the screen. The procedure below will generate a new column of numbers called 'ohms', created by dividing the 'yvalue' column by 'x-value'. Type the following: 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. 2

3 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 menu item. Highlight the items corresponding to the x and y axes (Xwave and Ywave) and click Do It. A simple graph will appear: The appearance of the graph can be modified by positioning the cursor directly over the trace and double-clicking. The Modify Trace Appearance dialog box appears. You can also choose the corresponding item from the Graph> Modify Trace Appearance menu. 3

4 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. To modify the axes, position the cursor over the bottom axis line. The cursor changes to this shape:. This indicates the cursor is over the axis and also that you can move the axis (and the corresponding plot area edge) to a new position. Double-click directly on the axis. The Modify Axis dialog appears: 4

5 Note the Live Update checkbox in the top/right corner of the Modify Axis dialog. When it is checked, changes that you make in the dialog are immediately reflected in the graph. When it is unchecked, the changes appear only when you click Do It. 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: 5

6 Click the Minor Ticks checkbox so it is checked. Click the Ticks and Grids tab: Choose Inside from the Location pop-up. Choose the 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. Your graph should now look like this: 6

7 Clicking on the bottom axis one more time will bring up the Modify Axis dialog box again.. You can adjust the position of the markers relative to the axis 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" Finally click on the Axis Label tab to add labels to your graph: 7

8 You can add legends and other text to your graph, See the users manual for further details. 2. Regression Statistics 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. Igor will draw the best straight line to the points and generate some statistical information at the bottom of the screen. For the above graph, the following is generated: 8

9 This says that the value of 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: 9

10 Now when you select Analysis > Quick Fit > line, the result of the fit will appear as on the graph (which you can move to any location on the plot). 10

11 Extrapolating a Fit After the Fit is Done 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 use the Quick Fit menu, Igor created a wave named fit_y-values to show the fit results. 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_y-values 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. 11

12 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: Weighted and Unweighted Fit Consider the following data: 12

13 To include error bars, tick the Error Bars box in the Modify Trace window. Plotting the data gives the graph shown overleaf. The error bars are drawn using the values in the err_y column. 13

14 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 data columns. 14

15 Adjust the Weighting and Residual menu to _none_, check the X Range Full Width of Graph and Add Textbox to Graph checkboxes, which will display the results of the fit on your graph as well as the command window. 15

16 Weighted Fit: When you include error bars on your graph, you expect data points with small errors to be more believable than data points with large errors. Thus you should expect a 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: 16

17 The weighted plot is shown below. Note that the points with the largest error bars have been almost ignored by the straight line. (Of course, you can fit any function to your data; the straight line is used here as an example.) 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 quadratic function, of the form ax 2 + 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 For example, consider the following data: 17

18 The resulting graph is shown below. The equation of the line of best fit is 2 y x 0.17x (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 mathematical 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: 18

19 You can fit this by defining 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. 19

20 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. 20

21 Click Do It to obtain the line of best fit. 5. Plotting Functions Here are the steps required to plot a function: 1. Decide how many data points you want to plot. 21

22 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 evaluate the function over a different domain, you need to reexecute the SetScale command with different parameters. This redefines x for the wave. Then you need to reexecute the waveform assignment statement. For example, SetScale/I x, 0, 2*PI, wave0 // plot function from x=0 to x=2π wave0 = 3*sin(x) + 1.5*sin(2*x + PI/6) If you want 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. 22

23 6. Plotting Multiple Curves on the same Axes Consider the following data with common x-values, but two different y-values. 23

24 Select Windows > New Graph as before and highlight the x and y columns. Click Do It and adjust the markers as desired, for example: 24

25 When the data contains two or more sets of numbers such as the following: The data sets do not need to contain the same number of points. Select Windows > New Graph to plot the first set of data: 25

26 Then select Windows >Append Traces to Graph to obtain the second set. Tidy the graph as desired. The text "Plotting two graphs together" was created using the Graph > Add Annotation menu. 26

27 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 4x 2 3x 8 and some data: 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, 100, wave0 // plot function from x=0 to x=100 wave0=sqrt(x) wave1=x/10 Display wave0 wave1 27

28 Gives the graph: 28