FPL Statistics Group

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1. Microfibril Angle Estimation From X-Ray Diffraction Patterns
2. The Initial 6, Fit 6, Initial 11, and Fit 11 or Fit 11,4 buttons
3. Getting data to and from the applet
4. The Load, Reset, Clear All, Clear, and Zoom buttons
5. The Buttons 1, 2, 3, 4, and 5 at the top of the plot
6. Writing results to files
7. Running the applet on a demonstration data file
8. Documentation
9. The nonlinear least squares code
10. Installation of the application
11. Differences between the applet and the application
12. Format.java
13. Rubberband.java
14. Support
15. Bugs

Microfibril Angle Estimation From X-Ray Diffraction Patterns

Ideally the fitting process could be entirely automated. However, the fit involves a 11 parameter nonlinear regression and if initial estimates of the parameters are off, human intervention is required. For the most part the initial estimates that are automatically generated work well, but occasionally they fail. Currently this leads to a relatively fast but tedious (if you have hundreds of diffraction patterns) process in which a user clicks the Initial 6, Fit 6, Fit 11 or Fit 11,4, and Next buttons in sequence.

The Initial 6, Fit 6, Initial 11, and Fit 11 or Fit 11,4 buttons

The Initial 6 button leads to an automatic calculation of initial estimates of six parameters --- a, the baseline of the data, b1, the height of the first major peak above the baseline, b2, the height of the second major peak above the baseline, mu1, the center of the first major peak, sigma1, which is the half width of the first major peak at approximately 61% of its maximum height above the baseline, and sigma2, which is the half width of the second major peak at approximately 61% of its maximum height above the baseline. (In LaTeX, the 6 parameter model is "intensity = a + b_1 \times \exp(-(angle - \mu_1)^2/(2 \sigma_1^2)) + b_2 \times \exp(-(angle - (\mu_1 + 180))^2/(2 \sigma_2^2))".)

The Initial 6 results are plotted as a blue overlay on the data. This overlay can be quite far from a good fit and still represent adequate starting values for the 6 parameter fit. A user will quickly get an idea of how good this initial 6 parameter fit needs to be to yield a decent final 6 parameter fit. If, as occasionally happens, the initial automatic parameter estimates are too poor to yield a good final fit, then the user must provide improved initial estimates. This can be done in two ways. The user can type initial estimates into the text fields next to the a, b1, b2, mu1, and sigma1 buttons or the user can use the mouse to identify good initial values:

• To use the mouse to identify an initial a value, click the a button. A horizontal blue line will appear at the height corresponding to the current a value. Now click the mouse on the plot at a height that is approximately even with the plot's baseline. The first horizontal blue line will be replaced with a new one that corresponds to the height selected by the mouse click. This new a value will also appear in the text field next to the a button. In addition, the old initial fit overlay will be replaced by a new (cyan) overlay based on the new initial parameter values.

• To use the mouse to identify an initial b1 value, click the b1 button. A horizontal blue line will appear at the height corresponding to the current a + b1 value. Now click the mouse on the plot at a height that is approximately even with the leftmost main peak's maximum. The first horizontal blue line will be replaced with a new one that corresponds to the height selected by the mouse click. The new b1 value (calculated as click height minus the a value) will also appear in the text field next to the b1 button. In addition, the old initial fit overlay will be replaced by a new (cyan) overlay based on the new initial parameter values.

• To use the mouse to identify an initial b2 value, click the b2 button. A horizontal blue line will appear at the height corresponding to the current a + b2 value. Now click the mouse on the plot at a height that is approximately even with the rightmost main peak's maximum. The first horizontal blue line will be replaced with a new one that corresponds to the height selected by the mouse click. The new b2 value (calculated as click height minus the a value) will also appear in the text field next to the b2 button. In addition, the old initial fit overlay will be replaced by a new (cyan) overlay based on the new initial parameter values.

• To use the mouse to identify an initial mu1 value, click the mu1 button. A vertical blue line will appear at the x value corresponding to the current mu1 value. Now click the mouse on the plot at an x value that is approximately at the midpoint of the leftmost main peak. The first vertical blue line will be replaced with a new one that corresponds to the x value selected by the mouse click. The new mu1 value will also appear in the text field next to the mu1 button. In addition, the old initial fit overlay will be replaced by a new (cyan) overlay based on the new initial parameter values.

• To use the mouse to identify an initial sigma1 value (which is used for both sigma1 and sigma2), click the sigma1 button. A vertical blue line will appear at the x value corresponding to the current mu1 value. A second vertical blue line will appear at the x value corresponding to mu1 + sigma1. Now click the mouse on the plot at an x value that is approximately equal to an improved mu1 + sigma1 estimate. (Ideally this should be at a point at which the curve is at about 60% of its maximum height. However the initial sigma1 value does not have to be very close at all to the correct value in order for the subsequent nonlinear least squares to succeed.) The second vertical blue line will be replaced with a new one that corresponds to the x value selected by the mouse click. The new sigma1 value (calculated as the click x value minus mu1) will also appear in the text field next to the sigma1 button. In addition, the old initial fit overlay will be replaced by a new (cyan) overlay based on the new initial parameter values.

Before proceeding with a 11 parameter fit we need to consider the possibility that the initial estimate of the rotation (parameter "rot") of the wood cells should not be 0 degrees. As noted in the 2005 paper, if the front faces of the wood cells in a specimen are not perpendicular to the X-ray beam, then the location of the 8 bright spots will change. As illustrated in Figure 31 of the paper, if the front faces are perpendicular to the beam, the complete broadened profile should contain left and right profiles with central peaks. As illustrated in Figure 32 of the paper, if the front faces of the wood cells are rotated 22.5 degrees in a counterclockwise direction (looking down at the specimen from above), the complete profile should contain a left profile with 2 noncentral peaks and a right profile with a central peak. If a user sees this pattern, they could click the nc,c (this stands for noncentral, central) button on the right panel prior to performing the 11 parameter fit. As illustrated in Figure 33 of the paper, if the front faces of the wood cells are rotated 45 degrees in a counterclockwise direction, the complete profile should contain left and right profiles that each contain 2 noncentral peaks. If a user sees this pattern, they could click the nc,nc button on the right panel prior to performing the 11 parameter fit. Finally, as illustrated in Figure 34 of the paper, if the front faces of the wood cells are rotated 67.5 degrees in a counterclockwise direction (or -22.5 degrees in a clockwise direction), the complete profile should contain a left profile with a central peak and a right profile with 2 noncentral peaks. If a user sees this pattern, they could click the c,nc button on the right panel prior to performing the 11 parameter fit.

The program permits a user to change the initial 11 parameter estimates by changing the values displayed in the text fields in the lower half of the right hand panel.

A user performs a 11 parameter fit by clicking on either the Fit 11 button or the Fit 11,4 button. If the Fit 11 button is clicked, one nonlinear least squares fit is performed and the resulting predicted intensity values are plotted as a red overlay. A smoothing of the observed intensity data is plotted as a green overlay. The final parameter estimates are displayed in the "MFA", "rot", "tilt", "sdFB_lp", "sdFB_rp", "sdRL_lp", "sdRL_rp", "a", "bFB", "bRL", and "bRdL" text fields. The MFA estimate also appears in the panel at the top of the window. If the fit is the first 11 parameter fit of the data set then the MFA estimate appears next to the 1 button. If the fit is the second 11 parameter fit of the data set then the MFA estimate appears next to the 2 button. And so on. When more than one fit is performed, the ID of the fit that corresponds to a minimum mean sum of squares is placed in the box to the right of ``ID_min'' in the top panel. The corresponding minimum mean sum of squares is placed in the box to the right of ``mss_min'' in the top panel. Currently, the program permits at most five 11 parameter fits of a particular data set. (Of course one can always reload the data set in order to obtain additional fits. However this should seldom be necessary.) See below for a description of how results are saved to a file.

If the Fit 11,4 button is clicked (this is our standard protocol), four fits are performed. They differ only in the initial estimate of the rotation. The four fits use -22.5 degrees, 0 degrees, 22.5 degrees, and 45 degrees as the initial rotation estimates. Of these four fits, the fit associated with the smallest sum of squares is reported in the appropriate box on the top panel.

Getting data to and from the applet

Here is an excerpt from the mfa_demo_input file that is the default applet data file:

03ar1erX 
   -0.1364E+03    0.3084E+03 
   -0.1363E+03    0.3084E+03 
   -0.1362E+03    0.3125E+03 
   -0.1361E+03    0.3144E+03 
   -0.1360E+03    0.3144E+03 
   -0.1359E+03    0.3144E+03 
   .                         
   .                         
   .                         
    0.2231E+03    0.3064E+03 
    0.2232E+03    0.3016E+03 
    0.2233E+03    0.3026E+03 
    0.2234E+03    0.3084E+03 
    0.2235E+03    0.3084E+03 
    0.2236E+03    0.3084E+03 
12br1erX 
   -0.1364E+03    0.3259E+03 
   -0.1363E+03    0.3259E+03 
   -0.1362E+03    0.3275E+03 
   -0.1361E+03    0.3343E+03 
   -0.1360E+03    0.3343E+03 
   -0.1359E+03    0.3343E+03 
   .                         
   .                         
   .                          

We describe below how to obtain a Java application version of this applet that can be run locally on your machine with access to your file system. It can read the data file directly from your file system and write the results files directly to your file system. However, for quite good security reasons Java applets cannot read from or write to your file system. Thus if you do not want to bother downloading and installing the application version of this applet, but do want to run it on your data, you must anonymous ftp the data file to www1.fpl.fs.fed.us and put it in the pub/data directory. Then, after you start the applet (see below), replace "mfa_demo_input" in the first applet window with the name of your data file, and "mfa_demo_output" in the first applet window with the prefix that you want for your output files. Note that these names should be unique to you to avoid intermixing your results with those of another user.

The Load, Reset, Clear All, Clear, and Zoom buttons

The Reset, Clear All, Clear, and Zoom buttons can be used to remove "glitches" in the data. In particular:

• A user excludes rectangular regions of data by pushing a mouse button down at one corner of the rectangle, holding the button down while moving the pointer to the opposite corner of the rectangle, and then releasing the button. While a user is performing this movement, an animated red rectangle appears that outlines the current exclusion region. After the button is released the outline of the rectangle turns black, and it can no longer be moved.
• If a user wants to look at only the data that has not been excluded, the user should press the Zoom button. A sequence of zooms can be performed.
• Currently, the program does not permit a user to unzoom a single zoom. However a user can reactivate all of the data by pressing the Reset button at the bottom of the page. A user can see all of the inactivated rectangles by performing a fit and then clicking the appropriate recall button at the top of the page.
• The data in an inactivated rectangle can be reactivated if the rectangle is "cleared." A user clears a rectangle by clicking a mouse button in it (all rectangles that contain this point will be cleared) and then clicking on the Clear button at the bottom of the page. All rectangles that are shown on the current page (in the current "zoom state") will be cleared if the user clicks the Clear All button at the bottom of the page.

The Buttons 1, 2, 3, 4, and 5 at the top of the plot

After a 11 parameter fit has been performed, an estimate of the microfibril angle appears in one of the boxes at the top of the page. Up to 5 fits can be performed on any one data set (of course, additional fits can be performed by reloading the data set). If i < 5 fits have been performed, and the Fit 11 or Fit 11,4 button is clicked, the MFA estimate from the fit will appear in text field i + 1 at the top of the page. (If there are four or five empty fields at the top of the page, and the Fit 11,4 button is clicked, the results from all four fits will appear at the top. If one to three fields are available at the top of the page, and the Fit 11,4 button is clicked, only the best of the four fits will appear at the top.) At any time prior to a click of one of the Load, Back, Next, or Stop buttons, a fit can be recalled by clicking the button (buttons 1 -- 5) corresponding to the fit at the top of the page.

Writing results to files

Running the applet on a demonstration data file

Documentation

The nonlinear least squares code

Installation of the application

The code is available in compressed tar or Windows 98 and later zip form. Given the way that the code is currently written you will need to place the following directories and associated files under a directory in your CLASSPATH (see below). The creation of the subdirectories is done automatically if you are untarring the compressed tar file on a UNIX box. On a Windows box, the creation of the subdirectories under the directory in which you have unzipped the program can be done by running the install.bat program.

• corejava
  • Format.java
  • Format.class
• optimization
  • Lmder_fcn.java
  • Lmder_fcn.class
  • Lmdif_fcn.java
  • Lmdif_fcn.class
  • Minpack_f77.java
  • Minpack_f77.class
• rubberband
  • Rubberband.java
  • Rubberband.class
  • RubberbandRectangle.java
  • RubberbandRectangle.class
  • RubberbandRectangleX.java
  • RubberbandRectangleX.class
• sorts
  • Real_Sorts_f77.java
  • Real_Sorts_f77.class
• SPV_graphics
  • SPVGraph.java
  • SPVGraph.class
  • SPVGrint.java
  • SPVGrint.class
  • TicDraw.java
  • TicDraw.class
  • TicID.java
  • TicID.class

You will then need to place the other classes (MFA_application.class, MFA_application1.class, MFA_application_canvas.class, Nlin6.class, Nlin11.class, Spots8.class, Pdown_application.class, Pright_application.class, and Pup_application.class) together in a directory and type

java MFA_application

while you are in that directory to run the application. (You would have to type this at a DOS command line under Windows.)

For a UNIX machine, your CLASSPATH will be set in your .cshrc file if you are running under the C-shell.

For a WINDOWS machine, your CLASSPATH will probably already include the "current working directory." Thus if you install MFA_application.class, MFA_application1.class, MFA_application_canvas.class, Nlin6.class, Nlin11.class, Spots8.class, Pdown_application.class, Pright_application.class, and Pup_application.class in a directory, and the corejava, optimization, rubberband, sorts, and SPV_graphics subdirectories under that directory, then if you type java MFA_application in the directory, the program should run.

Of course for this to work, you will need a Java runtime environment (JRE) on your machine. If your machine does not currently include a JRE, you can obtain one for free at http://java.sun.com/j2se/desktopjava/index.jsp (Solaris, Linux, or Windows) or http://devworld.apple.com/java/ (Apple). (There are free sites on the Web for other machines such as IBM and HP UNIX boxes.) You will need to follow the associated installation instructions to get the JRE set up on your system.

Differences between the applet and the application

On our machines the application runs faster than the applet.

Format.java

Here is what Cornell and Horstmann have to say about the use of code from their book:

NOTE: People have often asked what the licensing requirements for using the sample code in a commercial situation are. You can freely use any code from this book for non-commercial use. However, if you do want to use the code as a basis for a commercial project, we simply require that every person on the development team for that project own a copy of Core Java.

Rubberband.java

Here is what Geary and McClellan have to say about the use of code from their book:

The CD that accompanies this book includes:

• All the source code for the Graphic Java Toolkit.
• Unit test applets for all GJT components, including HTML files for unit test applets.
• HTML documentation for all GJT classes.
• Numerous image files in .gif format developed by Pixelsite

Virtually all these programs are discussed throughout the book. Feel free to borrow, adapt, or extend these for your own purposes.

Support

Bugs

We welcome suggestions for improving this program. Please send suggestions and bug reports to the e-mail address given below.