a fit2d SAXS/WAXS primer

• disclaimer
• start-up
• display an image
• display a series of images
• background subtraction
• graphics output
• calibrated plots
• direct beam
• distance/wavelength calibration
• azimuthal integration
• cake
• special option: integrations with CAKE
• (projections)
• (calibrated 2D plots)
• 1D peak fitting of calibrated data
• final remark

disclaimer

a final hint

start-up

• Click the fit2D icon on the analysis PC.
  
• fit2d needs to reserve some initial memory space for reading in images. For the MedOptics detector  use 1024 by 1024 as number of bins.
• Use memory arrays (answer YES) for speedy data handling, don't use variance arrays (answer NO).
• Click O.K which gets you to the fit2d  main menu.

display an image

• goto SAXS/GISAXS > INPUT
• go all the way up in the file tree, until you get to the hard drives. The specuser directory of the data acquisition computer is mapped to drive H:\ on the analysis PC
• go to your user directory and then onto the corr subdirectory
• INPUT an image
  
• set the scale: SAXS/GISAXS > Z-SCALING; choose "LOG SCALE" and set "USER MIN/MAX" to 15 and 15000: these are the default values to see at a glance, whether the MedOptics detector is happy - I want you to use this z-scale, while optimizing the CCD exposure
• NOTE: white regions indicate that the exposure was too long and that the detector is oversaturated - immediately reduce the exposure time by a factor of 10 !!!
• get back to SAXS/GISAXS menu by hitting EXIT
• NOTE: this will be the default in many submenus and I won't mention it again
• the default false color scheme ("geographic") is very powerful - I want you to use this scheme, while optimizing the CCD  exposure
• see manual for other choices (Black & White etc.)
• use SAXS/GISAXS > ZOOM IN to zoom into a region; use  ZOOM OUT or FULL  to zoom out or get back to the full image, respectively
• use the REMEMBER ROI  / FORGET ROI  toggle switch to remember / forget the Region Of Interest  (ROI) defined by your zoom choice for successive images

display a series of images

• go back to main menue > FILE SERIES > COMPOSITE
• input first and last file and FILE INCREMENT (for instance increment=2 reads in every other file)
• SUBTRACT: NO
• ROI: as needed YES or NO
• NO. PER ROW: aim for square arrays for best quality; if some images are missing to fill the array, empty images are given in black
  
• RE-BIN NO.: the image size for a composite image gets too large, if the resolution is not reduced by adding adjacent pixels together ("binning"). Increase the suggested binning number by 1, since fit2d tends to underestimate, how much memory it needs.
  

notes:

• only files with identical names other than the file number can be combined into a series (otherwise make renamed copies of the files)
• this feature is very useful to create an overview of all data

background subtraction

• read in background image using INPUT
• click EXCHANGE
• read in data image via INPUT
• click MATH > SCALED SUB: scaled subtraction allows finetuning a background scaling parameter of the form signal - factor*background which can be adjusted after the inital attempts - I usually use a factor of 1 for starters
  
• finetune the scalefactor by going up or down in 1% or 10% steps
• a good value for the factor is found when the far corner of the detector shows intensity close to zero - you will need to reset the z-scaling parameter (1 to 15000 is often a good range) - you should still be able to see the detector noise
• a constant offset of 20 ("pedestal") was used for the automatic image correction. If the subtraction factor is below 90% or above 110%, the pedestal should be removed first (can also be done in the math menu), and then use the scaled subtraction
  
• you can save the background-subtracted image using OUTPUT to create a file in tiff format for further processing at a later time

simple operations in pixel space

• use SAXS/GISAXS > DISPLAY > SLICE to make a 1D cut through the image
• use SAXS/GISAXS > DISPLAY > PROJECTION to project a range of data onto a given axis
• you first define the projection axis with 2 clicks and then the projection range with 2 clicks
• projection take a bit more work than the 1D cut, but yields better statistics
• horizontal and vertical projections are very useful for GISAXS images

graphics output

• use OUTPUT > TIFF16 to save processed images for further processing at a later time; such output can be read with fit2d again
• in order to keep track of GISAXS images during beamtime, I recommend using an electronic log:
  
• use Alt-PrtScr to copy the active window (which in this case would be the fit2D window)
• paste the image into MS Powerpoint or MS Word or some program of your choice using Ctrl-V or the paste function
• you can email these log files to your advisor or collaborator so that they are informed how things are going
• these logs are also extremely useful, in case you want to get back to me with a question after the run; in particular a program like Powerpoint allows you to mark up features with arrows, add comments etc.
  
• only if you want to use fit2D for publication-style graphics: use PRINT to save fit2d graphics output to a postscript file
• provide as path for the output file H:\<my user directory>, so that all files remain on the data acquisition computer; use the file extension .ps to facilitate further processing (in fact you may want to make a ps subdirectotory for the output)
• with the free program Ghostview or with Adobe Reader Professional such postscript files can be converted to convenient image formats such as PNG or JPEG for use in publication-quality graphics
• the postscript file can also be sent directly to a color postscript printer
• NOTE: please DO NOT use the black&white printer at the beamline for image output - it uses up the toner in no time
• use OUTPUT > CHIPLOT for xy plots
• an automatic path is generated putting the file back into the corr directory with its original name and extension .chi
• these files can be imported as ASCII into Excel , Origin, etc. for further processing

calibrated plots

direct beam position

• first task is always to find the direct beam mark (through an attenuator!). I usually make sure that at least one set of calibration data is collected for each detector configuration. Calibration files typically contain "AgBeh" or "beam" in their name and I keep track of them in my log.
• zoom into the beam mark to limit the fitting range
• go to SAXS/GISAXS > BEAM CENTRE > 2D GAUSSIAN FIT and click on the beam mark
• the program will remember this position, unless a new beam center calibration is performed; fit results are provided on the fit2d ASCII window
  

distance & wavelength calibration

• Usually I measure the x-ray wavelength to better than 1% from the mono calibration (checked at each beginning of a run or sometime at the end) using the CHESS energy analyzer
  
• Estimate the sample/detector distance L_est with a ruler (WAXS) or a tape measure (SAXS) to about 10%.
• I use a Ag behenate standard (d-spacing d001=58.38 A, corresponding to a q-value of 1.0763 nm-1) which works for the full range of sample-to-detector distances available (100mm to 1500mm).
  
• fit the direct beam mark as described in the previous section
• use SAXS/GISAXS > INTEGRATE to do an angular integration of the intensity - see next section for a detailed description of the menue features
• follow the instructions in the "integration" section - I should have provided you with the wavelength
• for a first sample-detector distance use the L_est value from above
• do the integration in wavevector space (more robust)
• zoom in onto the first behenate peak and click on the maximum - in the left upper corner of the fit2d graphics window the q_est value is displayed
• do a simple calculation to get the calibrated distance L_cal :    L_cal  = L_est * q_est / 1.0763 nm-1
• now the detector is self-consistently calibrated using the well-known q-value of the first Ag behenate ring
• sanity check: redo the integration by clicking EXCHANGE and then INTEGRATE, now using L_cal - the first q maximum should be right at the correct value!

notes

• this simple procedure yields a precision better than 1% for SAXS and GISAXS - this is sufficient !!!
• the procedure yields only a precision of 2-3% for GIWAXS, which is often sufficient for diffuse scatterers like polymers
• note: if the sample is off-center by 1 mm, this already corresponds to an error of 1% at 100 mm distance
  
• if crystallographic precision (<1%) is needed in GIWAXS, images and beam images should be taken at 2 distances using a calibrated spacer, so that an absolute measurement of the scattering angle is performed; L_cal gets determined by fitting several diffraction spots or powder rings taken at different distances
  
• a pragmatic way of handling the GIWAXS calibration is using the behenate calibration for a first orientation during the measurements, and do the more precise procedure afterwards
• moving the detector is not recommended for the new detector stage
  

azimuthal integration

• choose an appropreation section of the image by zooming in; specifically the region close to the edge of the detector should be removed
• use the REMEMBER ROI feature for  integration of multiple images
• go to SAXS/GISAXS > INTEGRATE
• integration needs a fair amount of input data, however, these will be saved, and can be recalled for the next image to be analyzed
• the important input parameters are:
• pixel size: 46.9 microns for the MedOptics detector in both directions
  
• sample to detector distance L_cal (see section above)
  
• wavelength λ: will be provided by me
• the direct beam coordinates were already determined in the previous step
  

• scattering vector Q (inverse nm)
• scattering angle 2theta (deg)
• d-spacing (Angstroem)

• CONSERVE INT. : NO is recommended in combination with other fit2d features
• POLARIZATION  : does not explain whether it is s- or p-polarization, so if I really care, I choose NO and do it myself. This factor does not have effect on SAXS, and also for WAXS from organics, scattering angles are still smaller than 20 deg with the MedOptics camera, so this correction is not very important either.
• GEOMETRY COR. takes care of the transformation from a planar area detector to angle space (for math freaks: it's the Jacobian), so for this one I use: YES

• MAX. ANGLE: I use the default suggested by fit2d
• SCAN BINS: a value of about 500-1000 yields smooth curves
• MAX. D-SPACING: depends on your sample:
  
• for WAXS, 100 Å is a good start
  
• for SAXS, 2000 Å will do for all D1 can resolve
  

notes:

• You only have to set-up all of these parameters once, and then you can go through your hundreds of images, provided the scattering geometry remained the same
• You can save the numeric output data using SAXS/GISAXS > OUTPUT and choose option CHIPLOT for further analysis of the integrated curves with your own favorite software. The default values in the CHIPLOT menu will result in an ASCII file with a small header and the plot values written as an x and a y column of values (don't try to understand the settings). You can choose/modify the filename using the FILE NAME option.
  
• You can save any plots using SAXS/GISAXS > PRINT; the plot is written to a postscript file.
• Before you INPUT the next file to process, use EXCHANGE to get the program into the right mode. This is important in the SAXS/GISAXS menu, some of the other menus are more forgiving. 
• If you forget to use EXCHANGE, you will have to click FULL a couple of times to display an image. Make sure to reset the pixel size in the INTEGRATE menue to the correct value, the next time you use INTEGRATE - they are still set to the step size of the 1D output plot, and without correcting this, you will get some very stange output..
  

cake plots and sector integration

• for textured samples, i.e. if powder rings have structure or for partial powder rings, you may want to fit the angular width of these features. Here the CAKE menu comes handy: CAKE converts the x,y image to a calibrated polar plot, where the x axis can be 2-Theta (deg), q (inverse nm), or d (Å), and the y axis is the azimuth angle around the beam
• so cake yields another 2D image, which however is very suitable to determine angular widths
• the 2D plot can also be used to yield 1D integrated plots for radial and angular intensity distributions
  

• START AZIMUTH: choose in first quadrant for a continuous output angular range
  
• END AZIMUTH: go in counter-clockwise direction from start azimuth
• INNER RADIUS: can be as small as the direct beam position
• OUTER RADIUS: can be as far out as the image extends
• note: the CAKE plot will always provide a 360 deg range starting from the START AZIMUTH and going in counter-clockwise direction.
  

• 1 DEG AZ : YES if 1deg steps yield decent output,  NO - for a finer grid
  
• AZIMUTH BINS: 200-500 steps, depending on the angular range, yields smooth curves
• RADIAL BINS: 200-500 looks good
• note: for this transformation you will appreciate how lightning-fast fit2d cranks through the data - try the same in Origin!
• note: the usual fit2d features seem to have some problem with the transformed plot. In particular the pixel size does not come out right. However, choosing 1 DEG AZ. : YES, or similar, provides a simple angular bin size (of 1 deg) for further processing. Ideally slices or projections (integration of intensity over a range onto a line) could be used to determine angular width.
  

• some other parameters as explained in INTEGRATE above
• after the transformation, go to ASPECT RATIO and choose NO for a full size plot
  
• for printing or writing the CAKE plot to a spreadsheet see below.

special option: integrations with CAKE

• By setting azimuthal bins to 1, a single 1-D radial 2-Theta or Q-space scan can be obtained which is integrated over a sector whose angular width is given by the azimuth parameters. This way the integration region and the signal-to-noise ratio can be better controlled and problematic regions (edges, bad spots) can be better avoided than using INTEGRATE.

• By setting the number of radial bins to 1, and selecting the ''cake'' as an sector with specific radial vales, an integration of intensity versus azimuth may be obtained. This is very useful for texture analysis. In the P3HT case, the azimuthal width characterizes, how parallel the P3HT lamellae are with regard to the substrate.
  

• before you INPUT the next image, hit EXCHANGE: this recalls the previous 2D data image settings (and the detector pixel size before the transform !!).
  
• If you forget to EXCHANGE, chack INTEGRATION parameters carefully, and fix whatever looks wrong - in particular pixel sizes, and radial range.
  
• use REMEMBER ROI to save your integration region - this way you will get the same region each time in a file series: you can skip START AZIMUTH etc. and directly proceed to INTEGRATE. By default this feature is enabled on fit2d start-up.
  
• At times I have gotten stuck in CAKE beyond rescue - in the worst case close fit2d and restart from scratch.

(projections)

• horizontal projection
• click on the left limit of the range keeping the cross hair at the same height as the direct beam mark ( white cross).
• click on the right limit of the range keeping the crosshair at the same height as the direct beam mark
• choose top and bottom of the projection range with the cursor
• you will get the calibration menu, as in INTEGRATE or CAKE (2 pages) - check that calibration parameters are correct
• the third page just informs you about the units in x and y - just hit return
• the plot will show, often with some strange range or scaling
• zoom in to the relevant range
• see graphic output how to save the data to an ASCII xy table for use with other programs (Excel, Origin, etc.)

• vertical projections
• click on the top of the range keeping the crosshair above the direct beam mark
• click on the bottom of the range keeping the crosshair in line with the dircet beam mark - choosing a poit above the mark is fine
• do not exchange the order of inputs, or you may not get the range you wanted
• now continue as described above for the horizontal case
• the range displayed is even crazier as for horizontal - ignore all of the negative q-range when you zoom in
• note that in a GISAXS detector image, the Yoneda peak occurs at alf_i+alf_c, or in q-space, q_Y  = k {(sin(alf_i)+sin(alf_c)}
  

(calibrated 2D plots)

• determine the (q_x_min, q_y_min) values of the left bottom corner point of the image from the beam center and Ag behenate calibration
• determine the stepsize per pixel q_x_step and q_y_step
  
• generate a plot using commands from above, then rescale the plot axes to these values:
• go to the keyboard interface: MAIN > KEYBOARD
  
• now typ the following command on the ASCII screen which will prompt you for the four values determined above: AXES SCALES > q_x_min, q_x_step, q_y_min, q_y_step
• switch back to graphical interface: IMAGE; this has to be done after each step for changes to take effect on the image
  
• other useful commands to generate publication-grade figures include
  
• remove default labels: SET X-LABEL STYLE > no; SET Y-LABEL STYLE > no
  
• make numbers larger: SET ENUMERATION STYLE ; in menu choose color BLACK and size 2
• define major ticks: SET TICK POSITIONS
• define minor ticks: SET AXES STYLE
• define user region of image: REGION
• high quality output: PUBLICATION QUALITY
  
• for more detailed information see reference manual
  
• if a series of images is to be reformatted, it is worth while to learn how to write a fit2d macro
  
• PRINT to postscript file
  
• a program like ghostview (available free on the internet) can reformat the postscript to a graphics file format like png or jpeg for use in publications
• unfortunately 1D slices from the rescaled plot do not conserve the calibration and are plotted in relative pixel units
• calibrated projections onto a line can be obtained using PROJECTION. Please check the fit2d manual for details (I still have to work this out).

1D peak fitting of calibrated data

• before you get started, the Z-SCALING mode has to be set to LINEAR (in any menu you happen to be in). In order to make data visible again, if you come from LOGARITHMIC, use FULLY AUTOMATIC or WEAK PEAKS. These features work for the LINEAR scale, but yield poor scaling in the LOG scale.
  
• goto MAIN > MFIT > INITIALIZE
  
• provide rough starting parameter:
• use POLYNOMINAL for the background; a polynom of 6th order works for me
• choose model for peaks (GAUSSIAN, etc.) and follow instructions
• provide starting values for each peak
  
• starting curves are shown that should look reasonable
• EXIT
• OPTIMISE should give you a nice fit
• RESULTS displays the fit parameters in your chosen calibrated coordinates which can be saved to a file using SAVE
• ASCII OUTPUT can be optained using CHIPLOT (to be tested)
  
• PRINT the output, if you want to use the graphics (see "calibrated 2D plots")

final remark