Radial Profile 

  A radial profile plot widget is created when the user selects Radial
  Profile for the mouse mode in the ROI and depresses a mouse button
  at the center of the desired radial profile, drags the mouse to the
  radial edge of the profile, and releases the mouse button.

  Functions above the radial profile plot include:

    GaussShow - pops up a widget with the original fit data, a 2-D
    model of the gaussian, the residuals of the fit, and a contour
    map of the residuals with or without the image overlaid.  The user
    can specify the minimum and maximum value to be imaged for the
    raw data, model data, and residuals.  When generating a contour
    map the user specifies the number of levs that are evenly spread
    between z1 and z2.  The raw image, model image, and/or the residual
    image may be saved to a fits file.  The Done button closes the
    widget.

    Smooth - Smooth smoothes the radial profile with a boxcar smooth
    over the number of pixels specified by the user (Pix).  Undo resets
    the smooth width to 1.

    Save -  There are 3 different files that may be saved from the
    radial profile widet:
      2D image - the radial profile vector is expanded into a 2-D
      image the size of the ROI.

      Centroid - the centroid solutions of all images that are ON
      are saved to the user specified text file.

      Radial Profile - Save current radial profile to a text file, 
      with the following columns: Radius, Mean, Standard Deviation of the
      Mean (or Median), Encircled Energy, Number of Points within the radius,
      Number of Points Rejected (masked) within the Radius, Standard Error of
      the Mean (Median), Signal to Noise (Mean or Median), and Signal to Noise
      (Pixel).  Comments at the top of the file include the profile center,
      radius, zoom factor, ROI coordinates, and the smooth factor.  A widget
      pops up for the user to enter the output file name. 
    
    Print - Print current radial profile to output file (postscript,
    encapsulated postscript, pict, tiff, or jpeg).  Pops up a widget 
    for the user to enter file name and output type.

    Help - Displays this file.

    Done - Closes the Radial Profile Widget.


  On the radial profile plot:

    On the lower right side of the plot the xcursor and ycursor values are
    displayed in yellow as the cursor is moved in the plot display.


  Below the radial profile plot:

    Ymin and Ymax:  The minimum and maximum plot value for the y-axis.
    These values are set automatically when Auto Scale is enabled.  If
    the user changes the values Auto Scale is disabled.  All subsequent
    radial profile plots will use the same scaling until Auto Scale is
    re-enabled.

    Auto Scale: The y-axis of the radial profile plot is scaled between
    the minimum and maximum of the profile vector.  The minimum and 
    maximum are computed for each profile.

    Log Scale: The y-axis is scaled logarithmically.

    Encircled Energy:  The user may select to plot the encircled energy
    instead of the radial profile.

    Overplot:  When overplot is selected subsequent profiles may be 
    overplotted on the first.  There are 6 distinct line styles to
    distinguish each plot.

    Error Plotting:  Errors associated with the radial profile may be
    overplotted on the profile (in red).  The options are None, Standard
    Deviation Error, and Standard Error.

    S/N Plot: If error plotting has been enabled the user may select to
    plot in a separate graphic window the signal to noise of the profile.

    ShowBox:  If a non-zero value for the WgtMoment-HalfBox has been
    specified, HalfBox will show the box in the ROI display.  If a 
    Weighted Moment centroid has been computed WgtMoment will show
    the data used in the computation in the ROI display.

    Profile:  The profile may be computed as the mean or median of pixels
    at each radius.

    XCenter: The x location of the radial profile center.  It is automatically
    set from the circle drawn in the ROI but may be updated by the user.

    YCenter: The y location of the radial profile center.  It is automatically
    set from the circle drawn in the ROI but may be updated by the user.

    Radius: The radius of the radial profile.  It is automatically set from
    the circle drawn in the ROI but may be updated by the user.

    Fitting:  The FWHM is required for centroid fitting using the 2-D
    Gaussian fit and is the default for determining the box width for
    the Weighted Moment algorithm.  (See HalfBox below.)  Calc FWHM
    will calculate an approximate FWHM from the radial profile and 
    update the FWHM field.  The user may alter the value in the field.
    
    Fit Circle: By default a square region of data is fit.  If Fit Circle
    is enabled pixels inside the box but outside the circle are masked.

    WgtMoment:  Additional parameters for the weighted moment algorithm are:
      HalfBox:  The user may specify a box half width in pixels
      for the fitting region.  This will override the default box half
      width of 1.5 sigma (0.637 * FWHM).

      CenterPeakUp:  By default, the weighted moment algorithm finds the
      maximum pixel in a box centered on the input X,Y center and extracts
      a new box about this maximum pixel.  If CenterPeakUp is disabled
      this step is omitted in the fitting process.

    Centroid Methods:

      Weighted Moment (CNTRD from the Astron Library), uses an early DAOPHOT
      "FIND" centroid algorithm that locates the position where the X and Y
      derivaties go to zero.  

      GaussFit is the mpfit2dpeak procedure from Craig B. Markwardt which
      uses his non-linear least squares fitter MPFIT.  The baseline level
      is assumed to be constant.

  A number of changes have been made to the radial profile plot window.
These changes are described below:

  Both the centroid and adjust radial profile functions have been moved
  to the radial profile window.  The profile may be adjusted by changing
  the x and y centers or radius in the appropriate boxes at the bottom
  of the widget.  The initial guess of the centroid center is defined
  in the same boxes while the full width half maximum may be computed
  from the radial profile (Calc FWHM button) or typed in the appropriate
  box.

  A number of new features have been added including:

  1. The user may choose between the mean and the median when computing
     the radial profile.

  2. Two methods are defined for computing the centroid, the weighted
     moment algorithm that has always been available and the 2D Gaussian
     fitting routine.  Either or both may be selected with the weighted
     moment routine the default.  When both are selected the results of
     both fits are printed in a box on the right side of the widget with 
     their errors and the differences between the fits in x and y and the 
     total error.  The radial profile generated from the weighted mean 
     center is plotted as a solid line and the profile generated from 
     the gaussian center is overlaid as a dashed line.

  3. The user may select the minimum and maximum values for the plot y
     axis to expand the y scaling.  If auto scale is turned off all future
     plots will use the same scaling.  Otherwise, the scaling is only
     valid for the current plot.

  4. The user may select to plot the encircled energy profile instead of
     the radial profile.

  5. The user may select to plot the associated errors over the radial
     profile.

  6. The user may select log scale or the default linear scale for the
     y-axis.

  7. If over plot is selected subsequent radial profile plots are overplotted
     on the current display with no erase.  Since there are six unique line 
     styles it is not recommended to overplot more than five profiles.

  8. The user may adjust the radial profile by changing the values of
     the profile x,y center or radius in the appropriate text boxes.
     The profile is updated with any change to these parameters.

  9. The user must enter a value for FWHM or calculate the value based
     on the profile data before centroiding.  If a 2-d gaussian is fit
     the user may display the data that was fitted, the model of the
     fit, the residuals, and a contour map of the residuals with the
     gaussshow button.

 10. The S/N Plot button produces a signal to noise plot of the profile.

  Radial Profile submenu in the ROI

    Save
      Save current radial profile to a text file, X,Y pairs.  Pops up a
      widget allowing user to enter file name.  The center of the
      radial profile is saved in the first line of the output file.

    Print
      Print current radial profile to output file (postscript, 
      encapsulated postscript, or pict).  Pops up a widget allowing
      user to enter file name and output type.

    Save Centroids
      Saves the centroid x and y values with associated file names to
      an ASCII text file.

    Set Color
      Sets the color of the radial profile circle drawn in the roi
      display.

    Align Centroids
      Moved to ROI Plot Menu.

    Adjust Radial Profile
      Moved to radial profile display

    Centroid
      Moved to radial profile display