Boulder Laboratory for 3-Dimensional Electron Microscopy of Cells

FILTERPLOT(1)						 	  FILTERPLOT(1)

NAME
  filterplot - plot filter created by 4 IMOD filter parameters

SYNOPSIS
  filterplot

DESCRIPTION
  Filterplot shows a graph of the filter function created by the four 
  parameters that are used in many IMOD programs: Sigma1, Sigma2, Radius1,
  and Radius2.  After you start the program, simply enter the parameters 
  to see the graph of the filter attenuation factor versus spatial frequency.
  Frequency is in reciprocal pixels and ranges from 0 to 0.5 in the graph,
  although the filter function does extend farther than 0.5 to cover the
  higher frequencies found at oblique angles in 2D images and 3D volumes.

  The filter is the product of two gaussian functions, the first one typically
  controlled by Sigma1 and the second one by Sigma2, Radius1, and Radius2.  If
  all values are positive or zero, then the first filter is in the form of a
  gaussian highpass filter given by:	
       (1. - exp(-r**2/(2*Sigma1**2)))
  The second filter is a gaussian-edged band-pass filter. This filter is
  flat between Radius1 --> Radius2 and decays symmetrically as a gaussian
  below Radius1 or above Radius2:
       exp(-(r-Radius)**2/(2.*sigma2**2))

  If either Sigma = 0, then that part of the filter is removed.

  The units are in fractional reciprocal lattice units,
  that is r goes from 0-->sqrt(2)/2   (0-->.5 on each axis)

  If Sigma1 is negative, the first filter is the second derivative of a
  gaussian, Del-squared G, with formula
       r**2*exp(-r**2/(2.*Sigma1**2))
  This filter alone is bandpass with a peak at 1.414*|Sigma1|, so Sigma2 and
  the Radii can be set to zero.

  If Sigma2 is negative, the second filter is inverted (1 minus the Gaussian
  band-pass filter).  This filter is then multiplied by the filter specified
  by sigma1 (if any).

  If Radius1 is negative, then the first filter is 0 out to |Radius1| and
  rises as an inverted gaussian from that point:
       (1. - exp(-(r-|Radius1|)**2/(2.*Sigma1**2)))
  The effective Radius1 for the second filter is then 0, but this filter can
  still be used to add lowpass filtering.

  Several modes of operation are possible:

  Gaussian low-pass filter (temperature factor)
  	:  Sigma1 & Radii = 0, use Sigma2

  Gaussian bandpass centered at Radius
  	:  Sigma1=0, 		use Radius1=Radius2 & Sigma2

  Gaussian-edged badpass between Radius1 & Radius2
  	:  Sigma1=0, 		use Radius1,Radius2 & Sigma2

  Gaussian bandpass (low-pass + high-pass)
  	: Radii = 0,		use Sigma1 & Sigma2

HISTORY
  Added to package, 6/19/08