topo
Version 2.05, September 2000
David L. Windt
Copyright (c) 1997-2000, David L. Windt. All rights reserved
The topo library is a set of IDL routines for analyzing 1D or 2D surface topography (i.e., surface roughness) data. I originally wrote these routines in order to analyze WYKO and AFM data of optical surfaces, but the routines are general, and can be used to analyze any type of 1D or 2D topography data.
The available routines are listed below. In particular, the routines xanlz_prof , xanlz_psd , and xanlz_surf are point-and-click (widget) applications for 1D profile analysis, 1D PSD analysis, and 2D surface analysis, respectively.
References
My understanding of surface roughness is based largely on the material contained in these two references:
1. J. M. Bennett and L. Mattsson, 'Introduction to Surface Roughness and Scattering' (Optical Society of America, Washington, D. C. 1989)
2. E. L. Church, 'Fractal surface finish', Applied Optics, 27 (8) 1518-1526 (1988)
See the README file in the topo directory for installation instructions.
Note: To use the topo library, you must be running IDL V5.1 or higher.
To load the topo library, at the IDL prompt type .run topostart:
IDL> .run topostart
Once the library has been loaded, you can use these routines as you would any IDL procedures and functions.
For instance, you might make up some 2D data like this:
IDL> x=vector(0.,100.,256)
IDL> y=x
IDL> z=randomn(seed,256,256)
and then try:
IDL> xanlz_surf,x,y,z
I've included in the extras.dir directory some sample data to play around with.
Try this:
IDL> rd_wyko,x,y,z,file='...path to topo.../extras.dir/wyko_example.dat'
IDL> rd_wyko,x,y,z,file='...path to topo.../extras.dir/wyko_example.dat',/swap_endian
and then:
IDL> xanlz_surf,x,y,z
Or this:
IDL> rd_digital_afm,x,y,z,file='...path to topo.../extras.dir/digital_afm_example.dat'
IDL> rd_digital_afm,x,y,z,file='...path to topo.../extras.dir/digital_afm_example.dat',/swap_endian
and then:
IDL> xanlz_surf,x,y,z
Last Updated: 2-Sep-2000
New routines and those that have changed since the last release (2.04, 1-Dec-1998) are marked with an asterix.
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NAME:
ANGLE2WAVES
PURPOSE:
Procedure to compute (and optionally plot) the spatial
wavelengths corresponding to scattering for incidence angle
ALPHA, wavelength LAMBDA, into scattering angles
ALPHA+/-DELTA(0) to ALPHA+/-DELTA(1)
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
ANGLE2WAVES,ALPHA,LAMBDA,DELTA,WAVES=WAVES
INPUTS:
ALPHA - A scalar or 1D array of incidence angles.
LAMBDA - Scalar specifying the incidence wavelength.
DELTA - 2-element array specifying the min and max scattering
angles to consider.
KEYWORD PARAMETERS:
WAVES - Output array of spatial wavelengths, having
dimensions [2,N_ELEMENTS(ALPHA)]. Units
are the same as for LAMBDA.
The following keywords only have an effect when ALPHA is an
array:
NOPLOT - Set to inhibit plotting the results.
All IDL PLOT graphics keywords.
PROCEDURE:
WAVES=FLTARR(2,N_ELEMENTS(ALPHA))
WAVES(0,*)=LAMBDA/2./SIN(DELTA(0)/2.*!DTOR)/
COS((ALPHA-DELTA(0)/2.)*!DTOR)
WAVES(1,*)=LAMBDA/2./SIN(DELTA(1)/2.*!DTOR)/
COS((ALPHA-DELTA(1)/2.)*!DTOR)
EXAMPLE:
Compute the range of spatial wavelengths (in angstroms)
corresponding to scattering for 30 degree incidence, with
scattering angles from 1 to 60 degrees (i.e., 30+/-1 to
30+/-60), for a photon wavelength of 100 angstroms:
ANGLE2WAVES,30.,100.,[1.,60.]
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
ANLZ_PROF
PURPOSE:
Perform 2D analysis of X,Y profile data. This procedure
combines the functionality of several TOPO routines, and
displays the results in a single composite plot, using the
PLOT_PROF, PLOT_H_DIST, PLOT_S_DIST, PLOT_AUTOCOV, and
PLOT_PSD routines.
This routines is called by the XANLZ_PROF widget application.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
ANLZ_PROF,X,Y
INPUTS:
X - 1D array of (equally spaced) lengths in angstroms.
Y - 1D array of heights in angstroms.
KEYWORD PARAMETERS:
PLOT - A 4-element vector indicating which plots are to be
made:
PLOT(0) - Set to 1 to plot profile.
PLOT(1) - Set to 1 to plot height and slope
distributions.
PLOT(2) - Set to 1 to plot autocovariance.
PLOT(3) - Set to 1 to plot PSD.
XREGION - 1D array of subscripts for X, specifying a
region-of-interest.
SUB_TILT - Set to subtract tilt, using SUB_TILT
HEIGHTS - Output array of heights (see HEIGHT_DIST), in units
determined by the value of TOPO.YUNITS_PTR (see
PROCEDURE below.)
HEIGHT_HIST - Output array of height histogram values (See
HEIGHT_DIST)
N_HEIGHTS - Number of heights to be used for HEIGHT_DIST
NOFIT_HEIGHT - Set to inhibit fitting the height histogram
with a gaussian.
SLOPES - Output array of slopes in degrees (See HEIGHT_DIST.)
SLOPE_HIST - Output array of slope histogram values (See
HEIGHT_DIST)
N_SLOPES - Number of slopes to be used for HEIGHT_DIST
NOFIT_SLOPE - Set to inhibit fitting the height histogram
with a gaussian.
TAU - Output array of lag lengths, in units determined by the
value of TOPO.XUNITS_PTR (see PROCEDURE below.)
AUTOCOV - Output array of autocovariance values, in units
determined by the value of TOPO.YUNITS_PTR (see
PROCEDURE below.) For example, if TOPO.YUNITS_PTR=1,
then the AUTOCOV units will be nm^2.
FIT_AUTOCOV - Same as FIT_TYPE keyword to PLOT_AUTOCOV.
FREQ - Output array of spatial frequencies, in units
determined by the value of TOPO.XUNITS_PTR (see
PROCEDURE below.) For example, if TOPO.XUNITS_PTR=1,
then the FREQ units will be 1/nm.
PSD - Output array of power-spectral-density values, in units
determined by the value of TOPO.YUNITS_PTR (see
PROCEDURE below.) For example, if TOPO.YUNITS_PTR=1,
then the PSD units will be nm^3.
ZERO_PAD - See PROF2PSD
HANNING - See PROF2PSD
KAISER - See PROF2PSD
RANGE - See PROF2PSD
FIT_PSD - Same as FIT_TYPE keyword to PLOT_PSD
Z_VALUE - Z parameter needed for Omega/nu/n PSD fits.
PRSTYLE - 5-element array specifying
[COLOR,LINESTYLE,THICK,PSYM,SYMSIZE] keywords for
profile plot. (except that PSYM and SYMSIZE are
ignored!)
HSTYLE - 5-element array specifying
[COLOR,LINESTYLE,THICK,PSYM,SYMSIZE] keywords for
height-histogram plot. (except that PSYM and SYMSIZE
are ignored!)
SSTYLE - 5-element array specifying
[COLOR,LINESTYLE,THICK,PSYM,SYMSIZE] keywords for
slope-histogram plot. (except that PSYM and SYMSIZE
are ignored!)
ASTYLE - 5-element array specifying
[COLOR,LINESTYLE,THICK,PSYM,SYMSIZE] keywords for
autocovariance plot.
PSTYLE - 5-element array specifying
[COLOR,LINESTYLE,THICK,PSYM,SYMSIZE] keywords for
PSD plot.
PRXAXIS - 4-element array specifyin
[XTYPE,XRANGE(0),XRANGE(1),XSTYLE] keywords for
profile plot.
AXAXIS - 4-element array specifyin
[XTYPE,XRANGE(0),XRANGE(1),XSTYLE] keywords for
autocovariance plot.
PXAXIS - 4-element array specifyin
[XTYPE,XRANGE(0),XRANGE(1),XSTYLE] keywords for
PSD plot.
PRYAXIS - 4-element array specifyin
[YTYPE,YRANGE(0),YRANGE(1),YSTYLE] keywords for
profile plot.
AYAXIS - 4-element array specifyin
[YTYPE,YRANGE(0),YRANGE(1),YSTYLE] keywords for
autocovariance plot.
PYAXIS - 4-element array specifyin
[YTYPE,YRANGE(0),YRANGE(1),YSTYLE] keywords for PSD
plot.
RESTRICTIONS:
The X values must be equally spaced.
X and Y must be in angstroms.
PROCEDURE:
Although X and Y must be in angstroms, the units for
displayed (and returned keyword) variables are determined by
the values of the relevant tags of the common block variable
TOPO.
That is, set TOPO.XUNITS_PTR to 0 for angstroms, 1 for nm, 2
for microns, and 3 for mm. Same goes for TOPO.YUNITS_PTR.
The precision of the fit parameters that are labelled on the
plots is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), TOPO.YPRECISION for height-related
parameters (e.g., rms roughness), and TOPO.SPRECISION for
slope-related parameters (e.g., rms slope.) For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
January, 1998 - Added call to TEK_COLOR (unless !D.NAME eq
'HP'), and when !D.NAME eq 'CGM', set the color
index for !p.color to black.
May, 1998 - Added PLOT keyword.
windt@astro.columbia.edu
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NAME:
AUTOCOV2PARS
PURPOSE:
Procedure to compute the rms roughness SIGMA and correlation
length L from the the autocovariance function, C(TAU).
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
AUTOCOV2PARS,TAU,C,SIGMA,L
INPUTS:
TAU - 1D array of lag lengths.
C - 1D array of autocovariance values.
OUTPUTS:
SIGMA - Rms roughness, in units determined by the units of C.
For example, if [C]=nm^2, then [SIGMA]=nm.
L - Correlation length, in same units as TAU.
PROCEDURE:
SIGMA=SQRT(C)
L = 2/SIGMA^4 * Integral(C^2)
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
AUTOCOV2PSD
PURPOSE:
Function to compute the power-spectral-density function S(F)
from the the autocovariance function, C(TAU).
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
S=AUTOCOV2PSD(TAUX[,TAUY],C)
INPUTS:
TAUX - 1D array of lag lengths along X direction.
TAUY - Optional 1D array of lag lengths along Y direction.
C - 1D or 2D array of autocovariance values.
OUTPUTS:
S - 1D or 2D array of power-spectral-density values.
KEYWORD PARAMETERS:
FX - 1D output array of spatial frequencies along X
direction.
FY - 1D output array of spatial frequencies along Y
direction.
POSITIVE_ONLY - Set to only compute S(F) for positive spatial
frequencies.
HANNING - Set to use a Hanning window function.
RANGE - 2-element array specifying the min and max spatial
frequency values to be considered.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
AUTOCOV_FIT
PURPOSE:
Function to fit the autocovariance function with either a
gaussian, and exponential, or a gaussian plus an exponential.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
Result=AUTOCOV_FIT(TAU,C,PARS,FIT=FIT)
INPUTS:
TAU - 1D array of lag lengths.
C - 1D array of autocovariance values.
FIT - Set to 0 to fit to a gaussian. Set to 1 to fit to an
exponential. Set to 2 to fit to a gaussian+exponential.
OUTPUTS:
Result - Fit function.
PARS - 1-D array of fit parameters.
PROCEDURE:
The autocovariance function is fit using either the GAUSS_FIT,
the EXPO_FIT, or the GAUSSEXPO_FIT functions. See the
documentation for these functions (in the windt library) for a
desciption of the elements of PARS.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
HEIGHT_DIST
PURPOSE:
Function to compute the height histogram from X,Y profile
data. The function can also be used to compute the slope
histogram, in conjunction with the PROF2SLOPE function.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
Result=HEIGHT_DIST(X,Y[,HEIGHTS])
INPUTS:
X - 1D array of (equally spaced) lengths.
Y - 1D array of heights.
KEYWORD PARAMETERS:
N_HTS - Integer specifying the number of bins to be used in
conjunction with the HISTOGRAM function.
RANGE - 2-element array specifying the min and max height
values to consider.
OUTPUTS:
Result - 1D array of density values. (See the HISTOGRAM
function.)
OPTIONAL OUTPUTS:
HEIGHTS - 1D array of height values; the i'th element of
Result is the density of heights in the i'th bin of
HEIGHTS.
PROCEDURE:
The HISTOGRAM function is used.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PARS2AUTOCOV
PURPOSE:
Function to generate an autocovariance function from an array
of parameters describing the function. This function is a
sort of inverse of the AUTOCOV_FIT routine.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
C=PARS2AUTOCOV(TAUX[,TAUY],P,TYPE=TYPE)
INPUTS:
TAUX - 1D array of lag lengths along X direction.
TAUY - Optional 1D array of lag lengths along Y direction.
P - Array of parameters describing the function. The number
of elements of P required depends on the value of the
TYPE keyword:
TYPE - Keyword specifying the functional form for C: 0 for
gaussian, 1 for exponential, 2 for
gaussian+exponential.
OUTPUTS:
C - 1D or 2D array of autocovariance values.
PROCEDURE:
TYPE=0 - Gaussian:
C=P(0)^2*EXP(-(TAU/P(1))^2)+P(2)
TYPE=1 - Exponential:
C=P(0)^2*EXP(-ABS(TAU)/P(1))+P(2)
TYPE=2 - Gaussian+Exponential:
C=P(0)^2*EXP(-(TAU/P(1))^2)+P(2)^2*EXP(-ABS(TAU)/P(3))+P(4)
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PARS2PSD
PURPOSE:
Function to generate a power-law power-spectral-density
function from an array of parameters describing the function.
This function is a sort of inverse of the PSD_FIT routine.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
S=PARS2PSD(FX[,FY],P)
INPUTS:
FX - 1D output array of spatial frequencies along X
direction.
FY - 1D output array of spatial frequencies along Y
direction.
P - 2-element array of parameters describing the power-law
function. P(0)= K_n, P(1)=n.
OUTPUTS:
S - 1D or 2D array of power-spectral-density values.
PROCEDURE:
For a 1D PSD function,
S=P(0)/(ABS(F)^P(1))
For a 2D PSD function,
S=GAMMA((P(1)+1)/2)/2./GAMMA(.5)/GAMMA(P(1)/2.)* $
P(0)/(ABS(F)^(P(1)+1))
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PLOT_AUTOCOV
PURPOSE:
Procedure to plot and optionally fit the autocovariance
function.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PLOT_AUTOCOV,TAUX[,TAUY],C
INPUTS:
TAUX - 1D array of lag lengths along X direction, in units
corresponding to the value of TOPO.XUNITS_PTR.
TAUY - 1D array of lag lengths along Y direction, in units
corresponding to the value of TOPO.YUNITS_PTR.
C - 1D array of autocovariance values, in units corresponding
to the value of TOPO.YUNITS_PTR.
KEYWORD PARAMETERS:
SIGMA - Output rms roughness, computed from C using
AUTOCOV2PARS, in units corresponding to the value of
TOPO.YUNITS_PTR.
CORR_LENGTH - Correlation length, computed from C using
AUTOCOV2PARS, in units corresponding to the
value of TOPO.XUNITS_PTR.
FIT_TYPE - Set to -1 for no fit, 0 for gaussian fit, 1 for
exponential fit, 2 for gaussian+exponential fit.
REGION - Set to interactively select a region-of-interest for
fitting, using GET_ROI.
CFIT - Output fit dependent variable.
TAUFIT - Output fit independent variable.
FIT_PARS - Fit parameters. (See AUTOCOV_FIT.)
FIT_COLOR - IDL graphics keyword for fit function.
FIT_THICK - IDL graphics keyword for fit function.
FIT_LINESTYLE - IDL graphics keyword for fit function.
NOLABEL - Set to inhibit labelling the SIGMA, L and fit
parameters values.
LABEL_POSITION - Integer specifying label position, as per
PLOT_TEXT.
Plus most IDL PLOT graphics keywords.
RESTRICTIONS:
The units for TAU and C must correspond to the values of the
relevant tags of the common block variable TOPO. That is, set
TOPO.XUNITS_PTR to 0 for TAU in angstroms, 1 for nm, 2 for
microns, and 3 for mm. Similarly, set TOPO.YUNITS_PTR to 0 for
C in angstroms^2, 1 for nm^2, 2 for microns^2, and 3 for mm^2.
The precision of the fit parameters that are labelled on the
plot is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), and TOPO.YPRECISION for height-related
parameters (e.g., rms roughness). For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PLOT_H_DIST
PURPOSE:
Procedure to compute, plot and optionally fit a height
histogram function.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PLOT_H_DIST,X,Y
INPUTS:
X - 1D array of lengths, in units corresponding to the value
of TOPO.XUNITS_PTR.
Y - 1D array of heights, in units corresponding to the value
of TOPO.YUNITS_PTR.
KEYWORD PARAMETERS:
N_HEIGHTS - Integer specifying the number of bins to be used
in conjunction with the HISTOGRAM function.
HIST - 1D ouput array of density values. (See the HISTOGRAM
function.)
HEIGHTS - 1D output array of height values; the i'th element
of HIST is the density of heights in the i'th bin
of HEIGHTS.
NOLABEL - Set to inhibit labelling the SIGMA, and L values.
LABEL_POSITION - Integer specifying label position, as per
PLOT_TEXT.
Plus most IDL PLOT graphics keywords.
RESTRICTIONS:
The units for X and Y must correspond to the values of the
relevant tags of the common block variable TOPO. That is, set
TOPO.XUNITS_PTR to 0 for X in angstroms, 1 for nm, 2 for
microns, and 3 for mm. Similarly, set TOPO.YUNITS_PTR to 0 for
Y in angstroms, 1 for nm, 2 for microns, and 3 for mm.
The precision of the fit parameters that are labelled on the
plot is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), and TOPO.YPRECISION for height-related
parameters (e.g., rms roughness). For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
PROCEDURE:
HEIGHT_DIST is used to compute the height histogram function.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PLOT_PROF
PURPOSE:
Procedure to plot a profile function.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PLOT_PROF,X,Y
INPUTS:
X - 1D array of lengths, in units corresponding to the value
of TOPO.XUNITS_PTR.
Y - 1D array of heights, in units corresponding to the value
of TOPO.YUNITS_PTR.
KEYWORD PARAMETERS:
OVERPLOT - Set for overplot.
NOLABEL - Set to inhibit labelling the SIGMA, and L values.
LABEL_POSITION - Integer specifying label position, as per
PLOT_TEXT.
Plus most IDL PLOT graphics keywords.
RESTRICTIONS:
The units for X and Y must correspond to the values of the
relevant tags of the common block variable TOPO. That is, set
TOPO.XUNITS_PTR to 0 for X in angstroms, 1 for nm, 2 for
microns, and 3 for mm. Similarly, set TOPO.YUNITS_PTR to 0 for
Y in angstroms, 1 for nm, 2 for microns, and 3 for mm.
The precision of the parameters that are labelled on the
plot is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), and TOPO.YPRECISION for height-related
parameters (e.g., rms roughness). For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PLOT_PSD
PURPOSE:
Procedure to plot and optionally fit the
power-spectral-density function.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PLOT_PSD,FX[,FY],S
INPUTS:
FX - 1D array of spatial frequencies along X direction, in
units corresponding to the value of TOPO.XUNITS_PTR.
For example, if TOPO.XUNITS_PTR=1, then [FX]=1/nm.
FY - 1D array of spatial frequencies along Y direction, in
units corresponding to the value of TOPO.XUNITS_PTR.
For example, if TOPO.XUNITS_PTR=1, then [FY]=1/nm.
S - 1D array of power-spectral-density values, in units
corresponding to the value of TOPO.YUNITS_PTR. For
example, if TOPO.YUNITS_PTR=1, then [S]=nm^3.
KEYWORD PARAMETERS:
OVERPLOT - Set for overplot.
SIGMA - Rms roughness, computed from S using PSD2PARS.
CORR_LENGTH - Correlation length, computed from S using
PSD2PARS.
FIT_TYPE - Set to -1 for no fit, 0 for power-law fit, 1 for
sigma/xi/h fit, and 2 for omega/nu/n fit. If
FIT_TYPE=2, then Z_VALUE must be provided. Note that
if FIT_TYPE is set to 0, then TWOD will be set to
zero as well; if FIT_TYPE is set to 1 or 2, then
TWOD will be set to 1.
Z_VALUE - Film thickness parameter needed for omega/nu/n PSD
model fit. Units for Z_VALUE are given by the
value of TOPO.XUNITS_PTR.
RANGE - 2-element array of frequency values defining the
region-of-interest for fitting.
REGION - Set to interactively select a region-of-interest for
fitting, using GET_ROI.
TWOD - Set to indicate that the 1D PSD being plotted is
actually a slice from a 2D PSD function, so that the
units are labelled properly. This keyword may be overwritten
if FIT_TYPE is specified.
SFIT - Output fit dependent variable.
FFIT - Output fit independent variable.
FIT_PARS - Fit parameters. (See PSD_FIT.)
FIT_COLOR - IDL graphics keyword for fit function.
FIT_THICK - IDL graphics keyword for fit function.
FIT_LINESTYLE - IDL graphics keyword for fit function.
NOLABEL - Set to inhibit labelling the SIGMA, L and fit
parameters values.
LABEL_POSITION - Integer specifying label position, as per
PLOT_TEXT.
Plus most IDL PLOT graphics keywords.
RESTRICTIONS:
The units for F and S must correspond to the values of the
relevant tags of the common block variable TOPO. That is, set
TOPO.XUNITS_PTR to 0 for F in angstroms, 1 for nm, 2 for
microns, and 3 for mm. Similarly, set TOPO.YUNITS_PTR to 0 for
S in angstroms^3, 1 for nm^3, 2 for microns^3, and 3 for mm^3.
The precision of the fit parameters that are labelled on the
plot is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), and TOPO.YPRECISION for height-related
parameters (e.g., rms roughness). For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
May 1998 - Added FIT_TYPE=1,2, and REGION and Z_VALUE keywords.
- F and S are now correctly converted according the
values of TOPO.XUNITS_PTR and TOPO.YUNITS_PTR
windt@astro.columbia.edu
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NAME:
PLOT_SLOPE
PURPOSE:
Procedure to plot a slope function.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PLOT_SLOPE,X,SLOPE
INPUTS:
X - 1D array of lengths, in units corresponding to the value
of TOPO.XUNITS_PTR.
SLOPE - 1D array of slope values, in degrees.
KEYWORD PARAMETERS:
OVERPLOT - Set for overplot.
NOLABEL - Set to inhibit labelling the SIGMA, and L values.
LABEL_POSITION - Integer specifying label position, as per
PLOT_TEXT.
Plus most IDL PLOT graphics keywords.
RESTRICTIONS:
The units for X must correspond to the value of the relevant
tag of the common block variable TOPO. That is, set
TOPO.XUNITS_PTR to 0 for X in angstroms, 1 for nm, 2 for
microns, and 3 for mm.
The precision of the rms slope parameter that is labelled on
the plot is determined by the value of the variable
TOPO.SPRECISION. For example, if TOPO.SPRECISION=3, then three
places to the right of the decimal will be displayed.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PLOT_S_DIST
PURPOSE:
Procedure to compute, plot and optionally fit a slope
histogram function.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PLOT_S_DIST,X,Y
INPUTS:
X - 1D array of lengths, in units corresponding to the value
of TOPO.XUNITS_PTR.
Y - 1D array of heights, in units corresponding to the value
of TOPO.YUNITS_PTR.
KEYWORD PARAMETERS:
N_SLOPES - Integer specifying the number of bins to be used
in conjunction with the HISTOGRAM function.
HIST - 1D ouput array of density values. (See the HISTOGRAM
function.)
SLOPES - 1D output array of slope values; the i'th element of
HIST is the density of slopes in the i'th bin of
SLOPES.
NOLABEL - Set to inhibit labelling the SIGMA, and L values.
LABEL_POSITION - Integer specifying label position, as per
PLOT_TEXT.
Plus most IDL PLOT graphics keywords.
RESTRICTIONS:
The units for X and Y must correspond to the values of the
relevant tags of the common block variable TOPO. That is, set
TOPO.XUNITS_PTR to 0 for X in angstroms, 1 for nm, 2 for
microns, and 3 for mm. Similarly, set TOPO.YUNITS_PTR to 0 for
Y in angstroms, 1 for nm, 2 for microns, and 3 for mm.
The precision of the fit parameter (i.e., rms slope) that is
labelled on the plot is determined by the value of the variable
TOPO.SPRECISION. For example, if TOPO.SPRECISION=3, then three
places to the right of the decimal will be displayed.
PROCEDURE:
PROF2SLOPE is used to compute the slope values; HEIGHT_DIST
is used to compute the slope histogram function.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PROF2AUTOCOV
PURPOSE:
Function to compute the autocovariance function from the
profile data.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
C=PROF2AUTOCOV(X,Y,TAU=TAU)
INPUTS:
X - 1D array of (equally-spaced) lengths.
Y - 1D array of heights.
OUTPUTS:
TAU - 1D array of lag lengths, in units of [X].
C - 1D array of autocovariance values, in units of [Y]^2.
KEYWORD PARAMETERS:
POSITIVE_ONLY - Set to compute the autocovariance function
for positive lag lengths only.
RESTRICTIONS:
The X values must be equally spaced.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PROF2PSD
PURPOSE:
Function to compute the power-spectral-density function from
the profile data.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
S=PROF2PSD(X,Y,F=F)
INPUTS:
X - 1D array of (equally-spaced) lengths.
Y - 1D array of heights.
OUTPUTS:
F - 1D array of spatial frequencies, in units of 1/[X].
S - 1D array of PSD values, in units of [Y]^3.
KEYWORD PARAMETERS:
POSITIVE_ONLY - Set to compute the psd function for positive
frequencies only.
RANGE - 2-element array specifying the min and max spatial
frequencies to be considered. Default is from
1/(length) to 1/(2*interval) (i.e., the Nyquist
frequency), where length is the length of the scan,
and interval is the spacing between points.
ZERO_PAD - Set this to an integer specifying the number of
zero-height points to add on either side of the
profile data.
HANNING - Set this to use a Hanning window function.
KAISER - Set this to use a Kaiser-Bessel window function
RESTRICTIONS:
The X values must be equally spaced.
PROCEDURE
S=Length*ABS(FFT(Y*Window),-1)^2
Where Length is as described above, and Window is the value of
the optional window function (Hanning or Kaiser-Bessel).
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
Nov 1998: When using the HANNING or KAISER keywords, the window
function is now normalized so that the integral of the PSD is
~constant, i.e., independent of your choice of window.
September 2000: Corrected a problem wherein the spatial
frequencies were computed incorrectly.
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NAME:
PROF2SLOPE
PURPOSE:
Function to compute the slope from the profile data.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
Result=PROF2SLOPE(X,Y)
INPUTS:
X - 1D array of (equally-spaced) lengths.
Y - 1D array of heights.
OUTPUTS:
Result - 1D array of slope values, in degrees.
RESTRICTIONS:
The X values must be equally spaced.
X and Y must have the same units.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PSD2RAVEPSD
PURPOSE:
Function to compute the radially-averaged PSD from a 2D PSD array.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
SR=PSD2RAVEPSD(FX,FY,S,FR=FR)
INPUTS:
FX - 1D array of spatial frequencies along X
direction.
FY - Optional 1D array of spatial frequencies along Y
direction.
S - 2D array of power-spectral-density values.
OUTPUTS:
SR - 1D array of radially-averaged PSD values.
FR - 1D array of spatial frequencies.
PROCEDURE:
The radially-averaged PSD is computed for a vector of FR values,
with FR = sqrt(FX^2+FY^2), and for FR values ranging from the
minimum spatial frequency to the maximum spatial frequency
along X or Y (whichever is smallest.)
The i'th value of SR, at a specific FR(i), is equal to the
average of all S values contained in the anulus defined by
FR(i)-.5*DFR < sqrt(FX^2+FY^2) <= FR(i)+.5*DFR, where DFR
is the spatial frequency increment.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1998
windt@astro.columbia.edu
September 2000: Corrected some problems with the way SR and FR
were computed that arose when FX and FY are unequal.
Eric Gullikson, LBL
EMGullikson@lbl.gov
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NAME:
PSD2PARS
PURPOSE:
Procedure to compute the rms roughness SIGMA and correlation
length L from the the power-spectral-density function S(F).
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PSD2PARS,F,S,SIGMA,L
INPUTS:
F - 1D array of spatial frequencies.
S - 1D array of power-spectral-density values.
OUTPUTS:
SIGMA - Rms roughness, in units of [S]^(1/3)
L - Correlation length, in units of 1/[F]
PROCEDURE:
SIGMA=SQRT(2*Integral(S))
L = 1/2/SIGMA^4 * Integral(S^2)
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PSDPARS2SIGMA_L
PURPOSE:
Procedure to compute the rms roughness SIGMA and correlation
length L from the scan LENGTH and the power-law parameters
K_N and N.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PSDPARS2SIGMA_L,K_N,N,LENGTH,SIGMA,L
INPUTS:
K_N - Power-law scaling factor.
N - Power-law exponent.
LENGTH - Scan length.
OUTPUTS:
SIGMA - Rms roughness.
L - Correlation length.
PROCEDURE:
SIGMA = SQRT(K_n*LENGTH^(N-1)/(N-1))
L = (N-1)^2*LENGTH/2/(2*N-1)
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PSDPARS_ANGLE2SIGMA_L
PURPOSE:
Function to compute the rms roughness SIGMA and correlation
length L from (a) the maximum spatial wavelength
corresponding to scattering for incidence angle ALPHA,
wavelength LAMBDA, into scattering angles ALPHA+/-DELTA(0) to
ALPHA+/-DELTA(1), and (b) the power-law parameters K_N and N.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
PSDPARS_ANGLE2SIGMA_L,K_N,N,ALPHA,LAMBDA,DELTA,SIGMA,L
INPUTS:
K_N - Power-law scaling factor.
N - Power-law exponent.
ALPHA - A scalar or 1D array of incidence angles.
LAMBDA - Scalar specifying the incidence wavelength.
DELTA - 2-element array specifying the min and max scattering
angles to consider.
OUTPUTS:
SIGMA - Rms roughness.
L - Correlation length.
PROCEDURE:
The ANGLE2WAVES procedure is used to compute the range of
spatial wavelengths corresponding to scattering at incidence
angle ALPHA, wavelength LAMBDA, into scattering angles
ALPHA+/-DELTA(i). The maximum wavelength is then used along
with the specified K_N and N to compute SIGMA and L, using
the PSDPARS2SIGMA_L routine.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
PSD_FIT
PURPOSE:
Function to fit a 1D array of power-spectral-density function
values with a power-law.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
Result=PSD_FIT(F,S,PARS)
INPUTS:
F - 1D array of spatial frequencies.
S - 1D array of power-spectral-density values.
OUTPUTS:
Result - Fit function.
PARS - 1-D array of fit parameters: PARS(0)=K_n, PARS(1)=N
KEYWORD PARAMETERS:
RANGE - 2-element array of min and max spatial frequencies to
be used for fitting. Default is to use the entire
range of data.
FFIT - Array of F values corresponding to the range used for
fitting.
TWOD - If TWOD is set, then the 1D array of PSD values is consider
to represent a slice (or radial average) of a 2D PSD function.
PROCEDURE:
A 1D PSD function is fit to the function
S=K_n/(ABS(F)^N)
A 2D PSD function is fit to the function
S=Gamma((N+1)/2)/(2*Gamma(1/2)*Gamma(N/2))*K_n/F^(N+1)
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
May 1998 - Added RANGE, FFIT and TWOD keywords.
- If a 2-sided PSD is provided, then fit function
returned is now only 1-sided (i.e., defined only for
positive frequencies).
windt@astro.columbia.edu
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NAME:
PSD_SIGMA_XI_H_FIT
PURPOSE:
Function to fit a power-spectral-density function with a
function of the form:
PSD(2*pi*F)=4 pi H sigma^2 xi^2 /(1 + abs(2*pi*F)^2 xi^2)^(1+H)
Note that this form refers to a 2D PSD function; thus it only
makes sense to use this program to fit a 1D array of
radially-averaged PSD values.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
Result=PSD_SIGMA_XI_H_FIT(F,S,PARS)
INPUTS:
F - 1D array of spatial frequencies.
S - 1D array of power-spectral-density values.
OUTPUTS:
Result - Fit function.
PARS - 1-D array of fit parameters: [sigma,xi,H]
KEYWORD PARAMETERS:
RANGE - 2-element array of min and max spatial frequencies to
be used for fitting. Default is to use the entire
range of data.
FFIT - Array of F values corresponding to the range used for
fitting.
RESTRICTIONS:
F and S must use the same length units.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1998
windt@astro.columbia.edu
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NAME:
PSD_OMEGA_NU_N_FIT
PURPOSE:
Function to fit a power-spectral-density function with a
function of the form:
PSD(2*pi*F)=Omega * (1-exp(-2*nu*(2*pi*F)^n*z)) / (2*nu*(2*pi*F)^n)
Note that this form refers to a 2D PSD function; thus it only
makes sense to use this program to fit a 1D array of
radially-averaged PSD values.
This form of the PSD comes from the stochastic model of thin
film growth and erosion, developed by D. Stearns,
Appl. Phys. Lett. 62, 1745-1747 (1993)
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
Result=PSD_OMEGA_NU_N_FIT(F,S,Z,PARS)
INPUTS:
F - 1D array of spatial frequencies.
S - 1D array of power-spectral-density values.
Z - z parameter (film thickness)
OUTPUTS:
Result - Fit function.
PARS - 1-D array of fit parameters: [Omega, nu, n]
KEYWORD PARAMETERS:
RANGE - 2-element array of min and max spatial frequencies to
be used for fitting. Default is to use the entire
range of data.
FFIT - Array of F values corresponding to the range used for
fitting.
COMMON BLOCKS
COMMON PSD_OMEGA_NU_N,Z
RESTRICTIONS:
F and S must use the same length units.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1998
windt@astro.columbia.edu
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NAME:
RD_DIGITAL_AFM
PURPOSE:
Read a Digital Instruments Nanoscope III AFM image.
CALLING SEQUENCE:
RD_DIGITAL_AFM,X,Y,Z
KEYWORD PARAMETERS:
FILE - name of Nanoscope III data file.
TILT_SUB - set to subtract tilt.
SPHERE_SUB - set to subtract a 2nd order polynomial
background.
HIST_EQUAL - set to perform histogram equalization of image.
SWAP_ENDIAN - set to use the SWAP_ENDIAN function to convert
the data file from 'big endian' to 'little
endian', or visa-versa. Useful for reading on a
Windows platform data files originally
stored on Unix or Mac platforms, or visa-versa.
OUTPUTS:
X - Vector of x-position values, in angstroms.
Y - Vector of y-position values, in angstroms.
Z - Array of height values, in angstroms.
MODIFICATION HISTORY:
David L. Windt, Bell Labs, 1992.
windt@astro.columbia.edu
Actually working: February 1998
November 1998: The procedure can now handle Nanoscope III
file version 0x0440003.
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NAME:
RD_GRIFFITH_AFM
PURPOSE:
Read a Joe Griffith AFM file.
CALLING SEQUENCE:
RD_GRIFFITH_AFM,X,Y,Z
KEYWORD PARAMETERS:
FILE - name of AFM data file, without the .arr ending. It is
assumed that both the .arr and .hed files exist.
TILT_SUB - set to subtract tilt.
SPHERE_SUB - set to subtract a 2nd order polynomial background.
HIST_EQUAL - set to perform histogram equalization.
OUTPUTS:
X - Vector of x-position values, in angstroms.
Y - Vector of y-position values, in angstroms.
Z - Array of height values, in angstroms.
MODIFICATION HISTORY:
David L. Windt, Bell Labs, 1991.
windt@astro.columbia.edu
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NAME:
RD_MICROMAP
PURPOSE:
Read a Micromap data file.
CALLING SEQUENCE:
RD_MICROMAP,FILE=FILE,X,Y,Z
KEYWORD PARAMETERS:
FILE - name of Micromap data file.
TILT_SUB - set to subtract tilt.
SPHERE_SUB - set to subtract a 2nd order polynomial background.
HIST_EQUAL - set to perform histogram equalization of image.
OUTPUTS:
X - Vector of x-position values, in angstroms.
Y - Vector of y-position values, in angstroms.
Z - Array of height values, in angstroms.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1998
windt@astro.columbia.edu
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NAME:
RD_WYKO
PURPOSE:
Read a WYKO TOPO-3D data file.
CALLING SEQUENCE:
RD_WYKO,FILE=FILE,X,Y,Z,HEADER=HEADER
KEYWORD PARAMETERS:
FILE - name of WYKO data file.
OFFSET - set OFFSET to skip an additional 512 bytes at the
beginning of the data file. This additional 512-byte
header is introduced by BASIC/UX when the file is
transferred from an LIF to an HFS disk.
TILT_SUB - set to subtract tilt.
SPHERE_SUB - set to subtract a 2nd order polynomial background.
HIST_EQUAL - set to perform histogram equalization of image.
SWAP_ENDIAN - set to use the SWAP_ENDIAN function to convert
the data file from 'big endian' to 'little
endian', or visa-versa. Useful for reading on a
Windows platform WYKO data files originally
stored on Unix or Mac platforms, or visa-versa.
OUTPUTS:
X - Vector of x-position values, in angstroms.
Y - Vector of y-position values, in angstroms.
Z - Array of height values, in angstroms.
OPTIONAL OUTPUT PARAMETERS:
HEADER - structure value containing the raw header information.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, March 1991.
August, 1997 - Added SWAP_ENDIAN keyword.
May, 1998 - Added SUB_TILT keyword
windt@astro.columbia.edu
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NAME:
RD_ZYGO
PURPOSE:
Read a ZYGO NewView data file.
CALLING SEQUENCE:
RD_ZYGO,FILE=FILE,X,Y,Z
KEYWORD PARAMETERS:
FILE - name of ZYGO data file.
TILT_SUB - set to subtract tilt.
SPHERE_SUB - set to subtract a 2nd order polynomial background.
HIST_EQUAL - set to perform histogram equalization of image.
OUTPUTS:
X - Vector of x-position values, in angstroms.
Y - Vector of y-position values, in angstroms.
Z - Array of height values, in angstroms.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, June 1998
windt@astro.columbia.edu
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NAME:
SUB_TILT
PURPOSE:
Function to subtract tilt (i.e., a straight line) from
profile data.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
Result=SUB_TILT(X,Y,CURVATURE=CURVATURE)
INPUTS:
X - 1D array of lengths.
Y - 1D array of heights.
KEYWORD PARAMETERS:
CURVATURE - Set to subtract a 2nd order polynomial instead of
a straight line.
OUTPUTS:
Result - The new profile data.
EXAMPLE:
NewY=SUB_TILT(X,Y)
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
SURF2AVE_PSD
PURPOSE:
Procedure to compute the average power-spectral-density
functions along X and Y from surface data.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
SURF2AVE_PSD,X,Y,Z,XAVEPSD=XAVEPSD,YAVEPSD=YAVEPSD,
FX=FX,FY=FY,XPSD=XPSD,YPSD=YPSD
INPUTS:
X - 1D array of lengths along X direction.
Y - 1D array of lengths along Y direction.
Z - 2D array of heights.
OUTPUTS:
FX - 1D array of spatial frequencies along X direction, in
units of 1/[X].
FY - 1D array of spatial frequencies along Y direction, in
units of 1/[Y].
XAVEPSD - 1D array of PSD values = average of XPSD along Y
direction, in units of [Z]^3.
YAVEPSD - 1D array of PSD values = average of YPSD along X
direction, in units of [Z]^3.
XPSD - 2D array of PSD values computed along X direction, in
units of [Z]^3.
YPSD - 2D array of PSD values computed along Y direction, in
units of [Z]^3.
KEYWORD PARAMETERS:
POSITIVE_ONLY - Set to compute the autocovariance function
for positive lag lengths only.
RANGE - 2-element array specifying the min and max spatial
frequencies to be considered. Default is from
1/(length) to 1/(2*interval) (i.e., the Nyquist
frequency), where length is the length of the scan,
and interval is the spacing between points.
ZERO_PAD - Set this to an integer specifying the number of
zero-height points to add on either side of the
profile data.
HANNING - Set this to use a Hanning window function.
KAISER - Set this to use a Kaiser-Bessel window function
PROCEDURE:
This function computes the 1D PSD functions along every line in
the X and Y directions of the image array, and then computes the
averages in X and Y of these 1D PSD functions. Note that SUB_TILT
is used on each line prior to computing the PSD.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
September 2000: Corrected a problem that caused SURF2AVE_PSD to fail
if X and/or Y contained an odd number of points.
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NAME:
SURF2PSD
PURPOSE:
Function to compute the 2D power-spectral-density function
from surface data.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
S=SURF2PSD(X,Y,Z,FX=FX,FY=FY)
INPUTS:
X - 1D array of lengths along X direction.
Y - 1D array of lengths along Y direction.
Z - 2D array of heights.
OUTPUTS:
Result - 2D PSD function, in units of [Z]^4.
FX - 1D array of spatial frequencies along X direction, in
units of 1/[X].
FY - 1D array of spatial frequencies along Y direction, in
units of 1/[Y].
KEYWORD PARAMETERS:
POSITIVE_ONLY - Set to compute the autocovariance function
for positive lag lengths only.
XRANGE - 2-element array specifying the min and max spatial
frequencies along X direction to be
considered. Default is from 1/(Xlength) to
1/(2*interval) (i.e., the Nyquist frequency), where
Xlength is the length of the scan along X, and
interval is the spacing between points.
YRANGE - 2-element array specifying the min and max spatial
frequencies along Y direction to be
considered. Default is from 1/(Ylength) to
1/(2*interval) (i.e., the Nyquist frequency), where
Ylength is the length of the scan alogn Y, and
interval is the spacing between points.
ZERO_PAD - Set this to an integer specifying the number of
zero-height points to add on either side of the
profile data.
HANNING - Set this to use a Hanning window function.
KAISER - Set this to use a Kaiser-Bessel window function
PROCEDURE:
S=XLength*YLength*ABS(FFT(Z*Window),-1)^2
Where XLength and YLength are as described above, and Window
is the value of the optional window function (Hanning or
Kaiser-Bessel).
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
Nov 1998: When using the HANNING or KAISER keywords, the window
function is now normalized so that the integral of the PSD is
~constant, i.e., independent of your choice of window.
September 2000: Corrected a problem wherein the spatial
frequencies were computed incorrectly. Also, non-isotropic
surfaces are now handled correctly. Much thanks to Eric
Gullikson, LBL, EMGullikson@lbl.gov
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NAME:
TOPOSTART
PURPOSE:
The start procedure for the TOPO surface topography library.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
At the IDL command line, type ".run TOPOSTART".
COMMON BLOCKS:
COMMON TOPO,TOPOHOME,TOPO
COMMON PLOT_PRINT,PRINTPARS (See PLOT_PRINT)
PROCEDURE:
The site-configuration file (topositeconfig.pro) is read,
defining widget fonts, etc. The topo save file is loaded
into IDL, using the RESTORE command.
RESTRICTIONS:
UNITS and PRECISION:
When using any of the topo plot procedures: PLOT_PROF,
PLOT_SLOPE, PLOT_H_DIST, PLOT_S_DIST, PLOT_AUTOCOV, and
PLOT_PSD; or the procedures ANLZ_PROF, XANLZ_PROF, XANLZ_PSD, and
XANLZ_SURF, the data length (X for 1D, or X and Y for 2D) and
height (Y for 1D, or Z for 2D) units MUST ALL BE IN
ANGSTROMS. However, the common block variable TOPO is used
to control the units that are actually displayed.
In particular, the variables TOPO.XUNITS_PTR and
TOPO.YUNITS_PTR determine the units for lengths and heights,
respectively; set TOPO.XUNITS_PTR to 0 for angstroms, 1 for
nm, 2 for microns, or 3 for mm. Same goes for
TOPO.YUNITS_PTR.
The precision of the fit parameters that are labelled on the
plots is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), TOPO.YPRECISION for height-related
parameters (e.g., rms roughness), and TOPO.SPRECISION for
slope-related parameters (e.g., rms slope.) For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
The TOPO.*UNITS_PTR and TOPO.*PRECISION variables can either
be set explicitly before executing any of the aforementioned
procedures, or they can be set transparently to the user be
selecting the appropriate menu items when using the
XANLZ_PROF, XANLZ_PSD, or XANLZ_SURF procedure.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
TOPO_X_CONVERT
PURPOSE:
Function to convert length variables according to the value
of the common block variable TOPO.XUNITS_PTR.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
NewX=TOPO_X_CONVERT(X)
INPUTS:
X - 1D array of length values, in angstroms.
OUTPUTS:
Result - 1D array of length values, in units specified by
TOPO.XUNITS_PTR, i.e., 1 => angstroms, 2 => nm, 3 =>
microns, and 4 => mm.
KEYWORD PARAMETERS:
TO_ANGSTROMS - Set to convert an input X from the units
specified by TOPO.XUNITS_PTR to angstroms.
COMMON BLOCKS:
COMMON TOPO
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
TOPO_Y_CONVERT
PURPOSE:
Function to convert height variables according to the value
of the common block variable TOPO.YUNITS_PTR.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
NewY=TOPO_Y_CONVERT(Y)
INPUTS:
Y - 1D array of height values, in angstroms.
OUTPUTS:
Result - 1D array of height values, in units specified by
TOPO.YUNITS_PTR, i.e., 1 => angstroms, 2 => nm, 3 =>
microns, and 4 => mm.
KEYWORD PARAMETERS:
TO_ANGSTROMS - Set to convert an input Y from the units
specified by TOPO.YUNITS_PTR to angstroms.
COMMON BLOCKS:
COMMON TOPO
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
windt@astro.columbia.edu
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NAME:
XANLZ_PROF
PURPOSE:
A widget application for 1D profile analysis. This program
is really a widget interface to the ANLZ_PROF routine.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
XANLZ_PROF[,X,Y,GROUP=GROUP]
OPTIONAL INPUTS:
X - 1D array of (equally-spaced) lengths, in angstroms.
Y - 1D array of heights, in angstroms.
KEYWORD PARAMETERS:
GROUP - Widget GROUP_LEADER keyword to XMANAGER.
COMMON BLOCKS:
COMMON TOPO
COMMON PLOT_PRINT
RESTRICTIONS:
The X values must be equally spaced.
X and Y must be in angstroms.
PROCEDURE:
Although X and Y must be in angstroms, the units for
displayed variables are determined by the values of the
relevant tags of the common block variable TOPO.
That is, set TOPO.XUNITS_PTR to 0 for angstroms, 1 for nm, 2
for microns, and 3 for mm. Same goes for TOPO.YUNITS_PTR.
The precision of the fit parameters that are labelled on the
plots is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), TOPO.YPRECISION for height-related
parameters (e.g., rms roughness), and TOPO.SPRECISION for
slope-related parameters (e.g., rms slope.) For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
The TOPO.*UNITS_PTR and TOPO.*PRECISION variables can either
be set explicitly before executing this procedure, or they
can be set transparently to the user be selecting the
appropriate menu items once the procedure is running.
If no data are passed, the user is prompted to enter the IDL
command string used to read in new data. This command string
*must explicitly define X and Y in angstroms*. For example,
if your data is in the form of a plain text (ASCII) file,
consisting of two columns of data, X and Y, then you can use
the EROM routine, as in
EROM,X,Y,FILE='MyProfile.dat'
If your data is not in this form then you will probably
need to write your own IDL procedure to read in the data,
with X and Y as explicit parameters, i.e.,
MY_PROCEDURE,X,Y
or
Result=MY_FUNCTION(X,Y)
Once the profile data are defined, this routine uses the
ANLZ_PROF routine to compute the height distribution, the
slope distribution, the autocovariance, and the
power-spectral-density, with optional fitting, and displays
the results in a composite plot that can be printed using
PLOT_PRINT. Various popup-widgets are used to adjust the
computations, fits and plots to the users preference.
No common blocks are used that prevent multiple instances
of this routine from being used.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
May 1998 - Added ability to specify range of F values used for
PSD fitting.
- Added ability to specify which plots are made, as in
the new PLOT keyword to ANLZ_PROF.
- Draw widget now gets resized when the base is
resized.
windt@astro.columbia.edu
ILLUSTRATION:
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NAME:
XANLZ_PSD
PURPOSE:
A widget application for 1D PSD analysis. This program
is essentially a widget interface to the PLOT_PSD routine.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
XANLZ_PSD[,F,S,GROUP=GROUP]
OPTIONAL INPUTS:
F - 1D array of spatial frequencies, in 1/angstroms.
S - 1D array of power-spectral-density values, in A^3.
KEYWORD PARAMETERS:
TWOD - Set to indicate that the F and S values correspond to
a 1D slice of a 2D PSD function, or a radially-averaged
PSD function.
GROUP - Widget GROUP_LEADER keyword to XMANAGER.
TITLE - Title for main widget.
COMMON BLOCKS:
COMMON TOPO
COMMON PLOT_PRINT
PROCEDURE:
Although F and S must be in angstroms, the units for
displayed variables are determined by the values of the
relevant tags of the common block variable TOPO.
That is, set TOPO.XUNITS_PTR to 0 for angstroms, 1 for nm, 2
for microns, and 3 for mm. Same goes for TOPO.YUNITS_PTR.
The precision of the fit parameters that are labelled on the
plots is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), TOPO.YPRECISION for height-related
parameters (e.g., rms roughness), and TOPO.SPRECISION for
slope-related parameters (e.g., rms slope.) For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
The TOPO.*UNITS_PTR and TOPO.*PRECISION variables can either
be set explicitly before executing this procedure, or they
can be set transparently to the user be selecting the
appropriate menu items once the procedure is running.
If no data are passed, the user is prompted to enter the IDL
command string used to read in new data. This command string
*must explicitly define F and S in angstroms*. For example,
if your data is in the form of a plain text (ASCII) file,
consisting of two columns of data, F and S, then you can use
the EROM routine, as in
EROM,F,S,FILE='MyProfile.dat'
If your data is not in this form then you will probably
need to write your own IDL procedure to read in the data,
with F and S as explicit parameters, i.e.,
MY_PROCEDURE,F,S
or
Result=MY_FUNCTION(F,S)
Once the profile data are defined, this routine uses the
PLOT_PSD routine to display the results along with an
optional fit.
No common blocks are used that prevent multiple instances
of this routine from being used.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1998
windt@astro.columbia.edu
ILLUSTRATION:
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NAME:
XANLZ_SURF
PURPOSE:
A widget application for 2D surface analysis.
CATEGORY:
Topographic analysis
CALLING SEQUENCE:
XANLZ_SURF[,X,Y,Z]
OPTIONAL INPUTS:
X - 1D array of (equally-spaced) lengths along X direction,
in angstroms.
Y - 1D array of (equally-spaced) lengths along Y direction,
in angstroms.
Z - 2D array of heights, in angstroms.
WINDOW_XSIZE - The horizontal size of the window for image display, in pixels.
Default is 380.
WINDOW_YSIZE - The vertical size of the window for image display, in pixels.
Default is 400.
COMMON BLOCKS:
COMMON TOPO
COMMON PLOT_PRINT
COMMON XANLZ_SURF
RESTRICTIONS:
The X and Y values must be equally spaced.
X, Y and Z must be in angstroms.
PROCEDURE:
Although X, Y and Z must be in angstroms, the units for
displayed variables are determined by the values of the
relevant tags of the common block variable TOPO.
That is, set TOPO.XUNITS_PTR to 0 for X and Y angstroms, 1
for nm, 2 for microns, and 3 for mm. Similarly, set
TOPO.YUNITS_PTR to 0 for Z in angstroms, 1 for nm, 2 for
microns, and 3 for mm.
The precision of the fit parameters that are labelled on the
plots is determined by the values of the variables
TOPO.XPRECISION for length-related parameters (e.g.,
correlation length), TOPO.YPRECISION for height-related
parameters (e.g., rms roughness), and TOPO.SPRECISION for
slope-related parameters (e.g., rms slope.) For example, if
TOPO.XPRECISION=3, then three places to the right of the
decimal will be displayed.
The TOPO.*UNITS_PTR and TOPO.*PRECISION variables can either
be set explicitly before executing this procedure, or they
can be set transparently to the user be selecting the
appropriate menu items once the procedure is running.
If no data are passed, the user is prompted to enter
the IDL command string used to read in new data. This
command string *must explicitly define X and Y*. For
example, if you're reading in WYKO TOPO-3D data, you can
use the RD_WYKO procedure, as in
RD_WYKO,X,Y,Z,FILE='MyProfile.dat'
You might also try the RD_DIGITAL_AFM procedure for reading
in data obtained with the Digital Instruments Nanoscope III
atomic force microscope.
If you cannot use RD_WYKO or RD_DIGITAL_AFM, then you will
need to write your own IDL procedure to read in the data,
with X, Y and Z as explicit parameters, i.e.,
MY_PROCEDURE,X,Y,Z
or
Result=MY_FUNCTION(X,Y,Z)
(The TOPO distribution includes some sample WYKO data, in a
file called 'wyko_example.dat'.)
Once the surface data are defined, the user can select
interactively 1D profiles along X or Y. These profiles are
plotted, as are the corresponding PSD functions. The user
can also select X or Y profiles for more detailed analysis
using the XANLZ_PROF routine, which can be called directly
from XANLZ_SURF.
MODIFICATION HISTORY:
David L. Windt, Bell Laboratories, May 1997
January, 1998 - When !D.NAME eq 'CGM', set the color index for
!p.color to black.
May, 1998 - Added analysis menu, with option of using XANLZ_PSD
on X-, Y- and radially-averaged PSD function.
Added WINDOW_XSIZE and WINDOW_YSIZE keywords.
windt@astro.columbia.edu
ILLUSTRATION:
