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.TH BACK 1 "Ultrasonics Laboratory"
.SH NAME
back - Back Projection
.SH SYNOPSIS
back [options...]
.SH DESCRIPTION
This program reconstructs an image by back projecting
filtered projection data.
Images can be reconstructed for first, second, third
and fifth generation scanners.
.PP
All images are reconstructed over
a 64 x 64 grid.
A larger image (128 x 128) can
be constructed by sequentially calculating
each quadrant with the 
.B q=
parameter and then putting all
of the images together (see g128(1)).
.PP
There are many parameters that can be set
from the command line.
A parameter is set by listing
its name, an equals sign and
then the new value.
In the lists that follow the default
value is shown.
.PP
The following parameters indicate
the geometry of the scanner.
.TP 13
.B k=50
The number of projections or traverses
used when scanning the object.
.TP
.B n=100
The number of detectors.
For first
generation scanners this is equal to the
number of rays per projection.
.TP
.B nfl=100
The number of flashes per traverse for
fifth generation scanners.
.TP
.B gamma=45
Half of the fan width in degrees for
second, third and fifth generation scanners.
.TP
.B r=1
The radius of the scanner circle.
For first generation scanners this corresponds
to half the length of each projection.
.TP
.B cen=0
gives the center of each input projection.
This can be calculated by 
.B cen
(1) and 
removes any offset in the projections
due to real-world hardware.
.TP
.B theta=0
The initial angle of the first projection.
This also can be used to rotate the final image.
.PP
There are also several parameters that
indicate the desired output image.
.TP 13
.B q=n
indicates which four quadrants (1,2,3,4) to reconstruct.
Normally the projection is done over all
four quadrants.
Using this parameter also changes the default 
values of the
.B gx, gy
and
.B gs
parameters.
.TP
.B gx=-1
The x-coordinate of the upper left
corner of the output picture.
This flag is also changed by the
.B q=
parameter.
.TP
.B gy=1
The y-coordinate of the upper left
corner of the output picture.
This flag is also changed by the
.B q=
parameter.
.TP
.B gs=2
The size of the final picture.
This flag is also changed with the
.B q=
parameter.
.TP
.B l=1
The number of lines to reconstruct when
the
.B -l
option is used.
.PP
The control parameters are:
.TP 13
.B if=for002.dat
The input file.
This file should contain 
.B k
projections/traverses
of 
.B nfl
flashes of
.B n
single precision data points.
.TP
.B of=pic.r
The output file.
The resulting picture will be
64 x 64 single precision floating point numbers.
.TP 
.B lf=line
The output file when reconstructing a line
of the image.
This option sets the
.B -l
flag.
.TP
.B y=0.0
The location of the line to reconstruct when
the 
.B -l 
flag is used.
.TP
.B skip=0
allows projection data to be skipped.
If this flag is used only one out of every
.B skip+1
projections are used.
All other data is ignored.
.PP
There are also several flags that control the
type of reconstruction to perform and the scanner
configuration.
.TP 13
.B -x
Lax's algorithm is used to reconstruct third
generation data.
Normally a parallel back projection algorithm is used.
.TP
.B -5
Fifth generation data is back projected.
.TP
.B -f
Fifth generation data is back projected after first
filtering the projection data.
.TP
.B -e
Data from a scanner with
detectors spaced equally along the
receiver plane is back projected.
This is the normal mode for this program..
This applies only for second, third and
fifth generation scanners.
.TP
.B -a
Data from a scanner
with detectors spaced along equal angles
around the transmitter origin is back projected.
Normally the detectors are assumed
to be equal-spaced.
This applies only for second, third and
fifth generation scanners.
.TP 
.B -o
The object is assumed to be circularly symmetric
and only the first projection is used to 
reconstruct the entire image.
Normally all of the projection data is used
to calculate the image.
.TP
.B -l
The resulting image is 
reconstructed only for a set of lines.
The number of lines to reconstruct
is set by the
.B l=
parameter.
This flag is normally off but gives
a considerable savings in time when only the
center line is of interest.
.TP
.B -c
The entire output grid is offset by a half a step.
This is useful when looking at the center line of 
the image.
.TP
.B -p
Do not print a summary
of the program parameters.
Normally all the parameters are written
to standard output.
.SH FILES
.TP 13
for002.dat
is the default input file.
.TP
pic.r
is the default (64 x 64)
output file.
.TP
line
is the default file for single line reconstructions.
.SH SEE ALSO
.B Filt
(1) and
.B cen
(1) can be used to prepare the data for backprojection.
.SH DIAGNOSTICS
An error message is printed if the command line
syntax is wrong or if an error is found
when opening files.
.SH BUGS
The final image is not divided by the number of
projections.