w
ell
as
an
y
o sets
and
nonlinearities
in
r
and
The
program
w
as
dev
elop
ed
on
a
PC
using
Windo
ws
NT
and
Op
enGL WND
KF
A
v
e b
y v
e
grid
of
data
w
as
collected
where
a
mark
er
w
as
plotted
on
the
screen
a
hand
placed
in
to
the
scan
b
eam
at
that
p
osition
and
data
tak
en
at
eac
h
successiv
e
calibration
p
oin
t
F
or
eac
h
of
these
t
w
en
t
y v
e
p
oin
ts
r
and
w
ere
computed
from
the
range nder
data
r
w
as
calculated
b
y
the
follo
wing
equation
P
I
ov
er
peak
P
r
arctan
Q
ov
er
peak
P
where
is
the
accum
ulated
data
o
v
er
a
giv
en
p
eak
output
directly
from
the
ov
er
peak
range nder s
serial
p
ort
and
the
signed
quadrature
AR
CT
AN
routine
w
as
used
to
map
through
of
phase
The
a
v
eraged
data
o
v
er
man
y
samples
for
the
p
oin
ts
w
as
written
to
a
le
along
with
the
exp
ected
screen
co
ordinate
v
alues r
ex
ex
This
le
w
as
read
in
to
MA
TLAB www mathworks c
om
and
the
co
e cien
ts
for
v
arious
tting
functions
w
ere
computed
These
w
ere
then
made
a
v
ailable
to
other
programs
for
mapping
the
range nder s
co
ordinates
to
screen
p
ositions
Numerical
Metho
ds
Linear
Least
Squares
Fit
The
ra
w
data
pro
duced
b
y
the
range nder
is
essen
tially
in
p
olar
co
ordinates
using
units
of
clo
c
k
time
for
mirror
angle
and
quadrature
phase
angle
for
range r
A
con
v
ersion
form
ula
is
needed
to
translate
this
data
in
to
the
appropriate
screen
raster
co
ordinates
used
b
y
the
graphics
routines
This
can
rst
b
e
accomplished
b
y
tting
the
measured
r
and
to
exp
ected
r
and
v
alues
computed
from
screen
co
ordi
in
in
ex
ex
nates
assuming
the
scanner
at
the
origin
Using
the
calibration
program
describ
ed
in
the
last
section
a
data
set
w
as
written
along
with
the
corresp
onding
exp
ected
screen
co
ordinates
in
p
olar
form
A
MA
TLAB
program
w
as
written
Lasercal m
to
try
v
arious
kinds
of
ts
to
the
data
and
solv
e
for
resp
ectiv
e
co
e cien
ts
The
follo
wing