Interferometry for High Resolution Absolute Distance Measuring
by Larger Distances
E. Oalhoff.
E.
Fischer, S.Kreuz, H.I. Tiziani
Universitat Stuttgart, lnstitut
fUr
Technische
Optik:
Pfaffenwaldring
9.
D 7000 Stuttgart 80
1. Introduction
There are some techniques of absolute remote distance measurement. Some
of
it deserve the title of
absolutness without restriction (triangulation e.g.) but are not useful measuring
at
distances
of
some
ten
metres because
of
practical reasons. The other techniques have
an
unambiguity range within the
measu
·
rement
is
absolute. Among the incoherent techniques the phase measurement
of
modulated light seem
to have reached some limitation
with
an resolution
of
less
than
1 mm. This limitation
is
set by
the
bandwidth
of
the photodctecror. The coherent techniques operate with two wavelengths to extend
the
unambiguity range of
the
classical interferometry. The unambiguity range
is
then half
the
synthetic
wa·
velength
and
can be adjusted quite arbiuarily from some ten micrometers
on
.
If
heterodyne detection
is
involved a relative resolution
of
the electronic phase measurement
of
10" is achievable.
As
is valid for
the phase measurement
of
intensity modulated light cascading
of
2
or
more stages
of
different synthetic
wavelength is necessary
in
order to improve the relative resolution
of
the whole system.
The
main advantage
of
the coherent technique is that a resolution below 1 micron is possible. In addi·
tion the signal·tcrnoise ratio (SNR) makes the effort
of
coherent detection attractive especially working
at large distance. In
Fig
.l the SNR
of
the detector signal is depicted for the coherent system discussed
in
this paper and the incoherent phase measuring technique depending
on
the
power
of
the light backIe·
flected by
the
object.
In
the following a set·
up
of
a doubJe heterodyne interferometer with
an
unambiguity range
of
100 me·
ues
and a resolution
of
0.1
mm
(corresponding to a relative resolution
of
106) will be described and
experimental results will be presented.
2_
SetUp
The
set·
up
is designed to yield a resolution
of
0.1 mm with an unambiguity range
of
100 metres. A
sketch
of
it is shown in Fig.2. Light
of
a monomode laser diode with wavelength
AI
is frequency·
shifted by a
SOO
MHz
acoustooptic modulator (AOM) in
order
to yield the second wavelength
Az
. This
corresponds to a synthetic wavelength
of
60
cm. Light
of
the wavelengths
A,.
~
is
used as reference
249
iii
..
:!?
a:
z
"
U)
"

P/
v
"

~
V
b)

~
•
 /
V
"
..
"""
"
..,.
»
Objektli
chtJe
i
stung
[dB)
Fi
g.l .SNR dependent
on
object light power for
a)
incoherent phase measuring, b) coherent heterodyne
detection on one wavelength (BW
15
MHz)
, c) double heterodyne detection (BW
15
MHz).
light, while the object
li
ght
is
shifted by means of two additional AOM with
n=80
resp.
f2=80.1
MHz
in
order
to provide double heterodyne reception
Ill
.
The
object and reference light gelS superim
po
sed
on
a photodetector. Dropping the dc(;omponent the signal after demodulation is given
by
(I)
i",=li",lcos(2n
(
M 
I+¥))
where
M=
If,
f,1
and A=(A, 
A,)IIAI

A,I
.
Zis
me
distance
10
be measured. ThusM=IOO kHz
is
the heterodyne frequency
of
the demodulated signa]
and
the unambiguity range
of
the measurement is
given
half
the synthetic wavelength AI2=
3Ocm
. TIle distance is evaluated from a measurement
of
the
phase
of
the heterodyne signals
of
a measuring and a control interferometer with fIxed paths. The ex
tended unambiguity range
of
100 metres is obtained
by
computing the results
of
two measurements
with slightly different synthetical wavelength
A=58
.9
cm
corresponding to a frequency shift
of
the
AOM
of
501.5 MHz.
In
order
10
maintain the phase resolution
of
27t13600
after more than 300 cycles
of
the unambiguity range, the relative stability
of
the
synthetic wavelength has to be better than 10".
Rewriting
cq
.l to
A=c
/dv(where
dv
denotes the frequency difference between the two wavelengths) it
can
be
seen that
in
this setup the stability
of
the phase
is
depending only on the frequency stability
of
the AOM and not on the frequency stability
of
the laser diode. This is an advantage
of
this approach
since a relative stability
of
an electronic oscillator
of
better
thanlO6
is state
of
the art.
In addition to the unavoidable noise in the detection process the decorrelation
of
the two speckle pat
terns created by the object light when measuring
at
rough surfaces causes a phase error
12
1.
The stan
dard deviation
of
this statistical phase error depends on
the
wavelength difference, the roughness
of
the
target
and its tilt. Measuring at a perpendicular oriented surface with a mean roughne
ss
of
10
~m
it
is
calculated to
be below 0.1 mm for the setup
in
question. This phase error increases when a misalign
250
menl between the object light
of
the two wavelengths occurs. Therefore the object and reference light
after the
80
resp.
80
.1 MHz
ADM
is
fed into two monomode fibres where couplers split the light for
the
co
ntr
ol
interferometer. The fibres guarantee the alignment
of
the light
of
the two wavelengths.
f·
ObjHlpfad
f1
•
10
lIMa
.
.......
_.
_
'OIl
•
~I:::=m
~='='
rt:::t
_
AOM
I
•
fa..
10.1
....
Fig.2: Double heterodyne interferometer sctup.
3. Results
Fig. 3 shows a 30 s stability measurement at a rougb surface at 20 m distance. The resolution
is
0.08
nun.
By
now
systematic
errors
reduce
the
accuracy
to
about
1
nun
.
Fig
. 4
shows
a
measurement
at
lOO
metres distance at a retroreflettor with an rmsphasedeviation
of
0.2
nun. It shows. that a stable phase
measurement
is
obtained at a distance
the
optical path length
of
which
is
about 40 times the coherence
length
of
the laserdiode used.
Literatur:
III
Z.Sodoik.. E.Fischer, Th.lttner u. H.l.Tiziani: Twowavelength double heterodyne interferome·
try using a matched grating technique.
Applied Optics. Vol.30 No.22.
1991
nl
Vry,U. et.al.: Higher order statistica1 propenies
of
speckle fileds
and
their application to rougb
surface
interferometry
lournal
of
the Optical Society
of
America. Vol .3 No.1,
1986
251
Siabilitat
smessung
...
,
,
...
,
...
,.,
Fig
.3:
Stability
measurement
at
a
rough
target
at
5
metres
distance
.
Az,..
"",
O.
08
mm
Slatrilitatsmessung
...
, .
,
...
,,.
Fig.4:
Stability
measurement
at
a
cornercube
at
100
metres
di
stance
. 6z,..=O.
34
mm
.