A three-dimensional position measuring system

A three-dimensional position measuring system

Citation for published version (APA):

Driessen, F. P. G., Lucassen, F. H. R., & Ven, van de, H. H. (1988). A three-dimensional position measuring

system. In Theory of robots : selected papers from the IFAC/IFIP/IMACS symposium, Vienna, Austria, 3-5

December 1986 / Ed. P. Kopacek, I. Troch, K. Desoyer (pp. 433-438). (IFAC proceedings series; Vol. 8803).

Pergamon.

Document status and date:

Published: 01/01/1988

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+_ C o p y r i g h t O IFAC'fheorv of Robots, V i e n n a , A u s t r i a 1 9 8 6 INTRODUCTlON I n t o d a y ' s j - n d u s t r i e s , a n d o n t h e f a c t o r y f l o o r ,

there is a fast growing interest in and usê of the

programble rulti-functional mnipulator or

ind6-trial robot. The industrial robot can be used

excellêntly as a fast and precise posiÈioning or

handling machine. However, in spi-te of its Mny

quaLi-ties concerning speed and precision, thê robot

also has its lini.taÈions. Due to the robot

dynam-ics, the positioning accuracy is inversely

propor-tional to the speed. Onê way of reducing Èhe

effect of the robot dynanics is to alter the ratio

b e t w e e n t h e m a s s a n d s t i f f n e s s , e . g . b y u s i n g n e w m t e r i a l s .

Ànother possibj,Iity is to dj-ninisb the negative

effects of the dynanics without changing the

dynm-ics thereelves. Now the aceracy and repeatability

of the nanipulator can be inproved by adiling sore

intelligence to the programed robot, i.e. by

changing its program j-n such a way that any

unwant-ed movemenÈ is compensatunwant-ed for. For thj,s, it is

essential that the dynamics of the robot arn axe

knom a pri-ori.

Recently, much attentj.on has been paial to the

anal-ysis of dynanic atructures of mnipulators (e.9.

À s a d a , 1 9 8 3 ; B o o k , 1 9 8 2 ) . o n t h e d e v ê l o p m e n t o f

dynanic robot models a measuring system with the

ability to reasure the position of a fixed. point of

the robot arm as a function of time could be most

useful. Such a measuring system could also be used

when checking robot perfomnce and validating

already developed models. T'lxe developrent of such

a s y s t e m i s t h e s u b j e c t o f t h i s s t u d y .

Basically, we are only interested in the position

of one point on the robot arm, narely the one at

the end of thê am, the Tool Center Point. various

m e a s u r e r e n t s h a v e s h o m ( e . 9 . B e l j a a r s , ' 1 9 8 4 ) t h a t

the most dominant eigen-frequencies are below 30H2.

These frequencies have a Mximl amplitude of

sev-eral m's. Furthermore, it has been shown that

most robot arns have a mximw acGracy of about

0,lm together wj-th a mxirum speed of 3 n,/s.

TOR-K

A THREE-DIMENSIONAL POSITION

MEASURING SYSTEM

F. P. G. Driessen, F, H. R. Lucassen and H. [f. van de Ven

Eirulhouen Unitersitt oJ Technology, Department of Electrical Engirtteing.

Measurement an(L Control Croup, PO Box 5lJ, NL-5600 NIB Eindhouen,

The NetherLantls

Abstract. when checking robot performnce, a measuring system with the abilj-ty to

measure both the static and dynanic behaviour of a roboÈ arm is essentlal. The system

can also be used to check on robot perfomnce and on valj-d.ity of already d.eveloped

mod.els. This device should be able to measurê the position of a fixed point on the

robot am, the so-called Tool Center Poj-nt, in three dj-nensions with an accuracy of

'lOpn,

together with a large scale bandwid.th of 30i{2.

The device uses three identical laser{pticaL distance measuring systere, each of which

measures the displacement of the Tool Center Point with respect to a reference point

belonging to that system.

Each distance measurerent system consists of a frêquency stabi-lized Laser, a tracking

systen and a laser interferometer, À useful laser stabilizatj-on basêd on theml

expansion has been developed, as well as an interferomeÈer detection unit and a

bj--directional interf erometer counter.

Kelryords. Àctuatorsi counting cirej-ts; data handlingi laser j-nterferometert position

controlr stabili-zationt tarcet trackinq.

l

l

I

i

l

I

t*

l

l 1

From these data the followinq specificati-ons can be

extracted :

- _{a pos j-tiqn measuring acilracy of at least 10tn}

with respect to all- three d.irensiore t

- a dynamic range of 0 - 5 m/s;

- _{a bandwidth} of 0 - 100H2 for vibrations of very

smLl anplitude (a fraction of a nillineter)

and 30 Hz for aq)litudes of up to several

mil-l i r e t e r s .

Àt the rcment there is no comercial

three-di,ren-sional position neasurj.ng mchine that satisfies

these specifications. Therefore we decj-ded Èo

develop a (lov-budget) neasuring system ourselves.

PRINCIPIE

the objectives and specifications show that

in-dj-rect measurements, e.g. by detemining angular

positions of the motor axis, is inadêquate. By

using laser<ptical techniques it is possj-ble to

i-ncrease the measurenent accuracy. Becker ( 1984)

describes a system which uses two LaserbeaG which

are consÈantly projected at the Tool cente! Point

(TcP). The position of the TcP is detereined by

angÍular neasurement of the laserbeans and

triangu-lation. The achieved acsracy is about 0.lm and

is bound to the inaccuratê angular measurerents.

P f e i f e r a n d H o f ( 1 9 8 5 a , 1 9 8 5 b ) b u i l t a l a b o r a t o r y

prototype which uses four laser interferometers.

This prototl4)e produced some very satisfying

rê-sults. Due to these results, we decided to use Èhe

principle of 1en9Èh measurement by laser

interfero-neters.

The principle is depicted in Fig. 1. Three laser

j-nterferometers, situated at the rêference points

x l , x 2 a t d * 3 . . u " o t . t h e d i s t a n c e t o t h e T c P ( y ) .

309

t .

3 1 0

F. P. G. Driessen. F. H. R.

b )

Eig. 'la. The mêasurement

b . M e a s u r e m e n t o f

of length Li

p r i n c i p l e .

displacement D. instead

The lengths L1, L2 and L3 can be converted into the

coordinates of y. The describing equations havê

t w o s o l u t i o n s , y a n d y r . t h e l a t t e r b e i n g t h e i m g e

of y and rey easily be onitted by proper choice of

t h e t h r e e l a s e r i n t e r f e r o m e t e r s . I n f a c t , a l a s e r

-interferometer measures displacement instead of

length. It can be shom that if the coordinates of

a starting point p are knom beforehandr the

equa-tj-ons for deternining y have exactly the same form

as when using length measurement. By usj-ng a

seni-automtic calibration cycle the efforts needed for

setting up the system is kept to a miniM.

T h e p o s i t i o n s o f t h e r e f e r e n c e p o i n t s * t ( i = 1 , 2 r 3 )

can be calculated in a calibration cycle: one x'

takes the place of y and three knom different TCP

p o s i t i o n s _{/ , 1 2 u r a -} y 3 r e p l a c e x I , x 2 a n d x 3 .

In order to registrate the robot novements, a1I

three length, c.q. d.istance measurements have to b€

done period.j-ca1ly. with a sample frequency of 100

Hz the nost j.mportant eigen-frequencies (up to 30

Hz) can be determined.

THE CONSTRUCTÍON OF THE SYSTEM FOR ONE REFERENCE POINT

Àlthouqh Èhe complete system consisÈs of thrêe

identical length reasuring systens, we will focus

our attention on only one measuring systêm

belong-ing to one reference point.

Each length measurement system consists of a

frequ-ency stabilized laser, a tracking System and an

interferometer as depicted in Fig. 2.

À stabilized, laser frequency is necessary in order

to avoid node jurping and for the itrprovement of

the acaracy of the system. The trackj-ng systêm

will focus thê laserbeam at the TCP independently

of iÈs novements. Thê interferoneter counts the

displacem€nt of the TCP with respect to the

reference point in terre of half*avelengths of the

l a s e r l i g h t .

L u c a s s e n a n d F L H . v a n d e V e n

It wiLl appear that a very j-trportant part of the

systen is enbodi-ed in the retroreflêctor. This is

an optical instrwent with the following

quali-t l e s :

- _{the inconing and reflected beare are always}

parallel, regardless of the incoRing angle;

- the distance beween both beare will change if

the centre of the retroreflector is mved

per-pendiolar Èo the direction of the fixed

in-contlng bean.

i n t e r f e r o m e t e r

F j - g . 2 . A s u b s y s t e m b e l o n g i n g t o a s i n g l e

reference point.

Figurê 3 shows two itrtplementatj-ons of the

retro-reflector. The corner cube or tripel is mde up of

three perpendicularly placed nirrors. The

so-called cats€ye consists of two half spheres with

the same refraction index but different radius.

1 x a ) F i q . 3 . T h e c o r n e r c u b e ( a ) r e t r o r e f l e c t o ï . b ) a n d ' c a t s - e y e r ( b ) LÀSER STÀ3ILIZÀTION

À laser constitutes the centre of the measurerent

system. In an interferometer an unstabilj-zed laser

cannot be used because' in qeneral, the spectrum of

the laser shows nore than one spectral line: the

Iaser modes. These modes are subjected to

frequen-cy drift, which my discharge into node-jwps, i.e.

complete vanishing of a mode and re-appearing at

another frequency.

Mode-jups should be avoided at any cost because

they influence all modes by changing the direction

o f t h e i r p o l a r i z a t i o n .

To prevent these negative effects, the laser should

b e s t a b i l i z e d . À s t a b i l i z e d l a s e r i s v e r y w e l l

-suited to interferential lengtsh measurement due to

its high light. intensity, j-ts smll divergence and

iÈs gEeat coherence length (the latter being

in-versely proportional to the sEll spectrum).

l a s e r s t a b il i z a l i o n

-fl. f2

, , [ ?

i

Éi:iï:i""*

A T'hree-dimensional Position Nleasuring S,vstem

I a s e r

c o n t r o l l e d c u r r e n l

. ) l l

F i g . 4 . T h e l a s e r D o p P l e r - p r o f j ' l e 9 ( f ) i n c l u d l n g

two laser modes.

In our experiments we used a 22 cm long He-Ne

plasm tube of 0'5 nW power. T'he wavelengÈh Ào of

lh. Ir"-n. liqht is apProxiEaÈely 6328 Á' The

am-plitude of the spectral lines fol"low a so-cal1ed'

Doppler-profile (t{aitland, 1969) which is a

Gaussian distribution around f^,

f ^ = $ ( c i s t h e s P e e d o f l i g È t a n d n t h e

.ËtraËÈion index). T"he modes can only exist if

they exceed a certain thrêshold t, see Fig' 4,

otheffise a mode-junP wil-L ocor' IÈ can be shom

that, alue to the chosen tube lengÈh of 22 o, the

successive modes are seParated by 685 MHz, so thê

Doppler-profile of about 1.2 GHz will screen two of

the modes.

one phenomenon which has not yet been fully

untler-stood is that the successive modes have a lineaÍ

perpend.icular Polarization' so they can be

seParat-ea ly polarizing filters. out laser stabilization

unit rust keep the two spectral lines uder the

Doppler-Profile until they have the same anplitude'

ro-àcco4>lisn this, it is necessary to measure the

difference of boÈh inÈensities' . The sPectral

fre-quencies of the laser are related to the tube

iengÈh. À length deviation AL results in a

fre-quency devi.atlon Àf as follows; At/f = -AL/L' This

neans, for exanple, that 0,05 pn tube exPansion

resulÈs in 1OO MHz frequency reducing' we have

chosen therÉI expansion as a vêry sinPle yet

effective way of adjusting the tube length. It is

irplemented. by a healing spiral mde of resistance

wire around the plasm tube. The control current

of Èhe spiral is provided by the dj-fference of the

intensities of both laser rcdes as staÈed above

( r i g . 5 ) .

To improve the PerforGnce of the stabilization a

PI (proportional and integïating) controller is

added. ï,ong term stability tests have strom a

stationary overall drift of 100 l4Hz which is, in

f a c t , q u i t e t o l e r a b l e .

Beat measurements also showed a repeatabj-lity

with-in 1OO MHz. The remj-ning frequency drift my well

be caused by drift in the fotodiodes or Èhe op-amps

i"n the Pl-controller.

THE TR,ACKING SYSTEM

For on-line distance measurements of a noving TooI

center Point the laser beam should be focused on

the TcP constantly'

The most effectj-ve way of achieving this is by

fixinq the laser tube and deflecting the laserbem

by means of a rotating mirror. since the TcP can

rcve in three dimensions, Èhe niror mst have (aÈ

Iêast) two degrees of freedon. The princi-ple of

the tracking system is ilLustrated in Fig' 6' In

swry, we distingui-sh a retroreflector attached'

to the TCP, a rotating mirror with its actuators, a

d.isplacement sensor, and a conÈroller. Ttre

track-ing system oPerates as follows. The distance

be-tween the incoming and reflected beaG at the TcP

will change if the TcP is rcved Perpendifllar to

the direction of these beaG. This novement of the

reflected bean will be spotted by Èhe sensor and,

j-n turn, the sensor wj-ll Provide control signals

which activate the actuators into rotating the

m.irror unt.il the reflected beam has reached its

original- position with respect to thê incoming

beam. lhe control-ler can be used to optimize the

D i O C € S .

F i g . 6 . T h ê T C P t r a c k i n g s y s t e m .

very high demnds are [Ede on the surface of èhê

niffor with lespect to Power loss, divergence' etc'

and on itg susPensj-on. In order to mj'nimize any

hysterese and (non-1i-near) friction, we have oPted

for cardan suspension with a fLexural pivot of

laninated springs. Four linear electromgnetic

dynamic transducers, two per degÍee of freedom' are

used as actuators for rotating the nirror' The

nirror and actuaÈors are nounteal in a heavy rigid

block of aluRinium. !{hen writing this article no

data about the transient response of this

deflect-ing uni-È was available'

c o n t r o l l e r

3 1 2

Basically, two types of displacement sensor can be

used, namely, a CcD-camera and a lateral

photo-diode. The latter is superior due to i-ts higher

speed, better resolution and because it

automti-cally indicates the centre of the bearepot on the

sensor .

THE INTERFEROMETER

The interferometer is the part of the system that

actualLy measures the displacenent of the TCp with

regard t.o Èhe reference point. In Fig. Z

retro-reflector À is atÈached to the (moving) _{TCp, and B}

is a fixed reference retroreflector.

the interferometer is able to detect êvery half

wavelength (of the He-Ne liqht) dj-splacement of

retroreflector À. For thj-s, a harmonic

i n t e r f e r e n c e s i g n a l w i t h a f r e q u e n c y f r " o

proportj-onal _{to the velocity of the}

TCÊ;-I zv_^- i

fr"o =

| --+- l, has to be detected. We are not

l " ^ l

only interested j.n the absolute value of Vr.D but

a l s o i n i t s s i q n . À s e c o n d l - n t e r f e r e n c e s i f r a : - ,

which is always present, my supply informtion

about the sign. In using a specially coated

sep-aration prism, a phase difference of plus or Enus

kn rad. depending on the sigm of VTCP will appear

between the two interference siqnalëi- This effect

i s i l l u s t r a t e d i n F j - g . 8 ( w i t h 0 = 1 / Í r a d . ) .

So the sigm of VTCp can be extracted flon the sigÍn

of the phase difference betweên both interference

s i g m a l s .

Fig. 7. The interferometer wiÈh two interference

beare.

To avoid rutua1 interference _{of the two laser}

modes , one rcde has Èo be removed b1r reans of a

polarizj-ng fj-tter. À high-speêd photodiode is

indispensable for the detection of the interference

signal.s. The mximm frequency to be detected as

16 Mllz corresponding with the mxinum pemitteat ?Cp

velocj-ty of 5 n/s.

The obtaj-ned photo orrent is very difficult to

tackle due to Íts enormous dynamic ranqe of

0-161,Í12, its smll atrplitude due to opfical losses,

and a relatively high and unstable DC corDonenÈ.

In fact, thê intêrference sigmal is an

"ólitude

rcdulatêd signal wj-Èh a very sÈIl modulatj-on

index.

We have developed an interference detestinq unit

that converts the photo arrent into a useiul bLock

signal of the sme frequency and a constant

anpti-tudê. This detecting uit coqrrises, anonqst ;ther

things, a low-at filter with a mt-off frequency

of approximtêly 0.3H2 and a cosparator. ThL con_

parator is mde up of several cascaded ECL line

receivers. ECL, emitter coupled logi.c, is a loqrc

F . P . G . D r i e s s e n , F. H. R. Lucassen and H. H. van de Ven

f o i E j 0 ? t 3 , 4 : e i ( o . t - € ) ) , b r U : e _ _{I a e}j ( o r r - 2 0 ) j ( o " t - € ) 9 : e F j - q . 8 . A p h a s e d i f f e r e n c e c a u s e d b y a s p e c j - a l c o a t e d p r i s m .

fanily that can be used up to very high frequency

( 1 0 0 I r { H z ) s w i t c h i n g n e t w o r k a p p l i c a t i o n s . W e u s e d

the line receivers as boosters and a Schnj-Èt

tri-gger. À laboratory prototlT)e of the detectinq

unit has given some very encouraging results.

For the detection of the pulses of the final rnter_

ference signall each representing a \À^

displacement, a counter is necessary. "

An up-down counter is necessary in order to repre_

sent the direction of TCp movements, thê counting

dj-rêction is mtched to the sign of the phase dif_

ference of Èhe two interference signals. Further

more, for dynanic operation, the counter contents

rust be sampled with _{a satrple tj-ne of 0. O 1 sec. , as}

discussed before. A seven-decade .11 ttltz sanpled

bi--dj-rectj-onal counter with nÍcroprocessor càntrol

has been developed.

fhe microprocessor takes care of the saq)Iing,

storage of data, and the error handling. It my be

emphasised that for the complete system, one nicro_

processor can conÈrol all three interferometers.

MEÀSUREMEI{| ERRORS

AÈ various _{sÈages of the system, measulement errors}

are introduced. Às stated i-n the introduction, the

total arcunt of errors my not exceed a position

neasurêeent. inaccurasy of 'l0pm. when dêfining a

measurerent work space of one cubic meter, the

mximum pemitted relative inaccuraclr is I 0 -5 . In

this case the rel-ative j-naceracy _{is defined}

as the

absolute error in the position of ,Èhe T€p related

to the work space size.

In the following we will disass sone measurement

efiors.

The only measurenent error introduced by the laser

is related to its frequency drifÈ. The overall

drift of thê stabiu-zed laser is plus or mj-nus 50

M H z , È h e l a s e r f r e q u e n c ; _{b e i n g 5 . t O I 4 t t z , i r y I y r n g} a r e l a t i v e e r r o r o f 1 0 - l .

The i.nterferometer causes several eryors to occur.

Íhe refraction index of the air, for instance,

directly related to the laser wave len+h. is nor a

constant but iÈ depends on, e.9. aÍr pressure,

vaPour pressure, tenperature and CO2 percentage of

t h e a i r .

Under norml circumstances this gives rj,se Èo a

relati-ve error of less than 10{.

The low-et filter of the interference detectinq

uniÈ also introduces an error. Very low Vmp

causes a very low interference frequency wfriètr can

1 , 2

-1

A T h r e e - d i m e n s i o n a l P o s i t i o n N l e a s u r i n g S y s t e m . ) l J

be filterêd out. Every sêcond that a low frequency

signal cannot pass the filter an error will occur'

when using a filter with a cut-off frequency of 0'3

H z t h i s e r r o r i s l e s s t h a n 0 . 3 x l l o = 0 . 1 p n P e r

second.. The period of time that thj-s type of error

occurs is probably a very smll fractj-on of the

Èotal arcunt of measuring time.

Ànother error rey be caused by the data handling'

!íhen converting the data into useful TCP

coordin-ates, numerj,cal errors are mde. However, these

errors can be mde sufficiently sEall by increasing

the accuracy of Èhe Processor.

Roughly speaking, the tracking systen causes three

types of êrÍorS. First we have the errors caused

by iqperfections of the Physical rêtroreflector,

i.e. Èhe mss corner cube or cats-eye' For the

Mss cornêr cube an optical Path length difference

appears when the angle of the incomj-ng beam

changes. T'his change in optical Path length

evid-ently results in a neasurement error'

For the cats-eye, the inconing and reflecÈing beare

are only parallel wtren there is a specifi"c distance

between them. If the inconing beam noves, the

reflecteal beam wj-Il no longer be Paraltel and this

causes a measurement error.

Reference uncertainty. As discussed before, the

reasurement Pri-nciPle is basêd on three reference

points. If the interferometer beLongj-ng to a

cer-tain reference Poi'nt cannot reasure a displacement

shen the TCP is noved on a sphere with that

refer-ence point as centre, the reference Point is

unam-biguous. Inversely, a reference point is

unanbigu-ous if all Points wiÈh equal oPtical' PaÈh lengÈh

are situated on a sPhere when rotatj-ng the mirror'

If Èhey are not on a sphere a measuremenÈ error

will occur when the eirror rotates'

The posj-tions of the reference points are

dêÈerman-ed by the raccidentalr Positions of the calibration

positj.ons during the calibration cycle' The extent

àf ttri" error is highJ-y dependent on the tyPe of

suspension of the roÈating nirror but is zero if

the turning point of the mirror coincides with the

beaming poinÈ of the Rirror, which we will call an

idêa1 rotatj-ng nirror.

Aining error. This error arises when the (ideal)

retroreflector is not correctly beamed due Èo

t r a c k i n g i l q r e r f e c È i o n s ( e . g . s l o m e s s ) ' I f t h e

inconing beam is not correctly fo$sed on the TcP

retroreflector, the dj-stance between the inconlng

and reflected beare wj-ll change, as will the

opti-cal Path length.

Ítle d.isplacenent sensor is abLe to detect this

êfrof-. iihen using an ideal rotating error, we

found that the aj'ning error can be calslaÈed

with the help of the error detected by the

disptacemenÈ S€nSor. In this sPecial case, the

aiming error can be comPletely comPenstated for'

CONC],USIONS

À three-dinensional Position measurinq system has

been presented. The measuring system can be

iÍplemented by three acsrate length or

desplacement measurements done by laser

interferometers .

As the total measurement system basically consists

of three identical subsystere we focused our

attention prj-mrilY on one sybsystem, mde up of a

laser plus stabilizationl a tracking syst4' and a

laser interferometer.

we devel,oPed a laser stabilization based upon

thelml exPansion which perforG satisfactorily'

In order to deternine the direction of the

displacement or velocity to be detected, an

interfêrometer princiPle with two interference

signals has Proved most usefull. For this PurPose,

a properly working high speed (17 lt'Hz) intêrference

detector has been designed and buj-lt, as well as a

sampled i-nÈerf erometer counter.

At the rcment the Èracking system, in particular

the rotating niror, j-s the bottle neck of the

system, due to the fact that it nakes high 'leEn'Is

on its nechanical construction and b€cause iuproper

design ÍEy cause considerable measurerent errors'

Ttre measurenent errors which are not introduced by

the tracking system are sufficiently smll with

r e s p e c t t o t h e p o s t u l a t e d s p e c i f i c a t i o n s '

Future resêarch will concentrate primrily on

invesÈigation of the transient rePonse of our

rotating nirror and on developing a mtched

controller in order to oPtinize the tracking

perf orMnce.

REFERENCES

À s a d a , t l . ( 1 9 8 3 ) . À g e o m e t r i c a l r e P r e s e n t a t i o n o f

mnipulator dynaRics and its apPlication to arm

d e s j . g n . _{A s l ' 1 8 J . D y n . S M & c , 1 0 5 , 1 3 1 - 1 3 5 . ' -.} B e c k e r , P . J . ( 1 9 8 4 ) . L a s e r t r i a n g u l a t l o n l u r d a e

genaue dreidimensionale vermessung von

Robotern. _@lc!te, 2, 47-50'

BeLjaars, J.w.rFJEa]; íhe dvnamic behavj'our

of an industrj.aL robot with tw9. degrees of

f r e e d o n . ( i n D u t c h ) . M . S c . T h e s i s ,

GF.*.tt and control Group, DePt' of

Electrical Engineering, Eindhoven Universj'ty of

Technology, The Netherlands'

B o o k , W . J . ( 1 9 S 2 ) . R e c u r s i v e l a g r a n q i a n d y n a n i c s

of flexj-ble manipulator arN via transforEation

mtrices. Proc. IFÀC syÍq)' CÀD of

ltultivariable Technological syst'

W . f a f a y e t t e , I n d i a n a , 5 - 1 7

r 4 a i t l a n d , À . , a n d M . D u n ( 1 9 6 9 ) . I a s e r P h y s i c s .

North-Holland Publishj-ng corPany, Areterdil.

P f e i f e r , T ' , a n d À . H o f ( 1 9 8 5 a ) . R à u m l i c h e s I,legmepsysten - 3-D-Interferometer.

Laserinterferometrie in der LangemeBtêchnik.

A u s s p r a c h e t a g a m 1 2 . u n d 1 3 . M a r z 1 9 8 5 , Braunschweig.

P f e i f e r , T . , a n d A . H o f ( 1 9 8 5 b ) .

Sêlbstkalibrierendes Ráunliches wegmeFsystem

zur Koordinatenbestimung im Ram. wI-z, 127 '