THE LASER SIGNATURE IN CALIBRATION OF THE

SERVOMECHANISM

Edward F. Plinski*, Antoni Izworski**, Jerzy S. Witkowski*

*Institute of Telecommunications and Acoustics,Wrocław University of Technology,

Wybrzeże Wyspianskiego 27, 50-370 Wrocław, Poland

**Institute of Engineering Cybernetics, Wrocław University of Technology,

Wybrzeże Wyspianskiego 27, 50-370 Wrocław, Poland

Keywords: Servo-mechanism, process automation, CO

laser, laser signature, adaptive system, expert system

Abstract: The laser signature, which can be observed as a result of the CO

laser tuning, is used as a standard for

calibration of the servomechanism. The servomechanism can be used for continuous investigations of the

laser signatures of different laser media. Finally, some convenient signatures useful for a laser marker or

single frequency laser operation can be find.

1 INTRODUCTION

When we consider the optical device called a laser,

than we can recognize two “sets” of frequencies

produced in the device: a set of emission line

frequencies

of the excited laser medium (or a

singular line, which takes part in laser operation),

and a set frequencies

possible to obtain in an

optical resonator – see Figure 1.

When the laser is tuned (Figure 2), then the laser

longitudinal mode, let us say

q+1

, restores the

profile of the emission line giving a laser output gain

curve – see Figure 1. The gain curve is observed

with each half-lengthwave λ/2 tuning ∆L (from a

node to node of the standing wave in the resonator

cavity), where L – length of the optical resonator.

The resonator tuning is indicated in Figure 1 with

the arrow. Bottom figure – the laser gain curve

obtained when the laser is tuned of half-lengthwave

(∆L – a translation of the laser mirror M

The picture is much more complicated, when the

excited laser medium creates many emission lines.

The CO

medium is a good example – see a model

of the laser signature given in Figure 3. A line

hoppings effect is observed (Mocker, 1968).

A spectrum of the CO

molecule consists a

number of emission lines grouped in many bands,

and branches.

emission line

optical resonator frequencies

q+1

q+2

q+3

∆

output power

laser gain curve

Figure 1: Mechanism of the laser generation (a model) on

frequency

q+1

in the range of the emission line with a

center at

. (

- frequencies of the laser medium

spectrum,

– resonant frequencies of the optical

resonator (longitudinal modes)).

The most useful for the CO

laser operation is a

band with the frequency center of appr. 10.4 µm.

The band consists of two branches P, and R, where

the strongest line P20 is the most attractive for the

Plinski E., Izworski A. and Witkowski J. (2004).

THE LASER SIGNATURE IN CALIBRATION OF THE SERVOMECHANISM.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 3-10

DOI: 10.5220/0001124500030010

 SciTePress

laser operation – (Witteman, 1987). When we tune

the laser resonator, then different resonant

frequencies (longitudinal modes) of the optical

resonator can be in coincidence with frequencies of

the emission lines of CO

laser medium.

∆λ

total

reflecting mirror

standing wave in the laser (optical) resonator

output mirror

resonator length L

Figure 2: The rough scheme of the laser. The laser can be

tuned with a piezo-ceramic transducer (see output mirror)

of a few values of the half-wave ∆L.

spectrum of the particle - emission lines

optical resonator frequencies

P18 P20

P22

P24

q+1

q+2

q+3

q+4

q+5

q+6

q+7

q+8

∆

output power

laser

signature

P18P20 P24

P22

Figure 3: The laser signature developing (a model), when

the laser resonator is tuned of a half-wavelength (from a

node to node). The names of the emission lines are

indicated (top). The line hoppings effect is shown

(bottom) during the signature developing

Of course, each line being in coincidence with

the resonant can take part in laser action.

Theoretically, the laser can operate on many

emission lines simultaneously. Fortunately for the

experiment, a strong competition exists between

different rotational levels in the CO

medium, and

the laser usually operates only on one chosen line, as

a consequence (Mocker, 1968). Exactly, on that line,

which center frequency

is the closest to the

resonant frequency

of the resonator. Figure 3

explains the effect. As seen, the resonant frequency

q+3

is the closest to the center of the emission line

P20. When the resonator is tuned, then we can

expect “jumps” from line to line (a line hoppings

effect). The observed picture of the output laser

power is called a laser signature (Waksberg, 1971).

The signature is reproducible with each half-

lengthwave λ/2 of the tuning ∆L (usually a few

signatures – a few λ/2). The laser signature is stable,

and easy to calculate for the chosen length L of the

optical resonator – see Figure 2 (Shiffner, 1972).

2 EXPERIMENTAL

The RF excited laser shown in Figure 4 is equipped

with aluminium electrodes with an area 380 x 20

(top), and 400 x 110 mm

(bottom), spaced by

2 mm. The laser head is fed with an RF generator of

2kW power via a matching circuit (Plinski

, 2000).

The negative branch unstable resonator consists of a

rear mirror M

with a radius of 430 mm and output

mirror M

with a radius of 370 mm.

top Al electrode

bottom Al electrode

shunt inductors

RF connector

mirror

Figure 4: Scheme of the slab-waveguide laser structure.

The mirror spacing, defined by a low expansion

Invar bar, is L = 402 mm in length for appr. confocal

operation, but it can be increased to 414 mm giving

a diverging output beam. The rear mirror M

mount

is fixed to a piezo-electric transducers (PZT), for

cavity length scanning (a few wavelengths). The

positive branch unstable resonator with a rear mirror

= 5800 mm and an output mirror M

= 5000

mm, giving a geometrical out-coupling of 16%,

creates the second structure of the laser used in the

experiment. Figure 5 shows a real result of the

investigations on the laser signatures. The laser is

tuned of ∆L = λ/2. The signal is registered with a

ICINCO 2004 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

HgCdTe detector, and a scope (compare to

Figure 3). When the laser is tuned we observe a line

hoppings effect.

A similar experiment is performed with the laser

equipped with a positive branch unstable resonator.

The result is shown in Figure 6. It presents a partly

well-ordered signature (WOLS effect, Plinski

2000), where P lines are splitted up by a few lines of

an R branch (10.6 µm band) – exactly, the lines

appear in the order: P24, R14, P22, P20, R18, P18,

P16, R16, P14.

P20

P22

P24

P18

P26P20

20.0

19.7

19.8

19.9

P[W]

Figure 5: The laser signature. Changes of the laser output

power with tuning (translation) the laser mirror (see

Figure

2).

The result is obtained on a 414 mm long optical

resonator. A diffraction grating is used to recognize

the CO

laser emission lines. The output laser beam

is deflected at the grating into different angles and

visualized at the UV screen (top).

P24

P22 P20 P18 P16 P14

R14 R18 R16

laser radiation

diffraction

grating

screen

Figure 6: Partly well-ordered signature (P lines)

obtained on a positive branch unstable resonator of the

slab-waveguide CO

laser. The pattern of the output laser

beam is visualized at the UV plate

We elaborated a numerical procedure, which

calculates the laser signature for given frequencies

of the emission lines, and given length L of the

optical resonator (the shape of the emission lines is

not taken into account) – see an example of the

calculations in Figure 7.

414 mm

P22

P20

P18

P16

P14

R14

P24

R18

Figure 7: Graphical representation of the laser signature

from Figure 6, calculated theoretically.

The series of signatures in line creates a specific

picture (histogram) of the carbon dioxide laser for

some strictly determined spectrum of the laser

medium.

3 AUTOMATION OF THE

INVESTIGATION PROCESS

The automatic control system consists a set of piezo-

ceramic transducers (PZT), and a micrometric screw

MS with a motor-driver MD. The process of the

calibration is done in four steps (see Figure 8):

1000 0

70 0

10,0 0,0

C D

2,5 5,0 7,5

650 850

Figure 8: Mutual relations between AO control signal on

the step motor , Up voltage on the piezoceramic transducer

PZT, and translation of the mirror L

– initial

position of the mirror, L

– final position).

o I-st step: voltage from 0 to 70 V on PZT with

0,1V resolution – the signature is recorded;

THE LASER SIGNATURE IN CALIBRATION OF THE SERVOMECHANISM

o II-nd step: jump from 70 to 0 V on PZT (move

back);

o III-rd step: 3 steps of the motor (move forward,

appr. 3 x 2,5 µm) to „hit” the section CD;

o IVth step: correction voltage on a PZT to „hit”

the signature obtained in the I-st step.

1 - transducers PZT tune the laser resonator

(translates the mirror M

) of a few λ/2 (it depends

on the kind of the PZT) – a lower trace,

2 - the PZT comes back to the same position (the

same length L of the resonator) – the 2 voltage on

the PZT is set on the initial value – a medium trace,

3 - the screw MS takes over the role of the

translator; the screw translates the laser mirror of the

same distance (a few λ/2) with suitable corrections

using PZT – a upper trace,

4 - the PZT takes over the role of the translator again

(see Figure 9)

laser medium

MD PZTMS

Figure 9: The scheme of the laser used in the experiment.

The laser can be tuned with a motor-driver MD equipped

with a micrometric screw MS, and piezo-ceramic

transducers PZT of a few values of the half-wave ∆L. M

– rear, total reflective mirror, M

– output mirror.

3.1 Details of the automation –

intensity recognition

The algorithm of the control of the calibration

process is given in Figure 10. The control object

under investigation is controlled by tuning the

micrometric screw MS to obtain the screw travel of

. The screw travel is equal to

∆

= 500 µm per

one turn, and the total operating length equals L

M max

= 20 mm. (Only part of the operating length is used

in the experiment: L

∈ [0 ; L

], where L

< L

M max

The screw is operated by a stepped motor enabling

to make 200 steps per one complete revolution of the

motor. Thus, an expected screw linear travelling is

equal to

∆

= 2.5 µm per one revolution of the

motor (Plinski

, 2003).

=2000; Um=70V

∆U

=Um/1000;

s=0; Wait (t1)

Up=0V; Wait (t2)

,i=read(U

)

i=i+1

Up=Um

Up=Up+∆U

Wait (t2)

s+2<s

s=s+3; Wait (t1)

Up=0V; Wait (t2)

STOP

Count Q(k)

for k=0,..,200;

Find k0;

rchive {s,k0};

Up=(k0+1) ∆Up

,j=read(U

);

=j+1

>350

Up=Up+∆U

Wait (t2)

Figure 10: Algorithm of the calibration process.

Another actuating track is a

piezoceramic

transducer (PZT) that enables to achieve the shift

within the range of L

∈ [0 ÷ 10 µm] for the input

voltage U

∈ [0 ÷ 70 V]. As shown above,

comparing the operating ranges of the step motor

and piezoceramic transducer, 4 steps of the motor

correspond to the control range that is obtained by

voltage changes U

from 0 V to U

= 70 V. The

informations that the object under control has moved

out is obtained due to the HgCdTe detector that

provides the informations on the intensity of the

laser beam. The time constant of the detector does

not exceed one millisecond.

It is recommended solution for the automation

processes used in industry (Solnik, 2000), as the

control member, the industrial controller

SAIA PCD2 is applied. The manual control mode

and monitoring of the current control parameters

may be realised with the operator’s terminal. On the

other hand, the operator’s station SCADA

(Supervisory Control And Data Acquisition) serves,

primarily, for creation of the experiment archives

and for storage of the database. All measuring and

actuating tracks are provided with galvanic isolation

that decreases the impact of disturbances upon

ICINCO 2004 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

operation of the system. Also because of the need to

decrease the disturbance impacts the experiment

results, the current standard has been used for

analogue signals.

As a turn with the motor results in the shift value

of L

with a relatively high error of appr. 1 µm, a

voltage correction procedure for the shift is

introduced. A real shift

∆

= 2.5 µm ± 1 µm is

introduced for the single step of the motor. The

change of the voltage U

in a full range results in 4

steps of the motor. In the correction procedure: first

- the voltage U

on the PZT is increased up to 70 V;

second – the voltage is decreased to 0 V, and 3 steps

of the motor are introduced. Then, a resultant shift of

the mirror equals

∆

= 7.5 µm ± 1 µm. As an exact

position of the mirror is unknown, the operating

system looks for the correction voltage U

resulting

in shifting the mirror to the place, which can be

reached by an ideal motor. In that way, periodic

executions, as above, allow increasing the mirror

shift of 3 × 2.5 µm for each cycle (with the

resolution of 0.01 µm).

Expressions (1) and (2) describe the value of the

shift L

versus a signal AO on the transducer C/A

and the voltage U

. Expression (3) gives the value of

the shift L

versus a number s of the motor step.

VUAO

AOU

70,1000,...,1,0,

1000

==⋅= , 1)

VVU

70,...,0,

10 =⋅=

, 2)

⎥

⎦

⎤

⎢

⎣

⎡

=⋅=

smsL

5.2

,...,1,0,5.2

. 3)

Measurements of the laser response

give at

least 1000 values, when the L

is changed in the

range as in (2):

{}

1000;,...,,

≥= nUUUU

DDD

. 4)

After next 3 steps of the motor, and putting U

= 0 V

on the PZT, the U

voltage can be increased

according to (1) giving a sequence of values AO =

0,1,…,350 on the transducer.

{}

35021

,...,,

DDD

VVVV =

. 5)

At least 151 responses

is taken from the

measurement range (4). The goal of the operation

system is to determine the index k of the response

, which corresponds to the voltage (for

the ideal step motor, and micrometric screw k = 0).

250−n

Expression below describes an assumed quality

function (classic one used in identifying processes,

and approximation quality evaluations):

()

∑

=−=

200,...,0,

750

kVUkQ

. 6)

The minimum value k0 is assumed to minimize the

functional Q(k):

(

)

(

)

kQkQ

k 2000

min

≤≤

. 7)

Searching for the extremum of the quality

function (6), and application of the result for the

mirror shift correction is typical for the adaptive

process problems. After the mirror translation with

the step motor, the operation system searches for the

optimum value of the correction voltage, and adapts

itself to an unknown situation. Fig. 10 shows the

control algorithm.

Collected data of the correction values during the

experiment allows building the knowledge base. The

base can be used in constructing the expert system.

3.2 Details of the automation –

spectrum recognition

The investigations shown above do not give

information about a spectral contents of the laser

radiation during the laser tuning. Different emission

lines are responsible for specific maxima observed at

the laser signature – see Figure 5. We elaborated

another experimental arrangement to recognize the

spectral contents of the laser output gain curve. The

arrangement from Figure 6 was rebuilt in a such

way, that the detector is allowed moving across the

splitted (with the diffraction grating) laser beam –

see Figure 11. An algorithm of the procedure is

given in Figure 12. The detector can assume a value

of its position L

in the range from L

= 0 [mm] to

200

= L

max

= 20 [mm] with a resolution of

∆L

= 0.1 [mm]. An active surface of the detector is

1 mm in diameter, thus moving step is enough to not

“loose” any emission line. The range of the

investigated frequencies

depends on the distance

of the detector from the diffraction grating.

THE LASER SIGNATURE IN CALIBRATION OF THE SERVOMECHANISM

P26

P24

P22

P20

P18

P16

P18

P20

P22

P24

P26

diffraction

grating

zero diffraction

order

I diffraction

order

Detector

laser beam

Figure 11: Arrangement for recognizing the spectral

contents of the laser output. A moving detector across the

splitted (with a diffraction grating) laser beam is used.

Organization of the procedure of the laser

spectrum response investigations is similar to the

procedure of the calibration given above. This time,

additionally, a full procedure of the laser response

spectrum scanning is used for each value of a laser

resonator length. It means, a detector is moved to

next values of the position L

νn

, and simultaneously a

detector output signal U

is read. The signal depends

on both a laser resonator length (a moving indicator

is “i”, like in the calibration procedure) and detector

position (a detector position indicator is “n”). It is

why a data base read during the experiment is two-

dimensional –

The procedure needs calculations of the substitute

of the total laser output power for a given length of

the laser optical resonator. In the arrangement the

detector measures only output laser power for some

frequency ranges

. It is why total laser power,

necessary for the calculations, is substituted by sums

(8) and (9), which are some approximations of the

integration in an integral domain

∑

=≅

200

njj

VIV

, 8)

∑

=≅

200

njj

UIU

, 9)

=2000; Um=70V

∆

=Um/1000;

s=0; Wait (t1)

Up=0V; Wait (t2)

I=0

for n=0,…,200 {L

n; Wait (t3);

i,n=read(U

); I=I+ U

i,n;

Archive U

i,n

}

i=I; i=i+1

Up=Um

Up=Up+

∆

Wait (t2)

s+2<s

s=s+3; Wait (t1)

Up=0V; Wait (t2)

STOP

I=0

for n=0,…,200

Wait (t3);

I=I+read(U

)}

j=I

=j+1

for k=0,..,200

Count Q(k);

Find k0;

Archive {s,k0};

Up=(k0+1)

∆

>350

Up=Up+

∆

Wait (t2)

Figure 12: An algorithm used for a spectral recognition of

the laser output.

Figure 13 shows an experimental result obtained

in the arrangement shown in Figure 11. The

observed signature shows a good order, according to

an order of the emission lines in the spectrum of a

molecule. The result is obtained for the laser

resonator length of appr. 406 mm. The effect is

called a Well-Ordered Laser Signature – WOLS

(Plinski

, 2000). The signature can be easy

calculated, and the result is shown in Figure 13.

ICINCO 2004 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

P 8

P10

P12

P14

P16

P18

P20

P22

Figure 13: Well-Ordered Laser Signature - experimental

result (see the theoretical result in Figure 14 – top)

The result is calculated for the resonator length

tuning of many half-lengthwaves

/2, to show the

developing of the signature with the resonator length

change. As seen, the well-ordered signature loses its

ordered picture with resonator length changes. In

that way it is possible (changing the length of the

resonator) to find other signature interesting for

many applications.

x 10 m

Figure 14: Example of the signatures calculated around of

the laser resonator length L = 406 mm. Well-ordered laser

signature is found (Plinski

, 2000).

One of the applications of the laser is using the

laser as a source of a stable radiation. The servo-

loop, which stabilize the laser radiation to the centre

of the emission line operates much easier, when a

passive (temperature) stabilisation is ensured. In this

case it is useful to operate on some length of the

resonator, where the laser signature is enough

“poor”. It means, the line hoppings effect is reduced

as much as possible. Figure 15 shows the result

obtained around the resonator length of 411.5 mm.

As seen, we observe only one line hopping during

the full translation of the laser mirror of

/2.

4.1146 4.1146 4.1146 4.1147 4.1147 4.1147 4.1147

4.1147

4.1148

4.1148 4.1148

4.1148 4.1148 4.1148 4.1149 4.1149 4.1149 4.1149

4.1149

4.115

4.115 4.115

[

]

x 10

[

Figure 15: A special case of the signature: an one line

jump during the half-wavelength tuning is observed.

To rich the possibility of the elaborated system, it

is possible to fill the same mechanical structure of

the laser with different gas mixtures of CO

containing different isotopes of C an O molecules, as

shown in Figure 16.

x 10 m

OCO

16 12 16

OCO

16 13 16

OCO

16 12 18

OCO

18 12 18

OCO

18 13 18

Figure 16: Theoretically calculated laser signatures

starting from the length L = 410.4 mm of the resonator for

different isotopes of carbon and oxygen molecules (data

base for the expert system)

As seen, different signatures can be observed for

the same length of the resonator.

4 CONCLUSIONS

Our investigations show, that it is possible to find a

suitable laser signature for many applications. One

of them is a single frequency operation of the laser.

THE LASER SIGNATURE IN CALIBRATION OF THE SERVOMECHANISM

To avoid as much as possible temperature drifts of

the laser mirrors we should choose the length of the

resonator, where the signature is very poor. It means,

the laser operates on one chosen line in a wide range

of the resonator tuning.

Another application is a trace gas analyzer. Some

gases show a quite narrow dips in the absorption

spectrum. Choosing a suitable signature we can tune

the laser very easy to desired emission lines, which

can be absorbed by investigated gas medium. A

good example is a trace analyzer, where the spectral

line P14 of the carbon dioxide laser is desired in

combinations with P16, or P18, or P20 lines.

The picture of the laser histogram can be easy

modified using different isotopes of the carbon

or/and oxygen molecules like O

, O

, or O

. Then, different

signatures can be observed for the same length of the

laser resonator.

Another aspect of the experiment is to create an

expert system. As shown, stable and reproducible

signatures of the CO

laser can be a good standard to

calibrate servomechanisms used for investigations of

the laser histograms (series of signatures in line).

The servomechanism coupled with a given structure

of the laser can be applied for investigations of the

laser signatures in the large range of the laser tuning

independently of the laser medium. The adaptive

system to control the laser mirror is used for the

corrections of the mirror position errors. The system

searches the optimum voltage correction value, to

find the optimal position of the laser mirror. The

information about the optimum control is collected

for each investigated position of the step motor

(number of the pitches). Created in that way the data

base will be used in further investigations to develop

the expert system, which should be helpful for the

investigations of the laser histograms of different

lasers.

The automation of the described process can help

with searching suitable laser signatures for different

laser experiments, ex. very sophisticated signatures

for some heterodyning experiments (Buholz, 1981),

or well-ordered signatures (Plinski

, 2000).

The elaborated system for identification of the

laser lines can be used as a diffractive mechanism of

the laser marker, where the control of the lines

generated by a laser is obvious (Plinski

, 2000).

Reassuming, a carbon dioxide laser can be

designed as a chip spectral device, where choosing a

suitable operation frequency can be very easy

realized (comparing to expensive, and complicated

devices, where one of the laser mirrors is replaced

by a diffraction grating, which stimulates the laser

operation on a chosen line).

It is necessary to remark, that the results of the

investigations above are possible to obtain rather on

the laser in a single-mode operation regime. Then

only longitudinal modes are excited in the laser

cavity (Siegman, 1986). It is why an unstable

resonator is used, which stimulates a single-

frequency operation of the laser. In that way, high-

order transverse modes (disturbing the picture of the

signature) are suppressed by definition.

REFERENCES

Buholz, N. E., Selected five-color operation of a CO

laser. In Optical Engineering, Vol. 20, 1981, pp. 325-

327.

Mocker, H. W., Rotational level competition in CO

lasers. In IEEE Journal of Quantum Electronics, Vol.

QE-4, 1968, pp. 769-776.

Plinski

, E. F., Witkowski, J. S., Abramski, K. M.,

Algorithm of RF excited slab-waveguide laser design.

In Journal of Physics D: Applied Physics, Vol. 33,

2000, pp. 1-4.

Plinski

, E. F., Izworski, A., Witkowski, J. S., Calibration

of an automatic system using a laser signature. In

Journal of Systemics, Cybernetics and Informatics,

Vol. 1, No. 2, 2003 (Ed. International Institute of

Informatics and Systemics).

Plinski

, E. F., Witkowski, J. S., Well-ordered laser

signature. In Optics Communications, Vol. 176, No.

1,2,3, 2000, pp. 207-211.

Plinski

, E. F., Witkowski, J. S., Abramski, K. M.,

Diffractive mechanism for laser marker. In Optics and

Laser Technology, Vol. 32, 2000, pp. 33-37.

Shiffner, G., Prediction of CO

laser signatures. In IEEE

Journal of Quantum Electronics, Vol. QE-8, 1972, pp.

877-881.

Siegman, A. E., Lasers, Mill Valley, University Science

Books, California, 1986

Solnik W., Zajda Z., Automation of oxygenation process

in biological treatment plants, in Datorzinate 2000,

ser. 5, Riga, Rigas Teh. Univ. Zinat. Raksti,

2000, 12-17.

Waksberg, A. L., Boag, J. C., Sizgoric, S., Signature

variations with mirror separation for small sealed CO

lasers. In IEEE Journal of Quantum Electronics, Vol.

QE-7, 1971, pp. 29-35.

Witteman, W. J., The CO

laser, Springer Series in Optical

Sciences, Berlin, New York, 1987.

ICINCO 2004 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL