Cones-assembled Grating for Long-range Fiber-optic Linear

Displacement Sensor

Zeina El Rawashdeh, Philippe Revel, Christine Prelle and Frédéric Lamarque

Laboratoire Roberval UMR 7337, Université de Technologie de Compiègne, 60200, Compiègne, France

Keywords: Fiber-optic Sensor, Geometric Modelling, Grating Geometric Design, Diamond Tool Fabrication,

Long-range Displacement.

Abstract: This paper presents the initial design of a new fiber-optic displacement sensor; it is used to measure the

linear displacement of an actuator performing a helical movement. This sensor consists of a set of

assembled cones, which constitute a reflective grating, and two fiber-optic probes. It is characterised by its

ability to measure the displacement along a millimetric range, with a high sub-micrometric resolution. In

this work, the geometric model of the sensor is presented as well in terms of single probe response in front

of a curved reflective surface as in terms of grating shape which authorizes the measurement principle. This

grating design makes the displacement measurement possible due to the overlap of the two probes simulated

output signals. The single probe measurement in front of a curved reflective surface demonstrates a good

agreement with simulation results. A prototype of the cones-assembled grating has been fabricated using a

high precision turning machine and a single-crystal diamond tool on an aluminium alloy; the geometric

parameters of the fabricated grating were evaluated with the help of a Nanofocus

µscan optical

profilometer. The agreement between the simulated geometric parameters and the real parameters is very

good.

1 INTRODUCTION

The need of miniature sensors is becoming essential

in modern sciences. Development of micro sensors

with high sensitivity, high resolution and high

dynamic range dominates the research field for

different commercial applications (Mukherjee,

2012). Among the different parameters in numerous

applications, is the displacement to be measured

with high accuracy, and wide dynamic range.

High resolution and long range contactless

displacement sensors are integrated in mechanical

systems, where highly precise performances are

required. (Fan, 2007) presented the design of a

measurement system, consisting of a mini LDGI

(linear diffraction grating interferometer) and a

focus probe, these two sensors are integrated into the

spindle system of a micro/nano-CMM (coordinate

measuring machine). The system accuracy is 30 nm

for a 10 mm displacement of the spindle.

Fiber-optic technology is chosen for the sensor

design because it can achieve contactless

measurements within a miniature probe size.

A particular interest in recent studies is to design

miniature fiber-optic displacement sensors with high

relative accuracy (nanometric resolution /millimetric

range; ratio ~ 10

-6

The study developed by (Lee, 2012) presented

the design of a fiber-optic displacement sensor with

large measurement range; it is composed of a

transmissive grating panel, a reflection mirror, and

two optical fibers as a transceiver. The measured

bidirectional movement demonstrated a peak to peak

accuracy of 10.5 µm, high linearity, resolution of 3.1

µm at the full bandwidth, signal-to-noise ratio of

27.7 during a movement of 16004 µm.

To satisfy the requirements of the target

application for the sensor, which is the on-line depth

measurement for drilled-holes, the surface of the

sensor grating must be axis-symmetrical, and

consequently the surface has to be curved (convex).

(Zhao, 2000) presented a novel fiber-optic sensor for

small internal curved surface measurement. The

measurement principle is based on beam reflection,

and it gives high vertical resolution of 0.1 µm with 8

µm measuring error.

(Patil, 2011) developed a generalised

mathematical model able to do the simulation of any

147

El Rawashdeh Z., Revel P., Prelle C. and Lamarque F..

Cones-assembled Grating for Long-range Fiber-optic Linear Displacement Sensor.

DOI: 10.5220/0005432001470155

In Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology (OSENS-2015), pages 147-155

ISBN: 978-989-758-092-5

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

configurations of fiber-optic sensors. It is based on

ray tracing approach and different matrix

transformations such as translational, reflection or

rotational are used. In addition, (Bingshi, 2008)

studied the influence of the fiber-optic displacement

sensor parameters on its performances, focusing

on geometrical parameters such as the numerical

aperture, the radius of fiber core, the lateral

separation of transmitting and receiving fibers,

the angle between the two fibers and the

reflector curvature radius. (Utou, 2006) have

carried out various experiments in order to verify the

effects of various parameters on the accuracy

measurement of a fiber-optic displacement sensor,

for example: orientation between sensor tip and

target surface, i.e. angularity, the effect of varying

reﬂectivity of targets’ surfaces, the effect of

various transparent material thickness over the

target reﬂective surface and the displacement of a

surface in an arc-path away from the stationary

tip of a sensor. It was found out that the higher the

values of transparent material thickness, the lower

the sensitivity values obtained from the fiber-optic

sensor probe. The result from the experiment of the

angle variation between target and sensor has shown

that the sensor sensitivity reduces for angles higher

than 20°.

Finally, (Gaikwad, 2012) developed a novel

intensity-modulated fiber optic displacement sensor

with a convex reflector, in which the sensing

structure was described, and the derivations of

geometric and Gaussian mathematical models were

demonstrated.

This paper introduces first a geometrical model

of a convex surface reflector, together with its

experimental validation. Then, the modelling of the

long-range measurement is done which gives the

geometrical parameter of a set of assembled cones

which constitute an axi-symetrical grating. The

grating have been fabricated with a high precision

turning machine together with a single-crystal

diamond tool, in order to obtain high geometric

precisions and a good surface quality (R>95%,

polished-mirror surface).

These fabricated cones have been geometrically

characterised for future use of the sensor, where high

performances regarding its sensitivity, measurement

range and resolution are required for online depth

measurement while machining.

2 SENSOR PRINCIPLE

The sensor consists of two fiber-optic probes

associated to a high reflective surface. Each probe

has one emission fiber and four reception fibers.

The sensor performances when it is associated to a

planar surface have been already analysed (Alayli,

1998, Girão 2001). When translating the flat mirror

perpendicularly to the probe axis, the sensor

response curve is obtained (Figure 1).

Figure 1: Response curve of the fiber-optic displacement

sensor.

The preferred working zone of the sensor is zone (3)

because of its linearity and high sensitivity.

However, the measurement range of this zone is too

small (<200 µm). So, in order to increase the linear

zone, the displacement direction of the flat mirror is

different from the normal vector orientation of its

surface resulting in the multiplication of the nominal

range value by (sin ε)

-1

factor where ε is the

inclination angle related to the grating axis. By

repeating the tilting mirror configuration, a grating is

obtained. For an inclination angle ε of several

degrees, the sensor resolution can be reached to 15

nm and the measurement range can be increased to

several millimeters as a function of the grating steps

number. It is possible to do long-range

measurements if the non-linear signal during the

transition between two consecutive steps is

avoided. To do so, two probes are used, to ensure a

continuous displacement measurement over the

long-range by alternately switching between the

probes in order to avoid strong non-linearity due to

the illumination of two grating steps at the same

time. A sensor prototype was successfully modelled,

designed and tested (Prelle, 2006).

The objective of the current work is to develop a

sensor able to measure precisely the linear

displacement of an actuator performing a helical

movement. For this new application, the sensor

Figure 2: Measurement principle with a 3D grating.

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

148

reflective grating has to have a 3D shape in order to

provide a valid measurement even if the sensor

rotates along its axis of symmetry, as shown in the

figure 2.

3 GEOMETRIC MODEL OF THE

REFLECTIVE SURFACE

3.1 Convex Surface Modelling

The influence of the curved reflector on the sensor

performances was modelled. The reflective grating

of the sensor is a set of assembled cones, which

implies that the sensor reflector surface is convex.

This property will modify the sensor performances

as compared to the previous existing sensor with

grating composed of an assembly of flat mirrors

(Prelle, 2006, Khiat 2010). In order to observe the

influence of the convex surface on the sensor

performances, different geometric parameters were

considered. These parameters are shown in Table 1

and figure 3.

Table1: Geometric model parameters.

Symbol

Definition

Ø The probe diameter (mm)

Radius of curvature (mm)

M Tangential point

Normal vector to tangent

Initial distance between the reflector

and the probe (mm)

α The incidence angle



The angle between n

and the

symmetrical axis of the probe



The spacing between the emission

fiber and the reception fiber

The spacing between the normal

vector of the flat surface and the

reflected beam from the curved

surface intercepted by the sensor

The aim of this theoretical model is to analyse the

sensor performances when it is associated to a

convex reflector, and compare these performances to

a planar reflector. For that, the response curve of the

sensor was generated in the two cases (Flat surface

and convex surface), by detecting the light intensity

of the sensor as a function of the displacement (d

)

and the radius of curvature (R

In the model two conditions were taken into

account to ensure that the light is detected by the

sensor.

(a)

(b)

Figure 3: Schematic diagram of the reflected light model:

(a) Flat mirror, (b) convex mirror.

These conditions are illustrated in the following

equations:

α < β – 2 × δ (1)

emission

+ e < X

+∆ < R

emission

+ e + D

reception

(2)

Where β = arcsin(0.46), α and δ are defined in Table

1, R

emission

is the radius of the emission fiber, and

reception

is the diameter of the reception fiber.

The variables δ and ∆ are calculated geometrically

for each point (X

, Y

Figure 4 represents the results of several radii of

curvature (R

) as a function of the displacement (d

Cones-assembledGratingforLong-rangeFiber-opticLinearDisplacementSensor

149

Figure 4: Response curves for several radii of curvature.

The flat mirror configuration is used as the

reference. It is clear that the higher the radius of

curvature is, better will be the normalised light

intensity detected in the linear part of the curve, in

consequence, better will be the sensor performance.

For R

= 15 mm, the signal light intensity reduces

sharply.

Table 2 represents the loss in sensitivity ratio

(Att) due to the convex form of the reflector, as a

function of different radii of curvature, where:

 Att : The loss in sensitivity ratio





: The linear sensitivity of a curved

reflector (mm

-1

)

 S

∞

: The linear sensitivity of a planar

reflector

3.2 Experimental Validation of the

Convex Surface Modelling

The geometric model previously described has been

validated experimentally by fabricating two pieces

of cylinders with different diameters: Piece (A) with

small diameters (40, 30, 20, 10 mm) and piece (B)

with large diameters (55, 50, 40, 35 mm). These two

pieces have been fabricated with a single crystal

diamond tool on a high precision turning machine

whose characteristics and performances are

described in section 5.

For each cylinder in the two pieces, the

calibration curve of the sensor has been obtained by

moving the sensor away from the cylinder reflecting

surface. The linear sensitivity has been calculated

for each curve, with a linearity criterion of 1 %.

Figure 5 illustrates the experimental set-up used; it

consists of the two reflecting pieces together with a

fiber – optic probe.

(A): small diameter piece

(B): large diameter piece

Figure 5: Experimental set-up.

Table 2: Loss in sensitivity

(mm)

1 5 10 15 20

∞

Att





∞

0.7 0.74 0.8 0.91 0.98 1

The experimental sensitivities (zone 3 of figure 1)

have been compared to the theoretical sensitivities in

Figure 6: Influence of the diameter of the reflective

convex surface on the sensor sensitivity.

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

150

order to test the precision of the geometric model

(Figure 6).

The previous figure illustrates the influence of

the cylinder diameter on the linear sensitivity of the

sensor (simulated and experimental). It reduces as

the cylinder diameter decreases.

This experiment validates the geometric model and

shows that it is preferred to have a diameter higher

than 35 mm for applications requiring high

sensitivity.

For the mentioned reasons, and to guarantee a

good performance of the sensor, the cones-

assembled grating has been fabricated from a 50 mm

diameter cylinder.

4 GRATING GEOMETRICAL

DESIGN

A geometrical model was developed to simulate the

functioning of the long-range displacement sensor.

As a result, the optimal dimensions for each step of

the grating are provided. These dimensions ensure

the measurement continuity over a millimetric range

with a sub-micrometric resolution. This geometrical

model takes into account the following two

conditions:

1. The distance between the probe and the grating

step has to be in the linear zone (zone 3 of

figure 1).

2. The overlap between two successive signals is

fixed at 30 µm to avoid the linear measurement

discontinuity during the steps transition.

The grating geometrical model is based on the

algorithm shown in figure 7.

Figure 8 shows the geometric parameters

considered for a step in the cones-assembled grating,

where:

 l: The step length (µm)

 h

: The step height (µm)

 ε:The step angle (°)

 γ: the angle at the bottom of the step (°)

The model optimizes the dimensions to get the best

limit of resolution which depends on the value of ε.

The more ε is, the smallest will be the limit of

resolution.

Figure 8 shows the successive

algorithm sequences used to simulate the

functioning of the measurement principle. The

geometric model of the convex surface explained

above leads to the best limit of resolution of a single

fiber-optic probe used as a simple displacement

sensor.

Figure 7: Algorithm of the geometrical model.

Figure 8: Geometrical parameters of the cones-assembled

grating.

The algorithm figured out the values of each

geometric parameter:

 The step length (l) is 1541 µm

 The segment (h

) is 253 µm

 The angle (γ) is 130°

 The step angle ε is 7.17°

The theoretical limit of resolution is 24 nm with an

overlap between the two signals of 30 µm.

Figure 9 shows the theoretical displacements

calculated with Matlab software, where:

 Theoretical axial position (µm): The position of

the sensor in the classical case (without

inclination)

 Theoretical lateral position (µm): The position

of the sensor in the lateral case (with

inclination)

It is clear that the lateral displacement range

Cones-assembledGratingforLong-rangeFiber-opticLinearDisplacementSensor

151

Figure 9: Theoretical axial position (µm) vs. theoretical

lateral position (µm).

(801.0 µm) is higher than the axial one (100.1µm),

by a factor of sin 7.17°.

5 CONICAL GRATING

FABRICATION

After the geometrical model phase, the fabrication

technique has to be taken into account, and that

includes the performances of the turning machine, as

well as the fabricating tool whose geometrical

design, particularly, its radius of curvature

influences the fabrication procedure and its final

product.

A machining program has been used, in which

all these constraints have been taken into

consideration.

5.1 Fabricating Elements

Characteristics

In the case of 3D axis – symmetrical pieces, the high

precision rotating spindle coupled with single crystal

diamond tool provide high geometrical precisions as

well as good surface qualities. That is important for

the sensor based on cones-assembled grating, where

the light reflection influences the sensor sensitivity

and range.

The machine used for the fabrication technique is

a high precision turning machine (Figure 10).

The machine is a prototype lathe with T slide

architecture. On the Z-axis a magnetic bearing

spindle is fixed, and on the X-axis is fixed the tool

holder. The two hydrostatic slides (X and Z) are

fixed on a 1.5 ton granite block; this block is

supported by a high frequency vibration-filtration

system.

The hydrostatic bearings minimise the friction

forces to ensure a high rigidity as well as a straight

tool trajectory. For each axis, the straightness error

is 0.3 µm for a total displacement of 100 mm.

The two slides are actuated with the help of two

linear motors; the displacement is measured by an

optical encoder with a 4 nm limit of resolution.

The two motors are controlled numerically with

the help of PMAC card.

On the Z-axis, a high precision rotating spindle is

fixed together with magnetic bearings in order to

avoid friction loss and to ensure the right trajectory

during rotation.

This machine proved highly geometrical

precisions regarding the dimensions of the fabricated

pieces as well as high surface qualities (Gautier,

2008).

In order to obtain high surface roughness less

than 15 nm, it is preferred to use a single – crystal

diamond tool, thanks to its good qualities, such as:

hardness, good thermal conductivity and the low

waviness of the cutting edge (Yuan, 1996).

An aluminium alloy 2017 has been used to fabricate

the grating.

Figure 10: High precision turning machine.

5.2 Influence of the Tool Radius of

Curvature on the Geometry

The radius of curvature of the fabricating tool has

not been considered in previous studies. The more it

is sharp; the better will be the step profile at the

bottom of the steps (Figure 11). In the actual

prototype, this angle (γ) was fixed at 130°. However,

when the value of the angle γ is too high, the non-

0 200 400 600 800 1000 1200 1400 1600

100

150

200

250

300

Theoretical lateral position (micrometer)

Theoretical axial position (micrometer)

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

152

useful zone of the grating at the bottom of the steps

will increase. As a consequence, in future works, the

value of γ has to be optimised between 90° and 130°

which will enhance the sensor performance.

Figure 11: The tool radius of curvature.

5.3 Description of the Machining

Program

In order to have a good surface roughness for the

sensor grating, the depth cut has to be between 5 and

10 µm (Gautier, 2008).

The machining program is divided into two main

parts: In the first part, every step is machined by

achieving seven successive cuts (Figure 12).

The second part is the last finishing cut which allows

getting the final form of the overall grating.

In this prototype, ten steps were machined to

generate the sensor reflector grating.

For every step, two successive trajectories were

programmed: Firstly, from point A to point B as

shown in the figure 12 in order to get into the

material and to generate a slope respecting the value

of the angle ε. The second trajectory is from point B

to point C (Figure 12) to get out from the material

following the angle γ. Afterwards, the tool turns

back to its initial position A to re-do another cut.

Figure 12: Machining technique.

However, the contact point between the tool cutting

edge and the material as well as the tool radius of

curvature, both are not the same in the two

successive trajectories (Figure 13).

In the first six cuts, the depth was fixed to 20

µm. The seventh cut was done at 10 µm.

Figure 13: Machining contact points.

The length of the first trajectory has been reduced by

5 µm so that during the last finishing cut (the 8

the depth of the machined material is at 5 µm of

precision which ensures optimal cutting conditions.

At the last finishing cut, the depth in the first

trajectory has been fixed at 5 µm.

The lubrication flow has been increased and finally

the feederate speed was decreased to 50µm/s, in

order to obtain a high surface quality (polished-

mirror).

6 GEOMETRICAL

CHARACTERISATION OF THE

FABRICATED CONES

A grating prototype has been fabricated using the

single-crystal diamond tool, following the described

program in order to reach the theoretical dimensions

identified in the geometric model (Figure 14).

This fabricated grating have been characterised

geometrically using the Nanofocus

µscan optical

profilometer to measure the steps profiles and

compare them to the theoretical dimensions (Figure

14).

Figure 15 shows the profile of the measured

grating. The average value of the angle ε on the ten

Figure 14: Geometrical characterisation of the grating

using the Autofocus sensor.

anofocus

R=100 µ

Theor

Practice

Tool

Second contact point

First contact point

Ten ste

Cones-assembledGratingforLong-rangeFiber-opticLinearDisplacementSensor

153

steps is 7.25°.

The average of the measured height is (196.2 ±

2.1 µm) for a theoretical height of 194 µm, the

average of the measured length is (1539.6 ± 4.1µm)

for a theoretical one of 1541.8 µm.

These results are very good for an initial

prototype.

Figure 15: Profile of the measured steps after fabrication.

7 CONCLUSIONS

This paper presents the design of an original fiber-

optic displacement sensor, which will be used to

measure the linear displacement of an axis

performing a helical movement.

First, the geometric model of the sensor principle

was presented in order to obtain the theoretical

geometric parameters. These parameters lead to the

optimal cones-assembled grating, masterpiece of the

long-range displacement measurement principle.

Then, a 10 steps grating prototype of the sensor

was fabricated using a high precision turning

machine with the help of a single crystal-diamond

tool on an aluminium alloy in order to obtain high

precision in the fabricated dimensions, as well as

high reflectivity which ensures good sensor

sensitivity and linearity.

The conical grating prototype was characterised

using Nanofocus

µscan optical profilometer and

the measured parameters are close to the theoretical

ones.

In a near future, this grating will be used together

with two fiber-optic probes to measure on-line the

translation of an axis along several millimeters when

the measuring head of the spindle rotates at 360°

during the translation.

ACKNOWLEDGEMENTS

The Authors would like to thank Cetim (Centre

Technique des Industries Mécaniques) for the

support of this work.

The authors would like to thank B. Bosschaert,

N. Delias and P. E. Karcher, students in Univeristy

of technology of Compiègne, for their help in the

fabrication of the conical grating.

REFERENCES

T. Mukherjee, T.K. Bhattacharyaa, 2012. A Miniature,

High Sensitivity, Surface Micro-machined

Displacement Sensor with High Resolution. The 2012

IEEE/ASME International Conference on Advanced

Intelligent Mechatronics, Kaohsiung, Taiwan.

K.C. Fan, Z. F. Lai, P. Wu, Y. C. Chen, Y. Chen, G. Jager,

2007. A displacement spindle in a micro/nano level,

Measurement Science and Technology

doi :10.1088/0957-0233/18/6/S07.

A. D. Gaikwad, J. P. Gawande, A. K. Joshi, R. H. Chile,

2012. An Intensity-modulated optical fibre

displacement sensor with convex reflector,

International journal of advanced research in

electrical, electronics, and instrumentation

engineering, vol. 1, Issue 1.

Y.G. Lee, Y.Y. Kim, C.G. Kim, 2012. Fiber optic

displacement sensor with a large extendable

measurement range while maintaining equally high

sensitivity, linearity, and accuracy. Review of

Scientific Instruments 83, 045002(2012); doi:

10.1063/1.3698586.

Y. Zhao, P. Li, C. Wang , Z. Pu, 2000. A novel fiber-optic

sensor for small internal curved surface measurement.

Sensors and Actuators A, vol. 86, pp. 211-215.

S.S. Patil, A.D. Shaligram, 2011. Modeling and

experimental studies on retro-reflective fiber optic

micro-displacement sensor with variable geometrical

properties. Sensors and Actuators A, Vol. 172, pp.

428-433.

X. Bingshi, X. Wen , Y. Dong, 2008. A theoretical

analysis on parameters of fiber optic displacement

sensor. Proc. of SPIE, Vol. 7129, pp. 1-6.

F. E. Utou, J. Gryzagoridis, B. Sun, 2006. Parameters

affecting the performance of ﬁber optic displacement

sensors. Smart Mater. Struct. 15 (2006) S154–S157,

doi: 10.1088/0964-1726/15/1/025.

Y. Alayli, D. Wang, M. Bonis, 1998. Optical fiber

profilometer with submicronic accuracy. Proc. SPIE,

3509.

P.M.B.S. Girão, O.A. Postolache, J.A.B. Faria, J.M.C.D.

Pereira, 2001. An overview and a contribution to the

optical measurement of linear displacement, IEEE

Sens. J. pp. 322–331.

C. Prelle, F. Lamarque, P. Revel, 2006. Reflective optical

sensor for long-range and high-resolution

displacements. Sensors and Actuators A, vol. 127.

A. Khiat, F. Lamarque, C. Prelle, Ph. Pouille, M. Leester-

Schadel and S. Büttgenbach, 2010. Two-dimension

fiber optic sensor for high-resolution and long

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

154

range linear measurements. Sensors and Actuators

A, vol. 158, Issue 1.

A. Gautier, H. Khanfir, P. Revel, R.Y. Fillit, 2008. Polish-

miror finish surfaces obtained by high precision

turning, Int. J. Machining and Machinability of

Materials, Vol. 4, Nos. 2/3.

Z.J. Yuan, M. Zhou, S. Dong, 1996. Effect of diamond

tool sharpness on minimum cutting thickness in

ultraprecision machining, J. Mater. Proc. Tech. 62 (4),

pp. 327–330.

Cones-assembledGratingforLong-rangeFiber-opticLinearDisplacementSensor

155