A capacitors were obtained by segmenting the annular electrodes

     
   A tilt sensor is an
instrument that is used for measuring the tilt in multiple axes of a reference
plane. Tilt sensors measure the tilting position with reference to gravity, and
are used innumerous applications. They enable the easy detection of orientation
or inclination. Similar to mercury switches, they may also be known as tilt
switches or rolling ball sensors.

        These instruments have become more
popular over the years, and are being adapted for increasing numbers of high
end applications. For example, the sensor provides valuable information about
both the vertical and horizontal inclination of an airplane, which helps the
pilot to understand how to tackle obstacles during the flight. By knowing the
current orientation of the plane, and the angle at which the plane is inclined
to the earth’s surface, stunt pilots, i.e. the Red Arrows, can put on a
fascinating air show. Tilt sensors are an essential decision making tool for
the pilots.

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There are different types of tilt
sensors used in industries nowadays. They are

·        
Variable capacitive type.

·        
Variable resistive type.

·        
Optical type.

 

 

·       
Variable capacitive type

                                                             Figure 1.1  Variable Capacitive Tilt Sensor

 

               Capacitive
tilt sensors have excellent sensitivity, insofar as they would not be
significantly affected by temperature and mechanical misalignment and they are
highly reliable, owing to the absence of friction or wear within. Moreover,
capacitive tilt sensors are economically feasible and easy to manufacture,
given their low-cost materials and simple structure. Furthermore, electric
field shielding is easier with capacitive sensors than with magnetic sensors.
These sensors are composed of three parts: two electrodes and a common
electrode (or a metallic ball) forming two capacitors. When the sensor tilts
with an object, analog outputs in relation to the inclination can be realized
easily by measuring the difference between two capacitors. However, this kind
of sensor suffers from a limited measurement range, e.g., from ?45? to 45?, which depends on the
measurement mechanism used and the parameters for the inner structure of the
sensor itself. A planar-capacitive tilt sensor with concentric annular
electrodes is proposed for further expansion of inclination measurement range.
Four segmented annular planar capacitors were obtained by segmenting the
annular electrodes in the sensor head. By using dielectric liquid that crosses
the center of electrodes as a sensing pendulum. This sensor is developed to
determine the inclination angle by detecting the values of segmented annular
planar capacitors.

·      
Variable resistive type

            Figure 1.2 Variable Resistive Tilt Sensor

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

         The
measuring principle of the variable resistive inclinometer is based on a
voltage divider scheme with ac electrical potential detection. (a) shows the
schematic diagram of the working principle for the proposed inclinometer. A
ring-shape metal resistor and a disk metal grounding electrode were deposited
on a glass substrate for the sensing elements. A free liquid metal droplet in
the sensor chamber was used as the pendulum mass for tilt sensing. The
structure of the proposed inclinometer is like a variable resister where the
liquid metal droplet is the output port for reading the resistance value of the
ring-shape resistor. The equivalent circuit of the proposed inclinometer is
presented in (b). Since the position of the liquid-metal droplet is always
located at the lowest position of the sensor chamber such that the level of the
“voltage divider” is defined by the position of the metal droplet. ac signals
were applied for electrical potential measurements. In addition, a lock-in
detection scheme was used for the signals reading such that the background
noise can be removed. The output voltage of the inclinometer corresponding to
the tilt-angle can be represented as

  ? V = Vin  r_??.

                  L

where_V is the output voltage, Vin the
input voltage, r the radius of the sensing electrode, L the
length of the sensing electrode and ? is the tilt-angle (rad). Since L=2?r,
the equation can be presented as follows such that the output of the measured
results is independent to the size of the sensor:

?V = Vin_??.

             2?

 

                                 2.INTERFEROMETRY

 

Interferometry  is a family of techniques in which waves, usually electromagnetic waves, are superimposed causing the phenomenon of interference in order to extract information.  Interferometry is an important investigative
technique in the fields of astronomy, fiber optics
, engineering   metrology
, optical metrology, oceanography, seismology, spectroscopy  (and
its applications to chemistry), quantum
mechanics, nuclear and particle
physics, plasma
physics, remote
sensing, biomolecular
interactions, surface profiling, microfluidics,
mechanical stress/strain measurement, velocimetry, and optometry.

 

Interferometers are widely used in science and industry for the
measurement of small displacements, refractive index changes and surface
irregularities. In analytical science, interferometers are used in continuous
wave Fourier transform spectroscopy to analyze light containing features
of absorption or emission associated with a substance or mixture. An astronomical interferometer consists of two or more separate
telescopes that combine their signals, offering a resolution equivalent to that
of a telescope of diameter equal to the largest separation between its
individual elements.

Interferometry makes use of the principle
of superposition to combine waves in a way that will cause the result of their
combination to have some meaningful property that is diagnostic of the original
state of the waves. This works because when two waves with the same frequency combine,
the resulting intensity pattern is determined by the phase difference between
the two waves that are in phase will undergo constructive interference while
waves that are out of phase will undergo destructive interference. Waves which are
not completely in phase nor completely out of phase will have an intermediate
intensity pattern, which can be used to determine their relative phase
difference. Most interferometers use light or some other form of electromagnetic wave.

Interferometry has been used in defining and calibrating length standards. When the metre was defined as
the distance between two marks on a platinum-iridium bar, Michelson and Benoît used interferometry to
measure the wavelength of the red cadmium line in the new standard, and also
showed that it could be used as a length standard. Sixty years later, in 1960,
the metre in the new SI system was defined to be equal to
1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic
spectrum of the krypton-86 atom in a vacuum. This definition was replaced in 1983
by defining the metre as the distance travelled by light in vacuum during a
specific time interval. Interferometry is still fundamental in establishing the calibration chain in length measurement.

Interferometry is used in the calibration of slip gauges (called gauge blocks in the US) and in coordinate-measuring machines. It is also
used in the testing of optical components.

 

 

 

2.1 Fabry
– Perot (F – P) Interferometer

 

              The Fabry-Perot interferometer uses the phenomenon of multiple beam
interference that arises when light shines through a cavity bounded by two
reflective parallel surfaces. Each time the light encounters one of the
surfaces, a portion of it is transmitted out, and the remaining part is
reflected back. The net effect is to break a single beam into multiple beams
which interfere with each other. If the additional optical path length of the
reflected beam (due to multiple reflections) is an integral multiple of the light’s
wavelength, then the reflected beams will interfere constructively. More is the
number of reflection inside the cavity, sharper is the interference maximum.
Using Fabry-Perot (FP) interferometer as a spectroscopic tool, concepts of
finesse and free spectral range can be understood.

                The basic principle of working
of the Fabry-Perot interferometer is schematically explained in the adjacent
figure.

                                                           
Figure 2.1  Fabry Perot Interferometer principle

      

             The Fabry-Pérot interferometer
consists of two reflecting mirrors that can be either curved or flat .In the
Fabry-Perot interferometer the separation between two semi-silvered glass
plates can be varied. One plate remains stationary with respect to the frame of
the instrument whilst the other is mounted on a nut threaded on an accurate
screw.

             The adjustment of the Fabry -Perot
interferometer is in many ways similar to that of Michelson. In the Fabry –
Perot interferometer, the multiple beam interference fringes from a plane
parallel plate illuminated near normal incidence are used. The inner surfaces
are coated with partially transparent films of high reflectivity and are parallel,
so that they enclose a plane parallel plate of air. The plates themselves are
made slightly prismatic, in order to avoid disturbing effects due to
reflections at the outer uncoated surfaces.

            Only certain wavelengths of light
will resonate in the cavity: the light is in resonance with the interferometer
if and only if m(

/2) = L, where L is the distance between the
two mirrors, m is an integer, and

 is the
wavelength of the light inside the cavity. When this condition is fulfilled,
light at these specific wavelengths will build up inside the cavity and be
transmitted out the back end for specific wavelengths. By adjusting the spacing
between the two mirrors, the instrument can be scanned over the spectral range
of interest.

 

 

                                   3. SENSOR
DESIGN

 

 

                                                            
F

                                                   
Figure 3.1 Schematic diagram of sensor

 

Figure
3.1 shows the schematic diagram and physical picture of the developed F-P tilt
sensor that comprises of two silica capillary tubes, a standard single mode
fiber (SMF) and a liquid mercury marble as an inertial component. A microscale
mercury marble of ~13.3 ?l in volume and ~1.3 mm in diameter, working as a
light reflector, was injected with a pipettor into a larger silica capillary
tube serving as a sleeve tube with an inner diameter of 1.3 mm which confined
the liquid metal droplet and guided it when an inclination was applied. Another
smaller SiO2 capillary tube of 125 ?m in inner diameter was used as a ferrule
into which a SMF was inserted. Then, the assembly extended into the
aforementioned sleeve tube. The separation between the fiber end and the
mercury endface was controlled to set the initial F-P cavity length as 96 ?m .
After that, the capillary tube and the SMF were held together by an epoxy
adhesive  such that the air cavities at
both sides of the liquid marble were approximately set as 10 mm and 5 mm,
respectively.

 

Figure 3.2  Physical picture of F P tilt sensor

 

 

 

 

 

           The
use of a mercury marble with an appropriate weight instead of a mercury droplet
is to reduce the capillary force caused by the dynamic contact angle hysteresis
(CAH) that resists the droplet motion, thereby lowering the measuring threshold
relevant to the sensitivity. In consideration of the fact that a low surface
wettability contributes to a small dynamic CAH, the surface hydrophobicity of
the capillary tube is regulated by cleaning the tube with acetone solution at
25?C for 5 minutes and
then immersing it into an aqueous HDFT hydrophobic solution. Figure 3.3
compares the scanning electron microscope (SEM) images of a 500-?m-thick
silicon wafer with a 300-nm-thick oxide layer before and after the
hydrophobicity treatment. It can be clearly observed that the treatment is
conducive to the improvement of surface roughness and micro-defects on
substrate.

 

 

      
                                             Figure 3.3  Before  and  After Hydrophobicity Treatment                                                                                                        

 

 

 

           The
measured contact angles of the mercury and water marbles on a hydrophobic SiO2
substrate via drop shape analysis device (FM40MK2 Easy Drop) are given in
Fig.3.4 . The former exhibited a contact angle of ~135º after hydrophobic
treatment, which was obviously superior to ~101º of the latter. The results
revealed that the liquid mercury offered a larger contact angle, which
accounted for the choice of mercury marble as a liquid pendulum, compared with
other liquids such as deionized water, ethanol or magnetic fluid.

 

 

Figure 3.4 Contact angle
of water and mercury drop

 

 

 

 

 

 

4.PRINCIPLE

 

 

      

         Tilt is a static measurement where gravity is
the acceleration being imposed, depending on the externally applied inclination
and interfacial behaviour between liquid marble and substrate. Thus, a
lumped-parameter model was established to understand the liquid marble
dynamics. Assuming that the tilt angle (?) of the sensor is 0º when its
sensing direction is perpendicular to the direction of gravity. As seen in
Fig.4.1, when the sensor rotates anticlockwise from 0º to 90º, the liquid
marble will move downward, therefore making the known initial air cavity
lengths (L1 and L2) as L1-?L
and L2+?L
at its both sides, respectively.

 

 

                                                   

 

                                                           
Figure 4.1 Sensor Alignment

 

 

The
change of the cavity length L1 is primarily due to the sliding motion of
liquid marble and the deformation of its curved edge. In view of the complexity
of establishing an accurate model for the latter related to its mobility and
hysteresis, the curved contour edge deformation was regarded as a part of its
sliding motion. Accordingly, based on the ideal gas law, the internal pressures
P1 and P2 in two micro-cavities can be approximated as

  

 

     ——- ( 1 )

where P0,
which is equal to the atmospheric pressure, is the initial internal pressure in
the micro-cavities.

           During motion, the liquid marble is
subjected to the resisting force f that is involved with the capillary
force induced by dynamic CAH between the advancing contact angle ?a and
receding contact angle ?r, the air damping and the contact-line friction
in which the damping/friction force is assumed to be linearly related to the
traveling velocity of the droplet for analysis simplicity. Therefore, the
damping/friction force is ignored for determination of the static tilt angle ?
caused by a gravity driving force. Then we can arrive at the following
relation

——-
 ( 2 )

 where m is the mass of the
liquid marble and S is the cross-sectional area of the capillary sleeve
tube. Since the relative motion between liquid marble and capillary substrate
occurs when the capillary force is overcome, f in Eq.(2) is an angle of
inclination-related surface tension force, which can be modulated by substrate
roughness, surface wettability and liquid/vapor surface tension .

In
view of the hysteresis for the sliding liquid marble with this
semicircle-straight shape, the equation to determine the critical resisting
force f for the internal surface of capillary sleeve tube is
approximated as

 

——- ( 3 )

where K is
a correction factor; w is the width of the liquid marble (w??d),
where d is the inner diameter of the capillary tube), and ? is
the liquid/vapor surface tension that can be confirmed by calibration
experiments. Note that the curved edge of liquid marble will to a certain
extent occur to deform during it moves along the capillary substrate due to
contact angle hysteresis-dependent omnipresent heterogeneities on interfacial
surfaces, which will affect the accurate determination of w and ? in
Eq.(3). Hence, the correction factor K in Eq.(3) should be fitted to
balance the resisting force, the weight and the internal air pressures imposing
on the marble under the critical conditions in order to initiate sliding for
estimating motion behaviors of the mercury marble.

The
following step is to figure out the change (?L)
of F-P cavity length in Eq.(1). Referring to Fig.4.1 again, the movement of the
liquid marble in silica sleeve tube causes the change of L2 and then
generates the F-P interference. The reflected light intensity Ir can be
approximately given by

——–
( 4 )

where
R1 and R2  are the
reflective values of the mercury marble/air and the fiber end/air interfaces,
respectively; Ii is the incident intensity from the laser; ? is
the coupling coefficient of cavity length loss; ? is the phase
difference between two adjacent beams in micro-air cavity, which is
approximated as 4?L/?, where L is the of F-P cavity length
and ? is the wavelength of incident light. In fact, Ir in Eq.(4)
can reach the maximum value when ? equals to (2m+1)? wherein m=0,
1, 2 and etc. Hence, according to the measured spectrum of Ir/Ii,
the current value of cavity length (L2) can be calculated by

——— ( 5 )

Accordingly,
?L
and L1 in Eq.(1) can be solved.
In this case, the air pressures (P1 and P2) in two micro-cavities
and the tilt angle (?) to be solved are then obtained by Eqns.(1)-(3).
It is worth mentioning that the thermal deformation of the F-P cavity tends to
disturb the initial force balance due to varied air pressures in air cavity and
then cause L1 and L2 to change in the opposite trend, thus producing
the measurement error in tilt angle. More importantly, the mercury marble will
accelerate the evaporation as the temperature rises, thereby deteriorating the
sensor performance. This phenomenon restricts the current sensor to working at
room temperature. In addition, due to the existence of an F-P cavity, the
sensor response to external pressures is related to the mechanical strength of
cavity and epoxy adhesive used to seal the cavity. In other words,
high-strength cavity and epoxy adhesive can suppress the disturbance of ambient
pressures on the liquid marble motion. For this reason, the temperature and
pressure sensitivity of this sensor is not considered now.

                                      5 .
MEASUREMENT

 

 

 

         The measuring arrangement for tilt
measurement is shown in the above block diagram. A broadband laser (ALS-CL-17)
is used to illuminate the F-P sensor, and the corresponding reflection spectrum
is monitored by an AQ6370C optical spectrum analyzer (OSA) with a wavelength
resolution of 0.02 nm through the use of an optical circulator.Circulator is an
optical device which allows bidirectional transmission of optical signals
through the same path.

         Tthe cavity length L2, i.e., the
separation between the fiber end and mercury marble, can be extracted by
setting k=1 in Eq.(5), where ?m and ?m+1 are the adjacent
peak/dip wavelengths of the interference spectrum. In this way, the tilt angle ?
can be fitted on basis of the aforementioned model.

         As
mentioned above, the liquid/vapour surface force, holding a critical drop, is
related to the CAH. For this purpose, the positions of the liquid metal marble
in the capillary sleeve tube were observed at typical tilt angles in the range
of 0-90° induced by low acceleration (0-1 g) by using a camera, along with a
contour tracing algorithm. The advancing and receding contact angles (?a and
?r) at various tilt angles can then be extracted with an image feature
extraction algorithm                           

x

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