Free Access
Issue
Eur. Phys. J. Appl. Phys.
Volume 90, Number 3, June 2020
Article Number 30501
Number of page(s) 9
Section Photonics
DOI https://doi.org/10.1051/epjap/2020200036
Published online 08 July 2020

© EDP Sciences, 2020

1 Introduction

Water column pressure is a fundamental oceanography requirement towards obtaining data related to Bio-Geo-chemical parameters [1]. Current pressure sensors, adequate for all basic measurements, have limitations such as low response rate, operating frequency (Hz), possible electromagnetic interference with surroundings that can cause electrical circuit damages which restrict their applications in harsh environments [2]. Optical sensors have many advantages over conventional pressure sensors which are light weight, robust, small in size, anti- corrosive, anti electromagnetic, very fast response time, high accuracy [3,4]. Fiber optic pressure sensor mechanisms are divided into four categories based on modulation of frequency, phase modulation, modulation of wavelength, and modulation of polarization [57]. Out of these, wavelength modulation is simpler to interpret data, has lower cost and can detect signals from multiplexed sensors [8]. With these advantages, Fiber Bragg Grating (FBG) based sensors can be used effectively for oceanic applications [911].

Juncheng et al. developed an epoxy free high temperature fiber optic pressure sensor [12]. They made a sensor head with fused silica resulting in low temperature dependence and higher operating temperature (700 °C). Allwood et al. proposed high sensitive fiber Bragg grating pressure transducer with reported sensitivity of 0.116 pm/KPa [13]. They also reported a low-cost edge filter interrogation technique instead of high cost solid state interrogators. To improve pressure sensitivity and reduce temperature effect on pressure measurement, Frantisek et al. proposed a pressure sensor based on lateral deformation of FBG and membrane deformation [14]. Here, the applied pressure range is from 0–2 bar only and peak measurement requires high resolution 10 pm, precise spectrum analyser. However standard bare FBG pressure sensitivity is 0.00304 pm/MPa,which is much lower for practical sensing applications and due to fragile nature of FBG, some packaging technology has been required to improve the sensitivity [14]. Jun Huang et al. developed and tested a diaphragm type FBG pressure sensor with temperature compensation in the region of 0–1 MPa [15]. They showed that their sensor sensitivity is 1.57 pm/KPa with less hysteresis. However, while increasing the pressure sensitivity, higher temperature cross-sensitivity could not be avoided. To address this problem, many techniques have been reported, such as embedding FBG in polymer or Bonding FBGs on cantilever structure [16,17]. Hsu et al. developed a temperature compensated FBG based gas pressure sensor with a single FBG by applying an axial strain on it [18]. To compensate the temperature effect they applied constructive stress on the sensor. Another group developed a depth sensor for under water remote operated vehicles (ROV), with temperature compensation and tested in lab by combining FBG with an optical Extrinsic Fabroy-Perot Interferometer (EFPI) sensor [10]. A low-cost diaphragm based fiber bragg grating pressure sensor design for ocean applications has been presented and tested with different thickness of copper diaphragms [19].

In this paper, two designs for temperature compensated high-sensitive, low-cost and stable diaphragm based FBG pressure sensor are reported and discussed. Different types of metal diaphragms with varying thickness were used for this study. Theoretical and experimental comparison for the best one has been carried out. The mechanical deformation of the diaphragm was calculated theoretically and validated through ANSYS finite element simulation software. The mathematical relationship between FBG wavelength and pressure applied has been reported. Also, by the diaphragm properties, the sensitivity was calculated by using MATLAB. Proposed sensor designs are capable to measure up to 300 m depth of water with a resolution of 0.001 MPa, with linearity of 99.99% by using proper encapsulation methods and sealants. Proposed sensor design is easy to fabricate with low cost and low maintenance, also allows user to change the FBG on diaphragm with less effort. Samples are taken with the frequency of 25 Hz which is equal to sensors response time of 40 ms. Experiments were carried out for testing sensitivity and repeatability of both the sensor designs.

2 Sensor structure

The FBG is a device commonly used in telecommunications technology and sensing. Fabricated by creating a periodic modulation of Refractive Index (RI) in the core of single mode (SM) fibre. Usually the FBG acts as a spectral filter such that, it reflects narrow band wavelength and transmits the remaining wavelengths, when the fibre is illuminated with a broad band source. The condition for the reflecting wavelength is showed in equation (1) and it is called Bragg’s condition [2]. (1)

where neff is effective refractive index of grating in the fiber core, λB is central wavelength of the fiber grating, Λ is grating period. Here we used a standard telecommunication fiber (SMF-28) for all our experimentation [20,21]. When an external perturbation is applied on fiber there is change in core guided mode index called effective refractive index of the fiber which is equal 1.44728 for SMF-28. The magnitude of refractive index change is 10−4 to 10−5 [22]. The effective refractive index is proportional to the concentration of the core dopant(mole% GeO2) [23]. When an FBG is subjected to external perturbations both neff and Λ will change, which leads to shift in Bragg wavelength [24]. So, in response to change in strain, the total wavelength shift is given by [25] (2) (3)

The first term in the above equation (3) represents the strain of the grating period due to the extension of the fiber. Suppose we have a length L of a fiber with an inscribed FBG in it. If we apply a stress on the fiber of ΔL then we will have an relative strain . At the same time if the FBG has a length LFBG it will experience astrain but since the FBG is in the fiber, then . Since the Bragg displacement with extension equals the displacement of the grating period with the same extension and, therefore, the first term in equation (3) is the unit.

The second term in equation (3) is the photo-elastic coefficient (Pe), the variation of the index of refractionwith strain. When an extension is applied to the fiber, the two terms in equation (3) produce opposite effects, one by increasing the distance between gratings so that it will increase the wavelength and other by decreasing the refractive index change thus decreasing the bragg wavelength. For a single mode fiber, central wavelength shift caused by strain and temperature change is given by equation (4) [2] (4)

where pe is the effective photo elastic coefficient of the fiber, is given by (5)

P11, P12 are photo elastic coefficients 0.121, 0.270 respectively, μ is Poisson’s ratio value of 0.17, and by substituting neff values, we can ob tain Pe = 0.22. Δɛ is the strain change, α is thermal expansion coefficient of silica and ξ is thermo-optic coefficient ofsilica, and ΔT is the temperature variation. According to equation (4) the shift in wavelength varies linearly with both temperature and pressure. Here all experiments are done at constant room temperature so we neglected the second term in equation (4) (6)

From the above equation (6), wavelength shift due to effective refractive index is negligible, and therefore shift in wavelength is dominated by mechanical strain in the FBG when compare to effective refractive index change.

There are two models for the proposed FBG pressure sensor. One is the closed air cavity setup and, another one is the open-air cavity setup. 3D view of a closed air cavity setup is shown in Figure 1, and experimental sensor head is shown in Figure 2. This setup is made with a stainless steel annular ring with a thickness of 2.5 mm, copper diaphragm and a stainless steel disk with a thickness of 2.5 mm with a diameter of 60 mm. Annular ring and disk have four ‘O’ ring grooves to form a closed air cavity between diaphragm and disk, which reduces the pressure leakage. Here, the diaphragms are made with the copper sheet in circular shape with the diameter of 60 mm and thickness of 0.05 mm and 0.25 mm.

The schematic design of the open-air cavity setup is shown in Figure 3. This has an oil-filled hand pump to create pressure inside the system and to apply on the diaphragm which creates positive pressure. By pressing plunger, oil is pushed from the reservoir through hosepipe and it is connected to a stainless-steel plus-shaped adapter with proper connectors. When pressure measurement is needed, system need to connect a reference pressure gauge so the second port of the adapter is connected to a digital pressure gauge to measure the real-time pressure variations in the system. The third port is closed with an end cap to a pressure releasing mechanism. A stainless-steel disk 5 mm thick with a centre hole to pass the oil is welded on the fourth end of the connector. On top of welded stainless-steel disk, the diaphragms of copper and stainless-steel materials with different thickness are mounted. An annular ring with an inner diameter of 30 mm, the outer diameter of 60 mm and thickness of 3 mm, is fixedon metal diaphragms. The total system is now closed to maintain the pressure. By using fine adjustment screws in the system, pressure can be increased or decreased precisely. In both setups, FBG is fixed on top of the diaphragm with a cyano-acrylate glue, such that it is passing through the centre of the diaphragm. When pressure acts on the diaphragm, shape deformation takes place and strain develops in FBG which causes a wavelength shift proportional to pressure change. The diaphragm displacement and real-time variations is measured by using the ANSYS Finite Element simulation software [26]. Deformation of the diaphragm is calculated theoretically by (7)

where D is the diaphragm deformation, q is applied pressure on diaphragm, a radius of the diaphragm, and k is the bending stiffness of the diaphragm. (8)

E is Young’s modulus of the diaphragm, μ is the Poisson’s ratio of the diaphragm, and h is the diaphragm thickness.

As shown in Figures 2 and 3 the spring element of the pressure sensor is a plane circular diaphragm, on which deformation or strain would be produced when liquid or gas pressure is applied. Based on small deformation theory [27], the radial strain (ɛr) and tangential strain (ɛt) on the diaphragm can be calculated by (9) (10)

where p is the measured pressure, E is the Young’s modulus of the plate, μ is the Poisson’s ratio of shell, R is the radius of plate, r is the measuring distance from center, h is the diaphragm thickness. When pressure applied on the center of the diaphragm tangential strain will develop in it, which is equal to the axial strain of the FBG (11) (12)

where ɛaxis is axial strain in FBG. The FBG strain sensitivity can be obtained from substituting equations (6) and (4) into (2). An FBG of central wavelength 1559 nm, typical strain sensitivity is 0.001 nm/μɛ. (13)

where K is typical strain sensitivity of the sensor. From equation (13) sensitivity of the sensor is depends on thickness and radius of a particular material.

thumbnail Fig. 1

3D view of Closed air cavity setup.

thumbnail Fig. 2

Closed air cavity pressure sensor head.

thumbnail Fig. 3

Schematic 3D-design of open-air cavity pressure measurement system.

3 Simulation analysis

To validate the performance of the proposed FBG sensor models and to calculate the pressure sensitivity, simulation studies are performed. In our proposed models, metal diaphragm works as a pressure transducer. Different thickness of copper and 304-grade stainless steel are used as pressure transducers in the sensor design. The analysis is dived into two computational steps. In the first step need to create model of the sensor design and perform the global analysis on it. The result of the first step was used for the second, which gives a detailed analysis of the diaphragm deformation. The structure parameters of diaphragms are used in simulation and calculations are given in Table 1. The solid model and global analysis of the sensor design in simulation software are shown in Figure 4. The maximum deformation of the copper diaphragm with a thickness of 0.05 mm in closed air cavity with pressure variation of 0 to 0.04 MPa and in an open-air cavity with pressure variation of 0 to 0.1 MPa is shown in Figures 5a and 5b. The detailed deformation values of the other diaphragms with different thicknesses under different pressure variations are given in Table 2. The maximum displacement of the diaphragm takes place at the center, and it is decreased along the radius direction.

Table 1

Structure parameters.

thumbnail Fig. 4

ANSYS models of plates: (a) Solid model. (b) Finite element model.

thumbnail Fig. 5

Results of ANSYS simulation: (a) Displacement cloud of copper diaphragm with thickness of 0.05 mm under 0.04 MPa. (b) Displacement cloud of copper diaphragm with thickness of 0.05 mm under 0.1 MPa.

Table 2

Diaphragm deformations.

4 Experimental setup

The schematic diagram of experimental setup is shown in Figure 6. The agile, tunable broadband light source with a wavelength range 1528−1568 nm allows interrogation at multi KHz frequencies with high accuracy 1 pm. A three port fiber optic circulator is connected with broad band source, sensor and optical interrogator. The light from broad band source is launched into the sensor via port1 of the optical circulator and the reflected light from FBG sensor is sent to interrogator which is connected to port 3 via port 2. High precession and reliable Smartscan solid state FBG interrogator model is used as the optical interrogation system. This system has two channels for interrogation of FBGs, and in each channel, 16 FBGs can be interrogated simultaneously. This whole system works on wavelength division multiplexing (WDM).

thumbnail Fig. 6

Schematic diagram of experimental setup.

4.1 Closed air cavity pressure measurement

Closed air cavity pressure measurement setup is shown in Figure 7. The sensor head is made with a metal diaphragm, metal disk, and rubber O rings. From bottom to top, first, we kept a metal disk with a thickness of 5 mm and a diameter of 60 mm. On top of the metal disk, we made two O ring grooves with a diameter of 50 mm and 45 mm.Second, a metal annular ring is made with an outer diameter of 60 mm and an inner diameter of 30 mm, with a thickness of 3 mm kept on these two O rings. Third on top of the metal annular ring are made two O rings groves with above-mentioned dimensions. A metal diaphragm is attached above these O rings so that a closed air cavity will form between metal disk and diaphragm. The depth of the cavity is equal to the thickness of the annular ring. On top of the diaphragm, one more annular ring with the same dimensions as above is attached. An acrylic-coated 10 mm long FBG sensor with central wavelength 1549.65 nm is pasted on metal diaphragm along the diameter with cyanoacrylate glue. When assembled this there is an air trapped between diaphragm and metal disk so that it forms a closed air cavity. We have dipped this total setup in a 4-meter water tank for pressure measurements. Top view of the sensor head is shown in Figure 8a, and when pressure acts on a diaphragm, it will deform in a downward direction, as shown in Figure 8b. The FBG’s fiber pigtail is connected to optical interrogator by using FC/APC connector and the interrogator is connected to the computer by network cable to see the reflected spectrum from sensor. Smartsoft software is used for the spectrum analysis. By using this software, frequency of data acquisition can be varied from 1–25 kHz. The sensor head is moved vertically three times in water column and pressure is measured at an interval of 10 cm from 0 to 4 m depth. The temperature of the water is measured at (27 °C).

thumbnail Fig. 7

Closed air cavity pressure measurement setup.

thumbnail Fig. 8

Closed air cavity sensor head: (a) Top view. (b) Front view.

4.2 Open-air cavity pressure measurement

The schematic 3D-design for an open-air cavity pressure measuring system is shown in Figure 3 and the experimental configuration is shown in Figure 9. Open-air cavity setup has an oil pump with a reference pressure gauge to know the applied pressure and a plunger to apply the pressure manually on the diaphragm. Two stainless steel tubes of 304 grade are cross welded in ‘+’ shape. The first end of the tubes is connected to an oil pump with a flexible rubber tube and suitable connectors to reduce the oil leakage. The second end is connected with a Keller digital manometer with model number LEO 1 is a microprocessor-controlled, accurate and versatile digital pressure measuring system, which is capable of measuring 300 bar pressurewith 0.1 bar resolution. The third end is closed by an end cap to restrict oil leakage and also can be used as a pressure release valve. A stainless-steel disk with a thickness of 5 mm, and diameter of 60 mm is mounted and welded on the fourth end. On top of the Stainless-steel disk we made an O ring grove with 50 mm diameter. Above this O ring, a metal diaphragm with different thicknesses (0.05, 0.25, 0.5 mm) and diameter of 60 mm is kept. On top of the diaphragm, an annular metal ring with an outer diameter of 60 mm and an inner diameter of 30 mm with a thickness of 3 mm is placed. Finally, the diaphragm is sandwiched between mounted disk and annular ring by using nuts and bolts. Top view of the sensor head is shown in Figure 10a

By pressing the plunger, oil travels from the reservoir through the hosepipe, and it will reach to stainless steel tubes so that the pressureinside the system at every point is identical since all four ends of the Stainless-steel tubes are closed, and there is no chance of oilleakage. So oil pressure acts on the diaphragm. Due to this, deformation takes place at the center of the diaphragm in positive Z-direction such that diaphragm is on XY plane towards open-air through the annular ring inner diameter and it acts as an open-air cavity. The deformed shape of the diaphragm is showed in Figure 10b. At the same time, the digital pressure gauge shows the real-time pressure of the system. The pressure is raised from 0–0.5 MPa with an interval of 0.01 MPa, and the temperature of the measuring system is at room temperature 27 °C. Due to deformation of the diaphragm, a lateral strain in the FBG is caused, and the wavelength shift in the FBG sensor is recorded for each interval of pressure.

The real time diaphragm deformations are measured in open-air cavity setup by using a Mitutoyo dial indicator attached with magnetic stand. The round scale in this indicator is able to adjust zero reading after each measurement cycle so that error in measurement is negligible and it can measure maximum deformation of diaphragm up to 10 cm with the resolution of0.01 mm. Before applying pressure, the tip of indicator is need to attach the diaphragm surface so that it will show some reading in indicator scale and that reading need to adjust to zero by rotating entire circular scale. When pressure acting on diaphragm, deformation occurs and it causes the tip displacement in vertically upward direction. The experimental setup is shown in Figure 11.

thumbnail Fig. 9

Open-air cavity pressure measurement setup.

thumbnail Fig. 10

Open-air cavity sensor head: (a) Top view. (b) Front view.

thumbnail Fig. 11

Diaphragm deformation with Dial gauge.

5 Results and discussions

5.1 Closed air cavity results

In closed aircavity method, to check the repeatability and performance of sensor the sensor-head was descended and ascended in a 4 meters deep water tank. In both Open and Closed air cavity sensor measurements are done with 25 Hz frequency. Figure 12 shows wavelength shift with pressure variation measured by using a copper diaphragm with a thickness of 0.25 mm. Pressure sensitivity from the slope of the curve is 0.2286 nm/MPa and linearity of 96.29% is observed. The results are showed less repeatability, low sensitivity and experimental values deviated from theoretical curve, this may cause due to the fixing position of sensor on the diaphragm or deformation of diaphragm is not linear with pressure. Toincrease the pressure sensitivity and linearity of the sensor, the thickness of copper plate is reduced to 0.05 mm. The pressure variation with wavelength shift is shown in Figure 13. The pressure sensitivity is 24.59 nm/MPa, and the linearity of 99.72% is observed. To test for higher pressure range, the open-air cavity technique is adopted.

thumbnail Fig. 12

Wavelength shift with pressure variation measured by 0.25 mm thickness of copper plate by closed air cavity setup.

thumbnail Fig. 13

Wavelength shift with pressure variation measured by 0.05 mm thickness of copper plate by closed air cavity setup.

5.2 Open-air cavity results

In the open-air cavity setup, the range of pressure measurement can be increased by 10 times more than closed air cavity setup. Different thicknesses of copper and stainless steel diaphragms are tested. Repeatability of sensor is tested for three times with each diaphragm by increasing and decreasing the pressure from 0 to 5 MPa. Theoretical results are plotted with experimental results for each experiment. Copper diaphragm with thickness of 0.25 mm is tested under the pressure range from 0−0.5 MPa. Figure 14 shows the wavelength shift with pressure variation and the pressure sensitivity is calculated as 5.6097 nm/MPa with linearity of 99.64%. Figure 15 shows the wavelength shift variation with pressure by a copper diaphragm of thickness 0.05 mm. Pressure sensitivity measured with this diaphragm is 16.22 nm/MPa which is higher compared with 0.25 mm thickness plate. Here the pressure range is measured up to 0.1 MPa due tothe lesser thickness of diaphragm. Further, different thickness’s of copper and stainless steel diaphragms are tested for more sensor stability and linearity in 300 m depth of the ocean. Figure 16 shows the wavelength shift with pressure measured by using open-air cavity with thickness of 0.5 mm copper diaphragm, observed sensitivity is 2.7802 nm/MPa which is two times more than reported in [28] with linearity of 99.89%. Figure 17 shows the wavelength shift with pressure variation using 0.25 mm stainless steel plate with the sensitivity of 2.63 nm/MPa and linearity of 99.83%. Figure 18 shows the wavelength shift variation of FBG with pressure measured by open-air cavity setup and with 0.5 mm stainless steel plate. With the linearity of 99.79%, the sensitivity of the sensor is 1.305 nm/MPa (10 times more with double shell cylinder measurement) [29]. Figure 19 shows theoretical sensitivity with diaphragm thickness. From this one can able to choose the diaphragm with thickness for particular range of applications. Also shows that our experimental results are followed the theoretical curves. Theoretical results can be matched with experimental ones by setting up the FBG at location on the plate and need to be consider exact mechanical properties of the plate, where R is radius of diaphragm. Table 3 shows the experimental results of the proposed sensor designs.

thumbnail Fig. 14

Wavelength shift with pressure variation measured by 0.25 mm thickness of copper plate by open-air cavity.

thumbnail Fig. 15

Wavelength shift with pressure variation measured by 0.05 mm thickness of copper plate by open-air cavity.

thumbnail Fig. 16

Wavelength shift with pressure variation measured by 0.5 mm thickness of copper plate by open-air cavity.

thumbnail Fig. 17

Wavelength shift with pressure variation measured by 0.25 mm thickness of stainless steel plate by open-air cavity.

thumbnail Fig. 18

Wavelength shift with pressure variation measured by 0.5 mm thickness of stainless steel plate by open-air cavity.

thumbnail Fig. 19

Sensitivity variation with diaphragm thickness.

Table 3

Experimental results of the proposed sensor design.

6 Conclusions

Pressure measurements with different thickness of stainless steel and copper diaphragms with bare FBG are studied. The sensitivity of the sensor is tested with two different designs and with different metal diaphragms as pressure transducer. Results are indicating that the copper plate with 0.05 mm thickness is more sensitive and linear. In closed air cavity system, maximum pressure sensitivity of 24.59 nm/MPa is achieved and in the open-air cavity setup, maximum pressure sensitivity of 16.22 nm/MPa is achieved. Closed and open-air cavity linearities are observed to be 99.72% and 99.34% respectively.From the above analysis, suitable diaphragm can be chosen very easily for particular pressure range. An extended work is ongoing for the temperature compensation of sensor while measuring the pressure, by using single FBG and to enhance thesensitivity of sensor and for measuring temperature and pressure simultaneously in actual fields of ocean.

Acknowledgements

Authors would like to thank Prof. Balaji Srinivasn, Prof. in Department of Electrical Eng. IIT Madras for providing FBG sensors.

Author contribution statement

All the authors were involved in the theoretical analysis and experimental studies of the manuscript. Also, all the authors have read and approved the final manuscript.

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Cite this article as: Venkata Satya Chidambara Swamy Vaddadi, Saidi Reddy Parne, Sanjeev Afzulpurkar, Shivanand Prabhu Desai, Vijeesh Vadakke Parambil, Design and development of pressure sensor based on Fiber Bragg Grating (FBG) for ocean applications, Eur. Phys. J. Appl. Phys. 90, 30501 (2020)

All Tables

Table 1

Structure parameters.

Table 2

Diaphragm deformations.

Table 3

Experimental results of the proposed sensor design.

All Figures

thumbnail Fig. 1

3D view of Closed air cavity setup.

In the text
thumbnail Fig. 2

Closed air cavity pressure sensor head.

In the text
thumbnail Fig. 3

Schematic 3D-design of open-air cavity pressure measurement system.

In the text
thumbnail Fig. 4

ANSYS models of plates: (a) Solid model. (b) Finite element model.

In the text
thumbnail Fig. 5

Results of ANSYS simulation: (a) Displacement cloud of copper diaphragm with thickness of 0.05 mm under 0.04 MPa. (b) Displacement cloud of copper diaphragm with thickness of 0.05 mm under 0.1 MPa.

In the text
thumbnail Fig. 6

Schematic diagram of experimental setup.

In the text
thumbnail Fig. 7

Closed air cavity pressure measurement setup.

In the text
thumbnail Fig. 8

Closed air cavity sensor head: (a) Top view. (b) Front view.

In the text
thumbnail Fig. 9

Open-air cavity pressure measurement setup.

In the text
thumbnail Fig. 10

Open-air cavity sensor head: (a) Top view. (b) Front view.

In the text
thumbnail Fig. 11

Diaphragm deformation with Dial gauge.

In the text
thumbnail Fig. 12

Wavelength shift with pressure variation measured by 0.25 mm thickness of copper plate by closed air cavity setup.

In the text
thumbnail Fig. 13

Wavelength shift with pressure variation measured by 0.05 mm thickness of copper plate by closed air cavity setup.

In the text
thumbnail Fig. 14

Wavelength shift with pressure variation measured by 0.25 mm thickness of copper plate by open-air cavity.

In the text
thumbnail Fig. 15

Wavelength shift with pressure variation measured by 0.05 mm thickness of copper plate by open-air cavity.

In the text
thumbnail Fig. 16

Wavelength shift with pressure variation measured by 0.5 mm thickness of copper plate by open-air cavity.

In the text
thumbnail Fig. 17

Wavelength shift with pressure variation measured by 0.25 mm thickness of stainless steel plate by open-air cavity.

In the text
thumbnail Fig. 18

Wavelength shift with pressure variation measured by 0.5 mm thickness of stainless steel plate by open-air cavity.

In the text
thumbnail Fig. 19

Sensitivity variation with diaphragm thickness.

In the text

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