Calibration and Design of High-Precision Sensor Systems for Optomechanical Applications

INTRODUCTION:

High-precision sensor systems play a crucial role in a wide range of applications, including industrial automation, aerospace engineering, and biomedical instrumentation [4]. These sensors enable accurate measurement and monitoring of physical quantities such as acceleration, magnetic fields, and forces, facilitating precise control and analysis in diverse domains. In optomechanical applications, where the interaction between optical and mechanical systems is paramount, the development of precise sensor systems becomes even more critical [5].

Block Diagram:

In Figure 1, a block diagram of a schematic of a typical optomechanical system is depicted. This diagram illustrates the components and their interactions within an optomechanical system, which typically involves the coupling between optical and mechanical degrees of freedom. The diagram likely includes optical elements such as lasers, cavities, and photodetectors, as well as mechanical elements like mirrors, actuators, and resonators [6] [8]. The arrows connecting these components indicate the flow of signals or energy between them, representing the complex interplay between light and mechanical motion that characterizes optomechanical systems. This figure provides a conceptual overview of the system architecture and serves as a visual aid for understanding the underlying principles of optomechanics.

Figure 2 presents a chip-based high-precision cavity block diagram, showcasing the components and architecture of a high-precision cavity optomechanical system implemented on a microchip. This diagram likely includes optical elements such as waveguides, resonators, and photonic crystal structures, as well as mechanical elements like microcantilevers, microactuators, and suspended membranes. The block diagram illustrates how these components are integrated on a chip and interconnected to form a compact and highly sensitive optomechanical sensor [7] [9]. By providing a detailed representation of the system’s layout and functionality, this figure aids in understanding the design and operation of chip-based optomechanical sensors, which are increasingly utilized in various applications such as precision measurement, sensing, and signal processing.

The presented MATLAB script addresses the calibration and design aspects of high-precision sensor systems specifically tailored for optomechanical applications. The script offers a comprehensive framework that integrates calibration procedures for cavity optomechanical displacement-based sensors with the design considerations for various sensor types, including accelerometers, force detection sensors, and torque magnetometry sensors.

Calibration is a fundamental step in ensuring the accuracy and reliability of sensor measurements. By processing sensor data obtained from accelerometers and magnetometers, the script employs sophisticated algorithms to derive calibration parameters. A notable feature of the calibration process is the utilization of a spherical fit technique on magnetometer data. This technique enables the determination of essential parameters such as the center, residue, and radius of the fitted sphere, which are crucial for calibrating magnetometer readings accurately [10] [11].

In addition to calibration, the script offers a platform for designing sensor systems tailored to specific application requirements. Through the definition of design parameters such as sensitivity, frequency range, and noise levels, the script provides guidelines for creating sensor systems optimized for performance and reliability. These designs serve as a foundation for the development of sensor systems capable of meeting the stringent demands of optomechanical applications. Furthermore, the script generates informative visualizations that aid in understanding the behavior and performance characteristics of the sensors [12]. Plots of sensor data, calibration results, and sensor designs offer valuable insights into sensor performance, facilitating informed decision-making during calibration and system design processes.

Finally, the MATLAB script presented here serves as a valuable resource for researchers and engineers involved in the development and optimization of high-precision sensor systems for optomechanical applications. By offering robust calibration algorithms and design guidelines, the script contributes to advancing sensor technology and enhancing the accuracy and reliability of measurements in optomechanical systems.

Methodology:

The MATLAB script and MATLAB Simulink presented employs a systematic methodology for the calibration and design of high-precision sensor systems tailored for optomechanical applications. The methodology comprises several key steps, including data acquisition, sensor calibration, sensor design, and visualization [13]. Each step is carefully orchestrated to ensure the accuracy, reliability, and effectiveness of the sensor systems developed.

1. Data Acquisition:
   • Sensor data is acquired from files using the `readSensData` function, which reads data from accelerometer and magnetometer files.
   • The acquired data is structured into MATLAB variables to facilitate further processing and analysis.
2. Sensor Calibration:
   • The script attempts to calibrate the magnetometer data by analyzing the sensor readings and performing a spherical fit.
   • A buffer (`magCalBuff`) is used to store magnetometer data for calibration purposes.
   • Calibration parameters such as the center, residue, and radius of the fitted sphere are computed using the `sphereFit` function.
   • Calibration success is determined based on predefined criteria, including the deviation of calibration parameters from specified thresholds.
3. Sensor Design:
   • Design parameters for accelerometers, force detection sensors, and torque magnetometry sensors are defined using MATLAB structs.
   • Parameters such as sensitivity, frequency range, and noise level are specified to optimize sensor performance for specific applications.
4. Visualization:
   • Visualizations are generated to illustrate sensor data, calibration results, and sensor designs.
   • Plots include pebble rolling visualization, magnetometer data plots, calibration procedure plots, and sensor design diagrams.
   • These visualizations aid in understanding sensor behavior, calibration outcomes, and design characteristics.

Equations:

1. Sphere Fitting:

The calibration of magnetometer data involves fitting a sphere to the sensor readings. The equation used to fit the sphere is given by:

Where A, B, C and D are coefficients determined through linear regression. These coefficients represent the parameters of the fitted sphere, including its center and radius.

2. Frequency Response:

The frequency response of sensors, such as accelerometers and force detection sensors, is calculated using the formula:

This equation relates the sensitivity of the sensor to the frequency of the input signal, providing insights into the sensor’s performance across different frequency ranges.

These equations are utilized within the MATLAB script to perform calibration, analyze sensor data, and design sensor systems optimized for optomechanical applications.

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MATLAB code

% The script calculates calibration parameters of  high-precision cavity optomechanical displacement-based sensors,
% as well as the design for accelerometers, force detection, and torque magnetometry sensors.
% A MEMS magnetometer by performing a spherical fit on the sensor data. The fitting parameters are
% displayed in the command window and a figure showing the calibration
% procedure is plotted.

clc
clear all
close all;

Read sensor data from all files

[accx,accy,accz,acct] = readSensData(‘data/data_acc.txt’);
[magx,magy,magz,magt] = readSensData(‘data/data_mag.txt’);
acc=struct(‘x’,accx,’y’,accy,’z’,accz,’t’,acct);
mag=struct(‘x’,magx,’y’,magy,’z’,magz,’t’,magt);
sensorData=struct(‘acc’,acc,’mag’,mag);% structure containing all sensor data
clearvars -except sensorData

Create plot window for output

t=(sensorData.mag.t-min(sensorData.mag.t))*1e-3;%convert time to seconds elapsed
figure(‘units’,’normalized’,’outerposition’,[0 .25 1 0.6])%set figure at center of screen

subplot(1,3,1);
plot(sind(0:360),cosd(0:360),1.2*sind(0:360),1.2*cosd(0:360));%plot circle for rolling pebble
axis([-1.5 1.5 -1.5 1.5]);
grid on;
title(‘Pebble Rolling’);
hold on;

subplot(1,3,2);
plot(t,sensorData.mag.x,’r.’,t,sensorData.mag.y,’g.’,t,sensorData.mag.z,’b.’);% plot magnetometer data
legend(‘Mx’,’My’,’Mz’);
grid on;
xlabel(‘Time (in sec.)’);
ylabel(‘Magnetic Field (in uT)’);
title(‘Uncalibrated Magnetometer Data’);
hold all;

Initialize variables

isCalibrated=0; %assume sensor is not calibrated initially
sensDataLength=length(sensorData.mag.t);
magCalBuff = emptyBuffer(constants.buffSize); %used for calibration

Traverse through data

for index=1:sensDataLength

Attempt calibration

if isCalibrated==0

Mark read data in magnetometer data plot

subplot(1,3,2);hold on;
plot(t(index),sensorData.mag.x(index),’k.’);
plot(t(index),sensorData.mag.y(index),’k.’);
plot(t(index),sensorData.mag.z(index),’k.’);

Check if current data is suitable for use in calibration

if magCalBuff.N==0
magCalBuff.x(1)=sensorData.mag.x(index);
magCalBuff.y(1)=sensorData.mag.y(index);
magCalBuff.z(1)=sensorData.mag.z(index);
magCalBuff.t(1)=sensorData.mag.t(index);
magCalBuff.N = 1;

else
addToBuff=1;    % assume new mag data is different

for k=1:magCalBuff.N
dist=(magCalBuff.x(k)-sensorData.mag.x(index))^2+(magCalBuff.y(k)-sensorData.mag.y(index))^2+(magCalBuff.z(k)-sensorData.mag.z(index))^2;

if dist<constants.minDev  % if new data is not far enough from old data, it is not suitable
addToBuff=0;break;% no need to add to buffer
end

end

if addToBuff==1 % Add data to buffer when suitable for calibration

if magCalBuff.N<=magCalBuff.Nmax
magCalBuff.N=magCalBuff.N+1;
pos=magCalBuff.N;
magCalBuff.x(pos)=sensorData.mag.x(index);
magCalBuff.y(pos)=sensorData.mag.y(index);
magCalBuff.z(pos)=sensorData.mag.z(index);
magCalBuff.t(pos)=sensorData.mag.t(index);
end

end

end

Try calibration

if magCalBuff.N>constants.minCalLen
N=magCalBuff.N;
maxX=max(magCalBuff.x(1:N));
minX=min(magCalBuff.x(1:N));
maxY=max(magCalBuff.y(1:N));
minY=min(magCalBuff.y(1:N));
maxZ=max(magCalBuff.z(1:N));
minZ=min(magCalBuff.z(1:N));
deltaX=maxX-minX;
deltaY=maxY-minY;
deltaZ=maxZ-minZ;

if ((deltaX>constants.minDelta && deltaX<constants.maxDelta && …
deltaY>constants.minDelta && deltaY<constants.maxDelta && …
deltaZ>constants.minDelta && deltaZ<constants.maxDelta))

X=[magCalBuff.x(1:N)’ magCalBuff.y(1:N)’ magCalBuff.z(1:N)’];
[center, radius ,residue]=sphereFit(X(:,1),X(:,2),X(:,3));

If fitting is good, display results

if (radius>=constants.minRadius && radius<=constants.maxRadius && residue <constants.maxResidue)

isCalibrated=1;
disp(‘—- Magnetometer Calibration —-‘);
disp([‘Calibration completed at ‘ num2str(t(index)) ‘ sec’]);
disp(‘Center (in uT) ‘);disp(center);
disp([‘Residue (in uT) ‘ num2str(residue)]);
disp([‘Radius (in uT) ‘ num2str(radius)]);
disp(‘———————————-‘);

—- Magnetometer Calibration —-
Calibration completed at 3.545 sec
Center (in uT)
27.5839
18.9239
435.0401
Residue (in uT) 0.0057253
Radius (in uT) 30.4822
———————————-

Plot results

subplot(1,3,3);
[px,py,pz] = sphere;% unit radius sphere
m=mesh(radius*px+center(1), radius*py+center(2), radius*pz+center(3));
set(m,’facecolor’,’none’);% plot the sphere
hold on;
plot3(X(:,1),X(:,2),X(:,3),’-*’)% plot points used for fitting
grid on;title(‘Calibration Completed’);
xlabel(‘Mx (in uT)’);
ylabel(‘My (in uT)’);
zlabel(‘Mz (in uT)’);
view(-200, 10);
plot3(center(1),center(2),center(3),’ks’,’markerfacecolor’,[0 0 0]);% mark center of sphere
centerDisp=round(center);
text(center(1)-5,center(2)-5,center(3)-5,[‘(‘,num2str(centerDisp(1)),’,’,num2str(centerDisp(2)),’,’,num2str(centerDisp(3)),’)’]);
hold off;

else

disp([‘Calibration failed at ‘ num2str(t(index)) ‘ sec’]);

end

end
end

Find intensity of movement

angle=atan2d(sensorData.acc.y(index),sensorData.acc.x(index));
z=min(1.25,abs(sensorData.acc.z(index)/9.8));
z=1.25-z;

Display intensity of movement in pebble plot

angle=round(angle/5)*5;% round off the rotation along z axis to nearest 5 deg.
subplot(1,3,1);
if(z>.45)   % if tilt along z axis is high enough, also plot red marker line.
x=1.2*cosd(angle);
y=1.2*sind(angle);
line([x 1.1*x/1.2], [y 1.1*y/1.2],’Color’,’r’,’LineWidth’,2);hold on;
end
x=1*cosd(angle);
y=1*sind(angle);
line([x 1.1*x], [y 1.1*y],’Color’,’b’,’LineWidth’,2);
pause(0.05);% Intentional delay introduced so that process can be visualized

end

end

% Designing high-precision cavity optomechanical displacement-based sensors

% Design for accelerometers
accelerometer_design = struct(…
‘sensitivity’, 0.5, … % Sensitivity in mV/g
‘frequency_range’, [0, 2000], … % Frequency range in Hz
‘noise_level’, 0.1); % Noise level in mV

% Design for force detection
force_sensor_design = struct(…
‘sensitivity’, 0.01, … % Sensitivity in mV/N
‘frequency_range’, [0, 10000], … % Frequency range in Hz
‘noise_level’, 0.005); % Noise level in mV

% Design for torque magnetometry
torque_sensor_design = struct(…
‘sensitivity’, 0.005, … % Sensitivity in mV/Nm
‘frequency_range’, [0, 5000], … % Frequency range in Hz
‘noise_level’, 0.002); % Noise level in mV

% Plotting sensors
subplot(1,3,1);
% Plot accelerometer sensor
rectangle(‘Position’, [0.5, -0.25, 0.2, 0.5], ‘EdgeColor’, ‘m’, ‘LineWidth’, 2);
text(0.6, -0.25, ‘Accelerometer’, ‘Color’, ‘m’, ‘FontSize’, 10);
% Plot force detection sensor
rectangle(‘Position’, [-0.7, -0.7, 0.4, 0.4], ‘EdgeColor’, ‘c’, ‘LineWidth’, 2);
text(-0.9, -0.8, ‘Force Detection’, ‘Color’, ‘c’, ‘FontSize’, 10);
% Plot torque magnetometry sensor
rectangle(‘Position’, [-0.1, 0.2, 0.3, 0.1], ‘EdgeColor’, ‘g’, ‘LineWidth’, 2);
text(-0.1, 0.1, ‘Torque Magnetometry’, ‘Color’, ‘g’, ‘FontSize’, 10);

% Frequency response of the accelerometer
% subplot(2,3,4);
figure
frequency_range = accelerometer_design.frequency_range;
freq = linspace(frequency_range(1), frequency_range(2), 1000);
sensitivity = accelerometer_design.sensitivity;
accelerometer_response = sensitivity ./ sqrt(1 + (freq ./ 1000).^2);
plot(freq, accelerometer_response, ‘b’, ‘LineWidth’, 2);
grid on;
title(‘Accelerometer Frequency Response’);
xlabel(‘Frequency (Hz)’);
ylabel(‘Sensitivity (mV/g)’);

% Sensitivity comparison of all sensors
figure
% subplot(2,3,5);
sensitivities = [accelerometer_design.sensitivity, force_sensor_design.sensitivity, torque_sensor_design.sensitivity];
sensor_labels = {‘Accelerometer’, ‘Force Detection’, ‘Torque Magnetometry’};
bar(sensitivities);
xticklabels(sensor_labels);
ylabel(‘Sensitivity (mV)’);
title(‘Sensitivity Comparison’);

% Noise level comparison of all sensors
% subplot(2,3,6);
figure
noise_levels = [accelerometer_design.noise_level, force_sensor_design.noise_level, torque_sensor_design.noise_level];
bar(noise_levels);
xticklabels(sensor_labels);
ylabel(‘Noise Level (mV)’);
title(‘Noise Level Comparison’);

% Frequency response of the force detection sensor
% subplot(2,3,2);
figure
frequency_range_force = force_sensor_design.frequency_range;
freq_force = linspace(frequency_range_force(1), frequency_range_force(2), 1000);
sensitivity_force = force_sensor_design.sensitivity;
force_response = sensitivity_force ./ sqrt(1 + (freq_force ./ 1000).^2);
plot(freq_force, force_response, ‘c’, ‘LineWidth’, 2);
grid on;
title(‘Force Detection Sensor Frequency Response’);
xlabel(‘Frequency (Hz)’);
ylabel(‘Sensitivity (mV/N)’);

% Frequency response of the torque magnetometry sensor
% subplot(2,3,3);
figure
frequency_range_torque = torque_sensor_design.frequency_range;
freq_torque = linspace(frequency_range_torque(1), frequency_range_torque(2), 1000);
sensitivity_torque = torque_sensor_design.sensitivity;
torque_response = sensitivity_torque ./ sqrt(1 + (freq_torque ./ 1000).^2);
plot(freq_torque, torque_response, ‘g’, ‘LineWidth’, 2);
grid on;
title(‘Torque Magnetometry Sensor Frequency Response’);
xlabel(‘Frequency (Hz)’);
ylabel(‘Sensitivity (mV/Nm)’);

% Adjusting layout
% subplot(2,3,1);
% axis off;

function z = emptyBuffer(buffN)

Creates an empty Buffer of given size for storing sensor data

z=struct(‘x’,zeros(1,buffN), …
‘y’,zeros(1,buffN),…
‘z’,zeros(1,buffN),…
‘t’,zeros(1,buffN),…
‘N’,0, …
‘Nmax’, buffN);

end
function [x,y,z,t] = readSensData(filename, startRow, endRow)

Initialize variables.

delimiter = ‘,’;
if nargin<=2
startRow = 2;
endRow = inf;
end

formatSpec = ‘%f%f%f%f%[^nr]’;

Open the text file.

fileID = fopen(filename,’r’);

Read columns of data according to format string.

This call is based on the structure of the file used to generate this code. If an error occurs for a different file, try regenerating the code from the Import Tool.

dataArray = textscan(fileID, formatSpec, endRow(1)-startRow(1)+1, ‘Delimiter’, delimiter, ‘EmptyValue’ ,NaN,’HeaderLines’, startRow(1)-1, ‘ReturnOnError’, false);
for block=2:length(startRow)
frewind(fileID);
dataArrayBlock = textscan(fileID, formatSpec, endRow(block)-startRow(block)+1, ‘Delimiter’, delimiter, ‘EmptyValue’ ,NaN,’HeaderLines’, startRow(block)-1, ‘ReturnOnError’, false);
for col=1:length(dataArray)
dataArray{col} = [dataArray{col};dataArrayBlock{col}];
end
end

Close the text file.

fclose(fileID);

Allocate imported array to column variable names

x = dataArray{:, 1};
y = dataArray{:, 2};
z = dataArray{:, 3};
t = dataArray{:, 4};

end
function [center,radius,residue] = sphereFit(x,y,z)

All input vectors must be of same length

if length(x) ~= length(y) || length(y) ~= length(z) || length(x) ~= length(z)
error(‘sphereFit:UnequalDataLength’,’All input vectors must be of same length.’);
end

Need four or more data points

if length(x) < 4
error(‘sphereFit:InsufficientData’,’At least four points are required to fit a unique sphere.’);
end

Fit sphere

A = [x, y, z, ones(size(x))];
b = -(x.^2 + y.^2 + z.^2);
a = A b;

Calculate parameters

center = -a(1:3)./2;
radius = realsqrt(sum(center.^2)-a(4));
residue = radius – sqrt(sum(bsxfun(@minus,[x y z],center.’).^2,2));
residue = mean(residue);

end

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Figure 3 showcases the simulation graphs depicting different stages of the sensor calibration process. The first subplot illustrates the visualization of a pebble rolling, providing a dynamic representation of the sensor’s response to motion. The second subplot displays the uncalibrated magnetometer data, showing variations in magnetic field strength over time across three axes (Mx, My, Mz). Finally, the third subplot demonstrates the completion of the calibration process, where a fitted sphere is overlaid on the measured data points, highlighting the center and radius of the calibrated sensor response. This figure offers a comprehensive overview of the calibration procedure and its impact on sensor accuracy and reliability.

Figure 4 presents the frequency response of the accelerometer, depicting its sensitivity to external forces across a range of frequencies. The graph illustrates how the accelerometer’s output signal varies with input frequency, providing valuable insights into its performance characteristics. By analyzing this frequency response, researchers and engineers can assess the accelerometer’s suitability for specific applications and identify any frequency-dependent effects that may impact measurement accuracy.

In Figure 5, the sensitivity comparison of the accelerometer, force detection, and torque magnetometry sensors is depicted. This graph highlights the differences in sensitivity among the three sensor types, providing a basis for understanding their relative performance [15]. By comparing the sensitivities side by side, researchers can evaluate the trade-offs between sensor types and select the most appropriate option based on the application requirements.

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Figure 6 illustrates the noise level comparison of the accelerometer, force detection, and torque magnetometry sensors. This graph quantifies the amount of noise present in each sensor’s output signal, offering insights into their signal-to-noise ratio and overall measurement quality. By comparing the noise levels across different sensors, researchers can assess their performance in noisy environments and make informed decisions regarding sensor selection and deployment.

Figure 7 displays the frequency response of the force detection sensor, showcasing its sensitivity to external forces across a range of frequencies. Similar to the accelerometer frequency response, this graph provides valuable information about the sensor’s performance characteristics and frequency-dependent behavior. By analyzing this frequency response, researchers can evaluate the sensor’s dynamic range and frequency response range, aiding in sensor integration and application development.

Finally, Figure 8 presents the frequency response of the torque magnetometry sensor, highlighting its sensitivity to torque or rotational forces across different frequencies. This graph offers insights into the sensor’s ability to detect rotational motion and provides valuable information for applications requiring torque measurement. By analyzing the frequency response, researchers can assess the sensor’s performance in rotational motion detection and identify any frequency-dependent effects that may impact measurement accuracy.

MATLAB code explanation

This MATLAB script is designed to perform calibration of high-precision cavity optomechanical displacement-based sensors, along with designing accelerometers, force detection sensors, and torque magnetometry sensors. Additionally, it plots various graphs to visualize sensor data, calibration results, and sensor designs.

1. Initialization and Data Reading:
   • The script starts by clearing the command window, workspace, and closing all open figures.
   • Sensor data for accelerometers (`accx`, `accy`, `accz`, `acct`) and magnetometers (`magx`, `magy`, `magz`, `magt`) are read from text files using the `readSensData` function.
2. Plot Window Creation:
   • A plot window is created to display outputs. Three subplots are generated:
   • Subplot 1: A circle representing a rolling pebble.
   • Subplot 2: Uncalibrated magnetometer data (`Mx`, `My`, `Mz`) plotted against time.
   • Subplot 3: This subplot will be used for displaying calibration results.
3. Variable Initialization:
   • Variables like `isCalibrated`, `sensDataLength`, and `magCalBuff` are initialized.
4. Data Traversal and Calibration Attempt:
   • The script traverses through the magnetometer data to attempt calibration.
   • It marks the read data in subplot 2.
   • It checks if the current data is suitable for calibration and adds it to the buffer (`magCalBuff`) if appropriate.
   • Calibration is attempted if conditions are met. If successful, calibration results are displayed in the command window, and a sphere representing the calibration is plotted in subplot 3.
5. Intensity of Movement:
   • The intensity of movement is calculated based on accelerometer data.
   • It plots markers on subplot 1 to represent the intensity of movement during pebble rolling.
6. Sensor Design:
   • Designs for accelerometers, force detection sensors, and torque magnetometry sensors are defined as structures (`accelerometer_design`, `force_sensor_design`, `torque_sensor_design`).
7. Plotting Sensors:
   • The sensor designs are plotted on subplot 1.
8. Additional Graphs:
   • Additional graphs related to frequency response, sensitivity comparison, and noise level comparison of all sensors are generated in separate figures.
9. Helper Functions:
   • `emptyBuffer`: Initializes an empty buffer for storing sensor data.
   • `readSensData`: Reads sensor data from a text file.
   • `sphereFit`: Fits a sphere to the magnetometer data to perform calibration.

Outputs:

1. The script displays calibration results in the command window, including calibration completion time, center, residue, and radius of the fitted sphere.
2. It plots various graphs to visualize sensor data, calibration results, and sensor designs. These graphs provide insights into the behavior and performance of the sensors.

In short, this script provides a comprehensive analysis of sensor data and calibration procedures for high-precision sensors.

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MATLAB Simulink Part

Figure 9 presents a MATLAB Simulink model of a MEMS accelerometer, incorporating various blocks such as force, translational Simscape, optomechanical structure, and voltage. The simulation involves the interaction of these components to generate an output torque graph, force output graph, and voltage output graph, which are displayed on the oscilloscope. This figure provides a visual representation of the system dynamics and enables the analysis of how different inputs and components influence the sensor’s output behavior. By observing the output graphs, engineers can gain insights into the accelerometer’s performance under different operating conditions and validate the functionality of the Simulink model.

In Figure 10, a MATLAB Simulink model of a MEMS accelerometer is depicted along with the equations governing force, acceleration, torque, and sensitivity values utilized within the model. The model integrates these equations to simulate the accelerometer’s behavior and output response accurately. By incorporating mathematical expressions and system dynamics into the Simulink model, engineers can study the sensor’s performance, analyze its response to various inputs, and optimize its design parameters. This figure provides a comprehensive overview of the theoretical framework behind the accelerometer model, facilitating further analysis and refinement of the simulation.

Figure 11 showcases the output graphs generated from the MATLAB Simulink model of the MEMS accelerometer. The graphs display the force, voltage, and torque outputs, providing a visual representation of the sensor’s behavior under simulated conditions. By examining these output graphs, engineers can evaluate the sensor’s response to different inputs and assess its performance characteristics, such as sensitivity, dynamic range, and signal-to-noise ratio. This figure serves as a valuable tool for verifying the accuracy of the Simulink model, validating its predictions against experimental data, and informing design decisions for optimizing the accelerometer’s performance in real-world applications.

Conclusion

In conclusion, the MATLAB project presented demonstrates a comprehensive approach to the calibration and design of high-precision sensor systems tailored for optomechanical applications. Through meticulous data acquisition, sensor calibration, and design parameter specification, the project aims to enhance the accuracy and reliability of sensor measurements in demanding environments. The calibration procedure, which involves fitting a sphere to magnetometer data, offers a robust method for correcting sensor inaccuracies and ensuring precise measurement outcomes. By analyzing sensor readings and comparing them against predefined criteria, the script determines the success of calibration, providing valuable insights into sensor performance.

Furthermore, the project highlights the importance of visualization in understanding sensor behavior, calibration results, and design characteristics [14]. The generated plots and diagrams offer intuitive representations of sensor data, calibration outcomes, and sensor designs, facilitating comprehensive analysis and interpretation. Additionally, the integration of MATLAB Simulink models further enhances the project’s utility by providing a platform for simulating MEMS accelerometer systems. By simulating force, translational dynamics, and voltage outputs, the Simulink models enable researchers and engineers to explore sensor behavior in depth and optimize system performance [15]. Overall, the project underscores the significance of systematic methodologies and computational tools in advancing sensor technology for optomechanical systems, paving the way for improved accuracy, reliability, and performance in a wide range of applications.

References

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Keywords: High-Precision Sensor Systems, Optomechanical Applications

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