Single Particle Differentiation through 2D Optical Fiber Trapping and Back-Scattered Signal Statistical Analysis: An Exploratory Approach
Abstract
:1. Introduction
2. Materials and Methods
2.1. Optical Trapping Experiments
2.1.1. Fabrication of the Polymeric Lens for Optical Trapping
2.1.2. Optical Trapping and Particles Sensing Setup
2.2. Particles Trapping and Sensing Using the Polymeric Lens
2.2.1. Back-Scattered Signal Acquisition and Processing Steps
2.2.2. Particles Differentiation Using Back-Scattered Trapping Signal
Features
Time Doman-Derived Features
Frequency Doman-Derived Features
2.2.3. Statistical Analysis
2.2.4. Features Dimensionality Reduction Using Linear Discriminant Analysis (LDA)
3. Results and Discussion
3.1. Optical Trapping
3.2. Back-Scattered Signal Analysis
3.2.1. Time Domain Features Analysis
3.2.2. Frequency Domain Features Analysis
Discrete Cosine Transform (DCT)-Derived Features
Wavelet Features
3.3. Towards a Single Feature for Particles Class Differentiation
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Time Domain Features Analysis-Parwise Comparisons
Appendix B. Frequency Domain Features Analysis-Discrete Cosine Transform (DCT) Coefficients
Abbreviations
AUC | Area Under the Curve |
CMOS | Complementary Metal-Oxide-Semiconductor |
COTs | Conventional Optical Tweezers |
DAQ | Data Acquisition Board |
DCT | Discrete Cosine Transform |
E | Entropy |
FFT | Fast-Fourier Transform |
IQR | Interquartile Range |
IoT | Internet of Things |
Kurt | Kurtosis |
LDA | Linear Discriminant Analysis |
M | Mean |
OFT | Optical Fiber Tweezers |
OT | Optical Tweezers |
PBS | Phosphate Buffered Saline |
PCA | Principal Component Analysis |
Probability Density Function | |
PMMA | Poly(methyl methacrylate) |
PS | Polystyrene |
RBC | Red Blood Cell |
RI | Refractive Index |
RMS | Root Mean Square |
SD | Standard Deviation |
Skew | Skewness |
SMF | Single Mode Fiber |
SNR | Signal-to-noise Ratio |
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Solution | Solvent | Particles Type | Particles Diameter (d) | Particles RI | Nr. of Particles Used |
---|---|---|---|---|---|
1 | De-ionized water (n = 1.327) | Polystyrene microspheres | 8 m | 1.5731 [42] | 18 |
2 | PMMA microspheres | 8 m | 1.4843 [42] | 16 | |
3 | Living yeast cells | 6–7 m | 1.49–1.53 [43] | 16 |
Class | 1: “No Particle” | 2: “PMMA Particle” | 3: “PS Particle” | 4: “Living Yeast Cell” |
---|---|---|---|---|
Nr. of Particles | 16 | 16 | 18 | 16 |
Avg. nr. of signal portions per particle | 59 ± 0 | 57 ± 2 | 54 ± 5 | 59 ± 2 |
Total nr. of signal portions (all particles) | 949 | 919 | 971 | 939 |
Type | Group | Number | Feature/Parameter |
---|---|---|---|
Time Domain | Time Domain Statistics | 1 | Mean (M) |
2 | Standard Deviation (SD) | ||
3 | Root Mean Square (RMS) | ||
4 | Skewness (Skew) | ||
5 | Kurtosis (Kurt) | ||
6 | Interquartile Range (IQR) | ||
7 | Entropy ( E ) | ||
Time Domain Histogram | 8 | ||
9 | |||
Frequency Domain | Discrete Cosine Transform (DCT) | 10 | 1st Coefficient () |
11 | 2nd Coefficient () | ||
12 | 3rd Coefficient () | ||
13 | 4th Coefficient () | ||
14 | 5th Coefficient () | ||
15 | 6th Coefficient () | ||
16 | 7th Coefficient () | ||
17 | 8th Coefficient () | ||
18 | 9th Coefficient () | ||
19 | 10th Coefficient () | ||
20 | 11th Coefficient () | ||
21 | 12th Coefficient () | ||
22 | 13th Coefficient () | ||
23 | 14th Coefficient () | ||
24 | 15th Coefficient () | ||
25 | 16th Coefficient () | ||
26 | 17th Coefficient () | ||
27 | 18th Coefficient () | ||
28 | 19th Coefficient () | ||
29 | 20th Coefficient () | ||
30 | Number of coefficients that capture 98% of the original signal () | ||
31 | Total spectrum Area Under Curve (AUC) () | ||
32 | Maximum peak amplitude () | ||
33 | Total spectral power () | ||
Wavelet Packet Decomposition | 34 | Haar Relative Power 1st level () | |
35 | Haar Relative Power 2nd level () | ||
36 | Haar Relative Power 3rd level () | ||
37 | Haar Relative Power 4th level () | ||
38 | Haar Relative Power 5th level () | ||
39 | Haar Relative Power 6th level () | ||
40 | Db10 Relative Power 1st level () | ||
41 | Db10 Relative Power 2nd level () | ||
42 | Db10 Relative Power 3rd level () | ||
43 | Db10 Relative Power 4th level () | ||
44 | Db10 Relative Power 5th level () | ||
45 | Db10 Relative Power 6th level () |
Type of Wavelet | Wavelet Energy Level | 4 Classes Comparisons | Class 1 vs. Class 2 | Class 1 vs. Class 3 | Class 1 vs. Class 4 | Class 2 vs. Class 3 | Class 2 vs. Class 4 | Class 3 vs. Class 4 |
---|---|---|---|---|---|---|---|---|
Haar | 1st | ** | ** | ** | * | |||
2nd | ** | ** | ** | * | ||||
3rd | ** | * | ** | * | ||||
4th | ** | * | ** | * | ||||
5th | ** | ** | ** | ** | * | ** | ** | |
6th | ** | ** | ** | * | * | ** | ** | |
Db10 | 1st | ** | ** | ** | * | |||
2nd | ** | ** | ** | |||||
3rd | ** | ** | ** | ** | ||||
4th | ** | ** | ** | * | * | ** | ** | |
5th | ** | ** | ** | ** | * | ** | ** | |
6th | ** | * | ** | * | * | ** |
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Paiva, J.S.; Ribeiro, R.S.R.; Cunha, J.P.S.; Rosa, C.C.; Jorge, P.A.S. Single Particle Differentiation through 2D Optical Fiber Trapping and Back-Scattered Signal Statistical Analysis: An Exploratory Approach. Sensors 2018, 18, 710. https://doi.org/10.3390/s18030710
Paiva JS, Ribeiro RSR, Cunha JPS, Rosa CC, Jorge PAS. Single Particle Differentiation through 2D Optical Fiber Trapping and Back-Scattered Signal Statistical Analysis: An Exploratory Approach. Sensors. 2018; 18(3):710. https://doi.org/10.3390/s18030710
Chicago/Turabian StylePaiva, Joana S., Rita S. R. Ribeiro, João P. S. Cunha, Carla C. Rosa, and Pedro A. S. Jorge. 2018. "Single Particle Differentiation through 2D Optical Fiber Trapping and Back-Scattered Signal Statistical Analysis: An Exploratory Approach" Sensors 18, no. 3: 710. https://doi.org/10.3390/s18030710
APA StylePaiva, J. S., Ribeiro, R. S. R., Cunha, J. P. S., Rosa, C. C., & Jorge, P. A. S. (2018). Single Particle Differentiation through 2D Optical Fiber Trapping and Back-Scattered Signal Statistical Analysis: An Exploratory Approach. Sensors, 18(3), 710. https://doi.org/10.3390/s18030710