A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere
<p>Photograph and schematic of bio-inspired polarization sensor. (<b>a</b>) Photograph of sensor; (<b>b</b>) light path of scattered light; (<b>c</b>) directions of the six polarizers.</p> "> Figure 2
<p>Values for <span class="html-italic">V</span><sub>1_<span class="html-italic">ideal</span></sub>, <span class="html-italic">V</span><sub>2_<span class="html-italic">ideal</span></sub>, and <span class="html-italic">V</span><sub>3_<span class="html-italic">ideal</span></sub> when <span class="html-italic">d</span> = 0.5.</p> "> Figure 3
<p>Functional diagram of the section algorithm.</p> "> Figure 4
<p>Difference between <span class="html-italic">V</span><sub>1_<span class="html-italic">ideal</span></sub> and <span class="html-italic">V</span><sub>1_<span class="html-italic">AD</span></sub> when <span class="html-italic">d</span> = 0.5.</p> "> Figure 5
<p>Errors for <span class="html-italic">θ</span><sub>12</sub> when <span class="html-italic">d</span> = 0.5.</p> "> Figure 6
<p>Maximum of <span class="html-italic">V<sub>i_AD</sub></span> and accuracy limit for <span class="html-italic">θ</span> when <span class="html-italic">d</span> is between 0.05 and 0.95.</p> "> Figure 7
<p>(<b>a</b>) Schematics illustrating the integrating sphere; (<b>b</b>) Schematics illustrating the eccentric feature of the three centers; (<b>c</b>) Schematics illustrating how to use the central-symmetry method in calibration.</p> "> Figure 8
<p>(<b>a</b>) The separate influence of <span class="html-italic">O<sub>IS</sub></span> when <span class="html-italic">L<sub>IS</sub></span> = 0.05 mm and <span class="html-italic">α<sub>IS</sub></span> = 0°. (<b>b</b>) The separate influence of <span class="html-italic">O<sub>S</sub></span> on voltages when <span class="html-italic">L<sub>S</sub></span> = 0.02 mm and <span class="html-italic">α<sub>S</sub></span> = 70°.</p> "> Figure 9
<p>The integrated influence of <span class="html-italic">O<sub>IS</sub></span> and <span class="html-italic">O<sub>S</sub></span> when <span class="html-italic">L<sub>IS</sub></span> = 0.05 mm, <span class="html-italic">α<sub>IS</sub></span> = 0°, <span class="html-italic">L<sub>S</sub></span> = 0.02 mm, and <span class="html-italic">α<sub>S</sub></span> = 70°.</p> "> Figure 10
<p>The influence of <span class="html-italic">α<sub>S</sub></span> on the three voltage deviations after using the central-symmetry method.</p> "> Figure 11
<p>After using the central-symmetry method: (<b>a</b>) The influence of <span class="html-italic">L<sub>IS</sub></span> on ASD and percent; (<b>b</b>) the influence of <span class="html-italic">L<sub>IS</sub></span> on expectation and deviation percent.</p> "> Figure 12
<p>After using the central-symmetry method: (<b>a</b>) The influence of <span class="html-italic">L<sub>S</sub></span> on ASD and percent; (<b>b</b>) the influence of <span class="html-italic">L<sub>S</sub></span> on expectation and deviation percent.</p> "> Figure 13
<p><span class="html-italic">V</span><sub>1_<span class="html-italic">ideal</span></sub> and its derivative when <span class="html-italic">d</span> = 0.5.</p> "> Figure 14
<p>Overview of three types of calibrations.</p> "> Figure 15
<p>Photograph of indoor calibration setup.</p> "> Figure 16
<p>Error curves when only the section algorithm is used.</p> "> Figure 17
<p>Estimated voltage curves for <a href="#sec4dot3-sensors-19-03448" class="html-sec">Section 4.3</a> and noncontinuous points for <a href="#sec4dot4-sensors-19-03448" class="html-sec">Section 4.4</a>.</p> "> Figure 18
<p>Experimental data analysis when the central-symmetry method is also used.</p> "> Figure 19
<p>(<b>a</b>) Error curves when the central-symmetry method is also used; (<b>b</b>) error curves when the noncontinuous method is added.</p> "> Figure 20
<p>Summary of accuracies of three types of calibration.</p> "> Figure 21
<p>Theoretical calibration parameters replacing the corresponding indoor calibration parameters.</p> "> Figure 22
<p>Photograph of outdoor setup.</p> "> Figure 23
<p>Outdoor2 errors after calibration at 16:43:08. (<b>a</b>) Angle error; (<b>b</b>) degree error; (<b>c</b>) standard deviation; (<b>d</b>) the 40 measured samples.</p> "> Figure 24
<p>Outdoor replacement results without replacing <span class="html-italic">k</span>: (<b>a</b>) The compensation is not done; (<b>b</b>) the compensation is done.</p> "> Figure 25
<p>Outdoor replacement results when <span class="html-italic">k</span> was replaced: (<b>a</b>) The compensation is not done; (<b>b</b>) the compensation is done.</p> "> Figure 26
<p>Photograph of dynamic outdoor setup.</p> "> Figure 27
<p>Outdoor path offered by the inertial navigation system.</p> "> Figure 28
<p>Headings of the polarization sensor and the inertial navigation system.</p> "> Figure 29
<p>Heading deviations between the polarization sensor and the inertial navigation system.</p> ">
Abstract
:1. Introduction
2. Bio-Sensor for Navigation
2.1. Structure
2.2. Polarization Angle Calculation
2.3. Section Algorithm
2.4. Accuracy Limit for Different d Values
3. Calibration Method
3.1. Central-Symmetry Method with Integrating Sphere
3.2. Simulation of the Central-Symmetry Method
3.3. Noncontinuous Method
3.4. Calibration Parameters
3.5. Decoupling Method for Calibration Parameters
4. Indoor Results
4.1. Calibration Device
4.2. Section-Only Algorithm
4.3. Adding the (Integrating-Sphere) Central-Symmetry Method
4.4. Adding the Noncontinuous Method
4.5. Comparison of Three Calibration Methods
4.6. Analysis of Four Calibration Parameters
5. Outdoor Results
5.1. Static Outdoor Experiments
5.2. Dynamic Outdoor Experiments
6. Discussion
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Variable | Annotation |
---|---|
Vi_ideal | Theoretical voltages, i ∈ [1, 2, 3] |
Vi_AD | Theoretical voltages of 16-bit ADC, i ∈ [1, 2, 3] |
Vref | Reference voltage for logarithmic amplifier |
Vi | Voltages, i ∈ [1, 2, 3] |
Vimr | Voltages obtained using the central-symmetry method, also mean values of Vibr and Viar, i ∈ [1, 2, 3] |
Vinc | Voltages obtained using the noncontinuous method, i ∈ [1, 2, 3] |
Vbr | Voltage before 180° rotation |
Var | Voltage after 180° rotation |
Vicf | Theoretical voltages calculated by the calibration parameters in Equation (21) |
θ | Polarization angle |
θ12, θ13, θ23 | Polarization angles from three voltages |
θR | Rotational angle of precise rotary table in simulation |
θsec | Polarization angle obtained using the section algorithm |
d | Polarization degree |
dcm | Polarization degree obtained using the iterative least-squares estimation method, m ∈ [1, 2, 3, 4, 5, 6] |
da | Polarization degree determined by the authors |
OIS | Center of integrating sphere |
OS | Center of polarization sensor |
OR | Center of rotary table |
Lo | Length between the port and the photosensitive surface |
Eo | Irradiance at the center |
Ee | Irradiance at the off-axis edge |
E1, E2, E’1, E’2 | Irradiance at Point 1, 2, 1’, 2’ |
Lphoto | Length between OS and the photosensitive surface |
αIS | Eccentric angle between OR and OIS |
αS | Eccentric angle between OR and OS |
LIS | Eccentric distance between OR and OIS |
LS | Eccentric distance between OR and OS |
LR1 | Eccentric distance between OR and Point 1 |
LR2 | Eccentric distance between OR and Point 2 |
L1, L2, L1’, L2’ | Off-axis distance between OIS and Point 1, 2, 1’, 2’ |
BSD | Standard deviation of a 360° range before the central-symmetry method is used |
ASD | Standard deviation of a 360° range after the central-symmetry method is used |
gup | Gain of unpolarized light |
gtp | Gain of totally polarized light |
τM | Transmittance when the reference angle and main polarization angle of incident light are parallel |
τm | Transmittance when the reference angle and main polarization angle of incident light are orthogonal |
τf | Transmittance of blue filter |
Ein | Irradiance of incident light |
Ep | Irradiance at photodiode |
sr | Spectral responsivity of photodiode |
Ar | Active area size of photodiode |
kci | Constant value generated by the integrating sphere method, i ∈ [1, 2, 3] |
ki | Additive coefficient of calibration, i ∈ [1, 2, 3] |
kvi | Deviation parameter of reference voltage of logarithmic amplifier, i ∈ [1, 2, 3] |
kdm | Coefficient of non-ideal polarizer, m ∈ [1, 2, 3, 4, 5, 6] |
αm | Installation angles of polarizer, m ∈ [1, 2, 3, 4, 5, 6] |
Parameter | Theory | Indoor | Outdoor1 | Outdoor2 | Sun1 | Sun2 |
---|---|---|---|---|---|---|
α1 (°) | 0 | 0.7554 | 0.7813 | 0.9189 | 0.7887 | 0.9344 |
α2 (°) | 0 | 0.5500 | 0.8017 | 0.4385 | 0.8236 | 0.4540 |
α3 (°) | −120 | −117.6462 | −117.8128 | −118.0658 | −117.7964 | −118.0503 |
α4 (°) | −120 | −116.5699 | −116.3585 | −116.3233 | −116.3421 | −116.3078 |
α5 (°) | 120 | 123.0730 | 123.3667 | 122.9320 | 123.3727 | 122.9510 |
α6 (°) | 120 | 120.6994 | 120.6410 | 120.6542 | 120.6634 | 120.6634 |
k1 (mV) | 0 | −10.1519 | −7.4487 | −7.8456 | −7.4461 | −7.8455 |
k2 (mV) | 0 | 7.9230 | 8.8675 | 9.3682 | 8.8674 | 9.3681 |
k3 (mV) | 0 | −9.4542 | −18.5845 | −18.7583 | −18.5778 | −18.7604 |
kd1 | 0 | −0.0438 | −0.0229 | −0.0277 | −0.0203 | −0.0246 |
kd2 | 0 | −0.0365 | −0.0074 | −0.0153 | −0.0100 | −0.0158 |
kd3 | 0 | −0.0457 | −0.0118 | −0.0050 | −0.0127 | −0.0086 |
kd4 | 0 | −0.0492 | −0.0255 | −0.0163 | −0.0217 | −0.0166 |
kd5 | 0 | −0.0555 | −0.0151 | −0.0179 | −0.0136 | −0.0140 |
kd6 | 0 | −0.0166 | −0.0137 | −0.0217 | −0.0134 | −0.0172 |
kv1 | 1 | 1.0224 | 1.0064 | 1.0119 | 1.0066 | 1.0119 |
kv2 | 1 | 1.0081 | 1.0135 | 1.0029 | 1.0135 | 1.0029 |
kv3 | 1 | 1.0183 | 1.0070 | 1.0125 | 1.0054 | 1.0073 |
da | ----- | 0.5500 | 0.6550 | 0.7100 | 0.6600 | 0.7150 |
Origin-Accuracy (°) | ----- | ±0.0088 | ±0.0177 | ±0.0140 | ±0.0207 | ±0.0119 |
Accuracy (°) | ----- | ±0.009 | ±0.018 | ±0.014 | ±0.021 | ±0.012 |
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Wang, Y.; Chu, J.; Zhang, R.; Li, J.; Guo, X.; Lin, M. A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere. Sensors 2019, 19, 3448. https://doi.org/10.3390/s19163448
Wang Y, Chu J, Zhang R, Li J, Guo X, Lin M. A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere. Sensors. 2019; 19(16):3448. https://doi.org/10.3390/s19163448
Chicago/Turabian StyleWang, Yinlong, Jinkui Chu, Ran Zhang, Jinshan Li, Xiaoqing Guo, and Muyin Lin. 2019. "A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere" Sensors 19, no. 16: 3448. https://doi.org/10.3390/s19163448