Performance Analysis of a Noncontact Plastic Fiber Optical Fiber Displacement Sensor with Compensation of Target Reflectivity

<table>(a) <svg height="16.7875" id="M123" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 44.987499 16.7875" width="44.987499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.638)"><path d="M425 682q0 -40 -49 -59q-36 -13 -110 -13q-31 -18 -52.5 -49.5t-21.5 -67.5q0 -34 17.5 -57.5t45.5 -28.5q63 15 97 15q18 0 18 -16q0 -13 -22 -36t-34 -23q-50 0 -93 8q-47 -20 -80.5 -66.5t-33.5 -96.5q0 -76 84 -103q33 -11 75 -21q101 -26 101 -93q0 -51 -39 -95.5
t-76 -68.5l-22 20q60 69 60 111q0 21 -14 34t-55 22q-21 4 -63 16q-68 19 -101.5 52.5t-33.5 96.5q0 125 157 206q-27 10 -46 36t-19 58q0 84 103 152q-43 3 -71.5 21t-28.5 45q0 37 65 59l17 -6q-9 -14 -9 -33q0 -21 17.5 -36t51.5 -19q82 53 147 53q18 0 18 -17z" id="x1D709"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.675,16.725)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
q2 -89 11 -177z" id="x54"></path></g><g transform="matrix(.012,-0,0,-.012,15.314,16.725)"><path d="M655 0h-263v28q46 5 55.5 14.5t-5.5 34.5l-132 214q-69 -104 -122 -202q-19 -32 -10.5 -43.5t58.5 -17.5v-28h-229v28q44 5 70 17t47 40q47 59 164 239l-134 214q-33 50 -54 64t-74 20v28h246v-28q-44 -5 -52 -14t5 -28q32 -55 114 -182q66 102 99 162q19 33 10.5 44.5
t-57.5 17.5v28h228v-28q-56 -6 -80 -19.5t-58 -57.5q-45 -62 -121 -179l157 -246q35 -53 60.5 -70t77.5 -22v-28z" id="x58"></path></g>
<g transform="matrix(.017,-0,0,-.017,23.725,12.638)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,29.607,12.638)"><path d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5
h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" id="x1D451"></path></g><g transform="matrix(.017,-0,0,-.017,39.041,12.638)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg> and <svg height="16.875" id="M124" style="vertical-align:-3.35243pt" version="1.1" viewbox="0 0 44.974998 16.875" width="44.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.638)"><path d="M425 682q0 -40 -49 -59q-36 -13 -110 -13q-31 -18 -52.5 -49.5t-21.5 -67.5q0 -34 17.5 -57.5t45.5 -28.5q63 15 97 15q18 0 18 -16q0 -13 -22 -36t-34 -23q-50 0 -93 8q-47 -20 -80.5 -66.5t-33.5 -96.5q0 -76 84 -103q33 -11 75 -21q101 -26 101 -93q0 -51 -39 -95.5
t-76 -68.5l-22 20q60 69 60 111q0 21 -14 34t-55 22q-21 4 -63 16q-68 19 -101.5 52.5t-33.5 96.5q0 125 157 206q-27 10 -46 36t-19 58q0 84 103 152q-43 3 -71.5 21t-28.5 45q0 37 65 59l17 -6q-9 -14 -9 -33q0 -21 17.5 -36t51.5 -19q82 53 147 53q18 0 18 -17z" id="x1D709"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.675,16.725)"><path d="M631 18l-4 -26q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -63 14 -77.5t74 -19.5v-28h-262v28q62 5 76 19.5t14 77.5v402q0 62 -13 76t-73 19v28h248q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172q27 -52 89 -144
q49 -71 81 -104q31 -36 72 -47zM212 316h48q73 0 108 29q55 42 55 124q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247z" id="x52"></path></g><g transform="matrix(.012,-0,0,-.012,15.302,16.725)"><path d="M655 0h-263v28q46 5 55.5 14.5t-5.5 34.5l-132 214q-69 -104 -122 -202q-19 -32 -10.5 -43.5t58.5 -17.5v-28h-229v28q44 5 70 17t47 40q47 59 164 239l-134 214q-33 50 -54 64t-74 20v28h246v-28q-44 -5 -52 -14t5 -28q32 -55 114 -182q66 102 99 162q19 33 10.5 44.5
t-57.5 17.5v28h228v-28q-56 -6 -80 -19.5t-58 -57.5q-45 -62 -121 -179l157 -246q35 -53 60.5 -70t77.5 -22v-28z" id="x58"></path></g>
<g transform="matrix(.017,-0,0,-.017,23.712,12.638)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,29.594,12.638)"><path d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5
h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" id="x1D451"></path></g><g transform="matrix(.017,-0,0,-.017,39.028,12.638)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg> functions for each TX/RX fiber of the sample bundle. (b) <svg height="15.75" id="M125" style="vertical-align:-3.43843pt" version="1.1" viewbox="0 0 17.299999 15.75" width="17.299999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68
l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" id="x1D446"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.225,15.475)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
t325.5 101.5q114 0 204 -38z" id="x1D436"></path></g>
</svg>(<i>d</i>) functions for each RX fiber. Insets zoom on the close-range portion of the charts.</table>

Journal of Sensors

fig6

Figure 6

Figure 6: Performance Analysis of a Noncontact Plastic Fiber Optical Fiber Displacement Sensor with Compensation of Target Reflectivity 