M-Bonacci Zone Plates for Ultrasound Focusing
<p>Lens design procedure with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>j</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>: (<b>a</b>) design steps; (<b>b</b>) Fresnel regions (top), classification of M-bonacci Zone Plate (MbZP) regions after the binary sequence mapping (middle) and final transmittance function of the lens (bottom); and (<b>c</b>) resulting MbZP layout.</p> "> Figure 2
<p>Focusing profile of a lens with <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>j</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math> m, and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math> mm as a function of (<b>a</b>) the normalized axial coordinate and (<b>b</b>) the denormalized axial coordinate.</p> "> Figure 3
<p>MbZP layouts (left) and their normalized focusing profiles (right): (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. For all MbZPs, <math display="inline"><semantics> <mrow> <mi>j</mi> <mo>=</mo> <mn>9</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> m.</p> "> Figure 4
<p>Focusing profiles (blue lines) against axial distance for different values of <math display="inline"><semantics> <mi>γ</mi> </semantics></math> (rows) and <span class="html-italic">m</span> (columns), compared to their ideal counterparts (<math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>></mo> <mo>></mo> <mn>1</mn> </mrow> </semantics></math>) in red.</p> "> Figure 5
<p>(<b>a</b>) Normalized focal distances and (<b>b</b>) focal distance ratio as a function of the <math display="inline"><semantics> <mi>γ</mi> </semantics></math> parameter.</p> "> Figure 6
<p>Lens design example with <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> mm and <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>90</mn> </mrow> </semantics></math> mm: (<b>a</b>) Design procedure flow diagram, (<b>b</b>) resulting MbZP lens, and (<b>c</b>) numerically computed focusing profile.</p> "> Figure 6 Cont.
<p>Lens design example with <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> mm and <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>90</mn> </mrow> </semantics></math> mm: (<b>a</b>) Design procedure flow diagram, (<b>b</b>) resulting MbZP lens, and (<b>c</b>) numerically computed focusing profile.</p> "> Figure 7
<p>(<b>a</b>) Manufactured MbZP and (<b>b</b>) scheme of the experimental set-up.</p> "> Figure 8
<p>Experimental results: (<b>a</b>) measured intensity map, (<b>b</b>) measured (black squares) and simulated (blue line) focusing profiles for the MbZP built lens compared to the <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>></mo> <mo>></mo> <mn>1</mn> </mrow> </semantics></math> case (red line).</p> "> Figure 9
<p>(<b>a</b>) Numerically computed focal distances as a function of the working frequency; Experimental (black squares) and simulated (blue line) focusing profiles at (<b>b</b>) 1 MHz and (<b>c</b>) 1.1 MHz.</p> ">
Abstract
:1. Introduction
2. M-Bonacci Zone Plates
2.1. Design and Focusing Properties
2.2. -Parameter
3. Experimental Results and Discussion
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Pérez-López, S.; Fuster, J.M.; Candelas, P. M-Bonacci Zone Plates for Ultrasound Focusing. Sensors 2019, 19, 4313. https://doi.org/10.3390/s19194313
Pérez-López S, Fuster JM, Candelas P. M-Bonacci Zone Plates for Ultrasound Focusing. Sensors. 2019; 19(19):4313. https://doi.org/10.3390/s19194313
Chicago/Turabian StylePérez-López, Sergio, José Miguel Fuster, and Pilar Candelas. 2019. "M-Bonacci Zone Plates for Ultrasound Focusing" Sensors 19, no. 19: 4313. https://doi.org/10.3390/s19194313