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Keywords = missing-order Talbot effect

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13 pages, 7014 KiB

Open AccessArticle

Displacement Measurement Based on the Missing-Order Talbot Effect

by Liuxing Song, Kailun Zhao, Xiaoyong Wang, Jinping He, Guoliang Tian, Shihua Yang and Yaning Li

Sensors 2025, 25(1), 292; https://doi.org/10.3390/s25010292 - 6 Jan 2025

Viewed by 465

Displacement measurement is a crucial application, with laser-based methods offering high precision and being well established in commercial settings. However, these methods often come with the drawbacks of significant size and exorbitant costs. We introduce a novel displacement measurement method that utilizes the [...] Read more.

Displacement measurement is a crucial application, with laser-based methods offering high precision and being well established in commercial settings. However, these methods often come with the drawbacks of significant size and exorbitant costs. We introduce a novel displacement measurement method that utilizes the missing-order Talbot effect. This approach circumvents the need to measure contrast in the Talbot diffraction field, opting instead to leverage the displacement within the missing-order Talbot diffraction pattern. Our method only requires parallel light, an amplitude grating, and a detector to achieve displacement measurement. The measurement dynamic range can be adjusted by altering the grating period and the wavelength of the incident light. Through careful simulation and experimental validation, our method exhibits a correlation coefficient R surpassing

0.999

across a 30 mm dynamic range and achieves a precision superior to 3

μ

m. Full article

(This article belongs to the Special Issue Advances in Optical Sensing, Instrumentation and Systems: 2nd Edition)

► Show Figures

Figure 1

Figure 1
<p>Schematic and simulation of the Talbot effect. (<b>a</b>) Illustrates the formation of Talbot zones (red) where the 0th and ±1st diffraction orders overlap, creating periodic self-imaging, and missing-order Talbot zones (orange) that produce stripe-like images due to the absence of certain diffraction orders. (<b>b</b>) Shows the diffraction field for a 4 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m grating period under 632 nm illumination, with a Talbot distance of 50 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m, as calculated by FDTD. (<b>c</b>) Displays the diffraction field for a 100 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m grating period under the same illumination, with a Talbot distance of 32 mm, calculated using the angular spectrum method.</p> Full article ">Figure 2
<p>The diagram of diffraction propagation.</p> Full article ">Figure 3
<p>Localized amplification diagram of diffraction propagation.</p> Full article ">Figure 4
<p>The red dashed lines depict the stripe-like patterns that arise from the interference between the 0th and +1st orders, characterizing the missing-order Talbot images.</p> Full article ">Figure 5
<p>Simulation data of diffraction fields and detection results for a grating with a period of 100 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m under 632 nm plane wave illumination. (<b>a</b>) Shows the diffraction field in the missing-order region at distances ranging from 300 mm to 400 mm from the grating, with red arrows indicating the Talbot distances. (<b>b</b>) Displays the detection results and linear fit residual analysis within a dynamic range of 300 mm to 400 mm. (<b>c</b>) Illustrates the diffraction field in the missing-order region at distances between 350 mm and 360 mm from the grating. (<b>d</b>) Presents the detection results and linear fit residual analysis within a dynamic range of 350 mm to 360 mm. (<b>e</b>) Depicts the diffraction field in the missing-order region at distances from 355 mm to 356 mm. (<b>f</b>) Shows the detection results and linear fit residual analysis within a dynamic range of 355 mm to 356 mm. The correlation coefficient <span class="html-italic">R</span> and root mean square error (RMSE) are provided for each dynamic range.</p> Full article ">Figure 6
<p>Talbot zone diffraction and MTF analysis. (<b>a</b>) Talbot zone diffraction exhibiting periodic self-imaging. (<b>b</b>) MTF representation of periodic intensity fluctuations across displacement.</p> Full article ">Figure 7
<p>Algorithmic efficiency of displacement extraction algorithm.</p> Full article ">Figure 8
<p>Physical experimental setup for detecting relative displacement changes between grating and camera.</p> Full article ">Figure 9
<p>Measurement results of different dynamic ranges. (<b>a</b>) Measurement results of 1 mm dynamic range. (<b>b</b>) Measurement results of 10 mm dynamic range.</p> Full article ">

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