Super-resolution sensing with a randomly scattering analyzer

Letter
Open Access

Super-resolution sensing with a randomly scattering analyzer

Qiaoen Luo, Justin A. Patel, and Kevin J. Webb

Phys. Rev. Research 3, L042045 – Published 23 December 2021

Abstract

A randomly scattering analyzer located in the far field and with a fixed aperture, in front of a multielement detector, is introduced as a means to access enhanced sensing information associated with far-subwavelength spatial features. This sensing method allows improved spatial resolution with coherent fields scattered from a moving object, or some other relative change that causes a modified field incident on the detector aperture. Experimental optical speckle correlation data with a translated diffusing structure show the salient features, and understanding in relation to the experimental variables is supported by numerical simulations. The conclusion is that more heavily scattering analyzers provide better spatial resolution because the measurements are more sensitive to changes in the incident field. Such randomly scattering analyzers offer a dimension for sensitive coherent optical metrology related to various sensing and motion application domains requiring large offset distances.

Received 18 June 2021
Accepted 9 November 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.L042045

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Photonics

Functional materials Nanostructures

Imaging & optical processing Light scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Qiaoen Luo, Justin A. Patel , and Kevin J. Webb ^*

Purdue University, West Lafayette, Indiana 47907-2035, USA

^*Corresponding author: webb@purdue.edu

Article Text

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References

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Issue

Vol. 3, Iss. 4 — December - December 2021

Subject Areas

Optics

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Images

Figure 1
Experimental arrangement, where a coherent laser illuminates a randomly scattering slab and speckle images are captured through a random analyzer. An area of approximately 1.8 mm $\times$ 1.8 mm on the back of the random analyzer (the second scattering layer) was imaged (using a magnifying lens that is not shown) with a Photometrics Prime sCMOS ( $2048 \times 2048$ pixels) camera. The 4F system was used to regulate the speckle size and hence the number of speckle spots on the camera (for adequate resolution and useful statistical averaging). The diffusing slab was translated in small steps, and a speckle pattern was captured at each position through a linear polarizer (with the same same polarization as the incident laser beam). The measured data is presented as intensity correlations of these speckle patterns as a function of the translated slab position.
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Figure 2
The averaged normalized intensity correlation as a function of translation of the diffusing object (3-mm-thick acrylic slab containing 50-nm ${TiO}_{2}$ scattering having a reduced scattering coefficient of 4 ${cm}^{- 1}$ ), showing a varying decorrelation rate for the different analyzers. The more scattering the analyzer is, the faster the decorrelation becomes. With a thicker analyzer, we are able to sense subwavelength ( $< 850 nm$ ) translation of the diffusing object. For $Δ x = 952$ nm, the measured intensity correlations were 0.9550 (no analyzer), 0.8134 (one ground-glass slide), 0.4431 (3-mm acrylic slab), and 0.2978 (6-mm acrylic slab). Both types of acrylic random analyzer (with 50-nm ${TiO}_{2}$ scatterers) have a reduced scattering coefficient of 4 ${cm}^{- 1}$ .
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Figure 3
Experimental speckle correlation data with additional variables. (a) The more-scattering 3-mm-thick acrylic slab produced faster decorrelation when compared to one moving ground-glass slide (1 GG), because the larger spread of speckle intensity exiting the acrylic slab results in smaller speckle spots incident on the analyzer. (b) The rate of speckle decorrelation increased for smaller separation between the diffusing moving object (one ground-glass slide) and the analyzer (3-mm-thick acrylic slab), because of the reducing speckle size.
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Figure 4
The numerical simulation arrangement showing a section of one of the 6- $μ m$ -thick random analyzer slabs (the full breadth of the slab is wider than the displayed section). The randomly populated blue squares have side lengths of 200 nm and consist of dielectric material, with a fill fraction of 50%, while the gray regions are free space. The bottom and top rectangular sections are perfectly matched layers in a scattered field solution. A randomly generated speckle field (brown) was translated along the slab and in the $x$ direction. The speckle field had $E_{z}, H_{x}, H_{y}$ polarization, and the free-space wavelength was $λ = 850$ nm. The $y$ component of the time-average Poynting vector was measured at the detector plane (red), a distance of $λ / 4$ from the top boundary of the scattering slab.
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Figure 5
Numerical simulations of the transmitted intensity correlation as a function of translated random incident fields, with $λ = 850$ nm, showing the influence of (a) random analyzer scatter level and (b) speckle size. The fields are zero-mean circular Gaussian. The error bars correspond to $\pm σ_{e}$ , where $σ_{e}$ is the standard error in estimating the mean from the samples. Increasing the analyzer scatter and decreasing the speckle size both lead to more rapid decorrelation and hence greater sensitivity to spatial translation of the field.
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