We recently proposed a dual-slope technique for diffuse optical spectroscopy and imaging of scattering media. This technique requires a special configuration of light sources and optical detectors to create dual-slope sets. Here, we present methods for designing, optimizing, and building an optical imaging array that features m dual-slope sets to image n voxels. After defining the m × n matrix (S) that describes the sensitivity of the m dual-slope measurements to absorption perturbations in each of the n voxels, we formulate the inverse imaging problem in terms of the Moore-Penrose pseudoinverse matrix of S (S+). This approach allows us to introduce several measures of imaging performance: reconstruction accuracy (correct spatial mapping), crosstalk (incorrect spatial mapping), resolution (point spread function), and localization (offset between actual and reconstructed point perturbations). Furthermore, by considering the singular value decomposition formulation, we show the significance of visualizing the first m right singular vectors of S, whose linear combination generates the reconstructed map. We also describe methods to build a physical array using a three-layer mesh structure (two polyethylene films and polypropylene hook-and-loop fabric) embedded in silicone (PDMS). Finally, we apply these methods to design two arrays and choose one to construct. The chosen array consists of 16 illumination fibers, 10 detection fibers, and 27 dual-slope sets for dual-slope imaging optimized for the size of field of view and localization of absorption perturbations. This particular array is aimed at functional near-infrared spectroscopy of the human brain, but the methods presented here are of general applicability to a variety of devices and imaging scenarios.

中文翻译：

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用于双斜率漫射光学成像的源探测器阵列设计

我们最近提出了一种用于漫反射光谱和散射介质成像的双斜率技术。这种技术需要特殊配置的光源和光学检测器来创建双斜率集。在这里，我们提出了设计、优化和构建光学成像阵列的方法，该阵列具有 m 个双斜率集以对 n 个体素进行成像。在定义了 m × n 矩阵 (S) 后，该矩阵描述了 m 个双斜率测量对 n 个体素中的每一个中的吸收扰动的敏感性，我们根据 S (S+ ）。这种方法允许我们引入几种成像性能的度量：重建精度（正确的空间映射）、串扰（不正确的空间映射）、分辨率（点扩散函数）、和定位（实际和重建点扰动之间的偏移）。此外，通过考虑奇异值分解公式，我们展示了可视化 S 的前 m 个右奇异向量的重要性，其线性组合生成重建图。我们还描述了使用嵌入硅胶 (PDMS) 的三层网状结构（两个聚乙烯薄膜和聚丙烯钩环织物）构建物理阵列的方法。最后，我们应用这些方法来设计两个数组并选择一个来构造。所选择的阵列由 16 根照明光纤、10 根检测光纤和 27 个双斜率组组成，用于针对视场大小和吸收扰动的定位进行优化的双斜率成像。这种特殊的阵列旨在研究人脑的功能性近红外光谱，