线性化解相位恢复:近焦干涉理论
Abstract:
从共路结构中的平方律探测器进行相位重建传统上是一个非线性、非凸的逆问题,需要复杂的迭代算法。近焦干涉(NFI)能够独特地实现自参考相位重建的直接线性化。NFI利用相干波场在短距离自由空间传播(仅数个瑞利长度)过程中的纵向演化与未传播的原始波场之间的干涉。NFI方程对复波场除假设其为带限且在采样网格上完全表示外,不做任何其他假设。严格的理论表明,重建的复波场是唯一的,并连续依赖于测得的干涉项和单幅强度图像,从而确保稳定性。在数值实现中,NFI通过投影到离散六边形基底上,并结合无坐标克雷洛夫子空间最小二乘分析(LSA),应用于明场和纯暗场显微成像。在明场模式中,相位锁定于已知的背景场;在暗场模式中,采用数据驱动的自举方法为LSA提供初始估计,以解决自参考测量中常见的全局相位因子模糊性问题。含8比特噪声的数值模拟表明,仅需5次迭代即可恢复900个独立散射体。实验明场结果展示了远大于离焦衍射斑的样品成像能力。除唯一性和连续性保障外,NFI相较于当前先进定量相位成像技术的主要实际优势在于自校准:传播算子与复波场均直接从含噪测量中恢复,无需外部校准标准,即使仪器重新对准后仍可获得相同的重建结果。这些特性为跨设备和实验室的标准化定量相位成像奠定了基础,有助于其在医学诊断中的推广应用。 关键词:相位重建,共路干涉,近焦干涉,定量相位成像,自参考测量,明场显微,暗场显微,克雷洛夫子空间最小二乘分析,自校准,复波场重建
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