Amsterdam UMC, Location AMC, University of Amsterdam, Department of Biomedical Engineering and Physics, Amsterdam, The Netherlands, The Netherlands.
Amsterdam Cardiovascular Sciences, Atherosclerosis and Ischemic Syndromes, Amsterdam, The Netherlands, The Netherlands.
J Biomed Opt. 2022 Aug;27(8). doi: 10.1117/1.JBO.27.8.085001.
Optical coherence tomography (OCT) is an interferometric imaging modality, which provides tomographic information on the microscopic scale. Furthermore, OCT signal analysis facilitates quantification of tissue optical properties (e.g., the attenuation coefficient), which provides information regarding the structure and organization of tissue. However, a rigorous and standardized measure of the precision of the OCT-derived optical properties, to date, is missing.
We present a robust theoretical framework, which provides the Cramér -Rao lower bound σμOCT for the precision of OCT-derived optical attenuation coefficients.
Using a maximum likelihood approach and Fisher information, we derive an analytical solution for σμOCT when the position and depth of focus are known. We validate this solution, using simulated OCT signals, for which attenuation coefficients are extracted using a least-squares fitting procedure.
Our analytical solution is in perfect agreement with simulated data without shot noise. When shot noise is present, we show that the analytical solution still holds for signal-to-noise ratios (SNRs) in the fitting window being above 20 dB. For other cases (SNR<20 dB, focus position not precisely known), we show that the numerical calculation of the precision agrees with the σμOCT derived from simulated signals.
Our analytical solution provides a fast, rigorous, and easy-to-use measure for OCT-derived attenuation coefficients for signals above 20 dB. The effect of uncertainties in the focal point position on the precision in the attenuation coefficient, the second assumption underlying our analytical solution, is also investigated by numerical calculation of the lower bounds. This method can be straightforwardly extended to uncertainty in other system parameters.
光学相干断层扫描（OCT）是一种干涉成像模式，可提供微观尺度的断层成像信息。此外，OCT 信号分析有助于量化组织光学特性（例如衰减系数），从而提供有关组织结构和组织的信息。然而，迄今为止，OCT 衍生光学特性的精度还没有一个严格和标准化的衡量标准。
我们提出了一个稳健的理论框架，为 OCT 衍生光衰减系数的精度提供了克拉美-罗下限σμOCT。
我们使用最大似然方法和 Fisher 信息，当位置和焦点深度已知时，推导出用于σμOCT 的解析解。我们使用模拟的 OCT 信号验证了该解决方案，对于这些信号，使用最小二乘拟合过程提取衰减系数。
我们的解析解与没有散粒噪声的模拟数据完全吻合。当存在散粒噪声时，我们表明，在拟合窗口中的信噪比（SNR）高于 20dB 的情况下，解析解仍然成立。对于其他情况（SNR < 20dB，焦点位置不精确已知），我们表明，通过对模拟信号进行数值计算得到的精度与从模拟信号得出的σμOCT 一致。
我们的解析解为 SNR 高于 20dB 的信号提供了一种快速、严格且易于使用的 OCT 衍生衰减系数测量方法。数值计算下界还研究了焦点位置不确定性对衰减系数精度的影响，这是我们解析解的第二个假设。该方法可以直接扩展到其他系统参数的不确定性。
