Speckle in optical coherence tomography

Abstract

Optical coherence tomography (OCT) is a biomedical imaging modality that produces high-resolution cross-sectional images of tissues, using infrared light and low-coherence interferometry. For a thorough discussion of OCT, please refer to Chapter 5. As OCT is a coherent modality, its images are corrupted by speckle, giving them a grainy or mottled appearance. In this chapter, we discuss OCT speckle in detail. In Section 6.1, we start with a brief overview of speckle and its main characteristics, as discussed in the copious literature on the phenomenon. In Section 6.2, we introduce a simple model of OCT image formation in the single-backscattering regime. This permits us to define speckle and to understand its most important properties as a fundamental characteristic of coherent imaging. In Section 6.3, classification of different types of speckle are provided based on situations for which the model of Section 6.2 is not applicable, leading to different statistics of speckle when treated as a stochastic phenomenon. Both first- and second-order statistics are described in order to quantify the extent to which speckle is a corrupting influence on the image. In the former case, the magnitude of the speckle fluctuations is assessed using the contrast ratio. In the latter case, speckle size is assessed by virtue of the speckle correlation coefficient. To calculate the speckle correlation coefficient (a normalized autocorrelation function), a more detailed theory of OCT image formation is needed. In Section 6.4, we therefore introduce a linear, spatially variant (in the axial dimension) system framework for OCT. The sample's scattering potential is the input to the imaging system, and the output response is determined by the local point spread function (PSF) of the OCT system. The Fourier equivalent of the local PSF in the spatial frequency domain, the local (coherent) transfer function (TF), is used for the correlation-coefficient calculation. Based on this formalism, we demonstrate that speckle size is (almost) invariant over an A-scan, that is, as the scan axial position varies with respect to the illumination-beam focal plane. In Section 6.5, we extend our discussion to additional light-tissue interaction mechanisms relevant to OCT, in particular, multiple scattering, and how they affect the specific speckle realization (the image) and the statistics of speckle (calculated over an ensemble of image points). Even when the effects of multiply scattered light are included in the OCT detection model, both the speckle contrast ratio and the correlation coefficient will be, in general, sample-independent, given the OCT system parameters. In Section 6.6, we focus on scenarios for which analysis of speckle statistics can be used to either: Extract sample-specific information, or to assess the validity of the image-formation process, at progressively greater sample depths. In the first method, for sparsely distributed scatterers within the OCT resolution volume, the speckle contrast ratio is dependent on scatterer density. In the second, the correlation between multiple speckle patterns for a static sample under different illumination conditions can be used to assess the degree to which the recorded OCT images are corrupted by multiple scattering. Also, the correlation between multiple speckle patterns acquired from a dynamic sample, recorded at different times, can be used to extract useful sample-specific information, e.g., to quantify the extent to which scatterers at different spatial locations in the sample have moved between the images. Finally, in Section 6.7, we discuss both experimental and post-processing methods to improve OCT image quality by reducing the impact of speckle. Experimental validation of the main theoretical results and of speckle reduction methods is provided throughout the chapter using tissue-simulating phantoms, for which fine control of the sample structural and optical properties is possible. Additionally, we present a number of examples from the literature on biological samples showing the relevance of speckle, its analysis and exploitation, and the mitigation of its image-corrupting effects in OCT imaging.