Comparison of similar Mueller and Jones matrix method in catheter based polarization sensitive optical coherence tomography

Highlights

• We theoretically illustrate the discrepancy between the eigenvalue decomposition in Similar Jones matrix (SJM) and the polar decomposition in similar Mueller matrix (SMM).

• We find that the polar decomposition in SMM can separate diattenuation carrying different optical axis with phase retardation on sample, namely asymmetric non-coaxial diattenuation effect.

• We present a real incoherent averaging method in SMM and ind that incoherent averaging in SMM avoids a time-consuming global phase collection and more effectively reduce noise compared with complex coherent averaging in SJM.

Abstract

Catheter based polarization sensitive optical coherence tomography (PS-OCT) can provide composition information of coronary atherosclerotic plaque beyond the intensity based OCT, but it encounters a notable challenge that is how to reduce polarization properties variations owing to a rapidly rotating optical fiber in the catheter. Similar Jones matrix (SJM) and similar Mueller matrix (SMM) based polarization determination methods can provide a stable phase retardation imaging in a catheter based PS-OCT. In this paper, we systematically contrast SJM and SMM methods. Firstly, we theoretically illustrate the discrepancy between the eigenvalue decomposition in SJM and the polar decomposition in SMM. We find the SMM can reduce phase retardation error caused by non-coaxial diattenuation using polar decomposition. Secondly, we present a real incoherent averaging method in SMM. We find that incoherent averaging in SMM avoids a time-consuming global phase collection and more effectively reduce noise compared with complex coherent averaging in SJM. By polarization imaging for multiple biological tissues using a catheter based PS-OCT, we experimentally manifest that the areas with high diattenuation are highly correlated to the difference between images processed by SJM and SMM. At the same time, the SMM with incoherent averaging has a better performance than the SJM with coherent averaging especially at areas with low signal to noise ratio (SNR).

Introduction

Polarization sensitive optical coherence tomography (PS-OCT) is a promising functional extension of common OCT that enables depth-resolved imaging of polarization properties of biological tissues [1], [2], [3], [4], [5], [6], [7]. Among them, catheter based PS-OCT attracts broad attention in intravascular imaging, which offers composition information of coronary atherosclerotic plaque beyond the intensity image of arterial structure information available to conventional catheter based OCT [8], [9], [10], [11], [12], [13]. However, catheter based PS-OCT is a novel field that encounters several challenges. One notable challenge is how to reduce polarization properties variations when light travels through an optical fiber with a rapidly rotation in the catheter. Other challenges include depolarization and diattenuation, low signal to noise ratio (SNR) of PS-OCT signals and phase instability generated by optical fiber rapidly rotation and squeezing in the catheter [14], [15].

Commonly, two different input polarization states (SOPs) are used to eliminate the impact on tissue birefringence imaging owing to polarization properties variation of optical fiber in PS-OCT systems. Several methods determining the local phase retardation of samples are widely used in catheter based PS-OCT include Stokes vectors rotation angle method [16], [17], [18], [19], differential Mueller matrices method [20], [21] and so on. In addition, the spectral binning technique is applied to reduce polarization mode dispersion (PMD) effect due to the long fiber in catheter based PS-OCT [22], [23]. A polarization symmetry constraint method is used to recover optic axis orientation in catheter based PS-OCT [24]. Similar Jones matrix (SJM) is a widely used and accepted polarization determination method for PS-OCT, which performing eigenvalue decomposition of Jones matrix to acquire phase retardation of the sample based on matrix similarity [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]. Wang et al. [31] and Li et al. [33] also proposed catheter based PS-OCT systems using the SJM method. However, the catheter probes in these systems are tip-scanning and have a relatively large diameter, which are unsuitable for intravascular imaging. Learning the idea of SJM method, we proposed a similar Mueller matrix (SMM) method for polarization determination in catheter based PS-OCT [35], which is also based on matrix similarity. A matrix polar decomposition method [36], [37] is applied in SMM. The experimental results verify that the SMM method can provide a better imaging quality of phase retardation for biological tissue. However, the advancements of the SMM method compared with the SJM method are not theoretically illustrated in [35].

Diattenuation has a strong impact on the phase retardation measurement of the sample. The birefringence and diattenuation are two independent physical parameters that have different optic axes in real world, which can cause asymmetric non-coaxial diattenuation effect. SJM based on eigenvalue decomposition can only separate birefringence and diattenuation have the same axis of sample called as coaxial diattenuation, when there is an assumption for approximating a homogeneous Jones matrix [27], [30]. This assumption is reasonable, when diattenuation is not very large that mainly comes from tissues. However, the reflection of the reference surface or sample surface and noise will cause large asymmetric non-coaxial diattenuation in the catheter based PS-OCT. Whereas, the SMM can separate this asymmetric non-coaxial diattenuation by polar decomposition. SMM has a potential to reduce effect of asymmetric non-coaxial diattenuation on the phase retardation measurement.

Several algorithms are applied to improve the SNR and the quality of phase retardation images in SJM method including Bayesian maximum likelihood estimator [32], noise-stochastic corrected maximum a posteriori estimator [34] and so on. Whereas, averaging is a simple and widely-used approach. A complex coherent averaging is widely employed for measured Jones matrices [31], [33], [38], [39]. Since Jones matrices at each pixel have different phase offset caused by noise, a global phase collection for each pixel is necessary prior to coherence averaging. However, the noise model for the SMM method has not been proposed and analyzed yet. More importantly, to improve the quality of phase retardation image, an averaging method should be developed in the SMM method.

In this paper, we systematically contrast SJM and SMM methods. Firstly, we theoretically and experimentally illustrate the discrepancy between SJM and SMM methods. Since only two orthogonal polarization channels are used to acquire data in the presented catheter based PS-OCT, acquired Jones matrices need to be converted to Mueller matrices for SMM method, in which process does not alter any of the information. Nevertheless, the discrepancy between these two methods is matrix decomposing. The SMM is based on polar decomposition, but the widely used and accepted SJM is based on eigenvalue decomposition. Although Jones matrix can also be applied by a polar decomposition which has not been used for polarization determination in PS-OCT [40]. Here we only compare the SJM by eigenvalue decomposition with SMM. By constructing attenuation model and simulation results, we find the polar decomposition in SMM can separate asymmetric non-coaxial diattenuation effect. Whereas, SJM can only separate coaxial diattenuation. Asymmetric non-coaxial diattenuation can be generated by reflection of the reference or sample surface and noise. From experimental results, we also find that the areas with high diattenuation are highly correlated to the difference between images processed by SJM and SMM. The polarization contrasts of SMM are clearer than those of SJM method at areas with high diattenuation. SMM reduce effect of asymmetric non-coaxial diattenuation on the phase retardation measurement. Secondly, we compare complex coherent averaging in SJM with real incoherent averaging in SMM. By constructing average signals’ model with additive noise for SJM and SMM method, we find that the global phase will not affect incoherent averaging which avoids a time-consuming global phase collection for each pixel in the complex coherent averaging of SJM method. The simulation and experiment results both manifest that the SMM method with incoherent averaging has a better performance than the SJM method with coherent averaging. The peak signal to noise ratio (PSNR) of simulated images processed by the SMM method is higher than about 13 dB than that processed by the SJM method when the signal to noise ratio (SNR) is less than 3 dB. From experimental results after averaging, we also find that the polarization contrast of SMM is much clearer than that of SJM method at areas with low SNR.