Design considerations for polarization-sensitive optical coherence tomography with a single input polarization state

Abstract

Using a generalized design for a polarization-sensitive optical coherence tomography (PS-OCT) system with a single input polarization state (SIPS), we prove the existence of an infinitely large design space over which it is possible to develop simple PS-OCT systems that yield closed form expressions for birefringence. Through simulation and experiment, we validate this analysis by demonstrating new configurations for PS-OCT systems, and present guidelines for the general design of such systems in light of their inherent inaccuracies. After accounting for systemic errors, alternative designs exhibit similar performance on average to the traditional SIPS PS-OCT system. This analysis could be extended to systems with multiple input polarization states and could usher in a new generation of PS-OCT systems optimally designed to probe specific birefringent samples with high accuracy.

Keywords: (110.4500) Optical coherence tomography; (120.3890) Medical optics instrumentation; (230.5440) Polarization-selective devices.

Fig. 1

The generalized PS-OCT system. The detector collects two interferograms with orthogonal polarizations from interfered reference (E_r) and sample (E_s) arm light; inset shows the PS-detector used in this study. J_s or J_x : Jones matrix of the sample or polarization-controlling components in interferometer arm x = {src, ref, samp, det}, E_y: normalized Jones vector at y = {src, in, out}, src: source, det: detector, ref: reference, samp: sample, BS: non-polarizing beam splitter, Pol: linear polarizer, HWP: half-wave plate, L: lens, H: horizontal, V: vertical.

Fig. 2

Poincaré sphere representation of the calculation of birefringence. (a) Transformed light from the source (S_src) to the sample (S_in) is rotated by the sample (S_out) prior to measurement (S_I(z)). (b) A birefringent sample with optic axis θ rotates S_in about the vector [cos(2θ), sin(2θ),0], tracing out an arc of a circle on the sphere. (c) Optic axθ is proportional to the angle between the +U axis and (S′_in − S′_out), the projection of S_in − S_out in the Q-U plane. (d) Retardance η is proportional to the angle between S″_in and S″_out, where S″_x is the projection of S_x in the plane with normal vector [cos(2θ), sin(2θ),0] and containing point (cos(2θ), sin(2θ),0).

Fig. 3

Effects of polarization properties of the system on the accuracy of the birefringence measurement. (a) Simulated absolute retardance and optic axis error for the systems described in Table 1. Error is associated with a noisy version of the A-scan vector from Eq. 6 and locations of large error depend on E_in ( Media 1 and Media 2). (b) Location of nodes (black, associated with H: horizontal and V: vertical polarization states) and convergence loci (dashed lines) in the retardance-optic axis space. Nodes typically depress error; convergence loci lead to increased error. (c) Convergence points on Poincaré sphere (arrows) associated with the convergence loci in (b), derived from the intersections of contour lines for optic axis (black) and/or retardance (gray); the location of the H node (red circle) is independent of the system design. (d) Average absolute error (mean of logarithm) across the whole retardance-optic axis space as a function of the polarization state of E_r, modeled as a linear polarizer (LP) ( Media 3). (e) Average absolute error as a function of the rotation applied by the sample-to-detector Jones matrix ( ${\mathbf{J}}_{d-s}={\mathbf{J}}_{\mathit{det}}{\mathbf{J}}_{\mathit{samp}}^T$), modeled as a QWP ( Media 4).

Fig. 4

Measured birefringence parameters for the four experimental systems from Table 1. (a) Raw data. (b) Revised data after compensating for systemic non-idealities. The ideal behavior of these graphs is shown in the first column for comparison.

Fig. 5

Absolute error between ideal (set) and actual retardance and optic axis measurements for (a) simulations of compensated systems and (b) experimental data both before and (c) after compensation. Convergence loci for the compensated systems are overlaid as thin black lines in (b) and (c) as a visual aid.