Spatial frequency domain Mueller matrix imaging

Abstract

Significance: Mueller matrix polarimetry (MMP) and spatial frequency domain imaging (SFDI) are wide-field optical imaging modalities that differentiate tissue primarily by structure alignment and photon transport coefficient, respectively. Because these effects can be related, combining MMP and SFDI may enhance tissue differentiation beyond the capability of each modality alone.

Aim: An instrument was developed to combine MMP and SFDI with the goal of testing whether it enhances contrast of features in reflection mode.

Approach: The instrument was constructed using liquid crystal elements for polarization control, a digital light processing projector for generating sinusoidal illumination patterns, and a digital camera for imaging. A theoretical analysis shows that the SFD Mueller matrix is complex-valued and does not follow the same behavior as a regular Mueller matrix. Images were acquired from an anisotropic tissue phantom, an optical fiber bundle, and cerebellum, thalamus, and cerebrum tissues.

Results: The measurement results suggest that singly scattered, few scattered, and diffusely scattered photon paths can be distinguished in some of the samples investigated. The combined imaging modality yields additional spatial frequency phase information, which highlights paths having only a few scattering events.

Conclusions: The combination of MMP and SFDI offers contrast mechanisms inaccessible by each modality used alone.

Keywords: Mueller matrix; brain tissue; polarimetry; scattering; spatial frequency domain imaging; tissue anisotropy.

Fig. 1

(a) SFD Mueller matrix imaging system: PSG with polarizer (P1) and two LC retarders (LC1 and LC2), DLP projector, PSA with polarizer (P2) and two LC retarders (LC3 and LC4), objective (OBJ), and sCMOS camera (CAMERA). (b) A representation of how the sinusoid pattern for $f=5{\mathrm{cm}}^{-1}$ is displayed by the DLP projector pixels. (c) One of the 96 images acquired of bovine thalamus for vertical sinusoidal illumination at $f=5{\mathrm{cm}}^{-1}$.

Fig. 2

SFD Mueller matrix BRDFs from the para-aramid fiber embedded in a PDMS-based scattering and absorbing phantom: (a) the Mueller matrix BRDF at $f=0{\mathrm{cm}}^{-1}$, (b) the real part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$, and (c) the imaginary part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$. The maximum value of the black and white scale used for $F_{\text{r},11}$ at $f=0{\mathrm{cm}}^{-1}$ is twice the maximum value for $F_{\text{r},11}$ of $f=5{\mathrm{cm}}^{-1}$. The scale for the normalized SFD Mueller matrix elements is shown at the bottom of the figure. The spatial frequency sinusoidal pattern for $f=5{\mathrm{cm}}^{-1}$ was oriented horizontally. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.

Fig. 3

Diattenuation of the para-aramid fiber embedded in a PDMS-based scattering and absorbing phantom calculated using Lu-Chipman decomposition from the real part of the SFD Mueller matrix. Spatial frequency is listed above each image. Nonrealizable Mueller matrix pixels are depicted as blue. The spatial frequency sinusoidal pattern was oriented horizontally. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.

Fig. 4

SFD Mueller matrix BRDFs from the optic fiber bundle: (a) the Mueller matrix BRDF at $f=0{\mathrm{cm}}^{-1}$, (b) the real part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$, and (c) the imaginary part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$. The maximum value of the black and white scale used for $F_{\text{r},11}$ at $f=0{\mathrm{cm}}^{-1}$ is six times the maximum value for $F_{\text{r},11}$ of $f=5{\mathrm{cm}}^{-1}$. The scale for the normalized SFD Mueller matrix elements is shown at the bottom of the figure. The spatial frequency sinusoidal pattern for $f=5{\mathrm{cm}}^{-1}$ was oriented horizontally. The field of view of the images is 1.1 cm × 1.1 cm.

Fig. 5

SFD Mueller matrix BRDFs from the optic fiber bundle: (a) the Mueller matrix BRDF at $f=0{\mathrm{cm}}^{-1}$, (b) the real part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$, and (c) the imaginary part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$. The maximum value of the black and white scale used for $F_{\text{r},11}$ at $f=0{\mathrm{cm}}^{-1}$ is seven times the maximum value for $F_{\text{r},11}$ of $f=5{\mathrm{cm}}^{-1}$. The scale for the normalized SFD Mueller matrix elements is shown at the bottom of the figure. The spatial frequency sinusoidal pattern for $f=5{\mathrm{cm}}^{-1}$ was oriented vertically. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.

Fig. 6

Polarimetric purity indices (rows) for each spatial frequency (columns) of an optic fiber bundle. The color scale is shown with a discontinuity at unity, differentiating those regions where the matrix is a valid regular Mueller matrix from those that are not. The spatial frequency sinusoidal patterns were oriented horizontally. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.

Fig. 7

Polarimetric purity indices (rows) for each spatial frequency (columns) of an optic fiber bundle. The color scale is shown with a discontinuity at unity, differentiating those regions where the matrix is a valid regular Mueller matrix from those that are not. The spatial frequency sinusoidal patterns were oriented vertically. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.

Fig. 8

SFD Mueller matrix BRDF images of a caprine cerebellum: (a) the Mueller matrix BRDF at $f=0{\mathrm{cm}}^{-1}$, (b) the real part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$, and (c) the imaginary part of the SFD Mueller matrix BRDF multiplied by a factor of 5 at $f=5{\mathrm{cm}}^{-1}$. The maximum value of the black and white scale used for $F_{\text{r},11}$ at $f=0{\mathrm{cm}}^{-1}$ is four times the maximum value for $F_{\text{r},11}$ of $f=5{\mathrm{cm}}^{-1}$. The scale for the normalized SFD Mueller matrix elements is shown at the bottom of the figure. The spatial frequency sinusoidal pattern for $f=5{\mathrm{cm}}^{-1}$ was oriented horizontally. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.

Fig. 9

SFD Mueller matrix BRDF images of a bovine thalamus: (a) the Mueller matrix BRDF at $f=0{\mathrm{cm}}^{-1}$, (b) the real part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$, and (c) the imaginary part of the SFD Mueller matrix BRDF multiplied by a factor of 5 at $f=5{\mathrm{cm}}^{-1}$. The maximum value of the black and white scale used for $F_{\text{r},11}$ at $f=0{\mathrm{cm}}^{-1}$ is 3.5 times the maximum value for $F_{\text{r},11}$ of $f=5{\mathrm{cm}}^{-1}$. The scale for the normalized SFD Mueller matrix elements is shown at the bottom of the figure. The spatial frequency sinusoidal pattern for $f=5{\mathrm{cm}}^{-1}$ was oriented horizontally. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.

Fig. 10

SFD Mueller matrix BRDF images of a bovine cerebrum: (a) the Mueller matrix BRDF at $f=0{\mathrm{cm}}^{-1}$, (b) the real part of the SFD Mueller matrix BRDF at $f=5{\mathrm{cm}}^{-1}$, and (c) the imaginary part of the SFD Mueller matrix BRDF multiplied by a factor of 5 at $f=5{\mathrm{cm}}^{-1}$. The maximum value of the black and white scale used for $F_{\text{r},11}$ at $f=0{\mathrm{cm}}^{-1}$ is three times the maximum value for $F_{\text{r},11}$ of $f=5{\mathrm{cm}}^{-1}$. The scale for the normalized SFD Mueller matrix elements is shown at the bottom of the figure. The spatial frequency sinusoidal pattern for $f=5{\mathrm{cm}}^{-1}$ was oriented horizontally. The field of view of the images is $1.1\mathrm{cm}\times 1.1\mathrm{cm}$.