Sub-diffusive scattering parameter maps recovered using wide-field high-frequency structured light imaging.

This study investigates the hypothesis that structured light reflectance imaging with high spatial frequency patterns [Formula: see text] can be used to quantitatively map the anisotropic scattering phase function distribution [Formula: see text] in turbid media. Monte Carlo simulations were used in part to establish a semi-empirical model of demodulated reflectance ([Formula: see text]) in terms of dimensionless scattering [Formula: see text] and [Formula: see text], a metric of the first two moments of the [Formula: see text] distribution. Experiments completed in tissue-simulating phantoms showed that simultaneous analysis of [Formula: see text] spectra sampled at multiple [Formula: see text] in the frequency range [0.05-0.5] [Formula: see text] allowed accurate estimation of both [Formula: see text] in the relevant tissue range [0.4-1.8] [Formula: see text], and [Formula: see text] in the range [1.4-1.75]. Pilot measurements of a healthy volunteer exhibited [Formula: see text]-based contrast between scar tissue and surrounding normal skin, which was not as apparent in wide field diffuse imaging. These results represent the first wide-field maps to quantify sub-diffuse scattering parameters, which are sensitive to sub-microscopic tissue structures and composition, and therefore, offer potential for fast diagnostic imaging of ultrastructure on a size scale that is relevant to surgical applications.

volunteer exhibited γ -based contrast between scar tissue and surrounding normal skin, which was not as apparent in wide field diffuse imaging. These results represent the first wide-field maps to quantify sub-diffuse scattering parameters, which are sensitive to sub-microscopic tissue structures and composition, and therefore, offer potential for fast diagnostic imaging of ultrastructure on a size scale that is relevant to surgical applications.

Introduction
Light scattering in biological tissue is a complex process that occurs as photons traverse index of refraction mismatches along their propagation path. The index mismatches are associated with tissue morphology (e.g. cytoskeletal arrangement) and cellular ultrastructure (e.g. size and shape of nucleus, mitochondria, other cytoplasmic organelles). Measurements of scattering remission spectra have shown sensitivity to sub-cellular morphological changes in biological tissue [1][2][3][4][5][6][7][8]; these observations support the use of scattering as an endogenous and label-free contrast mechanism to differentiate between tissue types [8,9]. Scattering spectroscopy has important clinical implications for the diagnosis of cancers [10][11][12][13][14], and for the assessment of surgical margins to guide tumor resections [15][16][17]. While scatter remission spectra are sensitive to biological structure and morphology, the biological information that is encoded in collected spectra is dependent on the light transport regime that is sampled. Scattering interactions between photons and tissue can be described by a basic set of parameters including the frequency of scattering events, given by the scattering coefficient ( )  with the size distribution of scattering centers in bulk tissue [20], providing a noninvasive characterization of biological tissue structure; however, these measurements are averaged over a large tissue volume and are insensitive to changes in local tissue microstructure. Localized measurements of scatter remission have been developed to interrogate small tissue volumes of interest [6,21,22]. When near the source, they collect a population of photons that have experienced few scattering events, making the signal sensitive to the direction of individual scattering events [23-25]; light in this transport regime is termed sub-diffuse. Model-based interpretation of sub-diffuse remission spectra requires both s μ ′ and a parameter that describes the phasefunction-dependent probability of large-angle backscatter events which are likely to be collected during reflectance measurements [26][27][28]. For forward-directed scattering media, such as in biological tissue, the relative probability of large backscattering events is proportional to the weighted ratio of the 1st and 2nd Legendre moments of ( ) s P θ , given by 1 g and 2 g , as [24]. Approaches that have quantitated sub-diffusion scattering parameters in biological tissue have classically been limited to the sampling of small volumes, usually sub-mm [29,30]. Imaging of localized scatter has been achieved by mechanically scanning a fiber optic [6], and results suggest that contextual interpretation of heterogeneous spatial-variations in scatter remission may discriminate between tissue types and potentially guide clinical decisions [15]. However, these approaches can be timeintensive and studies published to date did not interpret the signal in terms of underlying scattering properties. This paper investigates the hypothesis that structured light imaging can be used to sample a sub-diffuse reflectance signal in a wide-field acquisition geometry and quantitate scattering properties relevant to anisotropic transport. for the non-absorbing case), a range of frequencies that limits the sampling of photons which experience few scattering events. The first assumption was addressed by Erickson et. al [34] who presented a Monte Carlo look up table to analyze SFDI signals in highly absorbing tissues. To date, no study has directly addressed the second assumption and quantitatively analyzed sub-diffuse remission collected from structured illumination imaging, although related work published by Konecky et. al [35], considered rotation of the incident illumination pattern to identify directional preferences for scatter within a wide field of view. This unique illumination pattern was characterized as a special case of diffuse light collection that was sensitive to the anisotropic orientation of scatterers on the order of the transport length ( ) quantitative scattering parameters. Here, we consider structured illumination imaging patterns with high spatial frequencies (i.e. X f >0.33 s μ ′ ) to sample reflectance in the sub-diffuse light transport regime and provide an analysis to extract wide field quantitative maps of subdiffusion scattering parameters that are sensitive to meso/micro-scale tissue structure, e.g. s μ ′ and γ .
In this study, wide-field imaging of a localized and sub-diffuse scatter signal is achieved by proper selection of the sampled x f which determines the sensitivity to depth within the medium and allows dynamic selection of the sampled transport regime (i.e. diffuse or subdiffuse). Low frequency patterns ( x f~0) approximate a uniform wide-field illumination, and the resulting signal is dominated by diffusely scattered light that has travelled a wide range of depths prior to remission. As x f is increased, the incident pattern is preserved at shallower depths, localizing the signal towards the surface; this principle serves as the basis for depthresolved tomography via SFDI [31], and more recently for direct sampling of scatter originating from the superficial tissue surface by using a single high frequency image [36]. Additionally, at high frequencies (

Structured illumination imaging device
A commercially available SFDI device (Modulated Imaging Inc., Irvine, CA, USA), shown schematically in Fig ( ) was calculated from the set of intensity images as at each pixel in the sampled field whereas the spatially variant DC amplitude ( ) The calibrated demodulated reflectance ( )

Monte Carlo model of structured light imaging
This study utilized a customized version of CUDA-accelerated Monte Carlo code that has been described in detail previously [37]. The model geometry was constructed to mimic a point-source incident on the air interface of a semi-infinite turbid medium with thickness of 100 cm and a maximal radial distance of 20 cm from the source location. The index of refraction of the medium and air were specified as medium n = 1.37 and air n = 1.0, respectively. Both source and detector were oriented normal to the medium/air interface with numerical apertures specified as NA = 0.15. Photons that scattered within the medium and remitted across the medium/air interface within the cone of acceptance for the detector were collected. The simulation returned the radial distance between incidence and remission ( ) ρ , which was discretely binned with a spacing of 0.1 mm.
Simulations were performed over a wide range of scattering parameters. The modified Henyey-Greenstein form of ( ) s P θ was selected to allow independent modification of 1 g and 2 g [38]. Optical properties were specified to simulate a range of s where the fitted parameters include η , which represents the collection efficiency of the detector, and i ζ , for [1,2,3,4]    wavelength range as defined previously by Michaels et. al [45]. Structured light images were acquired with the phantoms arranged on a black tray where the diameter of each sampled phantom was 25 mm within the full field of view [140 mm x 114 mm]. Images were generated for all phantoms in a single field of view with an exposure time that was automatically adjusted for each sampled wavelength, and each intensity was corrected for differences in exposure time. Images of phantoms were analyzed using Eq. Structured light imaging was also performed on the skin of a healthy volunteer. The imaged field of view included scar tissue from a previous superficial injury that had since healed. Color photographs of the sampled area were also taken. The skin measurements were analyzed using Eq. (6) from the full set of Monte Carlo simulations (i.e. all 18 phase functions), and reflectance maps were analyzed on a pixel-by-pixel basis.

Preliminary in vivo imaging of a superficial scar
Structured light imaging was performed on a healthy volunteer who had a superficial scar located on the posterior side of the left hand near the distal end of the second metacarpal bone, as shown in Fig. 6 ) images of demodulated reflectance intensity. The scar is distinguished by a bright area of contrast on the high frequency image in 6(c) and is highlighted by the red arrow; this contrast is absent in the diffuse image in 6(b). Figures 6(d) and 6(e) show spatial maps of s μ ′ and γ at 730 nm, respectively. Spectral descriptions of both parameters are provided in Figs. 6(f) and 6(g), with these spectra originating from point locations denoted by arrows: blue (indicating normal skin) and red (indicating the scar). The map of s μ ′ does not provide obvious contrast between the superficial scar and surrounding normal tissue. However, substantial contrast is observed in γ between normal and scar tissue both in the spatial map and spectral profiles, with a maximum difference of 25% at 850 nm. These data suggest that imaging of sub-diffuse scattering parameters may provide

Discussion and conclusions
This study investigated the use of structured light to image scattering properties quantitatively in turbid media that are relevant to anisotropic transport in the sub-diffusion regime. Monte Carlo simulated data were used to develop a semi-empirical model of demodulated reflectance, d R , in terms of dimensionless scattering expressed as absorption only introduces a 10% decrease in d R (data not shown). Previous work has shown that sub-diffuse scattering parameters can be estimated in the presence of strong absorbers by utilizing a model to estimate reflectance remission in the absence of absorption [39,40], a calculation that is informed by a basis set of chromophores, the specific absorption coefficients of the chromophores, and a model-based estimate of the photon path length within the medium [48,49]. In the present study the experimental device only samples four wavelengths, and does not provide adequate spectral information to fit both the scattering and absorption properties. Future investigations will consider optimization of the structured illumination design sample sets of wavelengths and spatial frequencies necessary to estimate scattering properties in the presence of strong biological absorbers.
It is also worth noting that the sub-diffusive imaging approach developed in the current study was tested and validated in homogenous optical media and then applied to heterogeneous tissue. The appropriateness of this transition is based on the principle that the sampled scatterers are relatively constant within the areas defined by the (local) spatial frequencies used in the illumination. Future investigations will consider the influence that structural heterogeneities (e.g. layered tissue) may have on the sub-diffuse parameter estimates.
The present study represents a proof-of-principle that structured light imaging can be used to map spatial variations in sub-diffuse scattering parameters quantitatively. While previous studies have achieved independent estimation of ( ) s μ λ ′ and metrics of the ( ) s P θ such as ( ) γ λ , they have been limited to microscopic fields of view (i.e. sub-mm length scale) [8,12,29,43]. The structured illumination imaging approach described here has three important benefits for imaging of scatter-based contrast in tissue: (1) the scatter properties are localized to the superficial tissue, (2) the sampled field of view is large (i.e. on the scale of tens of cm), and (3) measurement of remission at multiple spatial frequencies can be used to break the similarity relationship between scatter frequency and directionality. Independent assessment of spatial variations of multiple spectroscopically resolved parameters may provide a multidimensional basis for characterizing differences between tissue types.