1.1.

Illumination and Light Capturing Methods

In DOT systems different methods for illumination and light-capturing have been established. In DOT systems, two different setups can be distinguished: the first type employs noncontact illumination and light capturing while the second system type uses optical fibers in direct contact to the tissue to inject and detect light.^6,7,10 The optical fiber applications are limited with respect to functionality due to the need of contact gel in suitable containers, inflexibility, and high maintenance requirements. Furthermore, an integrated real shape 3-D reconstruction of tissues or phantoms embedded in contact gel is difficult or even impossible.^8,11 In noncontact DOT, problems arise due to refraction at surfaces, reflection, and intensity variations caused by the irregularity of the objects geometry.

1.2.

Reconstruction of Inner Tissue Structure

Mathematical models were developed to describe light transport inside tissue by employing finite element methods (FEM) or Monte Carlo simulations for image reconstruction and determining differences in absorption and scattering coefficients.^12–18 The use of such methods is strongly simplified due to the existence of highly sophisticated software toolboxes, e.g., TOAST (http://web4.cs.ucl.ac.uk/research/vis/toast/intro.html) or NIRFAST (http://www.dartmouth.edu/~nir/nirfast/), that offer a broad variety of adjustable parameters.¹⁹ Current methods for mesh creation are mainly based on segmented pre-MRI or CT scans, or rough approximations of the surface.^20–22 However, for a more accurate reconstruction, precise knowledge of the surface is inevitable.

1.3.

3-D Surface Scans and Reconstruction of the Object Shape

In addition to the development of reconstruction software, different surface capturing methods have been employed. DOT systems with integrated 3-D cameras, holographic scanners, or photoluminescence plates were developed. Another method to capture the shape of the object is to process pre-MRI or CT scans.^11,20–22 These systems have disadvantages regarding accuracy and/or handling, expenditure of time, availability and operating costs. For example, in semitransparent objects, 3-D cameras cannot distinguish between information from the surface and light originating from the subsurface. Photoluminescence plates capture only a shadow image of the object disregarding fine details of the surface.^3,8,12,19 Structured light 3-D scanners, which are widely used in a lot of industrial applications,^23–25 offer a cheap and flexible option for integration of a 3-D surface scanner into a DOT system. Libraries such as “Open Computer Vision” (open CV, http://opencv.willowgarage.com/wiki/) or “The Point Cloud Library” (PCL, http://pointclouds.org/) provide a multitude of suitable open source software components for utilization in optical imaging applications.²⁶

In this paper we present an approach for 3-D surface reconstruction of semi-transparent objects imaged by a DOT system, using a structured light projection setup in combination with polarization difference imaging (PDI). Combining these techniques allows for contactless image acquisition and also faster mesh generation for FEM-based image reconstruction algorithms.

2.1.

Polarization Difference Imaging

PDI is a relatively simple and fast technique, which allows the separation of light reflected by the real surface of an object from the signal originating from the subsurface.

In effect, in nonbirefringent media ballistic scattering does not alter the polarization state of light, while nonballistic scattering results in random polarization. By analyzing the polarization state of the reflected light, the real surface of the object can be extracted. Nevertheless, tissue penetration depth is correlated to multiple scattering events and inter-reflections ultimately resulting in a loss of polarization.

If polarizer and analyzer are aligned in the same orientation, ballistic scattered photons are recovered. To decrease the noise caused by photons randomly polarized in the same manner as the incident light due to inelastic scattering, the analyzer is turned orthogonal to the polarizer and the measured signal is subtracted. The calculated intensity of ballistic photons is

2.2.

Structured Light 3-D Reconstruction

A cloud of points on the object’s surface is captured using ray-plane intersection, which is then triangulated to obtain a discrete number of small surface elements. For the first step, gray-coded fringe patterns are projected onto the object. In the camera plane, the stripes seem shifted and curved due to the topology of the object. Here every stripe in the projected image is identified in the captured image by its binary gray-code.³¹ Provided the positions of camera and projector are known, the 3-D object position within the coordinate system of the camera is obtained by calculating the intersection point of the plane given by a projector stripe and the light ray detected by the camera.³² While examining tissue, it cannot be assumed that only direct surface reflections of fringe pattern are observed. Rather, photons originating from subsurface scattering must be accounted for. To this end, de-scattering properties of phase-shifting or PDI, which is used in this work, can be applied.²⁸

By rotating the object and repeating the previous procedure, local 3-D reconstructions from different viewpoints are acquired and can be merged to obtain global surface information. This data is used to provide boundary information for FEM-mesh creation on the one hand and to normalize images acquired during a DOT scan on the other hand (see Fig. 1).

An example for an experimental noncontact DOT setup with integrated PDI and structured light system is shown in Fig. 2.

Fig. 2

Experimental setup for a noncontact DOT system with integrated PDI and structured light projection system (on the right hand side). The laser beam describes the transmitted light path of the system (left-hand side). Transmitted light and fringe pattern can be captured by the same camera system. For 3-D surface shape reconstruction, the polarizer-analyzer orientation can be adjusted between 0 and 90 deg, and the object can be illuminated with fringe patterns by the projector.

2.3.

Workflow

The workflow of a DOT system is illustrated in Fig. 3. In the first step, the object is rotated on a stage while fringe pattern image sequences are collected to reconstruct a 3-D surface model. The same detector is used subsequently to acquire images of the object trans-illuminated by the laser. In the next step, the surface model data is needed for mesh generation on the one hand and intensity normalization of the images, captured in trans-illumination mode, on the other. Finally, the mesh is used for FEM-based solving of the forward model of light propagation within the object.¹⁹

Fig. 3

Workflow of a DOT system with integrated PDI and structured light projection. Hardware control, image acquisition, data reconstruction, and data analysis can be performed within one software application.

If the deviation between the solution of the forward model and the captured transmitted light data is minimized by parameter variation, the inversion of the forward problem can give an estimate for the distribution of the light absorption and scattering parameters ${\mu }_a$ and ${\mu }_s$. All of the components are integrated in one experimental setup.

2.4.

From Point Clouds to Mesh

In order to provide suitable information for tissue reconstruction applications like NIRFAST and TOAST, surface meshes have to be constructed out of the acquired point clouds. Such meshes usually consist of polygons, which in most cases form triangles for easier storage, rendering, and further processing of the data. Depending on the required accuracy, the density of points can be reduced first to reduce computing time. For the point cloud and surface reconstruction operations, the “Point Cloud Library”²⁶ is used. It provides implementations of several algorithms for both surface reconstruction and point cloud filtering/smoothing. For numerical iterative optimization purposes the “GNU Scientific Library” is used.³³

3.1.

Accuracy of the Method for Nontransparent Objects

To determine the accuracy of the 3-D scanning unit, a metallic cylinder of known radius $r_{\mathrm{cyl}}=7.7\mathrm{mm}$ was scanned from different angles. The resulting point clouds were merged into a 360-deg surface cloud. The final point cloud is shown in Fig. 4. For this measurement, the cylinder was aligned so that its symmetry axis coincides with the system’s rotation axis. Since the orientation of the rotation axis is known from the calibration procedure, it is possible to compare the distance of every point to the rotation axis with the actual cylinder radius.

Fig. 4

Point cloud reconstruction of a metal cylinder with radius $r_{\mathrm{cyl}}=7.7\mathrm{mm}$.

As presented in Fig. 5, the computed point cloud is in good agreement with the real shape of the cylinder. The mean error is 3.2% with a standard deviation of 2%, which is a satisfying result.

Fig. 5

Measurement of a test cylinder made of metal ($r_{\mathrm{cyl}}=7.7\mathrm{mm}$). The upper plot shows the computed radius for every point in comparison to the real cylinder radius, which is drawn as dashed line. The lower plot illustrates the relative error for every point. The mean error is 3.2% (dashed line) with a standard deviation of 2%. Note that the point indices are sorted by ascending $z$-values.

3.2.

Accuracy of the Method for Semitransparent Objects

Similar tests were performed on a semitransparent Agar-Agar cylinder (2% Agar-Agar Kobe I, Company Carl Roth GmbH Karlsruhe) of radius $r_{\mathrm{cyl}}=12.92\mathrm{mm}$. In order to determine the influence of PDI on the quality of the 3-D reconstruction, these measurements were carried out with and without using the PDI method. The following images illustrate the resulting point clouds of both measurements in comparison.

Figure 6 demonstrates that the absence of PDI leads to major reconstruction errors. This observation can be quantified by analyzing the cylinder radius as described in Sec. 3.1. As shown in Fig. 7(a), the usage of the PDI method suppresses most of the reconstruction errors. In addition, using PDI reduces the mean relative error from 19.3 to 7.4%. However, the errors still show a larger dispersion about the mean as compared to the metal cylinder. All the quantitative results are summarized in Table 1.

Fig. 6

(a) Point cloud reconstruction of an Agar-Agar cylinder with a radius $r_{\mathrm{cyl}}=12.92\mathrm{mm}$ using PDI technique. (b) Point cloud of the same cylinder measured without using PDI.

Fig. 7

Measurements of an Agar-Agar cylinder ($r_{\mathrm{cyl}}=12.92\mathrm{mm}$) with and without PDI. The dashed lines indicate the ideal cylinder radius in the upper and the mean errors in the lower plots (a) PDI measurement of an Agar-Agar cylinder. The mean error is 7.4% with a standard deviation of 7.9% (b) NonPDI measurement of the same cylinder. Here the mean error is 19.3% with a standard deviation of 60.5%. Note the different scaling of the y-axis. Point indices are sorted by ascending $z$-values in both cases.

Table 1

Validation results.

Based on these results, we conclude that the usage of PDI clearly improves the surface scans. However, our point cloud reconstructions of semitransparent objects do not reach the quality of nontransparent objects.

3.3.

Meshing of Nontransparent Objects

Both a photography of a nontransparent object (here a plastic mouse phantom) and the corresponding point cloud captured with the introduced setup via structured light, are shown in Fig. 8(a) and 8(b), respectively.

Fig. 8

(a) Photo of the phantom. (b) The point cloud image of the phantom. (c) and (d) Triangulated surface meshes with different node distances.

Such surface point clouds captured from different angles were merged into a 360-deg surface point cloud of the sample. We then used a triangulation algorithm implemented in NIRFAST to find a 3-D volume mesh for further processing. Preliminary results are shown in Fig. 8(c) and 8(d) with different node distances.

3.4.

Meshing of Semitransparent Objects

The main application of our approach is to handle tissue-like and semi-transparent objects using PDI. Figure 9(a) and 9(b) show both a photography of a typical HARIBO Gold-bear (HARIBO of America, Inc., Baltimore, MD) and its corresponding mesh as calculated from point cloud data obtained with our setup. As shown in Sec. 3.2, the absence of PDI leads to significant reconstruction errors and therefore the best results can be achieved by using PDI within a DOT system.

Fig. 9

(a) Photo of a typical HARIBO gold bear. (b) Volume mesh reconstructed from a PDI measurement of the same gold bear.