Setup for the liquid phantom experiments.

<p>The inclusion used was a black rod of 3.5 mm diameter. The rod was varied in depth (A), rotated in the x-y plane (B), tilted in x-y and z direction (C). A second rod was also used, at a different depth than the first rod, and intersecting the other one on a projection on the x-y plane (D).</p

Depth curve.

<p>The measured shift α is translated into the depth z/d₀ by using the relationship between α and z/d₀ obtained using diffusion theory. The depth curves shown here are based on different background optical properties, as indicated in the figure.</p

Experimental result of the vessel-structured rods located at depths z₁ = 16 mm and z₂ = 48.5 mm.

<p>(A) shows the averaged second derivative image overlaid with the recovered depth values. The histogram of the calculated depths for all pixels of the structure is shown in (B). The dotted bell curve corresponds to the actual depth location and the width to the error in depth based on 1 pixel uncertainty in finding the value of α<b>δD</b>.</p

Basic principles of the approach to depth discrimination for parallel-plate, transmission imaging of the breast.

<p>In panel (A), D_-<b>δD</b> is the detection fiber offset along –<b>δD</b>, and D_+<b>δD</b> is the detection fiber offset along +<b>δD</b>. The distance between the two fibers is δD. Panel (B) shows the transmitted intensity profiles (I_+<i>δD</i> and I_-<i>δD</i>) for both detectors as they are scanned along the <b>δ</b><b><i>D</i></b> direction. The two optical inhomogeneities located at different depths <i>z</i>₁ and <i>z</i>₂, respectively, appear shifted along <b>δ</b><b><i>D</i></b> by different amounts α₁δ<i>D</i> and α₂δ<i>D.</i></p

Experimental results from a rod inclusion at different depths.

<p>The figure illustrates clearly the offset between the location of the detected rod in the images collected with the two detectors, and how it increases with the depth of the inclusion.</p

Experimental result of the vessel-structured rods located at depth z = 48.5 mm.

<p>(A) shows the averaged second derivative image overlaid with the recovered depth values. The histogram of the calculated depths for all pixels of the structure can is shown in (B). The dashed line is a Gaussian centered at the actual location of the rod.</p

Geometrical configurations used for Monte Carlo simulations.

<p>(A) Spherical inclusions at different depths (12 and 28 mm). (B) Intersecting cylindrical inclusions located at different depths (12 and 28 mm). In both cases, the total thickness (i.e. the separation along <b>z</b> of the source S and the two detectors D_-<b>x</b> and D_+<b>x</b>) is 40 mm.</p

Vessel like structures.

<p>For mimicking more complex structures, black rods, shaped in a more vessel like fashion, have been used. Experiments were run with the deeper structure alone as well as both together.</p

Inner product approach to depth discrimination.

<p>The approach is based on binary versions of the second-derivative images measured with the two detectors, [<b>B</b>_-δD(<b>x</b>)] and [<b>B</b>_+δD (<b>x</b>)] detectors. (A) For specific inhomogeneities at <b>x</b>₁ and <b>x</b>₂), we consider 4 mm×4 mm windows <b>B</b>_-δD(<b>x</b>₁) and <b>B</b>_-δD(<b>x</b>₂)centered at <b>x</b>₁ and <b>x</b>₂, and (B) a set of 4 mm×4 mm windows shifted along <b>δD</b> by β<b>δD</b> (with 0≤ β ≤1). (C) When the inner product <b>B</b>_-δD(<b>x</b>_i) <b>B</b>_+δD(<b>x</b>_i+β_i,max<b>δD</b>)] shows a maximum, we set α_i = β_i,max.</p

Experimental results from the rod inclusions seen in <b>Figure 5</b>.

<p>In 9A and 9B, the actual depth is shown in black and the measured depths are shown in dark grey with error bars in light grey. (C) shows the tilted rods, where the actual rod is shown in black, the measured one is displayed with the thick grey line and the depth dependent error by the thin grey lines. (D) shows the second derivative image of D_-<b>x</b>, overlaid with the pixelwise calculated depth.</p