]> PMI: Medium Structure

The Medium Structure

The Medium structure defines the optical properties, imaging geometry, the volume to be reconstruction (where appropriate), and all the known optical perturbations in the volume (if any). Together with the SD structure, the Medium structure is the fundamental structure for defining the forward and inverse problems to be solved by the PMI toolbox.

Summary of Medium Fields

Muao	Average Optical Absorption [1/cm]
Muspo	Average Transport Scattering Length [1/cm]
idxRefr	Index of Refraction [-]
Geometry	Imaging Geometry
Slab_Thickness	Thickness in Slab Models [cm]
CompVol	Specify Voxels in Forward Matrix
Object	Define Perturbations

Detailed Descriptions

Medium.Muao, Medium.Muspo, Medium.idxRefr

Medium.Muao, Medium.Muspo, and Medium.idxRefr define the average optical properties of the tissue. Medium.Muao is the optical absorption coefficient (inverse absorption length) in 1/cm. Medium.Muspo is the transport scattering coefficient (inverse transport scattering length) in 1/cm. Medium.idxRefr is the index of refraction. The diffusion approximation breaks down for small scattering coefficient, so Medium.Muspo should be at least 1.0. While the diffusion approximation is valid, the infinite slab solution can fail to converge if the absorption coefficient is too small so small absorption coefficients should be avoided as well.

Medium.Geometry, Medium.Slab_Thickness

Medium.Geometry is a text string that defines the imaging geometry to be used. Currently supported values are 'infinite' (infinite medium, no boundaries), 'semi' (semi-infinite medium, boundary at $z = 0$ ), and 'slab' (infinite slab, boundaries at $z = 0$ and $z = Z$ ).

For infinite media, Medium.Slab_Thickness is not used. For semi-infinite medium, the sign of Medium.Slab_Thickness is used to determine whether the tissue is in the $+ z$ or $- z$ direction (if the thickness is positive, then the tissue is on the $z > 0$ side of the plane). For slab geometries, Medium.Slab_Thickness specifies both the thickness of the slab and whether it lies above or below the $z = 0$ plane (the tissue is located between $z = 0$ and $z = Z$ where $Z$ is given by Medium.Slab_Thickness).

Medium.CompVol

Medium.CompVol is a structure that declares the volume being imaged. There is more than one way to specify the volume; the string Medium.CompVol.Type tells the toolbox which method is being used. The values of Medium.CompVol.Type currently recognized by the toolbox are "uniform", "computed", and "list".

If Medium.CompVol.Type is set to "uniform" then the volume of the voxels (assumed to be the same for all voxels) is calculated by multiplying together Medium.CompVol.XStep, Medium.CompVol.YStep, and Medium.CompVol.ZStep. The centers of the voxels are at the $(x, y, z)$ locations obtained by calling the Matlab function meshgrid() with the vectors Medium.CompVol.X, Medium.CompVol.Y, and Medium.CompVol.Z as its arguments. In other words, there is one voxel for every possible combination of the elements of Medium.CompVol.X, Medium.CompVol.Y, and Medium.CompVol.Z. NOTE: X, Y, and Z must contain regularly-spaced intervals. The toolbox is not smart enough to detect non-uniform grids for you.
"Uniform" types, however, are cumbersome and they also contain redundant information. They exist largely as for historical reasons and will hopefully someday find their long-deserved death. The simpler way to set up the imaging volume is with the "computed" type. In this case, Medium.CompVol.XStep, Medium.CompVol.YStep, and Medium.CompVol.ZStep not only give the volume of the voxels but also the spacing between adjacent voxels. For computed volumes, Medium.CompVol.X, Y, and Z, instead of specifying all values, specify just the end-points and the given step sizes are used to fill in all the other values. specify just the end-points of the list; the interval is taken For example, if Medium.CompVol.XStep is 1.0 and Medium.CompVol.XStep is [0.5, 3.0] then all the voxels will have X-coordinates of 0.5, 1.5, or 2.5.
Finally, if non-uniform grids are absolutely essential, Medium.CompVol.Type can be set to "list". Now, Medium.CompVol.X, Medium.CompVol.Y, and Medium.CompVol.Z are vectors that directly specify the $(x, y, z)$ location of every voxel and the vector Medium.CompVol.Volume gives the volume at every voxel (which need not be constant).

Medium.Object

Medium.Object is a vector of cells that contain structures defining perturbations to the optical properties. Each cell defines a single perturbation. All lengths are in centimeters, all optical properties are in inverse-centimeters. Perturbations should never overlap, but the toolbox is not smart enough to check for this explicitly. Every structure contains a field Medium.Object{}.Type that specifies what kind of perturbation it describes. The legal values for Type are "sphere", "block", and "image".

Object Field Structure Summary
Type	Field	Description
"Sphere"	Pos	Coordinates of center of sphere, $(r_{x}, r_{y}, r_{z})$
	Radius	Radius of the perturbation
	Mua	Vector of absorption coefficients, $μ_{a} (λ)$
	Musp	Vector of scattering coefficients, $μ_{s}^{'} (λ)$
"Block"	Pos	Coordinates of center of sphere, $(r_{x}, r_{y}, r_{z})$
	Dims	Lengths of each side of the block, $(l_{x}, l_{y}, l_{z})$
	Mua	Vector of absorption coefficients, $μ_{a} (λ)$
	Musp	Vector of scattering coefficients, $μ_{s}^{'} (λ)$
"Image"	Mua	Matrix of voxel absorption coefficients, $μ_{a} (:, λ)$
"Image"	Musp	Matrix of voxel scattering coefficients, $μ_{s}^{'} (:, λ)$

For spherical perturbations, the Object fields are Pos, Radius, Mua, and Musp. The position vector (to the center of the sphere) is in Object.Pos and the radius of the sphere is in Object.Radius. The optical properties of the sphere, at every wavelength, are recorded in Object.Mua and Object.Musp. Note that these are the actual optical properties and not the perturbations relative to background. Finally, the shape of the sphere is mapped on to the grid of voxels before the perturbation is calculated, so pixelation effects can become important when the radius becomes comparable to the voxel spacing.

Rectangular (block) perturbations are very similar to spherical perturbations. Again, Object.Mua and Object.Musp specify the optical properties and Object.Pos specifies the center of the perturbation. The final field, Object.Dims, is a vector that specifies the length of each side of the box $(l_{x}, l_{y}, and l_{z})$ .

The final perturbation type, "image", specifies the optical properties at every voxel and at every wavelength. Again, these are the actual optical properties and not the perturbations relative to background. The rows of the matrix contain the different voxels, the columns hold the different wavelengths. All wavelengths must be defined even if they aren't used in the measurement list.