]> PMI: SD Structure

The SD Structure

The SD structure is used to store all the information about the "imager" being modeled, including source position, detector position, measurement order, and optical wavelength (information about the imaging volume is stored in the Medium structure, described here). Fields that are not needed (for example, the modulation frequency SD.ModFreq for modeling a time-domain imager) do not need to be initialized.

Summary of SD Structure Fields

SrcPos	Source Positions [cm]
SrcAmp	Complex Source Amplitude
DetPos	Detector Positions [cm]
DetAmp	Complex Detector Amplitude
Lambda	Measurement wavelengths [nm]
ModFreq	Modulation Frequency [MHz]
TimeDelay	Delay to start of time gate [sec]
TimeGateWidth	Width of time gate [sec]
SrcOffset	Source Temporal Offset [sec]
DetOffset	Detector Temporal Offset [sec]
MeasList	Measurement List

Detailed Descriptions

SD.SrcPos and SD.DetPos

The $(x, y, z)$ source and detector locations are specified as $N \times 3$ matrices in the fields SD.SrcPos and SD.DetPos respectively. All lengths are in centimeters. For imaging geometries with a planar interface (i.e., everything except the "infinite" geometry), the air-tissue interface defines the $z = 0$ plane. Other than this, the origin of the coordinate system is completely arbitrary (the forward problem is translationally invariant so only the relative separations matter).

Except in the "infinite" imaging geometry, all fibers must be placed on the air-tissue ( $z = 0$ or $z = Z$ ) interface. Fibers that are not an in interface will be silently moved to the nearest interface.

All fibers have zero NA, zero radius, and point into the medium along the $\pm z$ direction.

SD.SrcAmp and SD.DetAmp

SD.SrcAmp and SD.DetAmp are matrices which hold the source amplitude and detector coupling coefficients respectively. For frequency-domain imagers, these are complex numbers (magnitude and phase), otherwise they should be real-valued and strictly positive. The size of the matrices are $N \times N_{wvl} \times N_{frq} \times$ where $N$ is the number of sources [detectors] defined in SD.SrcPos [SD.DetPos], $N_{wvl}$ is the number of wavelengths defined in SD.Lambda and $N_{frq}$ is the number of frequencies defined in SD.ModFreq (or $1$ if SD.ModFreq does not need to be defined).

Because every measurement involves both a source and a detector, only the product SD.SrcAmp(iSrc,iWvl,iFrq)*SD.DetAmp(iDet,iWvl,iFrq) can be observed (for whatever iSrc, iDet, iFrq, iWvl is appropriate to a given measurement) and not the individual SD.SrcAmp and SD.DetAmp components (doubling all the SD.SrcAmp and halving all the SD.DetAmp leaves the final measurement unchanged). This indeterminacy is intrinsic to the forward problem. The product of the source and detector amplitudes has dimensions of Watts (detected fluence times the active area of the detector).

SD.Lambda

SD.Lambda is a vector of imaging wavelengths. For fluorescence measurements, SD.Lambda contains both excitation and emission wavelengths and the measurement list is used to distinguish between the two processes. Wavelengths should be specified in nanometers.

SD.ModFreq

For frequency-domain imagers, the vector SD.ModFreq holds the source modulation frequencies, in Megahertz.

SD.TimeDelay

For time-domain imagers, the time $t = 0$ is, by definition, the time when the light enters the tissue. SD.TimeDelay gives the time interval between when the light entered the medium and the start of the measurement. SD.TimeDelay may be negative, although the intensity at negative times is always zero.

For correlation measurements, SD.TimeDelay is the relative delay between the two events (whatever they might be).

For both time-domain imaging and correlation imaging, the time delay should be specified in seconds.

SD.TimeGateWidth

For gated time-domain detectors, SD.TimeGateWidth is the width of the gate, in seconds (a step gate response is implicitly assumed). For photon counting systems or other binned detectors, SD.TimeGateWidth is the width of the individual bins (again, a step response is implicitly assumed). If the gate width is set to 0.0, then the convolution of the forward problem with the detector gate is skipped entirely (since a gate width of zero makes no sense experimentally).

SD.SrcOffset and SD.DetOffset

The delays in SD.TimeDelay assume that all source/detector fibers introduce exactly the same delay. In practice, the fibers all have slightly different lengths which leads to temporal fiber-to-fiber variation. SD.SrcOffset and SD.DetOffset are matrices of delay corrections that provide a way to model small fiber length variations on a per-source and per-detector basis. The actual time that the light enters the medium is 0+SD.SrcOffset and the time that the detector begins collecting light is SD.TimeDelay+SD.DetOffset.

All temporal offsets are given in seconds. The size of the matrix SD.SrcOffset (SD.DetOffset) is $N_{src} \times N_{wvl}$ ( $N_{\det} \times N_{wvl}$ ).

SD.MeasList

The measurement list is a table of indicies into the other SD fields that describes the parameters to use for each experimental measurement. The measurement list is explained in more detail here.