Instrumentation calibration protocol

• US 6,529,846 B2
• Filed: 11/30/2000
• Issued: 03/04/2003
• Est. Priority Date: 11/30/2000
• Status: Expired due to Fees

• Current Assignee: The Research Foundation for The State University of New York (State University of New York)
• Original Assignee: The Research Foundation for The State University of New York (State University of New York)
• Inventors: Graber, Harry L., Barbour, Randall L.
• Primary Examiner(s): Bui, Bryan
• Application Number:
  US09/727,037
• Publication Number:
  US 20020095266A1
• Time in Patent Office: 824 Days
• Field of Search: 702/85, 702/94, 702/104, 702/127, 356/39, 356/43, 356/45, 356/435-438
• US Class Current: 702/104
• CPC Class Codes: G01D 18/00 Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00

Abstract

A system and method for determining the relative losses and/or efficiencies of the individual channels of a multi-channel measurement system, such as a multi-channel optical tomography system. The system and method provide several independent estimates of the losses associated with each of the plurality of source and detector components, whereby statistical analysis of the independent estimates can be used to reveal system errors or misalignments.

Claims

1. A method of calibrating a multi-channel measurement system comprising:

directing energy through a source channel into a calibrating target medium at a source location on the target medium, wherein the properties of the calibrating target medium are known;

measuring the energy emerging from the calibrating target medium through a plurality of detector channels at a plurality of detector locations on the calibrating target medium;

processing the measured energy using an iterative proportional fitting technique to determine a relative value of energy loss in the calibrating target medium;

determining a proportional energy loss associated with at least one of the source channel and the detector channel based on the measured energy and the relative value of energy loss in the calibrating target medium; and

adjusting the gain of at least one of the source channel and the detector channels based on the proportional energy loss wherein the gain compensates for losses in at least one of the source channel and detector channel during measurements of an actual target medium.

2. The method of claim 1 wherein the energy is directed into the calibrating target medium at a plurality of source locations and the energy emerging from the calibrating target medium is measured at a plurality of detector locations.

3. The method of claim 2 wherein the energy is directed through a plurality of source channels to the plurality of source locations and the energy emerging from the calibrating target medium is directed through a plurality of detector channels from the plurality of detector locations.

4. The method of claim 3 wherein, for energy directed into the calibrating target medium at each source location, the energy emerging from the calibrating target medium is measured at each detector location.

5. The method of claim 2 wherein the energy is directed into the calibrating target medium at the plurality of source locations in series.

6. The method of claim 2 wherein the measured energy forms a matrix, the matrix having a first and second axis comprising rows and columns of elements, the measured energy emerging from the calibrating target medium at each of the plurality of detector locations for energy directed into the calibrating target medium at a source location being elements aligned along the first axis of the matrix, the measured energy emerging from the calibrating target medium at a detector location for energy directed into the calibrating target medium at each of the plurality of source locations being elements aligned along the second axis of the matrix.

7. The method of claim 6 wherein the iterative proportionate fitting technique comprises applying the following equations in an alternating process to generate a sequence of matrices:

${\left(R^{\mathrm{\prime <br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},{\left(R^{\mathrm{″<br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}{\underset{i^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{i^{\mathrm{\prime <br><br>}}<br><br>j}^{\mathrm{\prime <br><br>}}},\mathrm{\dots <br><br>}.$

where R is the matrix and the elements in R are the detector location measurements r_ij at detector location j and source location i, the sequence of matrices being generated until the sum of the elements in each row and the sum of the elements in each column of the last matrix generated are substantially equal, each matrix in the sequence of matrices being generated from the elements of the previous matrix in the sequence.

8. The method of claim 7 wherein determining the proportional energy loss further comprises generating a resulting matrix by dividing each element of the matrix of the measured energy by each element of the last matrix in the sequence of matrices.

9. The method of claim 8 wherein the proportional energy loss in the source channel is:

$\frac{n_{\mathrm{ij}}}{\underset{i^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n_{i^{\mathrm{\prime <br><br>}}<br><br>j}},$

where n_ij are the elements of the resulting matrix, j is the detector location and i is the source location.

10. The method of claim 8 wherein the proportional energy loss in the detector channel is:

$\frac{n_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},$

where n_ij are the elements of the resulting matrix, j is the detector location and i is the source location.

11. The method of claim 1 further comprising generating a deviation of a modeled detector measurement from the measured energy at a detector location.

12. The method of claim 11 wherein the deviation is:

${\mathrm{\Delta <br><br>}}_{\mathrm{ij}}=100<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{r_{\mathrm{ij}}-\mathrm{\mu <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>s_i<br><br>m_{\mathrm{ij}}<br><br>d_j}{r_{\mathrm{ij}}}$

where Δ

_ij is the deviation, j is the detector location, and i is the source location, r_ij is the measured energy at detector location, s_im_ijd_j is the modeled detector measurement, and μ

is a normalization constant defined as $\mathrm{\mu <br><br>}=\underset{i,j}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{\mathrm{ij}}/\underset{i,j}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>s_i<br><br>m_{\mathrm{ij}}<br><br>d_j.$

13. The method of claim 1 wherein a plurality of proportional energy losses associated with at least one of a source channel and a detector channel are determined.

14. The method of claim 13 further comprising determining a deviation between the plurality of proportionate energy losses.

15. A method of calibrating a multi-channel measurement system comprising:

directing energy through a plurality of source channels, each source channel directing the energy into a calibrating target medium at a source location on the calibrating target medium;

measuring the energy emerging from the calibrating target medium using a plurality of detector channels at a plurality of detector locations on the calibrating target medium, the energy measurements being taken from the plurality of detector locations for each source location;

processing the measured energy using an iterative proportional fitting technique, wherein the iterative proportional fitting technique comprises applying the following equations in an alternating process to generate a sequence of matrices;

${\left(R^{\mathrm{\prime <br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},{\left(R^{\mathrm{″<br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}{\underset{i^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{i^{\mathrm{\prime <br><br>}}<br><br>j}^{\mathrm{\prime <br><br>}}},\mathrm{\dots <br><br>}$

where R is a matrix of elements r_ij of energy measurements at each detector location j for each source location i, the sequence of matrices being generated until the sum of the elements in each row and the sum of the elements in each column of the last matrix generated are substantially equal, each matrix in the sequence of matrices being generated from the previous matrix in the sequence;

generating a resulting matrix by dividing each element of the matrix of energy measurements by each element of the last matrix in the sequence of matrices;

determining a proportional energy loss in at least one of a source channel and a detector channel, wherein the proportional energy loss in the source channel is;

$\frac{n_{\mathrm{ij}}}{\underset{i^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n_{i^{\mathrm{\prime <br><br>}}<br><br>j}},$

and, wherein the proportional energy loss in the detector channel is;

$\frac{n_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},$

where n_ij are the elements of the resulting matrix, j is the detector location and i is the source location.

16. A system for calibrating a multi-channel measurement system, comprising:

a source channel at a source location on a calibrating target medium, wherein the source channel directs energy into the calibrating target medium, and wherein the properties of the calibrating target medium are known;

a plurality of detector channels at a plurality of detector locations on the calibrating target medium, wherein the detector channels measure the energy emerging from the calibrating target medium at a plurality of locations on the calibrating target medium;

a means for processing the measured energy using an iterative proportional fitting technique to determine a relative value of energy loss in the calibrating target medium;

a means for determining a proportional energy loss associated with at least one of the source channel and the detector channel based on the measured energy and the relative value of energy loss in the calibrating target medium; and

a means for adjusting the gain of at least one of the source channel and the detector channels based on the proportional energy loss, wherein the gain compensates for losses in at least one of the source channel and detector channel during measurements of an actual target.

17. The system of claim 16 wherein the energy is directed into the calibrating target medium at a plurality of source locations and the energy emerging from the calibrating target medium is measured at a plurality of detector locations.

18. The system of claim 17 wherein the energy is directed through a plurality of source channels to the plurality of source locations and the energy emerging from the calibrating target medium is directed through a plurality of detector channels from the plurality of detector locations.

19. The system of claim 18 wherein, for energy directed into the calibrating target medium at each source location, the energy emerging from the calibrating target medium is measured at each detector location.

20. The system of claim 17 wherein the energy is directed into the calibrating target medium at the plurality of source locations in series.

21. The system of claim 17 further comprising means for generating a matrix based on the measured energy, the matrix having a first and second axis comprising rows and columns of elements, the measured energy emerging from the calibrating target medium at each of the plurality of detector locations for energy directed into the calibrating target medium at a source location being elements aligned along the first axis of the matrix, the measured energy emerging from the calibrating target medium at a detector location for energy directed into the calibrating target medium at each of the plurality of source locations being elements aligned along the second axis of the matrix.

22. The system of claim 21 wherein the iterative proportionate fitting technique comprises applying the following equations in an alternating process to generate a sequence of matrices:

${\left(R^{\mathrm{\prime <br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},{\left(R^{\mathrm{″<br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}{\underset{i^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{i^{\mathrm{\prime <br><br>}}<br><br>j}^{\mathrm{\prime <br><br>}}},\mathrm{\dots <br><br>}$

where R is the matrix and the elements in R are the detector location measurements r_ij at detector locations and source location i, the sequence of matrices being generated until the sum of the elements in each row and the sum of the elements in each column of the last matrix generated are substantially equal, each matrix in the sequence of matrices being generated from the elements of the previous matrix in the sequence.

23. The system of claim 22 wherein determining the proportional energy loss further comprises means for generating a resulting matrix by dividing each element of the matrix of the measured energy by each element of the last matrix in the sequence of matrices.

24. The system of claim 23 wherein the proportional energy loss in the source channel is:

$\frac{n_{\mathrm{ij}}}{\underset{i^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n_{i^{\mathrm{\prime <br><br>}}<br><br>j}},$

where n_ij are the elements of the resulting matrix, j is the detector location and i is the source location.

25. The system of claim 23 wherein the proportional energy loss in the detector channel is:

$\frac{n_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},$

where n_ij are the elements of the resulting matrix, j is the detector location and i is the source location.

26. The system of claim 16 further comprising means for generating a deviation of a modeled detector measurement from the measured energy at a detector location.

27. The system of claim 26 wherein the deviation is:

${\mathrm{\Delta <br><br>}}_{\mathrm{ij}}=100<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{r_{\mathrm{ij}}-\mathrm{\mu <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>s_i<br><br>m_{\mathrm{ij}}<br><br>d_j}{r_{\mathrm{ij}}}$

where Δ

_ij is the deviation, j is the detector location, and i is the source location, r_ij is the measured energy at detector location, s_im_ijd_j is the modeled detector measurement, and μ

is a normalization constant defined as;

$\mathrm{\mu <br><br>}=\underset{i,j}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>r_{\mathrm{ij}}/\underset{i,j}{\sum <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>s_i<br><br>m_{\mathrm{ij}}<br><br>d_j.$

28. The system of claim 16 wherein a plurality of proportional energy losses associated with at least one of a source channel and a detector channel are determined.

29. The system of claim 28 further comprising means for determining a deviation between the plurality of proportionate energy losses.

30. A system for calibrating a multi-channel measurement system comprising:

a plurality of source channels, each source channel comprising an energy source and a source fiber, each source fiber having a first end for receiving energy from the energy source and a second end for directing energy into a calibrating target medium at a source location on the calibrating target medium;

a plurality of detector channels for measuring energy emerging from the calibrating target medium, each detector channel comprising a detector and a detector fiber, each detector fiber having a first end for receiving energy emerging from the calibrating target medium at a detector location on the calibrating target medium and a second end for delivering the energy to the detector;

means for processing the measured energy using an iterative proportional fitting technique, wherein the iterative proportional fitting technique comprises applying the following equations in an alternating process to generate a sequence of matrices;

${\left(R^{\mathrm{\prime <br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>r_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},{\left(R^{\mathrm{″<br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}{\underset{i^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>r_{i^{\mathrm{\prime <br><br>}}<br><br>j}^{\mathrm{\prime <br><br>}}},\mathrm{\dots <br><br>}$

where R is a matrix of elements r_ij of energy measurements at each detector location j for each source location i, the sequence of matrices being generated until the sum of the elements in each row and the sum of the elements in each column of the last matrix generated are substantially equal, each matrix in the sequence of matrices being generated from the previous matrix in the sequence;

means for generating a resulting matrix by dividing each element of the matrix of energy measurements by each element of the last matrix in the sequence of matrices;

means for determining a proportional energy loss in at least one of a source channel and a detector channel, wherein the proportional energy loss in the source channel is;

$\frac{n_{\mathrm{ij}}}{\underset{i^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>n_{i^{\mathrm{\prime <br><br>}}<br><br>j}},$

and, wherein the proportional energy loss in the detector channel is;

$\frac{n_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>n_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},$

where n_ij are the elements of the resulting matrix, j is the detector location and i is the source location.

31. Computer executable software code stored on a computer readable medium, the code for calibrating a multi-channel measurement system comprising:

code to direct energy through a source channel into a calibrating target medium at a source location on the calibrating target medium;

code to measure the energy emerging from the calibrating target medium through a detector channel at a detector location on the calibrating target medium;

code to process the measured energy using an iterative proportional fitting technique to determine a relative value of energy loss in the calibrating target medium; and

code to determine a proportional energy loss associated with at least one of the source channel and the detector channel based on the measured energy and the relative value of energy loss in the calibrating target medium.

32. Computer executable software code stored on a computer readable medium, the code for calibrating a multi-channel measurement system comprising:

code to direct energy through a plurality of source channels, each source channel directing the energy into the calibrating target medium at a source location on the calibrating target medium;

code to measure the energy emerging from the calibrating target medium using a plurality of detector channels at a plurality of detector locations on the calibrating target medium, the energy measurements being taken from a plurality of the detector locations for each source location;

code to process the measured energy using an iterative proportional fitting technique, wherein the iterative proportional fitting technique comprises applying the following equations in an alternating process to generate a sequence of matrices;

${\left(R^{\mathrm{\prime <br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>r_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},{\left(R^{\mathrm{″<br><br>}}\right)}_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}{\underset{i^{\mathrm{\prime <br><br>}}=1}{\overset{N}{\sum <br><br>}}<br><br>r_{i^{\mathrm{\prime <br><br>}}<br><br>j}^{\mathrm{\prime <br><br>}}},\mathrm{\dots <br><br>}$

where R is a matrix of elements r_ij of energy measurements at each detector location j for each source location i, the sequence of matrices being generated until the sum of the elements in each row and the sum of the elements in each column of the last matrix generated are substantially equal, each matrix in the sequence of matrices being generated from the previous matrix in the sequence;

code to generate a resulting matrix by dividing each element of the matrix of energy measurements by each element of the last matrix in the sequence of matrices;

code to determine a proportional energy loss in at least one of a source channel and a detector channel, wherein the proportional energy loss in the source channel is;

$\frac{n_{\mathrm{ij}}}{\underset{i^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>n_{i^{\mathrm{\prime <br><br>}}<br><br>j}},$

and, wherein the proportional energy loss in the detector channel is;

$\frac{n_{\mathrm{ij}}}{\underset{j^{\mathrm{\prime <br><br>}}}{\sum <br><br>}<br><br>n_{{\mathrm{ij}}^{\mathrm{\prime <br><br>}}}},$

where n_ij are the elements of the resulting matrix, j is the detector location and i is the source location.