## Adaptive feature specific spectroscopy for rapid chemical identification |

Optics Express, Vol. 19, Issue 5, pp. 4595-4610 (2011)

http://dx.doi.org/10.1364/OE.19.004595

Acrobat PDF (1444 KB)

### Abstract

Spectroscopic chemical classification based on adaptive, feature-specific measurements has been implemented and demonstrated to provide significant performance gain over traditional systems. The measurement scheme and the decision model are discussed. A prototype system with a digital micro-mirror device as the adaptive element has been constructed and validates the theoretical findings and simulation results.

© 2011 Optical Society of America

## 1. Introduction

2. W. Pearman and A. Fountain, “Classification of chemical and biological warfare agent simulants by surface-enhanced Raman spectroscopy and multivariate statistical techniques,” J. Appl. Spectrosc. **60**(4), 356–365 (2006). [CrossRef]

4. H. Liu, H. Zhong, N. Karpowicz, Y. Chen, and X. Zhang, “Terahertz spectroscopy and imaging for defense and security applications,” Proc. IEEE **95**(8), 1514–1527 (2007). [CrossRef]

5. K. Maquelin, T. van Vreeswijk, H. Endtz, B. Smith, R. Bennett, H. Bruining, and G. Puppels, “Raman spectroscopic method for identification of clinically relevant microorganisms growing on solid culture medium,” Anal. Chem. **72**(1), 12–19 (2000). [CrossRef] [PubMed]

6. K. Maquelin, C. Kirschner, L. Choo-Smith, N. Van den Braak, H. Endtz, D. Naumann, and G. Puppels, “Identification of medically relevant microorganisms by vibrational spectroscopy,” J. Microbiol. Methods **51**(3), 255–271 (2002). [CrossRef] [PubMed]

*adaptive feature specific spectrometer*(AFSS), overcomes the limitations posed by the traditional approaches. Unlike the traditional systems where measurements are made by sampling across each spectral channel, the AFSS makes use of feature-based measurements wherein the feature vectors are adaptively reconfigured based on the information gathered from each measurement. The decision model used by this alternate design is based on sequential hypothesis testing—a multiple measurement framework, which constantly monitors the quality of information obtained after each measurement. Early simulation results have shown significant performance gains over the traditional spectrometers in the low SNR regions. An experimental prototype was constructed to validate the findings of our simulations. The experimental setup, assumptions and results are presented and discussed below.

## 2. Feature specific spectroscopy

7. A. Manz, N. Graber, and H. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuators B **1**(1–6), 244–248 (1990). [CrossRef]

8. D. Harrison, P. Glavina, and A. Manz, “Towards miniaturized electrophoresis and chemical analysis systems on silicon: an alternative to chemical sensors,” Sens. Actuators B **10**(2), 107–116 (1993). [CrossRef]

9. R. Kopelman and W. Tan, “Near-field optical microscopy, spectroscopy, and chemical sensors,” Appl. Spectrosc. Rev. **29**(1), 39–66 (1994). [CrossRef]

10. J. Chou, Y. Han, and B. Jalali, “Time-wavelength spectroscopy for chemical sensing,” IEEE Photon. Technol. Lett. **16**(4), 1140–1142 (2004). [CrossRef]

**m**

*is therefore mathematically represented as: where*

_{t}**s**is a length-

*p*column vector corresponding to the incoming spectrum to be classified and

**n**

*denotes a length-*

_{t}*p*column vector where each element corresponds to the noise contribution associated with the individual spectral channels (assumed below to be zero-mean AWGN with standard deviation

*σ*). The primary task of spectral classification involves the determination of the best match for the spectrum

_{n}**s**from a given spectral library

**S**.

**S**is a known

*p*×

*r*library with

*r*the number of spectra present.

11. H. Pal, D. Ganotra, and M. Neifeld, “Face recognition by using feature-specific imaging,” Appl. Opt. **44**(18), 3784–3794 (2005). [CrossRef] [PubMed]

12. M. Neifeld and P. Shankar, “Feature-specific imaging,” Appl. Opt. **42**(17), 3379–3389 (2003). [CrossRef] [PubMed]

13. P. Fellgett, “Conclusions on multiplex methods,” J. Phys. Colloques **28**, C2-165–C2-171 (1967). [CrossRef]

**s**is optically projected onto an arbitrary feature vector before making the measurement. The feature specific measurement

**m**

*is given by: where*

_{p}**P**is a

*q*×

*p*projection matrix consisting of

*q*length-

*p*feature vectors. Here,

**n**

*is a length-*

_{p}*q*column vector corresponding to the noise (again AWGN with standard deviation

*σ*). Since the projection of the incoming spectrum onto an arbitrary basis vector may be viewed as a linear combination of the individual spectral components, the overall signal strength of the measurement is increased relative to the noise contribution. This multiplexing improves the measurement SNR considerably when compared with the traditional measurements.

_{n}## 3. Detection frameworks—Sequential hypothesis testing

*H*

_{0}and

*H*

_{1}, the conditional probabilities of the hypotheses given a series of

*k*feature-specific measurements {

**m**

*}*

_{p}*may be expressed in terms of the likelihoods using Bayes’ theorem as: The likelihood of the*

_{k}*i*hypothesis is given by

^{th}**L**

*which is formulated as follows:*

_{i,k}**L**

_{01,k}is essentially the likelihood ratio and in most cases the hypotheses are assumed to be equiprobable. Hence, If the measurement at each iteration is given by {

**m**

*}*

_{p}*, a very generalized update procedure for the likelihood ratios Λ*

_{k}*may be designed. The likelihood ratio at the*

_{k}*k*step may be written as: as the likelihoods are the conditional probabilities which may be updated as follows:

^{th}_{0}and Θ

_{1}and the decision may then be made in the following fashion:

### 3.1. Extension of SHT to multiple hypotheses

*w*hypotheses where

*w*> 2, the likelihood ratios may be updated as: where Λ

*now is the*

_{i,j;k}*i,j*element of a

^{th}*w*×

*w*likelihood ratio matrix Λ. The elements of the Λ matrix are the pairwise likelihood ratios and represent the probability ratios Pr

*H*|{

_{i}**m**

*}*

_{p}*/Pr*

_{k}*H*|{

_{j}**m**

*}*

_{p}*. All the elements in a single row (except the diagonal elements) are compared with the respective thresholds to decide in favor of a particular hypothesis. The decision making process may be formulated as follows:*

_{k}## 4. Adaptivity

*ad hoc*techniques exist which may be used for synthesizing the feature vectors so that increased discrimination between the spectral projections is achieved. Principal component analysis [21] proves to be a reasonable choice in this regard, as the first principal component captures the direction of greatest variance among the competing spectra, the second component provides the direction of greatest remaining variance and so on. However, it is important to note that feature decomposition based on principal component analysis is

*ad hoc*in nature. It is possible to find a set of

*k*features which are more discriminatory than the first

*k*principal components. The current AFSS system utilizes feature vectors synthesized via principal component analysis; we are working on techniques for determining optimal feature vectors.

*b*

^{th}spectrum in the spectral library

**S**is denoted by

**S**

*, then the mean spectrum*

_{b}**S̄**is given by: The first

*q*principal components are defined as the

*q*eigenvectors of the signal covariance matrix

**C**corresponding to the

*q*largest eigenvalues given by: In order to implement the probabilistic information gained after each measurement, the likelihood ratios are used to evaluate the probability estimate of a hypothesis

*H*given a series of

_{j}*k*measurements {

**m**

*}*

_{p}*: where Λ*

_{k}*is the*

_{i,j;k}*i,j*element of the likelihood ratio matrix Λ

^{th}*. The*

_{k}*i,j*element of the likelihood ratio matrix is given by: Essentially, all the elements in a single column have been summed and normalized to determine the denominator in the elements of the particular column.

^{th}*Q*also known as the

_{k}*inter-class scatter matrix*, with the mean spectrum

**S̄**now the probabilistically-weighted mean given by: The

*q*eigenvectors of the inter-class scatter matrix [22

22. J. Ke, P. Baheti, and M. Neifeld, “Applications of adaptive feature-specific imaging,” Proc. SPIE **6575**, 657505 (2007). [CrossRef]

*q*largest eigenvalues are used as the feature vectors of our choice. The projection of the spectral library onto these feature vectors yields improved discrimination among the hypotheses which are probabilistically still in serious contention. Figure 1 shows a block diagram illustrating the step by step procedure of the measurement and detection scheme involved in the adaptive feature specific spectrometer.

## 5. Simulation results

*task SNR*(TSNR). TSNR is defined as the ratio of the class separation of the spectral library to the standard deviation of noise, where the class separation is represented by the minimum pairwise Euclidean distance between spectra in the library: Assuming the noise contribution to be AWGN with standard deviation

*σ*, the task SNR is

_{n}*q*= 1 i.e. we always work with the first principal component. In order to physically realize the feature vector which contains both positive and negative weights, we decomposed the features into two separate components—one consisting of just the positive weights and the other just the negative weights. This dual rail implementation has some noise implications due to the presence of two individual noise contributions. The measurements

**m**

_{+}and

**m**

_{−}corresponding to these two vectors are given by: where

**p**

_{+}and

**p**

_{−}are the decomposed feature vectors,

**n**

_{1}and

**n**

_{2}are the two decomposed noise vectors, and

**s**is the incoming spectrum. The actual measurement is obtained by finding the difference

**m**

_{+}–

**m**

_{−}which will be associated with a noise contribution

^{5}measurements required by the traditional systems. The performance curves of the traditional and the AFSS system cross each other near the 10 dB point. In the high TSNR region (10 dB – 50 dB), we can clearly see that the AFSS system is worse by a factor of 2 when compared with the traditional systems. This is a result of the dual rail implementation of the feature vectors. In spite of the noise implications of the dual rail implementation, the AFSS easily outperforms its traditional counterpart in the low TSNR regions. It is reasonable to consider the impact of the chosen error rate on the performance of the AFSS. However, as both the AFSS and traditional system utilize the same decision framework, the impact is expected to be similar in both cases, leaving the performance gain of the AFSS qualitatively unchanged. This belief is supported by initial investigations with other error rates.

## 6. Experimental implementation

*μ*m × 7.56

*μ*m and can tilt by approximately 12°. The DMD has an efficiency of 68% over a wavelength range of 420–700 nm. The individual mirrors on the DMD are appropriately controlled to implement the different feature vectors required for the adaptive feature specific measurements.

### 6.1. Calibration and library design

### 6.2. Improving the system SNR

**C**(a 640 × 640 identity matrix) are transmitted to the DMD and measurements (

**M**

*) are recorded for each case which are given by: where*

_{e}**S**

*is the incoming spectrum from the LED array. In order to overcome the limitations posed by the signal strength of the source spectrum, we considered blocks of columns to improve the overall system SNR. A block size of 4 proved to be ideal for the purpose of the experimental validation. A better system SNR was achieved by using S-matrix based signal reconstruction techniques for calibrating the AFSS system. S-matrices with very low condition numbers were used to make multiplexed measurements which provide significant SNR advantage. The measurements using the S-matrix based calibration scheme is given by where*

_{e}**M**is the measurement vector,

**C**corresponds to the new calibration matrix which is the S-matrix of appropriate size,

**S**

*is the incoming LED spectrum and*

_{e}**n**

*corresponds to the noise contribution. The multiplexed measurements may then be used to synthesize the LED spectrum by accurate reconstruction given by where*

_{e}**Ŝ**

*corresponds to the measured LED spectrum and*

_{e}**C**

^{−1}is the inverted calibration matrix. The noise contribution is very negligible.

## 7. Noise settings and experimental results

*x*is the samples per trigger and

*y*is the noise parameter. Once, the desired task SNR is set, the necessary standard deviation of noise may be evaluated using the class separation of the spectral library as follows: where

*σ*is the noise standard deviation and

_{n}*σ*is the class separation. The number of samples which needs to be acquired per trigger may be then set on the DAQ using the following equation:

_{l}## 8. Future work and conclusion

*ad hoc*in nature). Further research is being carried on in this regard to determine the globally optimal feature vectors. Information optimal features have already been designed and implemented in the imaging domain where they have proven to perform better than the adaptive feature specific schemes in the low task SNR regions [25

25. M. Neifeld, A. Ashok, and P. Baheti, “Task-specific information for imaging system analysis,” J. Opt. Soc. Am. A **24**(12), B25–B41 (2007). [CrossRef]

## Acknowledgments

## References and links

1. | Y. Sun and K. Ong, |

2. | W. Pearman and A. Fountain, “Classification of chemical and biological warfare agent simulants by surface-enhanced Raman spectroscopy and multivariate statistical techniques,” J. Appl. Spectrosc. |

3. | H. Liu, Y. Chen, G. Bastiaans, and X. Zhang, “Detection and identification of explosive RDX by THz diffuse reflection spectroscopy,” J. Appl. Spectrosc. |

4. | H. Liu, H. Zhong, N. Karpowicz, Y. Chen, and X. Zhang, “Terahertz spectroscopy and imaging for defense and security applications,” Proc. IEEE |

5. | K. Maquelin, T. van Vreeswijk, H. Endtz, B. Smith, R. Bennett, H. Bruining, and G. Puppels, “Raman spectroscopic method for identification of clinically relevant microorganisms growing on solid culture medium,” Anal. Chem. |

6. | K. Maquelin, C. Kirschner, L. Choo-Smith, N. Van den Braak, H. Endtz, D. Naumann, and G. Puppels, “Identification of medically relevant microorganisms by vibrational spectroscopy,” J. Microbiol. Methods |

7. | A. Manz, N. Graber, and H. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuators B |

8. | D. Harrison, P. Glavina, and A. Manz, “Towards miniaturized electrophoresis and chemical analysis systems on silicon: an alternative to chemical sensors,” Sens. Actuators B |

9. | R. Kopelman and W. Tan, “Near-field optical microscopy, spectroscopy, and chemical sensors,” Appl. Spectrosc. Rev. |

10. | J. Chou, Y. Han, and B. Jalali, “Time-wavelength spectroscopy for chemical sensing,” IEEE Photon. Technol. Lett. |

11. | H. Pal, D. Ganotra, and M. Neifeld, “Face recognition by using feature-specific imaging,” Appl. Opt. |

12. | M. Neifeld and P. Shankar, “Feature-specific imaging,” Appl. Opt. |

13. | P. Fellgett, “Conclusions on multiplex methods,” J. Phys. Colloques |

14. | F. Robey, D. Fuhrmann, E. Kelly, and R. Nitzberg, “A CFAR adaptive matched filter detector,” IEEE Aerosp. Electron. Syst. |

15. | I. Reed, R. Gagliardi, and L. Stotts, “Optical moving target detection with 3-D matched filtering,” IEEE Aerosp. Electron. Syst. |

16. | S. Kay, |

17. | C. Helstrom, |

18. | T. Wickens, |

19. | A. Wald, Sequential analysis (Dover Pubns, 2004). |

20. | P. Armitage, “Sequential analysis with more than two alternative hypotheses, and its relation to discriminant function analysis,” J. R. Stat. Soc. Ser. B (Methodol.) |

21. | I. Jolliffe, |

22. | J. Ke, P. Baheti, and M. Neifeld, “Applications of adaptive feature-specific imaging,” Proc. SPIE |

23. | Texas Instruments, .17 HVGA DMD Datasheet. |

24. | Multicomp Corporation, Multicomp RGB LED Array Datasheet. |

25. | M. Neifeld, A. Ashok, and P. Baheti, “Task-specific information for imaging system analysis,” J. Opt. Soc. Am. A |

**OCIS Codes**

(300.6190) Spectroscopy : Spectrometers

(280.4788) Remote sensing and sensors : Optical sensing and sensors

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: November 11, 2010

Revised Manuscript: February 11, 2011

Manuscript Accepted: February 21, 2011

Published: February 24, 2011

**Virtual Issues**

Vol. 6, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

D. V. Dinakarababu, D. R. Golish, and M. E. Gehm, "Adaptive feature specific spectroscopy for rapid chemical identification," Opt. Express **19**, 4595-4610 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-5-4595

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### References

- Y. Sun, and K. Ong, Detection technologies for chemical warfare agents and toxic vapors (CRC, 2005).
- W. Pearman, and A. Fountain, “Classification of chemical and biological warfare agent simulants by surfaceenhanced Raman spectroscopy and multivariate statistical techniques,” J. Appl. Spectrosc. 60(4), 356–365 (2006). [CrossRef]
- H. Liu, Y. Chen, G. Bastiaans, and X. Zhang, “Detection and identification of explosive RDX by THz diffuse reflection spectroscopy,” J. Appl. Spectrosc. 43, 414–417 (2004).
- H. Liu, H. Zhong, N. Karpowicz, Y. Chen, and X. Zhang, “Terahertz spectroscopy and imaging for defense and security applications,” Proc. IEEE 95(8), 1514–1527 (2007). [CrossRef]
- K. Maquelin, T. van Vreeswijk, H. Endtz, B. Smith, R. Bennett, H. Bruining, and G. Puppels, “Raman spectroscopic method for identification of clinically relevant microorganisms growing on solid culture medium,” Anal. Chem. 72(1), 12–19 (2000). [CrossRef] [PubMed]
- K. Maquelin, C. Kirschner, L. Choo-Smith, N. Van den Braak, H. Endtz, D. Naumann, and G. Puppels, “Identification of medically relevant microorganisms by vibrational spectroscopy,” J. Microbiol. Methods 51(3), 255–271 (2002). [CrossRef] [PubMed]
- A. Manz, N. Graber, and H. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sens. Actuators B 1(1–6), 244–248 (1990). [CrossRef]
- D. Harrison, P. Glavina, and A. Manz, “Towards miniaturized electrophoresis and chemical analysis systems on silicon: an alternative to chemical sensors,” Sens. Actuators B Chem. 10(2), 107–116 (1993). [CrossRef]
- R. Kopelman, and W. Tan, “Near-field optical microscopy, spectroscopy, and chemical sensors,” Appl. Spectrosc. Rev. 29(1), 39–66 (1994). [CrossRef]
- J. Chou, Y. Han, and B. Jalali, “Time-wavelength spectroscopy for chemical sensing,” IEEE Photon. Technol. Lett. 16(4), 1140–1142 (2004). [CrossRef]
- H. Pal, D. Ganotra, and M. Neifeld, “Face recognition by using feature-specific imaging,” Appl. Opt. 44(18), 3784–3794 (2005). [CrossRef] [PubMed]
- M. Neifeld, and P. Shankar, “Feature-specific imaging,” Appl. Opt. 42(17), 3379–3389 (2003). [CrossRef] [PubMed]
- P. Fellgett, “Conclusions on multiplex methods,” J. Phys. Colloques 28, C2–165–C2–171 (1967). [CrossRef]
- F. Robey, D. Fuhrmann, E. Kelly, and R. Nitzberg, “A CFAR adaptive matched filter detector,” IEEE Aerosp. Electron. Syst. 28(1), 208–216 (1992). [CrossRef]
- I. Reed, R. Gagliardi, and L. Stotts, “Optical moving target detection with 3-D matched filtering,” IEEE Aerosp. Electron. Syst. 24(4), 327–336 (1988). [CrossRef]
- S. Kay, Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory (Prentice Hall PTR, 1998).
- C. Helstrom, Statistical theory of signal detection (Pergamon Oxford, 1968).
- T. Wickens, Elementary signal detection theory (Oxford University Press, USA, 2002).
- A. Wald, Sequential analysis (Dover Pubns, 2004).
- P. Armitage, “Sequential analysis with more than two alternative hypotheses, and its relation to discriminant function analysis,” J. R. Stat. Soc., B 12(1), 137–144 (1950).
- I. Jolliffe, Principal component analysis (Springer verlag, 2002).
- J. Ke, P. Baheti, and M. Neifeld, “Applications of adaptive feature-specific imaging,” Proc. SPIE 6575, 657505 (2007). [CrossRef]
- Texas Instruments, .17 HVGA DMD Datasheet.
- Multicomp Corporation, Multicomp RGB LED Array Datasheet.
- M. Neifeld, A. Ashok, and P. Baheti, “Task-specific information for imaging system analysis,” J. Opt. Soc. Am. A 24(12), B25–B41 (2007). [CrossRef]

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