## White-light scanning interferometer for absolute nano-scale gap thickness measurement

Optics Express, Vol. 17, Issue 17, pp. 15104-15117 (2009)

http://dx.doi.org/10.1364/OE.17.015104

Acrobat PDF (890 KB)

### Abstract

A special configuration of white-light scanning interferometer is described for measuring the absolute air gap thickness between two planar plates brought into close proximity. The measured gap is not located in any interference arm of the interferometer, but acts as an amplitude-and-phase modulator of the light source. Compared with the common white-light interferometer our approach avoids the influence of the chromatic dispersion of the planar plates on the gap thickness quantification. It covers a large measurement range of from approximate contact to tens of microns with a high resolution of 0.1 nm. Detailed analytical models are presented and signal-processing algorithms based on convolution and correlation techniques are developed. Practical measurements are carried out and the experimental results match well with the analysis and simulation. Short-time and long-time repeatabilities are both tested to prove the high performance of our method.

© 2009 Optical Society of America

## 1. Introduction

1. S. E. EVLASOV, “Evaluating the quality of optical surfaces by the width of interference fringes”, Meas. Tech. , **12**, 942–943, (1969). [CrossRef]

2. G. W. Meindersma, C. M. Guijt, and A. B. De Haan, “Water Recycling and Desalination by Air Gap Membrane Distillation”, Environ. Prog. , **24**, 434–44, (2005). [CrossRef]

3. J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding,. “PMMA microfluidic devices with three-dimensional features for blood cell filtration”, J. Micromech. Microeng. , **18**, 095021, (2008). [CrossRef]

4. A. Dhinojwala and S. Granick, “Micron-gap rheo-optics with parallel plates”, J. Chem. Phys. , **107**, 8664–8667, 1997 [CrossRef]

5. C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, “Nanogap capacitors: sensitivity to sample permittivity changes,” J. Appl. Phys. , **99**, 24305, (2006). [CrossRef]

6. A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, “Supramolecular nanostamping: Using DNA as movable type,” Nano Lett. , **5**, 1061–1064, (2005). [CrossRef] [PubMed]

8. B. Karp and G. Adam, “Small gap width measurement with a finite X-ray source”, NDT&E International , **27**, 21–25, (1994) [CrossRef]

9. J. K. Kim, M. S. Kim, J. H. Bae, J. H.k Kwon, H. B. Lee, and S. H. Jeong, “Gap measurement by position-sensitive detectors”, Appl. Opt. , **39**, 2584–2591, (2000). [CrossRef]

10. D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, “Ultrasonic measurement of the inter-electrode gap in electrochemical machining”, Int. J. Mach. Tools Manuf. , **42**, 1259–1267, (2002). [CrossRef]

12. E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, “Novel mask-wafer gap measurement scheme with nanometer-level detectivity”, J. Vac. Sci. Technol., B , **17**, 2698–2702, (1999). [CrossRef]

13. E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, “Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography”, J. Vac. Sci. Technol., B , **14**, 3969–3973, (1996). [CrossRef]

14. D. C. Flanders and T. M. Lyszcarz, “A precision wide-range optical gap measurement technique”, J. Vac. Sci. Technol., B , **1**, 1196–1199, (1983). [CrossRef]

16. A. Courteville, R. Wilhelm, and F. Garcia, “A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy”, Proc. of SPIE , **6189**, 618918, (2006). [CrossRef]

17. Y. Yasuno, S. Makita, M. Itoh, and T. Yatagai, “Profilometry with line-field Fourier-domain interferometry”, Opt. Express , **13**, 695–701, (2005). [CrossRef] [PubMed]

22. P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer”, IEEE Photonics Technol. Lett. , **16**, 1349–1351, (2004). [CrossRef]

23. P. A. Flournoy, R. W. McClure, and G. Wyntjes, “White-Light Interferometric Thickness Gauge”, App. Opt. , **11**, 1907–1915, (1972). [CrossRef]

## 2. Methodology

### 2.1 Experimental configuration

*I*on the photodetector plane, without any interference pattern. When the moving mirror is driven by the PZT so that the length difference between two interference arms Δ is scanned, the continous variation of the

*I*will be acquired by the photodetector to form an

*I*—Δ curve, from which the gap thickness will be eventually derived.

### 2.2 Basic principle

*E*be the complex amplitude of the input beam, and

_{input}*E*,

_{1}*E*,

_{2}*E*, and

_{3}*E*the sequentially reflected beams from four different surfaces. A series of

_{4}*r*and

*t*denote the reflection and transmission amplitude coefficients at the corresponding surfaces, and their values can be easily calculated by Fresnel equations.

*h*,

*h*and

_{1}*h*are the thickness of the gap and the two plates, and

_{2}*n*,

_{a}*n*and

_{1}*n*their refractive indexes. According to the practical applications of micro gaps

_{2}*h*is much smaller than

*h*and

_{1}*h*. The incident angle is represented by α; and the refractive angles in two plates by β and γ.

_{2}_{1}and φ

_{2}are:

*a*,

*b*,

*c*

*d*and

*A*are positive constants, and

*C*to

_{1}*C*are functions of Δ. The negative sign in

_{7}*C*,

_{2}*C*,

_{3}*C*, and

_{4}*C*is due to the 180 phase shift introduced by reflection at the interface from a low refractive index media to a high one.

_{7}*C*to

_{1}*C*denote different components in the

_{7}*I*—

*Δ*signal, which is acquired by the photodetector when the PZT drives the moving mirror continuously. A simulated

*I*—

*Δ*signal by Matlab is presented in Fig. 2, where each

*C*produces one or two local curves and each curve includes a sharp peak with its side lobes, as shown in Fig. 2 (a) and (b). For instance, for

*C*only as Δ equals zero all the cos(

_{1}*4*πΔ/λ) functions obtain the maximum 1 for every wavelength, so a peak will occur at the position of Δ=0, i.e. the position where the PZT translates to make the length of two interference arms equal. The same goes for

*cos*[

*4*π(Δ+

*n*)/λ] and

_{a}h*cos*[

*4*π(Δ-

*n*)/λ] in

_{a}h*C*, so that two symmetrical downward peaks can be observed at Δ=

_{2}*n*and Δ=-

_{a}h*n*, respectively. As a result, the spacing between the peaks in the local curves denoted by

_{a}h*C*and

_{1}*C*is exactly the value of

_{2}*n*, and therefore the gap thickness can be determined by measuring this spacing, which forms the basic principle of our method. In normal situation the air refractive index

_{a}h*n*can be considered a consistent of 1.00028 [24

_{a}24. J. Zhang, Z. H. Lu, and L. J. Wang, “Precision refractive index measurements of air, N_{2}, O_{2}, Ar, and CO_{2} with a frequency comb”, Appl. Opt., 3143–3151, (2008). [CrossRef] [PubMed]

### 2.3 The influence from dispersion of the plates

*a*)

*For common white-light scanning interferometers*

*M*to

_{1}*M*are constant values; the third and fourth items in formula (5) result in two local curves in the

_{4}*I*—Δ signal, and the spacing between their peaks is expected to be a measure for the gap thickness. One practical case is simulated in Fig. 3, where a 20 µm air gap is included by a 200-µm-thick cover plate and another 300 µm plate and the cover plate is made of BK7 glass. The two local curves before and after consideration of the dispersion of the cover plate are presented in Fig. 3 (a) and (b) for comparison. In (a)

*n*is given by a constant, the refractive index of BK7 glass for the central wavelength of the light source. In (b)

_{1}*n*is a function of λ due to the actual dispersion as in Fig. 3 (d), and now no certain Δ can make the cosine functions in formula (5) get simultaneously the maximum for all the wavelengths. As a result, the widths of the local curves are extended, amplitudes of the peaks are reduced and their positions deviate from the ideal ones. If the cover plate is thicker or the dispersion of the material is more significant, the negative influence of the dispersion will be more evident to make the gap thickness measurement impossible.

_{1}*b*)

*For our proposed method*

*n*and

_{1}*n*with λ will not cause any change to the values of

_{2}*C*and

_{1}*C*in Eq. 4, nor the peak spacing denoting the gap thickness which is completely governed by

_{2}*n*. Even with significant dispersion in the cover plate, the Central Curve and Side Curve are the same as in Fig. 2 (a) and (b). Therefore, the dispersion of the air cavity’s walls does not affect our measurement at all.

_{a}h## 3. Signal processing methodology

*C*and

_{1}*C*can be included in the practically obtained

_{2}*I*—Δ signal. Other local curves, too far away from the location of Δ=0, will not be considered in the following analysis. Now the three local curves generated by

*C*and

_{1}*C*are named by Central Curve and Side Curves, and the three peaks dominating the gap thickness measurement are Central Peak and Side Peaks, respectively.

_{2}### 3.1 Signal processing for gap thickness larger than 10 µm

*I*—Δ signal. (A spare algorithm by calculating the centroid of the local curve to obtain the peak position is also developed.)

*I*to be 1W, the random noise with a substantial amplitude of 4mW is simulated and added into the signal, as shown in Fig. 4 (a). The Central and Side Curves are zoomed in (b) and (c), where the noise makes the peak positions hard to indentify precisely.

_{input}### 3.2 Signal processing for gap thickness between 1µm and 10 µm

*I*—Δ signal and thus it can be recorded separately, as shown in Fig. 5 (b). In practical measurements this procedure only needs to be operated for one time before measuring the gaps, thereafter this data can be used as a reference and subtracted from the obtained signals for gaps thinner than 10 µm. The signal in Fig. 5 (a) is processed and the data after subtracting the Central Curve is shown in Fig. 6, in which the two Side Peaks return to their ideal locations, 2 µm and -2 µm. Now the gap thickness can be characterized accurately by calculating the half spacing between these two downward peaks. If heavy noise exists in the signal, the convolution calculation introduced in the former section can still be employed.

### 3.3 Signal processing for gap thickness less than 1µm

*I*—Δ signal. But even after that the Side Peaks still deviate from their ideal locations because now even the two Side Curves are close enough to combine with one another. The simulated curve of a 400 nm gap after subtracting the Central Curve is illustrated in Fig. 7.

*C*and

_{1}*C*, have completely the same shape; the only difference exists in their amplitude and orientation (upward or downward). Therefore, if the acquired Central Curve in Fig. 5 (b) is placed upside down, it can be taken as the Side Curve by a ratio; and the influence of this ratio will be removed in the correlation calculation because correlation only cares about the shape of curves.

_{2}*I*—Δ signal for a 400 nm gap with a 2mW peak-to-peak random noise is simulated in Fig. 8 (a), and the results of the correlation calculation between it and the curves in the database are illustrated in (b). The gap thickness is determined as 400 nm exactly, from which one can see that the correlation calculation helps finding the gap thickness from the database in a high accuracy, even for cases with heavy noise.

## 4. Experiments

### 4. 1 Experimental setup

### 4. 2 Experimental Data for gaps with different thickness

26. Physik Instruments Piezo Stage Catalog, “Nanopositioning/Piezoelectrics”, (Physik Instruments2009) http://www.physikinstrumente.com/en/pdf_extra/2009_PI_Nanopositioning_Systems_Piezo_Stage_Catalog.pdf

28. V. Shilpiekandula and K. Youcef-Toumi, “Modeling and Control of a Programmable Filter for Separation of Biologically Active Molecules,” In Proceedings of American Control Conference , **1**, 394–399, (2005). [CrossRef]

28. V. Shilpiekandula and K. Youcef-Toumi, “Modeling and Control of a Programmable Filter for Separation of Biologically Active Molecules,” In Proceedings of American Control Conference , **1**, 394–399, (2005). [CrossRef]

### 4. 3 Repeatability of our experiments

## 5. Discussion

*n*λ/2, (

*n*=1, 2, 3…). The measurement range required in many applications is often much larger than hundreds of nanometers, but often tens or hundreds of microns. For these cases the laser interferometer is not suitable. Our approach can cover the gap thickness quantification from approximate contact to tens of microns; if larger range is needed, we just need to use an electromechanical actuator such as the voice coil motor to replace the PZT, with nothing else changed in the setup.

## 6. Conclusion

## Acknowledgments

## References and links

1. | S. E. EVLASOV, “Evaluating the quality of optical surfaces by the width of interference fringes”, Meas. Tech. , |

2. | G. W. Meindersma, C. M. Guijt, and A. B. De Haan, “Water Recycling and Desalination by Air Gap Membrane Distillation”, Environ. Prog. , |

3. | J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding,. “PMMA microfluidic devices with three-dimensional features for blood cell filtration”, J. Micromech. Microeng. , |

4. | A. Dhinojwala and S. Granick, “Micron-gap rheo-optics with parallel plates”, J. Chem. Phys. , |

5. | C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, “Nanogap capacitors: sensitivity to sample permittivity changes,” J. Appl. Phys. , |

6. | A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, “Supramolecular nanostamping: Using DNA as movable type,” Nano Lett. , |

7. | V. Shilpiekandula, “Progress through Mechanics: Small-scale Gaps,” Mech. , |

8. | B. Karp and G. Adam, “Small gap width measurement with a finite X-ray source”, NDT&E International , |

9. | J. K. Kim, M. S. Kim, J. H. Bae, J. H.k Kwon, H. B. Lee, and S. H. Jeong, “Gap measurement by position-sensitive detectors”, Appl. Opt. , |

10. | D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, “Ultrasonic measurement of the inter-electrode gap in electrochemical machining”, Int. J. Mach. Tools Manuf. , |

11. | http://www.keyence.com/products/vision/laser/lt9000/lt9000.php |

12. | E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, “Novel mask-wafer gap measurement scheme with nanometer-level detectivity”, J. Vac. Sci. Technol., B , |

13. | E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, “Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography”, J. Vac. Sci. Technol., B , |

14. | D. C. Flanders and T. M. Lyszcarz, “A precision wide-range optical gap measurement technique”, J. Vac. Sci. Technol., B , |

15. | R. L. Johnson, J. R. P. Angel, M. Lioyd-Hart, and G. Z. Angeli, “Miniature instrument for the measurement of gap thickness using poly-chromatic interferometry”, Proc. SPIE Int. Soc. Opt. Eng. , |

16. | A. Courteville, R. Wilhelm, and F. Garcia, “A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy”, Proc. of SPIE , |

17. | Y. Yasuno, S. Makita, M. Itoh, and T. Yatagai, “Profilometry with line-field Fourier-domain interferometry”, Opt. Express , |

18. | A. G. Podoleanu, “Unique interpretation of Talbot Bands and Fourier domain white light interferometry”, Opt. Express , |

19. | U. Schnell, R. Dandliker, and S. Gray, “Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target” Opt. Lett. , |

20. | P. Hlubina, D. Ciprian, J. Lunaek, and M. lesnak, “Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry”, Appl. Phys. B , |

21. | G. Coppola, P. Ferraro, M. Iodice, and S. D. Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer”, Appl. Opt. , |

22. | P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer”, IEEE Photonics Technol. Lett. , |

23. | P. A. Flournoy, R. W. McClure, and G. Wyntjes, “White-Light Interferometric Thickness Gauge”, App. Opt. , |

24. | J. Zhang, Z. H. Lu, and L. J. Wang, “Precision refractive index measurements of air, N |

25. | A. V. Oppenheim, A. S. Willsky, and I. T. Young, Signal and systems, Prentice-Hall, Englewood Cliffs, N. J. USA, 1983. |

26. | Physik Instruments Piezo Stage Catalog, “Nanopositioning/Piezoelectrics”, (Physik Instruments2009) http://www.physikinstrumente.com/en/pdf_extra/2009_PI_Nanopositioning_Systems_Piezo_Stage_Catalog.pdf |

27. | M. Gutierrez and K. Youcef-Toumi “Programmable Separation for Biologically Active Molecules”, Proceedings of 2006 ASM, Design Engineering Division , |

28. | V. Shilpiekandula and K. Youcef-Toumi, “Modeling and Control of a Programmable Filter for Separation of Biologically Active Molecules,” In Proceedings of American Control Conference , |

**OCIS Codes**

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(120.3940) Instrumentation, measurement, and metrology : Metrology

(120.4640) Instrumentation, measurement, and metrology : Optical instruments

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: May 28, 2009

Revised Manuscript: June 29, 2009

Manuscript Accepted: July 9, 2009

Published: August 11, 2009

**Citation**

Zhiguang Xu, Vijay Shilpiekandula, Kamal Youcef-toumi, and Soon Fatt Yoon, "White-light scanning interferometer for absolute
nano-scale gap thickness measurement," Opt. Express **17**, 15104-15117 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-15104

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### References

- S. E. EVLASOV, "Evaluating the quality of optical surfaces by the width of interference fringes," Meas. Tech. 12, 942-943 (1969). [CrossRef]
- G. W. Meindersma, C. M. Guijt, and A. B. De Haan, "Water Recycling and Desalination by Air Gap Membrane Distillation," Environ. Prog. 24, 434-44 (2005). [CrossRef]
- J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008). [CrossRef]
- A. Dhinojwala and S. Granick, "Micron-gap rheo-optics with parallel plates," J. Chem. Phys. 107, 8664-8667 (1997). [CrossRef]
- C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006). [CrossRef]
- A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005). [CrossRef] [PubMed]
- V. Shilpiekandula, "Progress through Mechanics: Small-scale Gaps," Mech. 35, 3-6 (2006).
- B. Karp and G. Adam, "Small gap width measurement with a finite X-ray source", NDT&E International 27, 21-25 (1994). [CrossRef]
- J. K. Kim, M. S. Kim, J. H. Bae, J. H.k Kwon, H. B. Lee, and S. H. Jeong, "Gap measurement by position-sensitive detectors," Appl. Opt. 39, 2584-2591 (2000). [CrossRef]
- D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, "Ultrasonic measurement of the inter-electrode gap in electrochemical machining," Int. J. Mach. Tools Manuf. 42, 1259-1267 (2002). [CrossRef]
- http://www.keyence.com/products/vision/laser/lt9000/lt9000.php
- E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999). [CrossRef]
- E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, "Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography," J. Vac. Sci. Technol. B 14, 3969-3973 (1996). [CrossRef]
- D. C. Flanders and T. M. Lyszcarz, "A precision wide-range optical gap measurement technique," J. Vac. Sci. Technol. B 1, 1196-1199 (1983). [CrossRef]
- R. L. Johnson, J. R. P. Angel, M. Lioyd-Hart, and G. Z. Angeli, "Miniature instrument for the measurement of gap thickness using poly-chromatic interferometry," Proc. SPIE Int. Soc. Opt. Eng. 3762, 245-253 (1999).
- A. Courteville, R. Wilhelm, and F. Garcia, "A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy," Proc. of SPIE 6189, 618918 (2006). [CrossRef]
- Y. Yasuno, S. Makita, M. Itoh, and T. Yatagai, "Profilometry with line-field Fourier-domain interferometry," Opt. Express 13, 695-701 (2005). [CrossRef] [PubMed]
- A. G. Podoleanu, "Unique interpretation of Talbot Bands and Fourier domain white light interferometry," Opt. Express 15, 9867-9876 (2007). [CrossRef] [PubMed]
- U. Schnell, R. Dandliker, and S. Gray, "Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target," Opt. Lett. 21, 528-530 (1996). [CrossRef] [PubMed]
- P. Hlubina, D. Ciprian, J. Lunaek, and M. lesnak, "Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry,"Appl. Phys. B 84, 511-516 (2006). [CrossRef]
- G. Coppola, P. Ferraro, M. Iodice, and S. D. Nicola, "Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer," Appl. Opt. 42, 3882-3887 (2003). [CrossRef] [PubMed]
- P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004). [CrossRef]
- P. A. Flournoy, R. W. McClure, and G. Wyntjes, "White-Light Interferometric Thickness Gauge," App. Opt. 11, 1907-1915 (1972). [CrossRef]
- J. Zhang, Z. H. Lu, and L. J. Wang, "Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb," Appl. Opt. 3143-3151 (2008). [CrossRef] [PubMed]
- A. V. Oppenheim, A. S. Willsky, and I. T. Young, Signal and systems (Prentice-Hall, Englewood Cliffs, N. J. USA, 1983).
- Physik Instruments Piezo Stage Catalog, "Nanopositioning / Piezoelectrics," (Physik Instruments 2009) http://www.physikinstrumente.com/en/pdf_extra/2009_PI_Nanopositioning_Systems_Piezo_Stage_Catalog.pdf
- M. Gutierrez and K. Youcef-Toumi, "Programmable Separation for Biologically Active Molecules", Proceedings of 2006 ASM, Design Engineering Division, 119, pp 13-20, (2006).
- V. Shilpiekandula and K. Youcef-Toumi, "Modeling and Control of a Programmable Filter for Separation of Biologically Active Molecules," In Proceedings of American Control Conference, 1, 394-399, (2005). [CrossRef]

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