## Algorithm and simulation for analysis of bioimages obtained by aperture diffraction based optical MEMS

Optics Express, Vol. 16, Issue 16, pp. 11937-11953 (2008)

http://dx.doi.org/10.1364/OE.16.011937

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### Abstract

This paper proposes a novel method to detect transparent living cells in a transparent microfluidic chamber by optical diffraction of an aperture or an aperture array. Through the analysis of the far-field diffraction pattern, one of the parameters of the cells, including the size, refractive index, or position, can be extracted by the analysis software developed in this paper. Calculations are carried out to discuss the key issues of this MEMS device, and our simulation is verified by diffraction patterns of transparent microparticles on fabricated apertures, recorded via a digital camera

© 2008 Optical Society of America

## 1. Introduction

1. J. James and H. J. Tanke, *Biomedical Light Microscopy* (Kluwer Academic Publishers, 1991). [CrossRef]

3. K. Chen, A. Kromin, M.P. Ulmer, B.W. Wessels, and V. Backman, “Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy,” Opt. Commun **228**, 1–7 (2003). [CrossRef]

*Escherichia coli*bacteria when they grew [7-9

7. F. Morhard, J. Pipper, R. Dahint, and M. Grunze, “Immobilization of antibodies in micropatterns for cell detection by optical diffraction,” Sens. Actuatuators B. **70**, 232–242 (2000). [CrossRef]

## 2. Device design

## 3. Mathematical derivatives

### 3.1 Diffraction calculation method for various apertures

*x,y*) on the aperture plane X-Y and sheds onto a point P’(

*x’, y’*) on the detection plane, the ray PP’ passes through a particular optical path. In our analysis, assuming the positions of these materials are known, the effective optical path for the ray is calculated by:

*n*is the refractive index of the material that the ray encountered,

_{k}*L*is the length that the ray travels inside the material, and the material can be the chamber, or the buffer, or the cells and their nuclei. Because some materials have optical absorption, for example, nuclei have higher optical density,

_{k}*Φ*is assumed to be a complex, with its real part relates to the phase of the ray and imaginary part relates to the optical loss.

*x’,y’*) on the detection plane is the integration of

*e*

^{ik}^{Φ}in the aperture area

*S*, which can be written as:

*k*=2

*π*/

*λ*is the wave number of the optical light,

*S*is the opening area of the aperture. For instance, a circular aperture on the X-Y plane with its center (

*a, b*) in the X-Y-Z coordinate system is expressed as (

*x*-

*a*)

^{2}+ (

*y*-

*b*)

^{2}=

*r*

^{2}, where

*r*is the radius of the aperture.

*x’, y’*) on the detection plane is the conjugate product of the amplitude in Eq. (2) and can be calculated by:

*x’, y’*) on the detection plane is calculated individually by shifting the location of each aperture, and later adding up their amplitudes altogether. The normalized optical amplitude at P’ is:

*i*represents each aperture,

*N*are respectively the numbers of the apertures along the X and Y axes in the aperture array,

_{x}, N_{y}*S*is the area of each aperture. Thus the light intensity at P’(

_{i}*x’, y’*) is expressed as:

*I*,

_{ax}*I*are respectively defined as

_{ay}*x’, y’*) and P”(

*x”, y”*) is:

*n*is the refractive index of the buffer, (

_{b}*x, y*) is the coordinate of P on the aperture plane. So the amplitude of the light at point P”(

*x”, y”*) is

*U*(

*x’, y’*) and should be calculated by

*x’, y’*) are computed by

### 3.2 Cells and chambers in diffraction calculations

*d*) is the center of the sphere in the X-Y-Z coordinate system, and

_{x}, d_{y}, t*R*is the radius of the sphere.

*x*and

_{cm}*y*, a cylindrical chamber can be depicted as:

_{cm}*R*is the radius of the cylindrical chamber,

_{ch}*h*and

_{1}*h*are respectively the distances from the bottom and the top of the chamber to the aperture.

_{2}*a*and

*b*are the half-widths of the two sides of the rectangular viewed from the top,

*h*and

_{1}*h*are the distances from the bottom and the top of the chamber to the aperture.

_{2}*a*and

_{1}*b*are the half-widths of the pyramid’s bottom rectangle,

_{1}*d*is the distance from the bottom of the chamber to the aperture, γ is the slant angle of the pyramid as drawn in Fig. 3, and

*h*is the height of the chamber.

## 4. Discussions

### 4.1 The diffraction patterns with various apertures

#### 4.1.1 Single aperture comparisons

#### 4.1.2 Aperture array

^{2}, without 3 cells, the light powers detected on the detector for the single aperture, 2 × 2 and 3 × 3 aperture arrays are 1.08, 4.24 and 10.3 μW, respectively; with 3 cells, their light powers are 1.48, 4.46 and 9.08 μW, respectively. Obviously the light power is greatly improved by the aperture array. Without cells, this amplification factor is around

*N*×

_{x}*N*, where

_{y}*N*and

_{x}*N*are the aperture numbers along the X and Y axes in the aperture plane, respectively. With 3 cells, this amplification factor is slightly decreased.

_{y}#### 4.1.3 Detection limits caused by different apertures

### 4.2 The diffraction patterns with various chambers

#### 4.2.1 The influence of basic chamber shapes

#### 4.2.2 The multi-layer and misaligned chambers

### 4.3 Movement of a cell

### 4.4 Detect the diffraction with a photodetector array

## 5. Experiments

## 6. Conclusions

## References and links

1. | J. James and H. J. Tanke, |

2. | M. Pluta |

3. | K. Chen, A. Kromin, M.P. Ulmer, B.W. Wessels, and V. Backman, “Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy,” Opt. Commun |

4. | S. C. Hill, R. G. Pinnick, P. Nachman, G. Chen, R. K. Chang, M. W. Mayo, and G. L. Fernandez, “Aerosolfluorescence spectrum analyzer: real-time measurement of emission spectra of airborne biological particles,” Appl. Opt |

5. | Y. Yang, Z. Zhang, X. Yang, J. H. Yeo, L. Jiang, and D. Jiang, “Blood cell counting and classification by nonflowing laser light scattering method,” J. Biomed. Opt |

6. | A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, “Bacteria size determination by elastic light scattering,” IEEE J. Sel. Top. Quantum Electron |

7. | F. Morhard, J. Pipper, R. Dahint, and M. Grunze, “Immobilization of antibodies in micropatterns for cell detection by optical diffraction,” Sens. Actuatuators B. |

8. | G. T. Williams, R. D. Bahuguna, H. Arteaga, and E. N. Le Joie, “Study of microbial growth I: By diffraction,” Proc. SPIE |

9. | P. M. St. John, R. Davis, N. Cady, J. Czajka, C. A. Batt, and H. G. Craighead, “Diffraction-based cell detection using a microcontact printed antibody grating,” Anal. Chem |

10. | F. D. King and S. E. Leblanc, “Method and Apparatus for particle measurement employing optical imaging,” CA2487233 (2005). |

11. | M. Born and E. Wolf, |

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(230.4000) Optical devices : Microstructure fabrication

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: May 28, 2008

Revised Manuscript: July 22, 2008

Manuscript Accepted: July 22, 2008

Published: July 25, 2008

**Virtual Issues**

Vol. 3, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Xiaodong Zhou, Daniel Puiu Poenar, Kai Yu Liu, Man Siu Tse, Chew-Kiat Heng, Swee Ngin Tan, and Nan Zhang, "Algorithm and simulation for analysis of bio-images obtained by aperture diffraction based optical MEMS," Opt. Express **16**, 11937-11953 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11937

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### References

- J. James and H. J. Tanke, Biomedical Light Microscopy (Kluwer Academic Publishers, 1991). [CrossRef]
- M. Pluta, Advanced Light Microscopy Vol. 2. Specialized Methods (PWN-Polish Scientific Publishers, Warszawa, Poland, 1988).
- K. Chen, A. Kromin, M.P. Ulmer, B.W. Wessels, and V. Backman, "Nanoparticle sizing with a resolution beyond the diffraction limit using UV light scattering spectroscopy," Opt. Commun. 228, 1-7 (2003). [CrossRef]
- S. C. Hill, R. G. Pinnick, P. Nachman, G. Chen, R. K. Chang, M. W. Mayo, and G. L. Fernandez, "Aerosol-fluorescence spectrum analyzer: real-time measurement of emission spectra of airborne biological particles," Appl. Opt. 34, 7149-7155 (1995). [CrossRef] [PubMed]
- Y. Yang, Z. Zhang, X. Yang, J. H. Yeo, L. Jiang, and D. Jiang, "Blood cell counting and classification by nonflowing laser light scattering method," J. Biomed. Opt. 9, 995-1001 (2004). [CrossRef] [PubMed]
- A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, "Bacteria size determination by elastic light scattering," IEEE J. Sel. Top. Quantum Electron. 9, 277-287 (2003). [CrossRef]
- F. Morhard, J. Pipper, R. Dahint, and M. Grunze, "Immobilization of antibodies in micropatterns for cell detection by optical diffraction," Sens. Actuatuators B. 70, 232-242 (2000). [CrossRef]
- G. T. Williams, R. D. Bahuguna, H. Arteaga, and E. N. Le Joie, "Study of microbial growth I: By diffraction," Proc. SPIE 1332, 802-804 (1991). [CrossRef]
- P. M. St. John, R. Davis, N. Cady, J. Czajka, C. A. Batt, and H. G. Craighead, "Diffraction-based cell detection using a microcontact printed antibody grating," Anal. Chem. 70, 1108-1111 (1998). [CrossRef]
- F. D. King and S. E. Leblanc, "Method and Apparatus for particle measurement employing optical imaging," CA2487233 (2005).
- M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

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