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

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References

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  1. J. James and H. J. Tanke, Biomedical Light Microscopy (Kluwer Academic Publishers, 1991).
    [CrossRef]
  2. M. Pluta, Advanced Light Microscopy Vol. 2. Specialized Methods (PWN-Polish Scientific Publishers, Warszawa, Poland, 1988).
  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]
  4. 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]
  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. 9, 995-1001 (2004).
    [CrossRef] [PubMed]
  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. 9, 277-287 (2003).
    [CrossRef]
  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]
  8. 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]
  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. 70, 1108-1111 (1998).
    [CrossRef]
  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, Principles of Optics (Cambridge University Press, 1999).

2004 (1)

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]

2003 (2)

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]

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]

2000 (1)

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]

1998 (1)

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]

1995 (1)

1991 (1)

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]

Alfano, R. R.

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]

Alimova, A.

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]

Arteaga, H.

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]

Backman, V.

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]

Bahuguna, R. D.

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]

Batt, C. A.

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]

Cady, N.

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]

Chang, R. K.

Chen, G.

Chen, K.

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]

Craighead, H. G.

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]

Czajka, J.

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]

Dahint, R.

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]

Davis, R.

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]

Fernandez, G. L.

Grunze, M.

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]

Hill, S. C.

Jiang, D.

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]

Jiang, L.

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]

Katz, A.

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]

King, F. D.

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

Kromin, A.

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]

Le Joie, E. N.

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]

Leblanc, S. E.

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

Mayo, M. W.

McCormick, S. A.

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]

Morhard, F.

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]

Nachman, P.

Pinnick, R. G.

Pipper, J.

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]

Rosen, R. B.

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]

Rudolph, E.

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]

Savage, H. E.

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]

Shah, M. K.

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]

St. John, P. M.

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]

Ulmer, M.P.

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]

Wessels, B.W.

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]

Williams, G. T.

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]

Xu, M.

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]

Yang, X.

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]

Yang, Y.

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]

Yeo, J. H.

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]

Zhang, Z.

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]

Anal. Chem. (1)

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]

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

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]

J. Biomed. Opt. (1)

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]

Opt. Commun. (1)

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]

Proc. SPIE (1)

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]

Sens. Actuatuators B. (1)

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]

Other (4)

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).

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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Figures (12)

Fig. 1.
Fig. 1.

Detection of cells by aperture diffraction (two cells with their nuclei are inside a pyramidal chamber). The circular aperture illuminated by laser generates a diffraction pattern on the detection plane which can be recorded by a CCD camera or a photodetector array. The buffer deflects the light beam, causing the light spot on P’ to actually appear on P”.

Fig. 2.
Fig. 2.

Apertures that can be used for optical diffraction, with the shapes of (a) circular, (b) rectangular, (c) circular with middle blocked, (d) rectangular with middle blocked, (e) an aperture array formed by the ones in (a)-(d), and we suppose each element of (e) is the same.

Fig. 3.
Fig. 3.

Various chamber shapes can be fabricated in the MEMS device for detecting the cells with an optical aperture. The chambers are: (a) cylindrical, (b) pyramidal, (c) cuboidal, and (d) conical. It is possible to fabricate a planar chamber in several layers in order to trap the cells, so (a)-(c) show stacked chambers of up to 3 layers. In MEMS fabrication, each layer of the chamber might be misaligned from the center of the aperture by fabrication error, so the central line of the aperture is drawn to indicate the possible misalignment. Both side and top views are drawn for each kind of the chambers.

Fig. 4.
Fig. 4.

Fabrication process of the MEMS device with an optical aperture and a two-layer pyramidal chamber. The steps are: (a) etch a small Si tip for the pyramidal chamber; (b) etch a wider pyramidal chamber and a channel on Si mold; (c) fabricate the aperture by a metal layer; (d) spin-coat PDMS on the bottom glass and stamp the PDMS with Si mold to form the microfluidics; (e) bond the PDMS microfluidics with an inlet/outlet pre-drilled glass cover.

Fig. 5.
Fig. 5.

The diffraction patterns without and with 3 cells, and their deducted diffraction patterns (obtained by deducting the diffraction pattern without cells from the one with cells), listed from left to right, for 3 single apertures in different shapes. The chamber is cuboidal with 16 μm × 14 μm in top view and 10 μm in height. (a)-(c) are calculated by a 1.2 μm × 0.8 μm rectangular aperture, (d)-(f) are by a 0.6 μm in radius circular aperture, and (g)-(i) are by an annular aperture with an outer radius of 0.6 μm and an inner radius of 0.3 μm. The detector is 30 cm × 30 cm and placed 10 cm away from the aperture. The refractive indices for the buffer and the chamber are respectively 1.33 and 1.46. The sizes and positions of 3 cells are set as following: the radii of the 3 cells and their nuclei are respectively (3, 3.5, 2.8) μm and (1, 0.9, 0.8) μm, the refractive indices of the cells and their nuclei are respectively (1.38, 1.4, 1.38) and (1.42, 1.45, 1.41), the nuclei have the optical absorptions of (1, 0.8, 1.2) μm-1, the X, Y, Z coordinates for the centers of the cells are respectively x = (2, 3, -4) μm, y = (4, -3, 2) μm and z = (5, 5.5, 5) μm, the X, Y, Z coordinates for the centers of the nuclei are respectively xn = (3, 3.5, -3) μm, yn = (4.3, -2.5, 1) μm and zn = (6, 7, 5.5) μm. In these diffraction patterns, X and Y represent the calculated points in the detection plane, and the color bar indicates the light intensity.

Fig. 6.
Fig. 6.

The diffraction patterns of a cylindrical chamber without and with 3 cells, and their deducted diffraction patterns, from left to right, for various aperture arrays. Each array element is a circular aperture of 0.6 μm in radius, (a)-(c) are calculated for a single aperture, (d)-(f) are for a 2 × 2 array with aperture intervals of 2.4 μm, (g)-(i) are for a 3 × 3 array with aperture intervals of 2.4 μm, (j)-(l) are for a 3 × 1 array with aperture intervals of 7.2 μm. The detector is 15 cm × 15 cm and 10 cm away from the aperture. The refractive indices for the buffer and the chamber are respectively 1.33 and 1.46. In (a)-(i), the chamber is 8 μm in radius, the 3 cells are exactly the same as in Fig. 5; in (j)-(l), the chamber is 10 μm in radius, the cells are the same as in Fig. 5, except each cell is at the center of each aperture, i.e., the X, Y coordinates for the centers of the cells are x = (-7.2, 0, 7.2) μm, y = (0, 0, 0) μm. In diffraction patterns, X and Y represent the calculated points in the detection plane, the color bar shows the light intensity.

Fig. 7.
Fig. 7.

The diffraction patterns of various shapes of one-layer chamber without and with 3 cells, and their deducted diffraction patterns, listed from left to right, with a single circular aperture of 0.6 μm in radius. All chambers are 15 μm high, the distance from the bottom of the chambers to the aperture is 3 μm. (a)-(c) are calculated with a cuboidal chamber with 16 μm × 14 μm in top view, (d)-(f) are with a cylindrical chamber in a radius of 8 μm, and (g)-(i) are with a pyramidal chamber whose bottom surface is 2 μm × 1.6 μm, and its slant angle (defined in Fig. 3) is 54.71°. (j)-(l) are with a conical chamber with a slant angle of 54.71°. The detector is 20 cm × 20 cm and 10 cm away from the aperture. The refractive indices for the buffer and the chamber are respectively 1.33 and 1.43. The sizes and positions of the 3 cells are set as following: the radii of the cells and their nuclei are respectively (3, 3.5, 2.8) μm and (1, 0.9, 0.8) μm, the refractive indices of the cells and their nuclei are respectively (1.38, 1.4, 1.38) and (1.42, 1.45, 1.41), the nuclei have optical absorptions of (1, 0.8, 1.2) μm-1, the X, Y, Z coordinates for the centers of the cells are respectively x = (0.5, 2, 3.5) μm, y = (1, 3, -3) μm and z = (8, 14, 11) μm, the X, Y, Z coordinates for the centers of the nuclei are respectively xn = (1, 2.5, 3) μm, yn = (1.3, 3.5, -3.2) μm and zn = (9, 15, 11.5) μm. For each diffraction pattern, X and Y represent the calculated points in the detection plane, and the color bar shows the light intensity.

Fig. 8.
Fig. 8.

The diffraction patterns for a 3-layer cuboidal chamber without and with 3 cells, and their deducted diffraction patterns, listed from left to right, with a single circular aperture of 0.6 μm in radius. The distance from the bottom of the chambers to the aperture is 3 μm. The refractive indices for the buffer and the chamber, as well as the parameters of the 3 cells are the same as those of Fig. 7. (a)-(c) are calculated with a 3-layer cuboidal chamber without any misalignment, the sizes of the top viewed rectangles for these layers (from bottom to top) are respectively 4 μm × 3.5 μm, 16 μm × 14 μm, and 20 μm × 17.5 μm, and the height of the 3- layers are respectively 4 μm, 4 μm, and 7 μm. (d)-(f) are with a 3-layer cuboidal chamber with each layer’s size the same as that of (a)-(c), but with some misalignments to the aperture. The misalignments of the centers of 3 chamber layers (bottom to top) to the center of the aperture along the X-axis are (2, 1.5, 0.5) μm, along the Y-axis are (1.5, 1, 0.5) μm. In these diffraction patterns, X and Y represent the calculated points in the detection plane, and the color bar indicates the light intensity.

Fig. 9.
Fig. 9.

The diffraction patterns of a cell moving along the X-axis in an 8 μm radius cylindrical chamber. The centers of the cell and its nucleus are respectively with (a) x = -3 μm, xn = -2.5 μm; (b) x = -1.5 μm, xn = -1 μm; (c) x = 0, xn = 0.5 μm; (d) x = 1.5 μm, xn = 2 μm; (e) x = 3 μm, xn = 3.5 μm; (f) x = 4.5 μm, xn = 5 μm. The chamber is 15 μm high, and the distance from its bottom to the aperture plane is 3 μm. The detector is 30 cm × 30 cm and 10 cm away from the aperture. The refractive indices for the buffer and the chamber are respectively 1.33 and 1.43. The radii of the cell and its nucleus are respectively 3 μm and 1 μm, the refractive indices of the cell and its nucleus are respectively 1.38 and 1.42, the nucleus has an optical absorption of 1 μm-1. The Y and Z coordinates for the center of the cell are respectively y = 0 and z = 8 μm, the Y and Z coordinates for the center of the nucleus are yn = 0.3 μm and zn = 1 μm. In the diffraction patterns, X and Y represent the calculated points in the detection plane, and the color bar indicates the light intensity, which is fixed in (a)-(f) to be 0 ∼ 1 (from purple to red).

Fig. 10.
Fig. 10.

The detected powers for the pixels in a one-dimensional photodetector array placed 1 mm away from the aperture, when a cell is moving with the conditions in (a)-(f) be the same as in Figs. 9(a)-(f). The photodetector array consists of ten 80 μm × 80 μm pixels, the flaw between two adjacent pixels is 20 μm. Starting from the origin, it is placed in a line in the first quarter of the X’-Y’ coordinate system (refer to Fig. 1). In these patterns, the horizontal axis shows the number of the pixel, 0 is the one closest to the center. The vertical axis shows the detected optical power on each pixel, when supposing a laser light intensity of 1 W/m2. The range of the pixel power in the vertical axis is fixed at 0 ∼ 0.016 μW.

Fig. 11.
Fig. 11.

The photos of the fabricated aperture and aperture arrays (left) and their diffraction patterns (without microparticles) obtained by experiments (middle) and simulations (right). From top to bottom: the annulus aperture with an inner diameter of 3 μm and an outer diameter of 7 μm; 1 × 3 aperture array with each element of 5 μm in diameter and 8 μm in interval; 3 × 3 aperture array with each element of 7 μm in diameter and 10 μm in interval. The scale bar of the microscope pictures is 20 μm.

Fig. 12.
Fig. 12.

The photos of the fabricated aperture and aperture arrays with polystyrene microparticles (left) and their diffraction patterns obtained by experiments (middle) and simulations (right). From top to bottom: the annulus aperture with an inner diameter of 3 μm and an outer diameter of 7 μm, when one particle exists; 1 × 3 aperture array with each element of 5 μm in diameter and 8 μm interval, when 9 particles exist; 3 × 3 aperture array with each element of 7 μm in diameter and 10 μm interval, when 9 particles exist. The microparticles are with a diameter of 5 μm and a refractive index of 1.59, and their positions are adumbrated on the left of the microscopic pictures.

Tables (1)

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Table 1. Detection limits of the radius and refractive index of a cell by various apertures. We suppose there is only one cell in a cylindrical chamber of 8 μm in radius and 10 μm in height. The cell has no nucleus, and we fixed its refractive index at 1.38 when calculating the detection limit of its size and fixed its radius at 3 μm when calculating the detection limit of its refractive index. The cell is at the center of the aperture (or aperture array), and 8 μm away from the aperture plane. The refractive indices for the buffer and chamber are 1.33 and 1.43, respectively. The detector is 20 cm × 20 cm and is placed 10 cm away from the aperture. We set the threshold of the normalized difference contrast to be 0.05.

Equations (11)

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Φ = k n k L k ,
U x' y' = e k Im ( Φ ) S S e ik Re ( Φ ) dS = e k Im ( Φ ) S [ S cos ( k Re ( Φ ) ) dS + i S sin ( k Re ( Φ ) ) dS ] ,
I x' y' = U x' y' × [ U x' y' * ] = e 2 k Im ( Φ ) S 2 { [ S cos ( k Re ( Φ ) ) dS ] 2 + [ S sin ( k Re ( Φ ) ) dS ] 2 } .
U x' y' = i = 1 N x × N y U i x' y' i = 1 N x × N y S i = i = 1 N x × N y e k Im ( Φ i ) S i e ik Re ( Φ i ) dS i i = 1 N x × N y S i ,
I x' y' = { m = I ax I ax n = I ay I ay e k Im ( Φ m , n ) S cos [ k Re ( Φ m , n ) ] dS } 2 + { m = I ax I ax n = I ay I ay e k Im ( Φ m , n ) S sin [ k Re ( Φ m , n ) ] dS } 2 [ S ( 2 I ax + 1 ) ( 2 I ay + 1 ) ] 2 ,
{ x' = x" x n b + x y' = y" y n b + y ,
( x d x ) 2 + ( y d y ) 2 + ( z t ) 2 = R 2 ,
{ ( x x cm ) 2 + ( y y cm ) 2 R ch 2 h 1 z h 2 ,
{ x x cm a y y cm b , h 1 z h 2
{ x x cm a 1 + ( z d ) tan γ y y cm b 1 + ( z d ) tan γ , d z d + h
{ ( x x cm ) 2 + ( y y cm ) 2 ( z d ) 2 ( tan γ ) 2 d z d + h ,

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