Abstract

We investigate improved image reconstruction of structured light illumination for high-resolution imaging of three-dimensional (3D) cell-based assays. For proof of concept, an in situ fluorescence optical detection system was built with a digital micromirror device as a spatial light modulator, for which phase and tilting angle in a grid pattern were varied to implement specific image reconstruction schemes. Subtractive reconstruction algorithms based on structured light illumination were used to acquire images of fluorescent microbeads deposited as a two-dimensional monolayer or in 3D alginate matrix. We have confirmed that an optical subtraction algorithm improves axial and lateral resolution by effectively removing out-of-focus fluorescence. The results suggest that subtractive image reconstruction can be useful for structured illumination microscopy of broad types of cell-based assays with high image resolution.

© 2012 Optical Society of America

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2012 (3)

2011 (1)

2010 (1)

2009 (6)

M. G. Somekh, K. Hsu, and M. C. Pitter, “Stochastic transfer function for structured illumination microscopy,” J. Opt. Soc. Am. A 26, 1630–1637 (2009).
[CrossRef]

J. H. Sung, J. Choi, D. Kim, and M. L. Shuler, “Fluorescence optical detection in situ for real-time monitoring of cytochrome P450 enzymatic activity of liver cells in multiple microfluidic devices,” Biotechnol. Bioeng. 104, 516–525 (2009).
[CrossRef]

K. Kim, D. J. Kim, E.-J. Cho, J.-S. Suh, Y.-M. Huh, and D. Kim, “Nanograting-based plasmon enhancement for total internal reflection fluorescence microscopy of live cells,” Nanotechnology 20, 015202 (2009).
[CrossRef]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef]

B. A. Justice, N. A. Badr, and R. A. Felder, “3D cell culture opens new dimensions in cell-based assays,” Drug Discovery Today 14(1–2), 102–107 (2009).
[CrossRef]

M. W. Tibbitt and K. S. Anseth, “Hydrogel as extracellular matrix mimics for 3D cell culture,” Biotechnol. Bioeng. 103, 655–663 (2009).
[CrossRef]

2008 (4)

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

M. G. Somekh, K. Hsu, and M. C. Pitter, “Resolution in structured illumination microscopy: a probabilistic approach,” J. Opt. Soc. Am. A 25, 1319–1329 (2008).
[CrossRef]

A. Bullen, “Microscopic imaging techniques for drug discovery,” Nat. Rev. Drug Discov. 7, 54–67 (2008).
[CrossRef]

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

2007 (5)

T. Oh, J. H. Sung, D. A. Tatosian, M. L. Shuler, and D. Kim, “Real-time fluorescence detection of multiple microscale cell culture analog devices in situ,” Cytometry A 71A, 857–865 (2007).
[CrossRef]

T. Fukano, A. Sawano, Y. Ohba, M. Matsuda, and A. Miyawaki, “Differential Ras activation between caveolae/raft and non-raft microdomains,” Cell Struct. Funct. 32, 9–15 (2007).
[CrossRef]

F. Pampaloni, E. G. Reynaud, and E. H. K. Stelzer, “The third dimension bridges the gap between cell culture and live tissue,” Nat. Rev. Mol. Cell Biol. 8, 839–845 (2007).
[CrossRef]

S. Delica and C. M. Blanca, “Wide-field depth-sectioning fluorescence microscopy using projector-generated patterned illumination,” Appl. Opt. 46, 7237–7243 (2007).
[CrossRef]

K. Kim, E.-J. Cho, Y.-M. Huh, and D. Kim, “Thin film-based sensitivity enhancement for total internal reflection fluorescence live-cell imaging,” Opt. Lett. 32, 3062–3064 (2007).
[CrossRef]

2006 (1)

J. El-Ali, P. K. Sorger, and K. F. Jensen, “Cells on chips,” Nature 442, 403–411 (2006).
[CrossRef]

2005 (3)

J.-A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2, 920–931 (2005).
[CrossRef]

D. A. Tatosian, M. L. Shuler, and D. Kim, “Portable in situ fluorescence cytometry of microscale cell-based assays,” Opt. Lett. 30, 1689–1691 (2005).
[CrossRef]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102, 13081–13086 (2005).
[CrossRef]

2004 (1)

L. H. Schaefer, D. Shuster, and J. Schaffer, “Structured illumination microscopy: artifact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165–174 (2004).
[CrossRef]

2003 (3)

T. Fukano and A. Miyawaki, “Whole-field fluorescence microscope with digital micromirror device: imaging of biological samples,” Appl. Opt. 42, 4119–4124 (2003).
[CrossRef]

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtractive of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[CrossRef]

M. Martinez-Corral, M. T. Caballero, C. Ibanez-Lopez, and V. Sarafis, “Optical sectioning by two-pinhole confocal fluorescence microscopy,” Micron 34, 313–318 (2003).
[CrossRef]

2002 (3)

2001 (3)

T. Xian and X. Su, “Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry,” Appl. Opt. 40, 1201–1206 (2001).
[CrossRef]

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

G. Boyer and V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik 112, 177–179 (2001).
[CrossRef]

2000 (2)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197, 1–4 (2000).
[CrossRef]

1999 (1)

J. A. Rowley, G. Madlambayan, and D. J. Mooney, “Alginate hydrogels as synthetic extracellular matrix materials,” Biomaterials 20, 45–53 (1999).
[CrossRef]

1998 (1)

T. Wilson, M. A. A. Neil, and R. Juskaitis, “Real-time three-dimensional imaging of macroscopic structures,” J. Microsc. 191, 116–118 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

1991 (1)

S. J. Hewlett and T. Wilson, “Resolution enhancement in three-dimensional confocal microscopy,” Machine Vis. Appl. 4, 233–242 (1991).
[CrossRef]

Agard, D. A.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Anseth, K. S.

M. W. Tibbitt and K. S. Anseth, “Hydrogel as extracellular matrix mimics for 3D cell culture,” Biotechnol. Bioeng. 103, 655–663 (2009).
[CrossRef]

Badr, N. A.

B. A. Justice, N. A. Badr, and R. A. Felder, “3D cell culture opens new dimensions in cell-based assays,” Drug Discovery Today 14(1–2), 102–107 (2009).
[CrossRef]

Bastiaens, P. I. H.

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197, 1–4 (2000).
[CrossRef]

Bazargan-Lari, A.

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

Blanca, C. M.

Boyer, G.

G. Boyer, “New class of axially apodizing filters for confocal scanning microscopy,” J. Opt. Soc. Am. A 19, 584–589 (2002).
[CrossRef]

G. Boyer and V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik 112, 177–179 (2001).
[CrossRef]

Bruke, B.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Bullen, A.

A. Bullen, “Microscopic imaging techniques for drug discovery,” Nat. Rev. Drug Discov. 7, 54–67 (2008).
[CrossRef]

Caballero, M. T.

M. Martinez-Corral, M. T. Caballero, C. Ibanez-Lopez, and V. Sarafis, “Optical sectioning by two-pinhole confocal fluorescence microscopy,” Micron 34, 313–318 (2003).
[CrossRef]

M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103 (2002).

Calatayud, A.

Cardoso, M. C.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Carlton, P. M.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Chen, N. G.

C. H. Wong, N. G. Chen, and C. J. R. Sheppard, “Study on potential of structured illumination microscopy utilizing digital micromirror device for endoscopy purpose,” in Biophotonics, Nanophotonics and Metamaterials, 2006, International Symposium on Metamaterials (IEEE, 2006), pp. 218–222.

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef]

Cho, E.-J.

K. Kim, D. J. Kim, E.-J. Cho, J.-S. Suh, Y.-M. Huh, and D. Kim, “Nanograting-based plasmon enhancement for total internal reflection fluorescence microscopy of live cells,” Nanotechnology 20, 015202 (2009).
[CrossRef]

K. Kim, E.-J. Cho, Y.-M. Huh, and D. Kim, “Thin film-based sensitivity enhancement for total internal reflection fluorescence live-cell imaging,” Opt. Lett. 32, 3062–3064 (2007).
[CrossRef]

Choi, J.

Cole, M. J.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Conchello, J.-A.

Cremer, C.

Davidson, M. W.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109, 5311–5315 (2012).
[CrossRef]

Dayel, M. J.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Delica, S.

Doblas, A.

Dowling, K.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

El-Ali, J.

J. El-Ali, P. K. Sorger, and K. F. Jensen, “Cells on chips,” Nature 442, 403–411 (2006).
[CrossRef]

Felder, R. A.

B. A. Justice, N. A. Badr, and R. A. Felder, “3D cell culture opens new dimensions in cell-based assays,” Drug Discovery Today 14(1–2), 102–107 (2009).
[CrossRef]

Fiolka, R.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109, 5311–5315 (2012).
[CrossRef]

French, P. M. W.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Fukano, T.

T. Fukano, A. Sawano, Y. Ohba, M. Matsuda, and A. Miyawaki, “Differential Ras activation between caveolae/raft and non-raft microdomains,” Cell Struct. Funct. 32, 9–15 (2007).
[CrossRef]

T. Fukano and A. Miyawaki, “Whole-field fluorescence microscope with digital micromirror device: imaging of biological samples,” Appl. Opt. 42, 4119–4124 (2003).
[CrossRef]

Gillett, B. M.

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

Griffis, E. R.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef]

Gustafsson, M. G. L.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109, 5311–5315 (2012).
[CrossRef]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef]

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102, 13081–13086 (2005).
[CrossRef]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

Haase, S.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Hanley, Q. S.

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtractive of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[CrossRef]

Hansen, E. W.

Heintzmann, R.

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtractive of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[CrossRef]

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy—a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19, 1599–1609 (2002).
[CrossRef]

Hewlett, S. J.

S. J. Hewlett and T. Wilson, “Resolution enhancement in three-dimensional confocal microscopy,” Machine Vis. Appl. 4, 233–242 (1991).
[CrossRef]

Hsu, K.

Huh, Y.-M.

K. Kim, D. J. Kim, E.-J. Cho, J.-S. Suh, Y.-M. Huh, and D. Kim, “Nanograting-based plasmon enhancement for total internal reflection fluorescence microscopy of live cells,” Nanotechnology 20, 015202 (2009).
[CrossRef]

K. Kim, E.-J. Cho, Y.-M. Huh, and D. Kim, “Thin film-based sensitivity enhancement for total internal reflection fluorescence live-cell imaging,” Opt. Lett. 32, 3062–3064 (2007).
[CrossRef]

Ibanez-Lopez, C.

M. Martinez-Corral, M. T. Caballero, C. Ibanez-Lopez, and V. Sarafis, “Optical sectioning by two-pinhole confocal fluorescence microscopy,” Micron 34, 313–318 (2003).
[CrossRef]

Jensen, J. A.

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

Jensen, K. F.

J. El-Ali, P. K. Sorger, and K. F. Jensen, “Cells on chips,” Nature 442, 403–411 (2006).
[CrossRef]

Jones, R.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Jovin, T. M.

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtractive of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[CrossRef]

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy—a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19, 1599–1609 (2002).
[CrossRef]

Juskaitis, R.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197, 1–4 (2000).
[CrossRef]

T. Wilson, M. A. A. Neil, and R. Juskaitis, “Real-time three-dimensional imaging of macroscopic structures,” J. Microsc. 191, 116–118 (1998).
[CrossRef]

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997).
[CrossRef]

Justice, B. A.

B. A. Justice, N. A. Badr, and R. A. Felder, “3D cell culture opens new dimensions in cell-based assays,” Drug Discovery Today 14(1–2), 102–107 (2009).
[CrossRef]

Kim, D.

J. Choi, K. Kim, and D. Kim, “In situ fluorescence optical detection using a digital micromirror device (DMD) for 3D cell-based assays,” J. Opt. Soc. Korea 16, 42–46 (2012).
[CrossRef]

J. Choi, J. H. Sung, M. L. Shuler, and D. Kim, “Investigation of portable in situ fluorescence optical detection for microfluidic 3D cell culture assays,” Opt. Lett. 35, 1374–1376 (2010).
[CrossRef]

K. Kim, D. J. Kim, E.-J. Cho, J.-S. Suh, Y.-M. Huh, and D. Kim, “Nanograting-based plasmon enhancement for total internal reflection fluorescence microscopy of live cells,” Nanotechnology 20, 015202 (2009).
[CrossRef]

J. H. Sung, J. Choi, D. Kim, and M. L. Shuler, “Fluorescence optical detection in situ for real-time monitoring of cytochrome P450 enzymatic activity of liver cells in multiple microfluidic devices,” Biotechnol. Bioeng. 104, 516–525 (2009).
[CrossRef]

K. Kim, E.-J. Cho, Y.-M. Huh, and D. Kim, “Thin film-based sensitivity enhancement for total internal reflection fluorescence live-cell imaging,” Opt. Lett. 32, 3062–3064 (2007).
[CrossRef]

T. Oh, J. H. Sung, D. A. Tatosian, M. L. Shuler, and D. Kim, “Real-time fluorescence detection of multiple microscale cell culture analog devices in situ,” Cytometry A 71A, 857–865 (2007).
[CrossRef]

D. A. Tatosian, M. L. Shuler, and D. Kim, “Portable in situ fluorescence cytometry of microscale cell-based assays,” Opt. Lett. 30, 1689–1691 (2005).
[CrossRef]

Kim, D. J.

K. Kim, D. J. Kim, E.-J. Cho, J.-S. Suh, Y.-M. Huh, and D. Kim, “Nanograting-based plasmon enhancement for total internal reflection fluorescence microscopy of live cells,” Nanotechnology 20, 015202 (2009).
[CrossRef]

Kim, J. J.

Kim, K.

Kner, P.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef]

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Leonhardt, H.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Leve, M. J.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Lichtman, J. W.

J.-A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2, 920–931 (2005).
[CrossRef]

Madlambayan, G.

J. A. Rowley, G. Madlambayan, and D. J. Mooney, “Alginate hydrogels as synthetic extracellular matrix materials,” Biomaterials 20, 45–53 (1999).
[CrossRef]

Martinez-Corral, M.

Matsuda, M.

T. Fukano, A. Sawano, Y. Ohba, M. Matsuda, and A. Miyawaki, “Differential Ras activation between caveolae/raft and non-raft microdomains,” Cell Struct. Funct. 32, 9–15 (2007).
[CrossRef]

Miyawaki, A.

T. Fukano, A. Sawano, Y. Ohba, M. Matsuda, and A. Miyawaki, “Differential Ras activation between caveolae/raft and non-raft microdomains,” Cell Struct. Funct. 32, 9–15 (2007).
[CrossRef]

T. Fukano and A. Miyawaki, “Whole-field fluorescence microscope with digital micromirror device: imaging of biological samples,” Appl. Opt. 42, 4119–4124 (2003).
[CrossRef]

Mooney, D. J.

J. A. Rowley, G. Madlambayan, and D. J. Mooney, “Alginate hydrogels as synthetic extracellular matrix materials,” Biomaterials 20, 45–53 (1999).
[CrossRef]

Munroe, P.

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtractive of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[CrossRef]

Nailon, J.

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtractive of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[CrossRef]

Neil, M. A. A.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197, 1–4 (2000).
[CrossRef]

T. Wilson, M. A. A. Neil, and R. Juskaitis, “Real-time three-dimensional imaging of macroscopic structures,” J. Microsc. 191, 116–118 (1998).
[CrossRef]

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997).
[CrossRef]

Oh, T.

T. Oh, J. H. Sung, D. A. Tatosian, M. L. Shuler, and D. Kim, “Real-time fluorescence detection of multiple microscale cell culture analog devices in situ,” Cytometry A 71A, 857–865 (2007).
[CrossRef]

Ohba, Y.

T. Fukano, A. Sawano, Y. Ohba, M. Matsuda, and A. Miyawaki, “Differential Ras activation between caveolae/raft and non-raft microdomains,” Cell Struct. Funct. 32, 9–15 (2007).
[CrossRef]

Pampaloni, F.

F. Pampaloni, E. G. Reynaud, and E. H. K. Stelzer, “The third dimension bridges the gap between cell culture and live tissue,” Nat. Rev. Mol. Cell Biol. 8, 839–845 (2007).
[CrossRef]

Parsons-Karavassilis, D.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Piston, D.

Pitter, M. C.

Rego, E. H.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109, 5311–5315 (2012).
[CrossRef]

Reynaud, E. G.

F. Pampaloni, E. G. Reynaud, and E. H. K. Stelzer, “The third dimension bridges the gap between cell culture and live tissue,” Nat. Rev. Mol. Cell Biol. 8, 839–845 (2007).
[CrossRef]

Rowley, J. A.

J. A. Rowley, G. Madlambayan, and D. J. Mooney, “Alginate hydrogels as synthetic extracellular matrix materials,” Biomaterials 20, 45–53 (1999).
[CrossRef]

Saavedra, G.

Sanchez-Ortiga, E.

Sandison, D. R.

Sarafis, V.

M. Martinez-Corral, M. T. Caballero, C. Ibanez-Lopez, and V. Sarafis, “Optical sectioning by two-pinhole confocal fluorescence microscopy,” Micron 34, 313–318 (2003).
[CrossRef]

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtractive of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[CrossRef]

G. Boyer and V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik 112, 177–179 (2001).
[CrossRef]

Sawano, A.

T. Fukano, A. Sawano, Y. Ohba, M. Matsuda, and A. Miyawaki, “Differential Ras activation between caveolae/raft and non-raft microdomains,” Cell Struct. Funct. 32, 9–15 (2007).
[CrossRef]

Schaefer, L. H.

L. H. Schaefer, D. Shuster, and J. Schaffer, “Structured illumination microscopy: artifact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165–174 (2004).
[CrossRef]

Schaffer, J.

L. H. Schaefer, D. Shuster, and J. Schaffer, “Structured illumination microscopy: artifact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165–174 (2004).
[CrossRef]

Schermelleh, L.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Sedat, J. W.

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Shao, L.

R. Fiolka, L. Shao, E. H. Rego, M. W. Davidson, and M. G. L. Gustafsson, “Time-lapse two-color 3D imaging of live cells with doubled resolution using structured illumination,” Proc. Natl. Acad. Sci. U.S.A. 109, 5311–5315 (2012).
[CrossRef]

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Sheppard, C. J. R.

E. Sanchez-Ortiga, C. J. R. Sheppard, G. Saavedra, M. Martinez-Corral, A. Doblas, and A. Calatayud, “Subtractive imaging in confocal scanning microscopy using a CCD camera as a detector,” Opt. Lett. 37, 1280–1282 (2012).
[CrossRef]

C. H. Wong, N. G. Chen, and C. J. R. Sheppard, “Study on potential of structured illumination microscopy utilizing digital micromirror device for endoscopy purpose,” in Biophotonics, Nanophotonics and Metamaterials, 2006, International Symposium on Metamaterials (IEEE, 2006), pp. 218–222.

Shuler, M. L.

J. Choi, J. H. Sung, M. L. Shuler, and D. Kim, “Investigation of portable in situ fluorescence optical detection for microfluidic 3D cell culture assays,” Opt. Lett. 35, 1374–1376 (2010).
[CrossRef]

J. H. Sung, J. Choi, D. Kim, and M. L. Shuler, “Fluorescence optical detection in situ for real-time monitoring of cytochrome P450 enzymatic activity of liver cells in multiple microfluidic devices,” Biotechnol. Bioeng. 104, 516–525 (2009).
[CrossRef]

T. Oh, J. H. Sung, D. A. Tatosian, M. L. Shuler, and D. Kim, “Real-time fluorescence detection of multiple microscale cell culture analog devices in situ,” Cytometry A 71A, 857–865 (2007).
[CrossRef]

D. A. Tatosian, M. L. Shuler, and D. Kim, “Portable in situ fluorescence cytometry of microscale cell-based assays,” Opt. Lett. 30, 1689–1691 (2005).
[CrossRef]

Shuster, D.

L. H. Schaefer, D. Shuster, and J. Schaffer, “Structured illumination microscopy: artifact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165–174 (2004).
[CrossRef]

Sia, S. K.

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

Siegel, J.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Somekh, M. G.

Sorger, P. K.

J. El-Ali, P. K. Sorger, and K. F. Jensen, “Cells on chips,” Nature 442, 403–411 (2006).
[CrossRef]

Squire, A.

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197, 1–4 (2000).
[CrossRef]

Stelzer, E. H. K.

F. Pampaloni, E. G. Reynaud, and E. H. K. Stelzer, “The third dimension bridges the gap between cell culture and live tissue,” Nat. Rev. Mol. Cell Biol. 8, 839–845 (2007).
[CrossRef]

M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103 (2002).

Su, X.

Sucharov, L. O. D.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Suh, J.-S.

K. Kim, D. J. Kim, E.-J. Cho, J.-S. Suh, Y.-M. Huh, and D. Kim, “Nanograting-based plasmon enhancement for total internal reflection fluorescence microscopy of live cells,” Nanotechnology 20, 015202 (2009).
[CrossRef]

Sung, J. H.

J. Choi, J. H. Sung, M. L. Shuler, and D. Kim, “Investigation of portable in situ fluorescence optical detection for microfluidic 3D cell culture assays,” Opt. Lett. 35, 1374–1376 (2010).
[CrossRef]

J. H. Sung, J. Choi, D. Kim, and M. L. Shuler, “Fluorescence optical detection in situ for real-time monitoring of cytochrome P450 enzymatic activity of liver cells in multiple microfluidic devices,” Biotechnol. Bioeng. 104, 516–525 (2009).
[CrossRef]

T. Oh, J. H. Sung, D. A. Tatosian, M. L. Shuler, and D. Kim, “Real-time fluorescence detection of multiple microscale cell culture analog devices in situ,” Cytometry A 71A, 857–865 (2007).
[CrossRef]

Swoger, J.

Tang, B.

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

Tatosian, D. A.

T. Oh, J. H. Sung, D. A. Tatosian, M. L. Shuler, and D. Kim, “Real-time fluorescence detection of multiple microscale cell culture analog devices in situ,” Cytometry A 71A, 857–865 (2007).
[CrossRef]

D. A. Tatosian, M. L. Shuler, and D. Kim, “Portable in situ fluorescence cytometry of microscale cell-based assays,” Opt. Lett. 30, 1689–1691 (2005).
[CrossRef]

Tibbitt, M. W.

M. W. Tibbitt and K. S. Anseth, “Hydrogel as extracellular matrix mimics for 3D cell culture,” Biotechnol. Bioeng. 103, 655–663 (2009).
[CrossRef]

Wang, L.

Webb, S. E. D.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

Webb, W. W.

Williams, R. M.

Wilson, T.

M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Leve, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001).
[CrossRef]

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197, 1–4 (2000).
[CrossRef]

T. Wilson, M. A. A. Neil, and R. Juskaitis, “Real-time three-dimensional imaging of macroscopic structures,” J. Microsc. 191, 116–118 (1998).
[CrossRef]

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997).
[CrossRef]

S. J. Hewlett and T. Wilson, “Resolution enhancement in three-dimensional confocal microscopy,” Machine Vis. Appl. 4, 233–242 (1991).
[CrossRef]

Winoto, L.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6, 339–342 (2009).
[CrossRef]

L. Schermelleh, P. M. Carlton, S. Haase, L. Shao, L. Winoto, P. Kner, B. Bruke, M. C. Cardoso, D. A. Agard, M. G. L. Gustafsson, H. Leonhardt, and J. W. Sedat, “Subdiffraction multicolor imaging of the nuclear periphery with 3D structured illumination microscopy,” Science 320, 1332–1336 (2008).
[CrossRef]

Wong, C. H.

C. H. Wong, N. G. Chen, and C. J. R. Sheppard, “Study on potential of structured illumination microscopy utilizing digital micromirror device for endoscopy purpose,” in Biophotonics, Nanophotonics and Metamaterials, 2006, International Symposium on Metamaterials (IEEE, 2006), pp. 218–222.

Xian, T.

Yang, G. J.

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

Zhong, M.

B. M. Gillett, J. A. Jensen, B. Tang, G. J. Yang, A. Bazargan-Lari, M. Zhong, and S. K. Sia, “In situ collagen assembly for integrating microfabricated three-dimensional cell-seeded matrices,” Nat. Mater. 7, 636–640 (2008).
[CrossRef]

Appl. Opt. (5)

Biomaterials (1)

J. A. Rowley, G. Madlambayan, and D. J. Mooney, “Alginate hydrogels as synthetic extracellular matrix materials,” Biomaterials 20, 45–53 (1999).
[CrossRef]

Biotechnol. Bioeng. (2)

M. W. Tibbitt and K. S. Anseth, “Hydrogel as extracellular matrix mimics for 3D cell culture,” Biotechnol. Bioeng. 103, 655–663 (2009).
[CrossRef]

J. H. Sung, J. Choi, D. Kim, and M. L. Shuler, “Fluorescence optical detection in situ for real-time monitoring of cytochrome P450 enzymatic activity of liver cells in multiple microfluidic devices,” Biotechnol. Bioeng. 104, 516–525 (2009).
[CrossRef]

Cell Struct. Funct. (1)

T. Fukano, A. Sawano, Y. Ohba, M. Matsuda, and A. Miyawaki, “Differential Ras activation between caveolae/raft and non-raft microdomains,” Cell Struct. Funct. 32, 9–15 (2007).
[CrossRef]

Cytometry A (1)

T. Oh, J. H. Sung, D. A. Tatosian, M. L. Shuler, and D. Kim, “Real-time fluorescence detection of multiple microscale cell culture analog devices in situ,” Cytometry A 71A, 857–865 (2007).
[CrossRef]

Drug Discovery Today (1)

B. A. Justice, N. A. Badr, and R. A. Felder, “3D cell culture opens new dimensions in cell-based assays,” Drug Discovery Today 14(1–2), 102–107 (2009).
[CrossRef]

J. Microsc. (5)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197, 1–4 (2000).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of in situ fluorescence optical detection system with structured illuminations using a DMD. L, fiber-coupled laser; BE, beam expander; RD, rotating diffuser; L1, L2, L3, L4, relay achromatic lenses; BS, beam splitter; OB, objective lens; Em, emission filter; CCD, charge-coupled device camera.

Fig. 2.
Fig. 2.

Binary patterns loaded onto a DMD for structured illuminations. The produced patterns were sinusoidal following Eq. (1).

Fig. 3.
Fig. 3.

Flow chart of the reconstruction algorithmic for conventional and subtractive SIM images.

Fig. 4.
Fig. 4.

3D image stacks and orthogonal views (y-cut) of fluorescent microbeads with 10 μm diameter in a 2D monolayer on a slide glass: (a) wide-field imaging, (b) conventional SIM, and (c) subtractive SIM with γ=0.07. Labels on x and z axis in the orthogonal views represent spatial scales (50 μm). Intensity profiles across the lines of the orthogonal views are also presented in terms of fluorescence normalized by the maximum: (d) wide-field imaging, (e) conventional SIM, and (f) subtractive SIM with γ=0.07.

Fig. 5.
Fig. 5.

Axial PSFs measured of wide-field imaging and from images of conventional and subtractive SIM (γ=0.07, 0.14 and 0.21).

Fig. 6.
Fig. 6.

3D image stacks and orthogonal views (y-cut) of 3D microbead assays in a 1 mm thick alginate gel matrix: (a) wide-field imaging, (b) conventional SIM, and (c) subtractive SIM (γ=0.07). Labels in the orthogonal views represent different spatial scales in the x and z axis (50 and 250 μm). Orthogonal views are also presented: (d) wide-field imaging, (e) conventional SIM, and (f) subtractive SIM with γ=0.07. Horizontal and vertical lines in the orthogonal views represent those along which intensity profiles are provided in Fig. 7.

Fig. 7.
Fig. 7.

Intensity profiles across the lines of the orthogonal views presented in Fig. 6 in terms of fluorescence normalized by the maximum: (a) z=900μm and (b) z=545μm along the x axis, (c) z=145μm and (d) z=238μm along the z axis. The intensity profile in the top, middle, and bottom of each figure is respectively from wide-field imaging, conventional SIM, and subtractive SIM with γ=0.07.

Fig. 8.
Fig. 8.

Grid pattern noise that appears in SIM: (a) θ=0, (b) π/4, (c) π/2, and (d) 3π/4. Reduced grid pattern noise: (e) mean fluorescence image of SIM, given by Eq. (8), and (f) subtractive SIM.

Equations (11)

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S(x,y)=1+cos[v0(xcosθysinθ)ϕ].
Iimage(x,y)=Iin-focus(x,y)IS(x,y)+Iout-of-focus(x,y),
Iimage(x,y)=ICON(x,y)+ISIN(x,y)sinϕ+ICOS(x,y)cosϕ.
Iin-focus(x,y)={ISIN(x,y)}2+{ICOS(x,y)}2.
[Iϕ=0Iϕ=2π3Iϕ=4π3]=R[ICONISINICOS],
R=[1011sin(2π3)cos(2π3)1sin(4π3)cos(4π3)],
[ICONISINICOS]=(RTR)1RT[Iϕ=0Iϕ=2π3Iϕ=4π3].
Ia=(Iθ=0+Iθ=π4+Iθ=π2+Iθ=3π4)4.
Ia=Iin-focus+pIout-of-focus,
Iw=Iin-focus+(p+q)Iout-of-focus,
Is=IaγIw=(1γ)Iin-focus+[pγ(p+q)]Iout-of-focus.

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