## Computational modeling of optical projection tomographic microscopy using the finite difference time domain method |

JOSA A, Vol. 29, Issue 12, pp. 2696-2707 (2012)

http://dx.doi.org/10.1364/JOSAA.29.002696

Acrobat PDF (806 KB)

### Abstract

We present a method for modeling image formation in optical projection tomographic microscopy (OPTM) using high numerical aperture (NA) condensers and objectives. Similar to techniques used in computed tomography, OPTM produces three-dimensional, reconstructed images of single cells from two-dimensional projections. The model is capable of simulating axial scanning of a microscope objective to produce projections, which are reconstructed using filtered backprojection. Simulation of optical scattering in transmission optical microscopy is designed to analyze all aspects of OPTM image formation, such as degree of specimen staining, refractive-index matching, and objective scanning. In this preliminary work, a set of simulations is performed to examine the effect of changing the condenser NA, objective scan range, and complex refractive index on the final reconstruction of a microshell with an outer radius of 1.5 μm and an inner radius of 0.9 μm. The model lays the groundwork for optimizing OPTM imaging parameters and triaging efforts to further improve the overall system design. As the model is expanded in the future, it will be used to simulate a more realistic cell, which could lead to even greater impact.

© 2012 Optical Society of America

## 1. INTRODUCTION

1. Q. Miao, A. P. Reeves, F. W. Patten, and E. J. Seibel, “Multimodal 3D imaging of cells and tissue: bridging the gap between clinical and research microscopy,” Ann. Biomed. Eng. **40**, 263–276 (2012). [CrossRef]

2. M. G. Meyer, M. Fauver, J. R. Rahn, T. Neumann, and F. W. Patten, “Automated cell analysis in 2D and 3D: a comparative study,” Pattern Recogn. **42**, 141–146 (2009). [CrossRef]

3. M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express **13**, 4210–4223 (2005). [CrossRef]

3. M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express **13**, 4210–4223 (2005). [CrossRef]

5. N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. **12**, 285–314 (2010). [CrossRef]

6. H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. **69**, 5357–5363 (2009). [CrossRef]

7. I. R. Çapoglu, C. A. White, J. D. Rogers, H. Subramanian, A. Taflove, and V. Backman, “Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method,” Opt. Lett. **36**, 1596–1598 (2011). [CrossRef]

8. C. Smithpeter, A. K. Dunn, R. Drezek, T. Collier, and R. Richards-Kortum, “Near real time confocal microscopy of cultured amelanotic cells: sources of signal, contrast agents and limits of contrast,” J. Biomed. Opt. **3**, 429–436 (1998). [CrossRef]

### A. Optical Projection Tomographic Microscopy

*a priori*in accordance with the size of the cells being imaged. For example, lung epithelial cells are approximately 10 μm in diameter, so the scan distance is set to 12 μm. The microcapillary has a similar RI to the optical gel and index-matching immersion fluid such that its cylindrical geometry is transparent and nonrefractive [3

3. M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express **13**, 4210–4223 (2005). [CrossRef]

### B. Modeling

9. N. Nakajima, “Phase retrieval from a high-numerical-aperture intensity distribution by use of an aperture-array filter,” J. Opt. Soc. Am. A **26**, 2172–2180 (2009). [CrossRef]

10. M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik **112**, 399–406 (2001). [CrossRef]

11. F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. **23**, 4140–4148 (1984). [CrossRef]

12. G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. **11**, 22–34 (1994). [CrossRef]

13. P. Török, P. R. T. Munro, and E. E. Kriezis, “Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A **23**, 713–722 (2006). [CrossRef]

14. I. R. Çapoglu, A. Taflove, and V. Backman, “Generation of an incident focused light pulse in FDTD,” Opt. Express **16**, 19208–19220 (2008). [CrossRef]

16. R. L. Coe and E. J. Seibel, “Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method,” J. Opt. Soc. Am. A **28**, 1776–1783 (2011). [CrossRef]

17. P. R. T. Munro and P. Török, “Calculation of the image of an arbitrary vectorial electromagnetic field,” Opt. Express **15**, 9293–9307 (2007). [CrossRef]

14. I. R. Çapoglu, A. Taflove, and V. Backman, “Generation of an incident focused light pulse in FDTD,” Opt. Express **16**, 19208–19220 (2008). [CrossRef]

18. J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antennas. Propag. **54**, 2531–2542 (2006). [CrossRef]

16. R. L. Coe and E. J. Seibel, “Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method,” J. Opt. Soc. Am. A **28**, 1776–1783 (2011). [CrossRef]

## 2. THEORY

**13**, 4210–4223 (2005). [CrossRef]

14. I. R. Çapoglu, A. Taflove, and V. Backman, “Generation of an incident focused light pulse in FDTD,” Opt. Express **16**, 19208–19220 (2008). [CrossRef]

19. P. Török, P. R. T. Munro, and E. E. Kriezis, “High numerical aperture vectorial imaging in coherent optical microscopes,” Opt. Express **16**, 507–523 (2008). [CrossRef]

### A. Illumination

7. I. R. Çapoglu, C. A. White, J. D. Rogers, H. Subramanian, A. Taflove, and V. Backman, “Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method,” Opt. Lett. **36**, 1596–1598 (2011). [CrossRef]

*et al.*use spherical variables of integration to discretize the aperture [14

**16**, 19208–19220 (2008). [CrossRef]

22. I. R. Capoglu, J. D. Rogers, A. Taflove, and V. Backman, “The microscope in a computer: Image synthesis from three-dimensional full-vector solutions of Maxwell’s equations at the nanometer scale,” Prog. Opt.57, 1–91 (2012). [CrossRef]

### B. Numerical Method

*vice versa*. In this scheme it is important to understand that the relative permittivity and permeability are directly linked to the complex RI (

23. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. **14**, 302–307 (1966). [CrossRef]

24. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. **114**, 185–200 (1994). [CrossRef]

25. J. A. Roden and S. D. Gedney, “Convolution PML (CPML): an efficient FDTD implementation of the CFS–PML for arbitrary media,” Microw. Opt. Technol. Lett. **27**, 334–339 (2000). [CrossRef]

**16**, 19208–19220 (2008). [CrossRef]

26. D. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. **27**, 1829–1833 (1980). [CrossRef]

### C. Resampling

19. P. Török, P. R. T. Munro, and E. E. Kriezis, “High numerical aperture vectorial imaging in coherent optical microscopes,” Opt. Express **16**, 507–523 (2008). [CrossRef]

27. T. Martin, “An improved near- to far-zone transformation for the finite-difference time-domain method,” IEEE Trans. Antennas Propag. **46**, 1263–1271 (1998). [CrossRef]

28. D. J. Robinson and J. B. Schneider, “On the use of the geometric mean in FDTD near-to-far-field transformations,” IEEE Trans. Antennas Propag. **55**, 3204–3211 (2007). [CrossRef]

28. D. J. Robinson and J. B. Schneider, “On the use of the geometric mean in FDTD near-to-far-field transformations,” IEEE Trans. Antennas Propag. **55**, 3204–3211 (2007). [CrossRef]

16. R. L. Coe and E. J. Seibel, “Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method,” J. Opt. Soc. Am. A **28**, 1776–1783 (2011). [CrossRef]

27. T. Martin, “An improved near- to far-zone transformation for the finite-difference time-domain method,” IEEE Trans. Antennas Propag. **46**, 1263–1271 (1998). [CrossRef]

29. T. Martin, “On the FDTD near-to-far-field transformations for weakly scattering objects,” IEEE Trans. Antennas Propag. **58**, 2794–2795 (2010). [CrossRef]

### D. Image Formation

19. P. Török, P. R. T. Munro, and E. E. Kriezis, “High numerical aperture vectorial imaging in coherent optical microscopes,” Opt. Express **16**, 507–523 (2008). [CrossRef]

*m-theory*of diffraction determines the contribution from each equivalent magnetic dipole across the infinite plane to find the electromagnetic field at any observation point on the infinite half plane extending to

**16**, 507–523 (2008). [CrossRef]

### E. Simulating a Projection

### F. Three-Dimensional Image Reconstruction

## 3. METHODS

31. 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]

32. N. Martini, J. Bewersdorf, and S. W. Hell, “A new high-aperture glycerol immersion objective lens and its application to 3D-fluorescence microscopy,” J. Microsc. **206**, 146–151 (2002). [CrossRef]

33. X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. **48**, 4165–4172 (2003). [CrossRef]

*imrotate*function with linear interpolation. The projection is the result of integrating every frequency, focal plane, and scan position [Eq. (13) and Fig. 4]. Reconstructions using the projections are performed with the MATLAB

*iradon*function using the Ram–Lak filter where the simulated projection is replicated 500 times to mimic OPTM acquisition every 0.72° over the entire 360° of rotation.

## 4. RESULTS

35. T. H. Chow, W. M. Lee, K. M. Tan, B. K. Ng, and C. J. R. Sheppard, “Resolving interparticle position and optical forces along the axial direction using optical coherence gating,” Appl. Phys. Lett. **97**, 231113 (2010). [CrossRef]

37. J. J. Schwartz, S. Stavrakis, and S. R. Quake, “Colloidal lenses allow high-temperature single-molecule imaging and improve fluorophore photostability,” Nat. Nanotechnol. **5**, 127–132 (2009). [CrossRef]

35. T. H. Chow, W. M. Lee, K. M. Tan, B. K. Ng, and C. J. R. Sheppard, “Resolving interparticle position and optical forces along the axial direction using optical coherence gating,” Appl. Phys. Lett. **97**, 231113 (2010). [CrossRef]

## 5. DISCUSSION

- 1. High-NA condensers preserve axial shape information more effectively when compared to low NA condensers.
- 2. High-NA condensers should be scanned in conjunction with the objective to equally weight all axial information of the object in the projections.
- 3. Refractive-index differences do not significantly affect reconstructions for data acquired using high NA condensers.
- 4. Improved scanning based on
*a priori*information is necessary for high-NA condensers to eliminate blooming effect.

38. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods **4**, 717–719 (2007). [CrossRef]

39. R. Drezek, A. Dunn, and R. Richards-Kortum, “Light scattering from cells: finite-difference time-domain simulations and goniometric measurements,” Appl. Opt. **38**, 3651–3661 (1999). [CrossRef]

40. R. Drezek, A. Dunn, and R. Richards-Kortum, “A pulsed finite-difference time-domain (FDTD) method for calculating light scattering from biological cells over broad wavelength ranges,” Opt. Express **6**, 147–157 (2000). [CrossRef]

41. H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. **34**, 518–520 (2009). [CrossRef]

## 6. CONCLUSION

## ACKNOWLEDGMENTS

## REFERENCES

1. | Q. Miao, A. P. Reeves, F. W. Patten, and E. J. Seibel, “Multimodal 3D imaging of cells and tissue: bridging the gap between clinical and research microscopy,” Ann. Biomed. Eng. |

2. | M. G. Meyer, M. Fauver, J. R. Rahn, T. Neumann, and F. W. Patten, “Automated cell analysis in 2D and 3D: a comparative study,” Pattern Recogn. |

3. | M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express |

4. | I. T. Young, “Quantitative microscopy,” IEEE Eng. Med. Biol. |

5. | N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. |

6. | H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. |

7. | I. R. Çapoglu, C. A. White, J. D. Rogers, H. Subramanian, A. Taflove, and V. Backman, “Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method,” Opt. Lett. |

8. | C. Smithpeter, A. K. Dunn, R. Drezek, T. Collier, and R. Richards-Kortum, “Near real time confocal microscopy of cultured amelanotic cells: sources of signal, contrast agents and limits of contrast,” J. Biomed. Opt. |

9. | N. Nakajima, “Phase retrieval from a high-numerical-aperture intensity distribution by use of an aperture-array filter,” J. Opt. Soc. Am. A |

10. | M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik |

11. | F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. |

12. | G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. |

13. | P. Török, P. R. T. Munro, and E. E. Kriezis, “Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A |

14. | I. R. Çapoglu, A. Taflove, and V. Backman, “Generation of an incident focused light pulse in FDTD,” Opt. Express |

15. | A. Taflove and S. C. Hagness, |

16. | R. L. Coe and E. J. Seibel, “Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method,” J. Opt. Soc. Am. A |

17. | P. R. T. Munro and P. Török, “Calculation of the image of an arbitrary vectorial electromagnetic field,” Opt. Express |

18. | J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antennas. Propag. |

19. | P. Török, P. R. T. Munro, and E. E. Kriezis, “High numerical aperture vectorial imaging in coherent optical microscopes,” Opt. Express |

20. | B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A |

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

22. | I. R. Capoglu, J. D. Rogers, A. Taflove, and V. Backman, “The microscope in a computer: Image synthesis from three-dimensional full-vector solutions of Maxwell’s equations at the nanometer scale,” Prog. Opt.57, 1–91 (2012). [CrossRef] |

23. | K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. |

24. | J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. |

25. | J. A. Roden and S. D. Gedney, “Convolution PML (CPML): an efficient FDTD implementation of the CFS–PML for arbitrary media,” Microw. Opt. Technol. Lett. |

26. | D. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. |

27. | T. Martin, “An improved near- to far-zone transformation for the finite-difference time-domain method,” IEEE Trans. Antennas Propag. |

28. | D. J. Robinson and J. B. Schneider, “On the use of the geometric mean in FDTD near-to-far-field transformations,” IEEE Trans. Antennas Propag. |

29. | T. Martin, “On the FDTD near-to-far-field transformations for weakly scattering objects,” IEEE Trans. Antennas Propag. |

30. | A. C. Kak and M. Slaney, |

31. | M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. |

32. | N. Martini, J. Bewersdorf, and S. W. Hell, “A new high-aperture glycerol immersion objective lens and its application to 3D-fluorescence microscopy,” J. Microsc. |

33. | X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. |

34. | C. Guiffaut and K. Mahdjoubi, “Perfect wideband plane wave injector for FDTD method,” in |

35. | T. H. Chow, W. M. Lee, K. M. Tan, B. K. Ng, and C. J. R. Sheppard, “Resolving interparticle position and optical forces along the axial direction using optical coherence gating,” Appl. Phys. Lett. |

36. | J. P. Brody and S. R. Quake, “A self-assembled microlensing rotational probe,” Appl. Phys. Lett. |

37. | J. J. Schwartz, S. Stavrakis, and S. R. Quake, “Colloidal lenses allow high-temperature single-molecule imaging and improve fluorophore photostability,” Nat. Nanotechnol. |

38. | W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods |

39. | R. Drezek, A. Dunn, and R. Richards-Kortum, “Light scattering from cells: finite-difference time-domain simulations and goniometric measurements,” Appl. Opt. |

40. | R. Drezek, A. Dunn, and R. Richards-Kortum, “A pulsed finite-difference time-domain (FDTD) method for calculating light scattering from biological cells over broad wavelength ranges,” Opt. Express |

41. | H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. |

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(110.2990) Imaging systems : Image formation theory

(180.6900) Microscopy : Three-dimensional microscopy

(290.0290) Scattering : Scattering

(050.1755) Diffraction and gratings : Computational electromagnetic methods

**ToC Category:**

Microscopy

**History**

Original Manuscript: September 21, 2012

Revised Manuscript: November 2, 2012

Manuscript Accepted: November 7, 2012

Published: November 30, 2012

**Virtual Issues**

Vol. 8, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Ryan L. Coe and Eric J. Seibel, "Computational modeling of optical projection tomographic microscopy using the finite difference time domain method," J. Opt. Soc. Am. A **29**, 2696-2707 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-29-12-2696

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### References

- Q. Miao, A. P. Reeves, F. W. Patten, and E. J. Seibel, “Multimodal 3D imaging of cells and tissue: bridging the gap between clinical and research microscopy,” Ann. Biomed. Eng. 40, 263–276 (2012). [CrossRef]
- M. G. Meyer, M. Fauver, J. R. Rahn, T. Neumann, and F. W. Patten, “Automated cell analysis in 2D and 3D: a comparative study,” Pattern Recogn. 42, 141–146 (2009). [CrossRef]
- M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13, 4210–4223 (2005). [CrossRef]
- I. T. Young, “Quantitative microscopy,” IEEE Eng. Med. Biol. 15, 59–66 (1996). [CrossRef]
- N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. 12, 285–314 (2010). [CrossRef]
- H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J. Chang, and V. Backman, “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy,” Cancer Res. 69, 5357–5363 (2009). [CrossRef]
- I. R. Çapoglu, C. A. White, J. D. Rogers, H. Subramanian, A. Taflove, and V. Backman, “Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method,” Opt. Lett. 36, 1596–1598 (2011). [CrossRef]
- C. Smithpeter, A. K. Dunn, R. Drezek, T. Collier, and R. Richards-Kortum, “Near real time confocal microscopy of cultured amelanotic cells: sources of signal, contrast agents and limits of contrast,” J. Biomed. Opt. 3, 429–436 (1998). [CrossRef]
- N. Nakajima, “Phase retrieval from a high-numerical-aperture intensity distribution by use of an aperture-array filter,” J. Opt. Soc. Am. A 26, 2172–2180 (2009). [CrossRef]
- M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik 112, 399–406 (2001). [CrossRef]
- F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984). [CrossRef]
- G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994). [CrossRef]
- P. Török, P. R. T. Munro, and E. E. Kriezis, “Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A 23, 713–722 (2006). [CrossRef]
- I. R. Çapoglu, A. Taflove, and V. Backman, “Generation of an incident focused light pulse in FDTD,” Opt. Express 16, 19208–19220 (2008). [CrossRef]
- A. Taflove and S. C. Hagness,Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
- R. L. Coe and E. J. Seibel, “Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method,” J. Opt. Soc. Am. A 28, 1776–1783 (2011). [CrossRef]
- P. R. T. Munro and P. Török, “Calculation of the image of an arbitrary vectorial electromagnetic field,” Opt. Express 15, 9293–9307 (2007). [CrossRef]
- J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antennas. Propag. 54, 2531–2542 (2006). [CrossRef]
- P. Török, P. R. T. Munro, and E. E. Kriezis, “High numerical aperture vectorial imaging in coherent optical microscopes,” Opt. Express 16, 507–523 (2008). [CrossRef]
- B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959). [CrossRef]
- M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1980).
- I. R. Capoglu, J. D. Rogers, A. Taflove, and V. Backman, “The microscope in a computer: Image synthesis from three-dimensional full-vector solutions of Maxwell’s equations at the nanometer scale,” Prog. Opt.57, 1–91 (2012). [CrossRef]
- K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966). [CrossRef]
- J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
- J. A. Roden and S. D. Gedney, “Convolution PML (CPML): an efficient FDTD implementation of the CFS–PML for arbitrary media,” Microw. Opt. Technol. Lett. 27, 334–339 (2000). [CrossRef]
- D. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27, 1829–1833 (1980). [CrossRef]
- T. Martin, “An improved near- to far-zone transformation for the finite-difference time-domain method,” IEEE Trans. Antennas Propag. 46, 1263–1271 (1998). [CrossRef]
- D. J. Robinson and J. B. Schneider, “On the use of the geometric mean in FDTD near-to-far-field transformations,” IEEE Trans. Antennas Propag. 55, 3204–3211 (2007). [CrossRef]
- T. Martin, “On the FDTD near-to-far-field transformations for weakly scattering objects,” IEEE Trans. Antennas Propag. 58, 2794–2795 (2010). [CrossRef]
- A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
- 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]
- N. Martini, J. Bewersdorf, and S. W. Hell, “A new high-aperture glycerol immersion objective lens and its application to 3D-fluorescence microscopy,” J. Microsc. 206, 146–151 (2002). [CrossRef]
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