## Point-spread function engineering to reduce the impact of spherical aberration on 3D computational fluorescence microscopy imaging |

Optics Express, Vol. 19, Issue 23, pp. 23298-23314 (2011)

http://dx.doi.org/10.1364/OE.19.023298

Acrobat PDF (5157 KB)

### Abstract

Wavefront encoding (WFE) with different cubic phase mask designs was investigated in engineering 3D point-spread functions (PSF) to reduce their sensitivity to depth-induced spherical aberration (SA) which affects computational complexity in 3D microscopy imaging. The sensitivity of WFE-PSFs to defocus and to SA was evaluated as a function of phase mask parameters using mean-square-error metrics to facilitate the selection of mask designs for extended-depth-of-field (EDOF) microscopy and for computational optical sectioning microscopy (COSM). Further studies on pupil phase contribution and simulated WFE-microscope images evaluated the engineered PSFs and demonstrated SA insensitivity over sample depths of 30 μm. Despite its low sensitivity to SA, the successful WFE design for COSM maintains a high sensitivity to defocus as it is desired for optical sectioning.

© 2011 OSA

## 1. Introduction

1. E. R. Dowski Jr and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. **34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

2. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express **16**(26), 22048–22057 (2008). [CrossRef] [PubMed]

3. S. C. Tucker and W. T. Cathey, and E. Dowski Jr., “Extended depth of field and aberration control for inexpensive digital microscope systems,” Opt. Express **4**(11), 467–474 (1999). [CrossRef] [PubMed]

5. P. M. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. E. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. A. Agard, and J. W. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U.S.A. **107**(37), 16016–16022 (2010). [CrossRef] [PubMed]

6. J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods **19**(3), 373–385 (1999). [CrossRef] [PubMed]

8. D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. **13**(1), 191–219 (1984). [CrossRef] [PubMed]

9. J.-A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods **2**(12), 920–931 (2005). [CrossRef] [PubMed]

8. D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. **13**(1), 191–219 (1984). [CrossRef] [PubMed]

12. S. Yuan and C. Preza, “3D fluorescence microscopy imaging accounting for depth-varying point-spread functions predicted by a strata interpolation method and a principal component analysis method,” in *Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVIII*, (SPIE, 2011), 79040M.

13. S. F. Gibson and F. Lanni, “Experimental Test of an analytical Model of Aberration in an Oil-Immersion Objective Lens Used in 3-dimensional Light Microscopy,” J. Opt. Soc. Am. A **9**(1), 154–166 (1992). [CrossRef] [PubMed]

14. P. Török, P. Varga, and G. Nemeth, “Analytical solution of the diffection integrals and interpretation of wave-front distortion when light is focused through a planar interface between materials of mismatched refractive indices,” J. Opt. Soc. Am. A **12**(12), 2660–2671 (1995). [CrossRef]

15. J. G. McNally, C. Preza, J.-A. Conchello, and L. J. Thomas Jr., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A **11**(3), 1056–1067 (1994). [CrossRef] [PubMed]

16. J. W. Shaevitz and D. A. Fletcher, “Enhanced three-dimensional deconvolution microscopy using a measured depth-varying point-spread function,” J. Opt. Soc. Am. A **24**(9), 2622–2627 (2007). [CrossRef] [PubMed]

12. S. Yuan and C. Preza, “3D fluorescence microscopy imaging accounting for depth-varying point-spread functions predicted by a strata interpolation method and a principal component analysis method,” in *Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVIII*, (SPIE, 2011), 79040M.

18. C. Preza and J.-A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A **21**(9), 1593–1601 (2004). [CrossRef] [PubMed]

19. G. Saavedra, I. Escobar, R. Martinez-Cuenca, E. Sanchez-Ortiga, and M. Martínez-Corral, “Reduction of spherical-aberration impact in microscopy by wavefront coding,” Opt. Express **17**(16), 13810–13818 (2009). [CrossRef] [PubMed]

20. S. Mezouari and A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. **28**(10), 771–773 (2003). [CrossRef] [PubMed]

1. E. R. Dowski Jr and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. **34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

22. H. Zhao, Y. C. Li, H. J. Feng, Z. H. Xu, and Q. Li, “Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system,” Opt. Laser Technol. **42**(4), 561–569 (2010). [CrossRef]

25. S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase plate to extend the depth of field of incoherent hybrid imaging systems,” Appl. Opt. **43**(13), 2709–2721 (2004). [CrossRef] [PubMed]

1. E. R. Dowski Jr and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. **34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

22. H. Zhao, Y. C. Li, H. J. Feng, Z. H. Xu, and Q. Li, “Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system,” Opt. Laser Technol. **42**(4), 561–569 (2010). [CrossRef]

23. G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. **48**(7-8), 779–785 (2010). [CrossRef]

**34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

22. H. Zhao, Y. C. Li, H. J. Feng, Z. H. Xu, and Q. Li, “Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system,” Opt. Laser Technol. **42**(4), 561–569 (2010). [CrossRef]

**42**(4), 561–569 (2010). [CrossRef]

23. G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. **48**(7-8), 779–785 (2010). [CrossRef]

## 2. Theory

### 2.1 Wavefront encoded PSF (WFE-PSF)

*λ*is the emission wavelength, and

### 2.2 Image formation model in the presence of SA

*O*and

## 3. Methods

### 3.1 Phase mask design patterns

**34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

23. G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. **48**(7-8), 779–785 (2010). [CrossRef]

**42**(4), 561–569 (2010). [CrossRef]

**34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

### 3.2 Computation of WFE-PSFs

13. S. F. Gibson and F. Lanni, “Experimental Test of an analytical Model of Aberration in an Oil-Immersion Objective Lens Used in 3-dimensional Light Microscopy,” J. Opt. Soc. Am. A **9**(1), 154–166 (1992). [CrossRef] [PubMed]

^{3}assuming that: a) the light point source is located at a different depth (

*n*= 1.33) below the coverslip; and b) a 60x/1.2 NA oil-immersion objective lens (RI,

_{water}*n*= 1.515) and an emission wavelength

_{oil}*λ*= 633 nm are used to image the point source.

_{emission}### 3.3 Simulated 3D images

^{3}. The origin of the

*x*plane is at the center of the grid, and the origin along the

_{o}y_{o}*z*axis is placed at the 100th

_{o}*x*plane. The (

_{o}y_{o}*x*,

_{o}*y*) coordinates of the three spheres are: (−5 μm, 5 μm), (0 μm, 0 μm), and (5 μm, −5 μm), from top to bottom. Objects 2 and 3 are similar to Object 1 except that the depths of all the spheres are increased by 10 μm and 20 μm, respectively, in order to allow simulation of images with larger amounts of SA. The RI of the 3 objects is assumed to be equal to 1.33, while the immersion medium of the lens is oil (i.e., RI = 1.515).

_{o}### 3.4 Metrics for phase mask design evaluation and selection

*Z*and

_{k}*Z*. For a 3D WFE-PSF without SA (

_{c}19. G. Saavedra, I. Escobar, R. Martinez-Cuenca, E. Sanchez-Ortiga, and M. Martínez-Corral, “Reduction of spherical-aberration impact in microscopy by wavefront coding,” Opt. Express **17**(16), 13810–13818 (2009). [CrossRef] [PubMed]

*Z*is determined from the conventional PSF. In general, a small NMSE

_{c}_{2D}value over a long range of

*z*indicates that the XY layers of the PSF are similar over the range, (i.e., the PSF is insensitive to defocus) and thus good EDOF is achieved in the WFE microscope.

_{i}_{2D}and NMSE

_{3D}were computed and plotted as a function of defocus and point source location, respectively, in order to investigate the sensitivity of the PSF to defocus and SA. The NMSE analysis was performed using WFE-PSFs on a 512 x 512 grid. PSFs computed on a larger grid were cropped to 512 x 512. Although cropping of the WFE-PSF can affect the values of NMSE

_{2D}and NMSE

_{3D}, we found that the effect was minimal and the results did not change significantly.

### 3.5 Merit function for phase mask parameter selection suitable for COSM

_{2D}and the NMSE

_{3D}, respectively, over the investigation range. In this study,

_{2D}value, (i.e. by increasing the sensitivity to defocus) while decreasing the value of the NMSE

_{3D}, (i.e. by lowering the sensitivity to SA). For all design parameter sets investigated (Section 3.1), Eq. (7) was calculated and the parameter set that yielded the largest

### 3.6 Computation of phase due to defocus and SA from 2D CCA-ATFs

*z*.

_{i}### 3.7 Computation of 2D Modulation Transfer Function (MTF)

## 4. Results

### 4.1 Effect of mask parameter α on the sensitivity of the CPM-PSF to defocus and SA

_{2D}computed for CPM PSFs without SA (

_{2D}decrease as the value of α increases indicating that better EDOF is achieved. This result is consistent with a prior reported result [1

**34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

_{3D}computed using PSFs with increasing amounts of SA (denoted by the increasing Z location of the point source which is equivalent to

### 4.2 Effect of mask parameters on the sensitivity of the GCPM-PSF to defocus and SA

_{2D}, computed for GCPM PSFs without SA (

_{2D}[Fig. 4(b)] indicating that the resulting 3D GCPM PSFs are similar in this case. When β = −3α [Fig. 4(c)], the NMSE

_{2D}plots show greater variability than the one observed when β = -α/3 [(Fig. 4(a)], and they also show a similar trend as the one observed for the CPM design [Fig. 3(a)]. Moreover in this case, the NMSE

_{2D}is lower for most α values than in other β cases, indicating a better achieved EDOF. This finding is consistent with prior reported results [23

**48**(7-8), 779–785 (2010). [CrossRef]

_{2D}is achieved at α = 150 for β = −3α

_{2D}plots (not shown) were obtained for PSFs with SA (for

_{3D}vs.

*z*, computed using PSFs with increasing amounts of SA obtained for different values of α when β = −3α. Similarly, Fig. 4(e) plots the computed NMSE

_{o}_{3D}for different values of β when α = 150. Among all conditions investigated in our study, the smallest NMSE

_{3D}is achieved for α = 150 when β = −3α.

### 4.3 Effect of mask parameters on the sensitivity of the SCPM-PSF to defocus and SA

_{2D}and NMSE

_{3D}. Some of the results from this study are summarized in Fig. 5 . The NMSE

_{2D}, computed from SCPM PSFs without SA, is plotted as a function of defocus for different α values when β = α/3 and ω = -π/2 [Fig. 5(a)]. Similar NMSE

_{2D}plots (not shown) were obtained for PSFs with SA (

_{3D}vs.

*z*, computed using PSFs with increasing amounts of SA obtained with the same parameter sets as in the case of the NMSE

_{o}_{2D}[Fig. 5(a)]. Overall, the trends observed in these results (Fig. 5) are similar with the ones for the GCPM case (Fig. 4).

### 4.4 Phase mask design selection for EDOF microscopy

_{2D}values over defocus as this supports the WFE-PSF’s insensitivity to defocus. In all the cases investigated for the CPM, GCPM and SCPM, these parameters also yielded the smallest NMSE

_{3D}.

_{2D}computed from PSFs without SA (

*z*= 0 μm) and with SA (

_{o}*z*= 20 μm) for the 3 selected CPM-based designs is plotted as a function of defocus in Fig. 6(a) and Fig. 6(b), respectively. Figure 6(c) plots NMSE

_{o}_{3D}computed using PSFs with increasing amounts of SA vs.

*z*for the 3 CPM-based designs. Among the 3 designs, the selected SCPM design (with α = 150, β = α/3 and ω = -π/2) achieves the best NMSE

_{o}_{2D}performance, while the selected GCPM design (α = 150 and β = −3α) achieves the best NMSE

_{3D}performance and an acceptable NMSE

_{2D}performance. Thus, from this comparison study, the GCPM design is selected for EDOF microscopy in the presence of SA.

### 4.5 Phase mask design selection for COSM

_{2D}computed from PSFs without SA (

*z*= 0 μm) and with SA (

_{o}*z*= 20 μm) is plotted as a function of defocus in Fig. 7(a) and Fig. 7(b), respectively. Figure 7(c) plots NMSE

_{o}_{3D}computed using PSFs with increasing amounts of SA vs.

*z*for the 3 CPM-based designs. As it is evident, the CCA-PSF has the largest sensitivity to both defocus and SA among the compared PSFs [Figs. 7(a-c)]. This is also confirmed by comparing the resulting peak

_{o}_{2D}and NMSE

_{3D}, and has the largest

### 4.6 Comparison of selected GCPM to the CCA-ATF phase

### 4.7 WFE-PSFs with selected designs

*z*range.

### 4.8 Simulated 3D intermediate images from EDOF microscopy

### 4.9 Simulated 3D intermediate images from WFE-COSM

## 5. Discussion

**34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

*xy*plane [Figs. 2(b) and 9(c)] compared to the CCA-PSF [Fig. 2(a)]. The large extend of the WFE-PSF in the

*xy*plane imposes new constraints on image dimensions used for the finite-discrete domain implementation of the forward and inverse imaging problems (due to the crosstalk between multiple fluorescence points in the underlying specimen), which increase computational complexity. The tradeoff between achieved EDOF and computational complexity can be controlled by the chosen α value.

**34**(11), 1859–1866 (1995). [CrossRef] [PubMed]

*f*(Fig. 12e). Thus, it is anticipated that the EDOF-GCPM design will yield final reconstructed images with lower SNR than GCPM designs with a smaller α value. Another finding from Fig. 12(e) is that for the GCPM designs investigated in this study, a limited amount of SA had very little impact on its MTF characteristics, while the α value had some impact on the MTF characteristics as discussed above. For applications with large noise or applications requiring high SNR, the α value must be carefully selected. Furthermore, in some cases, EDOF and SA insensitivity, associated with a high α value, might have to be traded off to reach a required SNR level.

_{p}27. O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,” Opt. Commun. **216**(1-3), 55–63 (2003). [CrossRef]

27. O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,” Opt. Commun. **216**(1-3), 55–63 (2003). [CrossRef]

## 6. Conclusion

## Acknowledgement

## References and Links

1. | E. R. Dowski Jr and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. |

2. | S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express |

3. | S. C. Tucker and W. T. Cathey, and E. Dowski Jr., “Extended depth of field and aberration control for inexpensive digital microscope systems,” Opt. Express |

4. | M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in |

5. | P. M. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. E. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. A. Agard, and J. W. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U.S.A. |

6. | J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods |

7. | J.-B. Sibarita, “Deconvolution Microscopy,” in |

8. | D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. |

9. | J.-A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods |

10. | C. Preza and J. A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A |

11. | Z. Kam, P. Kner, D. A. Agard, and J. W. Sedat, “Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc. |

12. | S. Yuan and C. Preza, “3D fluorescence microscopy imaging accounting for depth-varying point-spread functions predicted by a strata interpolation method and a principal component analysis method,” in |

13. | S. F. Gibson and F. Lanni, “Experimental Test of an analytical Model of Aberration in an Oil-Immersion Objective Lens Used in 3-dimensional Light Microscopy,” J. Opt. Soc. Am. A |

14. | P. Török, P. Varga, and G. Nemeth, “Analytical solution of the diffection integrals and interpretation of wave-front distortion when light is focused through a planar interface between materials of mismatched refractive indices,” J. Opt. Soc. Am. A |

15. | J. G. McNally, C. Preza, J.-A. Conchello, and L. J. Thomas Jr., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A |

16. | J. W. Shaevitz and D. A. Fletcher, “Enhanced three-dimensional deconvolution microscopy using a measured depth-varying point-spread function,” J. Opt. Soc. Am. A |

17. | C. Preza and V. Myneni, “Quantitative depth-variant imaging for fluorescence microscopy using the COSMOS software package,” in |

18. | C. Preza and J.-A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A |

19. | G. Saavedra, I. Escobar, R. Martinez-Cuenca, E. Sanchez-Ortiga, and M. Martínez-Corral, “Reduction of spherical-aberration impact in microscopy by wavefront coding,” Opt. Express |

20. | S. Mezouari and A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. |

21. | M. R. Arnison, “Phase control and measurement in digital microscopy,” Ph.D. dissertation (University of Sydney, Sydney, 2004). |

22. | H. Zhao, Y. C. Li, H. J. Feng, Z. H. Xu, and Q. Li, “Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system,” Opt. Laser Technol. |

23. | G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. |

24. | S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. |

25. | S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase plate to extend the depth of field of incoherent hybrid imaging systems,” Appl. Opt. |

26. | S. Ghosh, G. Grover, R. Piestun, and C. Preza, “Effect of double-helix point-spread functions on 3D imaging in the presence of sphereical aberrations,” in |

27. | O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,” Opt. Commun. |

**OCIS Codes**

(180.6900) Microscopy : Three-dimensional microscopy

(350.4600) Other areas of optics : Optical engineering

(110.7348) Imaging systems : Wavefront encoding

**ToC Category:**

Microscopy

**History**

Original Manuscript: August 15, 2011

Revised Manuscript: October 4, 2011

Manuscript Accepted: October 13, 2011

Published: November 1, 2011

**Virtual Issues**

Vol. 7, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Shuai Yuan and Chrysanthe Preza, "Point-spread function engineering to reduce the impact of spherical aberration on 3D computational fluorescence microscopy imaging," Opt. Express **19**, 23298-23314 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-23-23298

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### References

- E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt.34(11), 1859–1866 (1995). [CrossRef] [PubMed]
- S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express16(26), 22048–22057 (2008). [CrossRef] [PubMed]
- S. C. Tucker and W. T. Cathey, and E. Dowski., “Extended depth of field and aberration control for inexpensive digital microscope systems,” Opt. Express4(11), 467–474 (1999). [CrossRef] [PubMed]
- M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical imaging and microscopy: techniques and advanced systems, P. Török and F.-J. Kao, eds. (Springer-Verlag, Berlin, 2003), pp. 143–165.
- P. M. Carlton, J. Boulanger, C. Kervrann, J.-B. Sibarita, J. Salamero, S. Gordon-Messer, D. Bressan, J. E. Haber, S. Haase, L. Shao, L. Winoto, A. Matsuda, P. Kner, S. Uzawa, M. Gustafsson, Z. Kam, D. A. Agard, and J. W. Sedat, “Fast live simultaneous multiwavelength four-dimensional optical microscopy,” Proc. Natl. Acad. Sci. U.S.A.107(37), 16016–16022 (2010). [CrossRef] [PubMed]
- J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods19(3), 373–385 (1999). [CrossRef] [PubMed]
- J.-B. Sibarita, “Deconvolution Microscopy,” in Microscopy Techniques, J. Rietdorf, ed. (Springer Berlin / Heidelberg, 2005), pp. 1288–1291.
- D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng.13(1), 191–219 (1984). [CrossRef] [PubMed]
- J.-A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods2(12), 920–931 (2005). [CrossRef] [PubMed]
- C. Preza and J. A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A21, 1593–1601 (2004).
- Z. Kam, P. Kner, D. A. Agard, and J. W. Sedat, “Modelling the application of adaptive optics to wide-field microscope live imaging,” J. Microsc.226(1), 33–42 (2007). [CrossRef] [PubMed]
- S. Yuan and C. Preza, “3D fluorescence microscopy imaging accounting for depth-varying point-spread functions predicted by a strata interpolation method and a principal component analysis method,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVIII, (SPIE, 2011), 79040M.
- S. F. Gibson and F. Lanni, “Experimental Test of an analytical Model of Aberration in an Oil-Immersion Objective Lens Used in 3-dimensional Light Microscopy,” J. Opt. Soc. Am. A9(1), 154–166 (1992). [CrossRef] [PubMed]
- P. Török, P. Varga, and G. Nemeth, “Analytical solution of the diffection integrals and interpretation of wave-front distortion when light is focused through a planar interface between materials of mismatched refractive indices,” J. Opt. Soc. Am. A12(12), 2660–2671 (1995). [CrossRef]
- J. G. McNally, C. Preza, J.-A. Conchello, and L. J. Thomas., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A11(3), 1056–1067 (1994). [CrossRef] [PubMed]
- J. W. Shaevitz and D. A. Fletcher, “Enhanced three-dimensional deconvolution microscopy using a measured depth-varying point-spread function,” J. Opt. Soc. Am. A24(9), 2622–2627 (2007). [CrossRef] [PubMed]
- C. Preza and V. Myneni, “Quantitative depth-variant imaging for fluorescence microscopy using the COSMOS software package,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing Xvii, SPIE 7570 (SPIE, 2010), 757003.
- C. Preza and J.-A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A21(9), 1593–1601 (2004). [CrossRef] [PubMed]
- G. Saavedra, I. Escobar, R. Martinez-Cuenca, E. Sanchez-Ortiga, and M. Martínez-Corral, “Reduction of spherical-aberration impact in microscopy by wavefront coding,” Opt. Express17(16), 13810–13818 (2009). [CrossRef] [PubMed]
- S. Mezouari and A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett.28(10), 771–773 (2003). [CrossRef] [PubMed]
- M. R. Arnison, “Phase control and measurement in digital microscopy,” Ph.D. dissertation (University of Sydney, Sydney, 2004).
- H. Zhao, Y. C. Li, H. J. Feng, Z. H. Xu, and Q. Li, “Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system,” Opt. Laser Technol.42(4), 561–569 (2010). [CrossRef]
- G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng.48(7-8), 779–785 (2010). [CrossRef]
- S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol.14(2), 67–74 (2004). [CrossRef]
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