## Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging |

Optics Express, Vol. 19, Issue 27, pp. 26249-26268 (2011)

http://dx.doi.org/10.1364/OE.19.026249

Acrobat PDF (10395 KB)

### Abstract

Fresnel Incoherent Correlation Holography (FINCH) enables holograms to be recorded from incoherent light with just a digital camera and spatial light modulator. We previously described its application to general three dimensional incoherent imaging and specifically to fluorescence microscopy, wherein one complex hologram contains the three dimensional information in the field of view, obviating the need for scanning or serial sectioning. We have now further analyzed FINCH in view of linear system theory and in comparison to conventional coherent and incoherent two dimensional imaging systems. We demonstrate, theoretically and experimentally, improved resolution by FINCH, when compared to conventional imaging.

© 2011 OSA

## 1. Introduction

1. S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express **15**(15), 9394–9402 (2007). [CrossRef] [PubMed]

2. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. **38**(34), 6994–7001 (1999). [CrossRef] [PubMed]

3. N. T. Shaked, T. M. Newpher, M. D. Ehlers, and A. Wax, “Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics,” Appl. Opt. **49**(15), 2872–2878 (2010). [CrossRef] [PubMed]

4. V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Superresolved imaging in digital holography by superposition of tilted wavefronts,” Appl. Opt. **45**(5), 822–828 (2006). [CrossRef] [PubMed]

5. P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, “Phase microscopy of technical and biological samples through random phase modulation with a diffuser,” Opt. Lett. **35**(7), 1028–1030 (2010). [CrossRef] [PubMed]

6. T.-W. Su, S. O. Isikman, W. Bishara, D. Tseng, A. Erlinger, and A. Ozcan, “Multi-angle lensless digital holography for depth resolved imaging on a chip,” Opt. Express **18**(9), 9690–9711 (2010). [CrossRef] [PubMed]

8. O. Mudanyali, W. Bishara, and A. Ozcan, “Lensfree super-resolution holographic microscopy using wetting films on a chip,” Opt. Express **19**(18), 17378–17389 (2011). [CrossRef] [PubMed]

9. Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express **18**(8), 8213–8219 (2010). [CrossRef] [PubMed]

10. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. **32**(8), 912–914 (2007). [CrossRef] [PubMed]

12. B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. **22**(19), 1506–1508 (1997). [CrossRef] [PubMed]

13. N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. **48**(34), H120–H136 (2009). [CrossRef] [PubMed]

14. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express **15**(5), 2244–2250 (2007). [CrossRef] [PubMed]

15. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics **2**(3), 190–195 (2008). [CrossRef]

16. G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express **19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

17. B. Katz, D. Wulich, and J. Rosen, “Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution,” Appl. Opt. **49**(30), 5757–5763 (2010). [CrossRef] [PubMed]

18. B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express **18**(2), 962–972 (2010). [CrossRef] [PubMed]

19. B. Katz and J. Rosen, “Could SAFE concept be applied for designing a new synthetic aperture telescope?” Opt. Express **19**(6), 4924–4936 (2011). [CrossRef] [PubMed]

1. S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express **15**(15), 9394–9402 (2007). [CrossRef] [PubMed]

5. P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, “Phase microscopy of technical and biological samples through random phase modulation with a diffuser,” Opt. Lett. **35**(7), 1028–1030 (2010). [CrossRef] [PubMed]

## 2. FINCH system analysis

### 2.1. Mathematical analysis

_{1}(an objective lens in the case of an infinity corrected microscope system). A more general and extensive analysis is given in Ref [16

16. G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express **19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

*f*is the focal length of lens L

_{o}_{1},

*d*is the distance between the lens L

_{1}and the SLM,

*z*is the distance between the SLM and the camera,

_{h}_{ρ¯=(u,v)}are the coordinates of the camera plane and

*B, B*’ are constants. For the sake of shortening, the quadratic phase function is designated by the function

*Q*, such that

_{Q(b)=exp[iπbλ−1(x2+y2)]}, where λ is the central wavelength of the light.

*L*denotes the linear phase function, such that

_{L(s¯)=exp[i2πλ−1(sxx+syy)]}, and

*P*(

*R*) stands for the limiting aperture of the system, where it is assumed that the aperture is a clear disk of radius

_{H}*R*determined by the overlap area of the two interfering beams on the camera plane. The expression in the square brackets of Eq. (1) describes the transparency of the SLM. This transparency is a combination of a constant valued mask with a diffractive positive spherical lens of focal length

_{H}*f*. In the past we presented two methods to display these two masks on the same SLM. The older, and less efficient, method is to randomly allocate half of the SLM pixels to each of the two masks [10

_{d}10. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. **32**(8), 912–914 (2007). [CrossRef] [PubMed]

14. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express **15**(5), 2244–2250 (2007). [CrossRef] [PubMed]

16. G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express **19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

*θ*is one of the three angles used in the phase shift procedure in order to eliminate the bias term and the twin image from the final hologram [10

10. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. **32**(8), 912–914 (2007). [CrossRef] [PubMed]

14. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express **15**(5), 2244–2250 (2007). [CrossRef] [PubMed]

18. B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express **18**(2), 962–972 (2010). [CrossRef] [PubMed]

22. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. **22**(16), 1268–1270 (1997). [CrossRef] [PubMed]

_{1}. This wave is multiplied by the lens L

_{1}

*d*[convolved with

*z*till the camera [convolved with

_{h}*P*(

*R*), is considered as part of the hologram. Finally, the magnitude of the interference is squared to yield the intensity distribution of the recoded hologram. It is easy to see from Fig. 1(a) and by calculating Eq. (1), that as long as the source point is located on the front focal plane of L

_{H}_{1}, the interference occurs between a plane and a spherical (in the paraxial approximation) wave.

*θ*are recorded and superposed in order to obtain a complex hologram of the object point, given by,where

*C’*is a constant and

*z*is the reconstruction distance from the hologram plane to the image plane calculated to be,

_{r}18. B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express **18**(2), 962–972 (2010). [CrossRef] [PubMed]

*M*/

_{T}= z_{h}*f*. The PSF of the system is obtained by reconstructing digitally the Fresnel hologram given in Eq. (2) at a distance

_{o}*z*from the hologram plane. The expression of the hologram in Eq. (2) contains a transparency of a positive lens with focal distance

_{r}*z*and hence, according to Fourier optics theory [11], the reconstructed image is,where

_{r}*C”*is a constant,

*v is*the scaling operator such that

*ν*[

*a*]

*f*(

*x*)=

*f*(

*ax*),

*Jinc*is defined as

*Jinc*(

*r*) =

*J*

_{1}(

*r*)/

*r*and

*J*

_{1}(

*r*) is the Bessel function of the first kind, of order one.

*L*is added to the intensity obtained by Eq. (6) in order to distinguish it from the non-linear reconstruction discussed next.

*Jinc*function of Eq. (5). This diameter remains the same for both the linear and non-linear reconstructions, and is equal to 1.22

*λz*According to Eq. (3),

_{r}/R_{H}.*z*|

_{r}=*z*| and therefore, based on a simple geometrical consideration, the radius of the hologram, which is the radius of the overlap area between the plane and the spherical beams, is,where

_{h}-f_{d}*R*is the radius of the smallest aperture in the system up to, and including, the SLM. For the projection of the spherical wave exceeds beyond the plane wave projection and therefore the radius of the overlap remains as

_{o}*λf*(1.4·

_{d}/*R*) and 0.61·

_{o}*λf*(1.5·

_{d}/*R*) in cases of linear and non-linear reconstruction, respectively. Therefore the resolution improvement of FINCH over a regular incoherent microscope is about a factor of 1.4 and 1.5 for linear and non-linear reconstruction, respectively. The FINCH’s resolution improvement over a coherent imaging system is a factor of 2.

_{o}### 2.2. Discussion

*φ*is the largest angle difference between the interfered beams in the system and

*z*. Therefore, in order to keep the system as diffraction limited as possible, the distance between the SLM and the camera should satisfy the condition,

_{h}_{zh≥4Roδ/λ}. Increasing the distance

*z*, while keeping the optimal condition

_{h}*z*and

_{h}### 2.3. Alternative FINCH configurations

*f*

_{2}focal distance. When the various parameters are chosen such that there is a perfect overlap between the two spherical waves on the camera plane,

*B*there is a transfer function of a negative lens as the following,

*M*/

_{T}= z_{h}*f*as before. Next, we make use of the fact that the two spherical waves perfectly overlap on the camera plane, and based on simple geometrical considerations, the following two relations are obtained, Substituting Eqs. (15)–(17) into Eq. (13) yields that effective width of FINCH’s PSF in the general configuration is

_{o}**15**(5), 2244–2250 (2007). [CrossRef] [PubMed]

15. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics **2**(3), 190–195 (2008). [CrossRef]

## 3. Experimental methods

**32**(8), 912–914 (2007). [CrossRef] [PubMed]

15. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics **2**(3), 190–195 (2008). [CrossRef]

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

## 4. Experimental results

*z*position of 1380 mm at which we were able to resolve the smallest features in the USAF pattern using FINCH with

_{h}*I*)/(

_{max}-I_{min}*I*) is a standard quantity used to characterize resolution. In this work, we examined visibility of the horizontal features in group 9, element 3, i.e. the smallest features. To define

_{max}+ I_{min}*I*, we located the row of pixels in each of the three features that had the highest summed intensity. We then averaged all the pixel values from those rows. To define

_{max}*I*, we located the row of pixels in each of the gaps between the features that had the lowest summed intensity, and then averaged the pixel values from those rows. Visual inspection of the images and the visibility calculations demonstrate that FINCH images resolve the smallest features better than images from the comparable standard microscope configuration at all effective NAs of the objective. Using the SLM as a tube lens produced images which had similar resolution to the glass tube lens up to an aperture of 8 mm, the approximate minimum size of the aperture of the SLM when viewed at a 45° angle in our setup.

_{min}*z*, which we call

_{h}/f_{d}*z-ratio*, using a reduced aperture of 5 mm since this dramatically reduced the imaging resolution of the objective under normal microscope conditions. Images at varying

*z-ratios*from 0.85 to 2.4 were recorded and are shown in Figs. 8 and 9 . Visual inspection of the images shows that the resolution continues to improve as

*z-ratio*increases from 0.85 and reaches a peak around

*z-ratio =*1.8 ± 0.2. Visibility data is presented in Fig. 10 . The maximum is not exactly at

**19**(6), 5047–5062 (2011). [CrossRef] [PubMed]

21. P. Bouchal, J. Kapitán, R. Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express **19**(16), 15603–15620 (2011). [CrossRef] [PubMed]

*z-ratio*of 1 and 2. Note that at

*z-ratio =*0.85 the visibility in the smallest group of lines is zero and therefore this point of data is not included in the plot of Fig. 10. However this result fits the prediction that the resolution of FINCH for

*z-ratio*<1 is lower than that of a regular microscope; as seen in Fig. 7, the visibility of the smallest group of lines, with objective back aperture of 5 mm, is 0.1.

## 5. Conclusions

- 1. FINCH is a hybrid system in the sense that its MTF has the shape of a coherent imaging system but in the optimal conditions, its spatial bandwidth is equal to that of an incoherent system.
- 2. The width of the PSF of FINCH, and accordingly its resolution, is dependent on its configuration and on the ratio between the distance from the SLM to the camera and the focal length of the diffractive lens. In all the possible configurations, the condition to obtain maximum resolution occurs when there is a perfect overlap between the projections of the two different interfering beams (originating from the same point source) on the camera sensing plane.
- 3. Under the optimal condition described in item 2, FINCH can resolve better than a regular glass-lenses-based imaging system with the same numerical aperture. In terms of Rayleigh criterion the improvement is between 1.5 and 2 fold in comparison to incoherent and coherent systems, respectively.

21. P. Bouchal, J. Kapitán, R. Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express **19**(16), 15603–15620 (2011). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express |

2. | E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. |

3. | N. T. Shaked, T. M. Newpher, M. D. Ehlers, and A. Wax, “Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics,” Appl. Opt. |

4. | V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Superresolved imaging in digital holography by superposition of tilted wavefronts,” Appl. Opt. |

5. | P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, “Phase microscopy of technical and biological samples through random phase modulation with a diffuser,” Opt. Lett. |

6. | T.-W. Su, S. O. Isikman, W. Bishara, D. Tseng, A. Erlinger, and A. Ozcan, “Multi-angle lensless digital holography for depth resolved imaging on a chip,” Opt. Express |

7. | M. Lee, O. Yaglidere, and A. Ozcan, “Field-portable reflection and transmission microscopy based on lensless holography,” Biomed. Opt. Express |

8. | O. Mudanyali, W. Bishara, and A. Ozcan, “Lensfree super-resolution holographic microscopy using wetting films on a chip,” Opt. Express |

9. | Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express |

10. | J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. |

11. | J. W. Goodman, |

12. | B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. |

13. | N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. |

14. | J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express |

15. | J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics |

16. | G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express |

17. | B. Katz, D. Wulich, and J. Rosen, “Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution,” Appl. Opt. |

18. | B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express |

19. | B. Katz and J. Rosen, “Could SAFE concept be applied for designing a new synthetic aperture telescope?” Opt. Express |

20. | Y. Tone, K. Nitta, O. Matoba, and Y. Awatsuji, “Analysis of reconstruction characteristics in fluorescence digital holography,” in |

21. | P. Bouchal, J. Kapitán, R. Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express |

22. | I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(090.1760) Holography : Computer holography

(090.1970) Holography : Diffractive optics

(090.2880) Holography : Holographic interferometry

(100.6890) Image processing : Three-dimensional image processing

(110.0180) Imaging systems : Microscopy

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.5060) Instrumentation, measurement, and metrology : Phase modulation

(180.2520) Microscopy : Fluorescence microscopy

(180.6900) Microscopy : Three-dimensional microscopy

(260.2510) Physical optics : Fluorescence

(090.1995) Holography : Digital holography

**ToC Category:**

Microscopy

**History**

Original Manuscript: October 19, 2011

Revised Manuscript: November 30, 2011

Manuscript Accepted: December 1, 2011

Published: December 8, 2011

**Virtual Issues**

Vol. 7, Iss. 2 *Virtual Journal for Biomedical Optics*

**Citation**

Joseph Rosen, Nisan Siegel, and Gary Brooker, "Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging," Opt. Express **19**, 26249-26268 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-27-26249

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### References

- S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. Denicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express15(15), 9394–9402 (2007). [CrossRef] [PubMed]
- E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt.38(34), 6994–7001 (1999). [CrossRef] [PubMed]
- N. T. Shaked, T. M. Newpher, M. D. Ehlers, and A. Wax, “Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics,” Appl. Opt.49(15), 2872–2878 (2010). [CrossRef] [PubMed]
- V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Superresolved imaging in digital holography by superposition of tilted wavefronts,” Appl. Opt.45(5), 822–828 (2006). [CrossRef] [PubMed]
- P. F. Almoro, G. Pedrini, P. N. Gundu, W. Osten, and S. G. Hanson, “Phase microscopy of technical and biological samples through random phase modulation with a diffuser,” Opt. Lett.35(7), 1028–1030 (2010). [CrossRef] [PubMed]
- T.-W. Su, S. O. Isikman, W. Bishara, D. Tseng, A. Erlinger, and A. Ozcan, “Multi-angle lensless digital holography for depth resolved imaging on a chip,” Opt. Express18(9), 9690–9711 (2010). [CrossRef] [PubMed]
- M. Lee, O. Yaglidere, and A. Ozcan, “Field-portable reflection and transmission microscopy based on lensless holography,” Biomed. Opt. Express2(9), 2721–2730 (2011). [CrossRef] [PubMed]
- O. Mudanyali, W. Bishara, and A. Ozcan, “Lensfree super-resolution holographic microscopy using wetting films on a chip,” Opt. Express19(18), 17378–17389 (2011). [CrossRef] [PubMed]
- Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express18(8), 8213–8219 (2010). [CrossRef] [PubMed]
- J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett.32(8), 912–914 (2007). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier optics, 3rd Ed., (Roberts and Company Publishers, 2005).
- B. W. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett.22(19), 1506–1508 (1997). [CrossRef] [PubMed]
- N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt.48(34), H120–H136 (2009). [CrossRef] [PubMed]
- J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express15(5), 2244–2250 (2007). [CrossRef] [PubMed]
- J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics2(3), 190–195 (2008). [CrossRef]
- G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express19(6), 5047–5062 (2011). [CrossRef] [PubMed]
- B. Katz, D. Wulich, and J. Rosen, “Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution,” Appl. Opt.49(30), 5757–5763 (2010). [CrossRef] [PubMed]
- B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express18(2), 962–972 (2010). [CrossRef] [PubMed]
- B. Katz and J. Rosen, “Could SAFE concept be applied for designing a new synthetic aperture telescope?” Opt. Express19(6), 4924–4936 (2011). [CrossRef] [PubMed]
- Y. Tone, K. Nitta, O. Matoba, and Y. Awatsuji, “Analysis of reconstruction characteristics in fluorescence digital holography,” in Digital Holography and Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DTuC13.
- P. Bouchal, J. Kapitán, R. Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express19(16), 15603–15620 (2011). [CrossRef] [PubMed]
- I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett.22(16), 1268–1270 (1997). [CrossRef] [PubMed]

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