## Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells |

Optics Express, Vol. 20, Issue 9, pp. 10295-10309 (2012)

http://dx.doi.org/10.1364/OE.20.010295

Acrobat PDF (1151 KB)

### Abstract

In this paper, we present an automated approach to quantify information about three-dimensional (3D) morphology, hemoglobin content and density of mature red blood cells (RBCs) using off-axis digital holographic microscopy (DHM) and statistical algorithms. The digital hologram of RBCs is recorded by a CCD camera using an off-axis interferometry setup and quantitative phase images of RBCs are obtained by a numerical reconstruction algorithm. In order to remove unnecessary parts and obtain clear targets in the reconstructed phase image with many RBCs, the marker-controlled watershed segmentation algorithm is applied to the phase image. Each RBC in the segmented phase image is three-dimensionally investigated. Characteristic properties such as projected cell surface, average phase, sphericity coefficient, mean corpuscular hemoglobin (MCH) and MCH surface density of each RBC is quantitatively measured. We experimentally demonstrate that joint statistical distributions of the characteristic parameters of RBCs can be obtained by our algorithm and efficiently used as a feature pattern to discriminate between RBC populations that differ in shape and hemoglobin content. Our study opens the possibility of automated RBC quantitative analysis suitable for the rapid classification of a large number of RBCs from an individual blood specimen, which is a fundamental step to develop a diagnostic approach based on DHM.

© 2012 OSA

## 1. Introduction

1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express **13**(12), 4492–4506 (2005). [CrossRef] [PubMed]

3. I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface **4**, 305–313 (2007). [CrossRef] [PubMed]

4. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A **73A**(10), 895–903 (2008). [CrossRef] [PubMed]

6. H. W. G. Lim, M. Wortis, and R. Mukhopadhyay, “Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer- couple hypothesis from membrane mechanics,” Proc. Natl. Acad. Sci. U.S.A. **99**(26), 16766–16769 (2002). [CrossRef] [PubMed]

7. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. **11**(3), 77–79 (1967). [CrossRef]

24. M. Mihailescu, M. Scarlat, A. Gheorghiu, J. Costescu, M. Kusko, I. A. Paun, and E. Scarlat, “Automated imaging, identification, and counting of similar cells from digital hologram reconstructions,” Appl. Opt. **50**(20), 3589–3597 (2011). [CrossRef] [PubMed]

1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express **13**(12), 4492–4506 (2005). [CrossRef] [PubMed]

3. I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface **4**, 305–313 (2007). [CrossRef] [PubMed]

25. P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. **30**, 468–470 (2005). [CrossRef] [PubMed]

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

27. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. **45**(5), 851–863 (2006). [CrossRef] [PubMed]

## 2. Off-axis digital holographic microscopy

25. P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. **30**, 468–470 (2005). [CrossRef] [PubMed]

*λ*=682 nm). The laser beam is divided into a reference wave and an object wave. The object wave is diffracted by the RBC samples, magnified by a 40 × /0.75NA microscope objective and interferes, in the off-axis geometry, with the reference wave to produce the hologram recorded via the CCD camera. The reconstruction and aberration compensation of the RBC wavefront is obtained by using the numerical algorithm described in [26

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

27. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. **45**(5), 851–863 (2006). [CrossRef] [PubMed]

## 3. Automated statistical quantification of multiple RBCs

*N*is the total number of pixels within single RBC,

*p*denotes the pixel size,

*M*the magnification of digital holography microscopy and

*i*pixel within the single cell representing the phase shift induced by the corresponding RBC as far as the phase value of the background is set to zero.

_{th}*k*[29], is also measured to characterize 3D morphology of RBCs. and is defined as a ratio of thickness at the center of the RBC to the thickness at a quarter of its diameter [see Fig. 2 ]. Since the thickness of a RBC is reflected by the phase value, the sphericity coefficient can be alternatively calculated by the phase value at the center of RBC and at a quarter of its diameter. While the projected surface of RBCs is viewed as circular form, the phase value in the center point and at a quarter of the diameter can be approximately measured by the average value within a 5 × 5 window over the RBC. The sphericity coefficient,

*k*as a morphological measurement is expressed as follows:where

*ph*and

_{c}*ph*are phase values at the center of RBC and at a quarter of its diameter, respectively.

_{d}## 4. Automated statistical classification of multiple RBCs

### 4.1 Parametric statistical method for classification of RBCs

*n*-variate random variable. An

*n*-dimensional random vector can be expressed as an 1 ×

*n*matrix,

*n*-dimensional location vector

*n*-variate normal distributions of reference and input RBCs, respectively. For the

*n*-variate hypothesis testing to check the equality of the

*n*-dimensional mean vectors between reference and input RBCs populations, the following likelihood ratio is applied [31]:where

*T*

^{2}has the

*Hotelling*’s distribution. For the statistical decision about whether the observed two

*n*-variate sampling distributions differ significantly, statistical hypothesis testing [31] is performed and then statistical

*p*-value is calculated by using the test statistic

*T*

^{2}value for the statistical decision. It is noted that the null hypothesis (

### 4.2 Nearest neighbor classification technique for classification of RBCs

*n*represents the number of features and

*i*

_{th}feature of corresponding types of RBCs. Since the Euclidean distance refers to the sum of the dissimilarity of individual features, a normalization of each feature must be carried out so that an arbitrary change of one feature will not affect the decision. Usually, this normalization process is done by replacing sample point in each feature, for example, sample point

## 5. Experimental results

### 5.1 Sample preparation

#### 5.2 3D sensing, imaging and segmentation of red blood cell (RBC)

4. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A **73A**(10), 895–903 (2008). [CrossRef] [PubMed]

### 5.3 Automatic statistical quantification and classification of red blood cells (RBCs)

*X*

_{1}, and the mean of the phase value,

*X*

_{2}, in the A part of a single RBC; Note that each property is considered a random variables. As shown in Fig. 8, the mean and standard deviation of RBCs with a stomatocyte shape for

*X*

_{1}are as 34μ

*m*

^{2}and 5μ

*m*

^{2}, respectively and are 97° and 9° for

*X*

_{2}, respectively. For RBCs with a discocyte shape, the mean and standard deviation of variable

*X*

_{1}are 42μ

*m*

^{2}and 8μ

*m*

^{2}

_{,}respectively, and are 74° and 15° for variable

*X*

_{2}, respectively. The standard deviations of random variable

*X*

_{1}and

*X*

_{2}in RBCs with a stomatocyte shape are smaller than those of RBCs with a discocyte shape. It is noted that the RBC with a stomatocyte shape tends to be more similar to each other than RBCs with a discocyte shape since stomatocytes are inclined to be much closer to the mean value. In addition, the mean of the phase value in the A part of the RBCs with a stomatocyte shape is larger than the RBCs with a discocyte shape while the mean of the projected surface area in the A part of RBCs with a stomatocyte shape is smaller than RBCs with a discocyte shape. It is noted that there was a difference of approximately 23° between the average phase values in the A part of the RBCs with the different types of shapes. Also, there was a difference of approximately 8μ

*m*

^{2}between the average projected surface area values in the A part of the RBCs with the different shapes. In addition, the overlapped area between two statistical distributions of the phase value is smaller than that of the projected surface area.

*p*-values were approximately 3.43×10

^{−13}and 1.36×10

^{−19}for the projected surface area (

*X*

_{1}), and mean phase value (

*X*

_{2}), respectively. This indicates that there is more separation between two statistical distributions of the mean phase value (

*X*

_{2}) than those of the projected surface area (

*X*

_{1}).

*X*

_{3,}and the mean phase value, random variable

*X*

_{4,}for a single RBC in the B part are used to analyze the distribution of the properties in RBCs having different shapes. The mean and standard deviation of variable

*X*

_{3}are calculated to be 10μ

*m*

^{2}and 5μ

*m*

^{2}respectively, and those of

*X*

_{4}are 81° and 12°, respectively, in RBCs with a stomatocyte shape. For RBCs with a discocyte shape in B part, the mean and standard deviation of random variable

*X*

_{3}are 18μ

*m*

^{2}and 5μ

*m*

^{2}respectively, and those for

*X*

_{4}are 60° and 11°, respectively. The mean projected surface area in the B part of the RBCs with a stomatocyte shape is about 8μ

*m*

^{2}smaller than that of RBCs with a discocyte shape while the standard deviation is very similar. Figure 9 shows a scatter plot of the relationship between the projected surface area and the mean of the phase value in A and B parts [see Fig. 6] in the RBC, respectively, where all single RBCs from the phase images of RBCs having the different shapes were investigated. As shown in Fig. 9, the projected surface area of the A or B parts of a single RBC is inversely proportional to the mean of the phase value in the A or B parts of both types of single RBCs. Furthermore, there is a strong correlation between the projected surface area and mean of the phase value in the A or B parts of both types of single RBCs. Also, Fig. 9 shows that there is a considerable separation between bivariate distributions or 3D morphology of the different types of RBCs.

*X*

_{1},

*X*

_{2}) or (

*X*

_{3},

*X*

_{4}) of the RBCs with two distinct types of shapes (stomatocyte shape and discocyte one), we have measured average statistical

*p*-value by using the table of

*Hotelling*’s distribution in reference [31], where the statistical hypothesis testing of Eq. (5) was performed. It is noted that the computed statistical

*p*-values for the two-dimensional random variable (

*X*

_{1},

*X*

_{2}) and (

*X*

_{3},

*X*

_{4}) are zero (<<10

^{−100}), which are the probability that the observed test statistic of Eq. (5) would occur in the same population (3D shape profile or 3D morphology for surface area and phase) in the A and B part. Therefore, these experimental results indicate that the joint statistical distributions for the 3D morphology (surface area and phase) of the RBCs can provide a good separation between RBCs having the different shapes.

*X*

_{5}, while in RBCs with a discocyte shape it is represented as

*X*

_{6}. The mean and standard deviation of random variable

*X*

_{5}are obtained as 31.1pg and 4.0pg, respectively, and those of

*X*

_{6}are 28.9pg and 4.0pg, respectively. It is noted that the averaged MCH values for both types of RBCs are approximately within the typical range of [27

27. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. **45**(5), 851–863 (2006). [CrossRef] [PubMed]

*p*-value was calculated by using the table of Student’s t distribution the computed statistical

*p*-value for checking of the equality of the location parameter is approximately 0.0002, which is the probability that the observed t-test statistic would occur in the same dry mass/MCH population. Therefore, from the above experimental results, we might investigate any distinctions of the hemoglobin concentration in the RBC with different types of shapes.

*k*defined in Eq. (2), which was taken as a random variable while each single RBC can be serviced as sample data.

*X*

_{7}and

*X*

_{8}are used to denote the random variables for the sphericity coefficient in RBCs with a stomatocyte shape and a discocyte one, respectively. The mean and standard deviation for random variable

*X*

_{7}in RBCs with a stomatocyte shape is calculated to be 0.54 and 0.21, respectively, while those values are 0.63 and 0.18, respectively, for

*X*

_{8}in RBCs with a discocyte shape. Figure 11 shows the statistical distribution for sphericity coefficient in RBCs with a stomatocyte shape and a discocyte one by taking the samples’ mean and standard deviation as population’s mean and standard deviation (There are approximately 100 samples for each class of RBCs). It is noted from Fig. 11 that most of the sphericity coefficients in both types of RBCs are smaller than 1.00 and the average sphericity coefficient in RBCs with a discocyte shape is a little bit larger than that in RBCs with a stomatocyte one.

## 6. Conclusion

33. F. A. Sadjadi and A. Mahalanobis, “Target-adaptive polarimetric synthetic aperture radar target discrimination using maximum average correlation height filters,” Appl. Opt. **45**(13), 3063–3070 (2006). [CrossRef] [PubMed]

## Acknowledgment

## References and links

1. | B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express |

2. | A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A |

3. | I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface |

4. | B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A |

5. | R. Barer, “Interference microscopy and mass determination,” Nature |

6. | H. W. G. Lim, M. Wortis, and R. Mukhopadhyay, “Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer- couple hypothesis from membrane mechanics,” Proc. Natl. Acad. Sci. U.S.A. |

7. | J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. |

8. | J. W. Goodman, |

9. | U. Schnars and W. Jueptner, |

10. | U. Schnars and W. P. O. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. |

11. | T. Kreis, |

12. | F. Dubois, L. Joannes, and J.-C. Legros, “Improved three-dimensional imaging with digital holography microscope using a partial spatial coherent source,” Appl. Opt. |

13. | T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. |

14. | Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE |

15. | E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. |

16. | Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. |

17. | P. Ferraro, S. Grilli, D. Alfieri, S. De Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital Holography,” Opt. Express |

18. | V. Micó, J. García, Z. Zalevsky, and B. Javidi, “Phase-shifting Gabor holography,” Opt. Lett. |

19. | A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express |

20. | B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. |

21. | T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. |

22. | L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express |

23. | P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. |

24. | M. Mihailescu, M. Scarlat, A. Gheorghiu, J. Costescu, M. Kusko, I. A. Paun, and E. Scarlat, “Automated imaging, identification, and counting of similar cells from digital hologram reconstructions,” Appl. Opt. |

25. | P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. |

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

27. | T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. |

28. | R. C. Gonzalez and R. E. Woods, |

29. | T. Tishko, T. Dmitry, and T. Vladimir, |

30. | B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. |

31. | C. Rencher, |

32. | E. Gose, R. Johnsonbaugh, and S. Jost, |

33. | F. A. Sadjadi and A. Mahalanobis, “Target-adaptive polarimetric synthetic aperture radar target discrimination using maximum average correlation height filters,” Appl. Opt. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(170.1530) Medical optics and biotechnology : Cell analysis

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(090.1995) Holography : Digital holography

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: January 24, 2012

Revised Manuscript: April 2, 2012

Manuscript Accepted: April 3, 2012

Published: April 19, 2012

**Virtual Issues**

Vol. 7, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Inkyu Moon, Bahram Javidi, Faliu Yi, Daniel Boss, and Pierre Marquet, "Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells," Opt. Express **20**, 10295-10309 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-9-10295

Sort: Year | Journal | Reset

### References

- B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express13(12), 4492–4506 (2005). [CrossRef] [PubMed]
- A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A24, 163–168 (2007). [CrossRef]
- I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface4, 305–313 (2007). [CrossRef] [PubMed]
- B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A73A(10), 895–903 (2008). [CrossRef] [PubMed]
- R. Barer, “Interference microscopy and mass determination,” Nature169(4296), 366–367 (1952). [CrossRef] [PubMed]
- H. W. G. Lim, M. Wortis, and R. Mukhopadhyay, “Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer- couple hypothesis from membrane mechanics,” Proc. Natl. Acad. Sci. U.S.A.99(26), 16766–16769 (2002). [CrossRef] [PubMed]
- J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
- U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2005).
- U. Schnars and W. P. O. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol.13(9), R85–R101 (2002). [CrossRef]
- T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).
- F. Dubois, L. Joannes, and J.-C. Legros, “Improved three-dimensional imaging with digital holography microscope using a partial spatial coherent source,” Appl. Opt.38(34), 7085–7094 (1999). [CrossRef] [PubMed]
- T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt.45(20), 4873–4877 (2006). [CrossRef] [PubMed]
- Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE94(3), 636–653 (2006). [CrossRef]
- E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt.39(23), 4070–4075 (2000). [CrossRef] [PubMed]
- Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett.29(15), 1787–1789 (2004). [CrossRef] [PubMed]
- P. Ferraro, S. Grilli, D. Alfieri, S. De Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital Holography,” Opt. Express13(18), 6738–6749 (2005). [CrossRef] [PubMed]
- V. Micó, J. García, Z. Zalevsky, and B. Javidi, “Phase-shifting Gabor holography,” Opt. Lett.34(10), 1492–1494 (2009). [CrossRef] [PubMed]
- A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express18(13), 14159–14164 (2010). [CrossRef] [PubMed]
- B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett.25(9), 610–612 (2000). [CrossRef] [PubMed]
- T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett.32(5), 481–483 (2007). [CrossRef] [PubMed]
- L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express16(1), 161–169 (2008). [CrossRef] [PubMed]
- P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt.14(1), 014018 (2009). [CrossRef] [PubMed]
- M. Mihailescu, M. Scarlat, A. Gheorghiu, J. Costescu, M. Kusko, I. A. Paun, and E. Scarlat, “Automated imaging, identification, and counting of similar cells from digital hologram reconstructions,” Appl. Opt.50(20), 3589–3597 (2011). [CrossRef] [PubMed]
- P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett.30, 468–470 (2005). [CrossRef] [PubMed]
- E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude and quantitative phase contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt.38(34), 6994–7001 (1999). [CrossRef] [PubMed]
- T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt.45(5), 851–863 (2006). [CrossRef] [PubMed]
- R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).
- T. Tishko, T. Dmitry, and T. Vladimir, Holographic Microscopy of Phase Microscopic Objects (World Scientific, 2011).
- B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt.14(3), 034049 (2009). [CrossRef] [PubMed]
- C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).
- E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996).
- F. A. Sadjadi and A. Mahalanobis, “Target-adaptive polarimetric synthetic aperture radar target discrimination using maximum average correlation height filters,” Appl. Opt.45(13), 3063–3070 (2006). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.