## Method for chromatic error compensation in digital color holographic imaging |

Optics Express, Vol. 21, Issue 22, pp. 26456-26467 (2013)

http://dx.doi.org/10.1364/OE.21.026456

Acrobat PDF (7273 KB)

### Abstract

This paper proposes an all-numerical robust method to compensate for the chromatic aberrations induced by the optical elements in digital color holographic imaging. It combines a zero-padding algorithm and a convolution approach with adjustable magnification, using a single recording of a reference rectangular grid. Experimental results confirm and validate the proposed approach.

© 2013 Optical Society of America

## 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]

8. M. K. Kim, “Full color natural light holographic camera,” Opt. Express **21**(8), 9636–9642 (2013). [CrossRef] [PubMed]

10. P. Tankam, Q. Song, M. Karray, J. C. Li, J.-M. Desse, and P. Picart, “Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry,” Opt. Lett. **35**(12), 2055–2057 (2010). [CrossRef] [PubMed]

11. U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. **35**(4), 977–982 (1996). [CrossRef]

12. A. Stadelmaier and J. H. Massig, “Compensation of lens aberrations in digital holography,” Opt. Lett. **25**(22), 1630–1632 (2000). [CrossRef] [PubMed]

13. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A **23**(12), 3177–3190 (2006). [CrossRef] [PubMed]

14. S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. **30**(20), 2706–2708 (2005). [CrossRef] [PubMed]

15. P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. **4**(1), 97–100 (2008). [CrossRef]

## 2. Theoretical background

### 2.1 Digital color holography scheme

*λ*in the red, green and blue domains [10

10. P. Tankam, Q. Song, M. Karray, J. C. Li, J.-M. Desse, and P. Picart, “Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry,” Opt. Lett. **35**(12), 2055–2057 (2010). [CrossRef] [PubMed]

10. P. Tankam, Q. Song, M. Karray, J. C. Li, J.-M. Desse, and P. Picart, “Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry,” Opt. Lett. **35**(12), 2055–2057 (2010). [CrossRef] [PubMed]

*M*×

*N*pixels sized

*p*×

_{x}*p*, providing real-time capabilities to the holographic set-up. For the study of large objects, a negative lens is placed just in front of the beam splitter, in the object optical path. Thus, a virtual object is produced in front of the sensor at a smaller distance than the initial one, and this enables the Shannon conditions to be fulfilled [11

_{y}11. U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. **35**(4), 977–982 (1996). [CrossRef]

13. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A **23**(12), 3177–3190 (2006). [CrossRef] [PubMed]

### 2.2 Numerical reconstruction

*A*of the reconstructed field at a plane (

_{r}*x*,

*y*) located at a distance

*d*from the sensor, retrieved from a recorded hologram

*H*, is written according to Eq. (1):In Eq. (1),

*w*(

*X*,

*Y*,

*λ*,

_{c}*R*) is a spherical reconstruction wave, whose parameters are its wavelength

_{c}*λ*and its curvature radius

_{c}*R*[3

_{c}3. P. Picart, P. Tankam, D. Mounier, Z. J. Peng, and J. C. Li, “Spatial bandwidth extended reconstruction for digital color Fresnel holograms,” Opt. Express **17**(11), 9145–9156 (2009). [CrossRef] [PubMed]

*w*is plane (i.e.

*w*= 1), and the wavelength is the same (

*λ*=

_{c}*λ*). The numerical focusing on the virtual or real image is obtained at a distance

*d =*±

*d*

_{0}(

*d*

_{0}: distance from the object to the sensor). There are several approaches to the numerical reconstruction of images in digital holography: the Fresnel transform [11

11. U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. **35**(4), 977–982 (1996). [CrossRef]

16. T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. **41**(4), 771–778 (2002). [CrossRef]

17. J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett. **34**(5), 572–574 (2009). [CrossRef] [PubMed]

18. S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. **36**(2), 103–126 (2001). [CrossRef]

19. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. **29**(14), 1668–1670 (2004). [CrossRef] [PubMed]

20. J. F. Restrepo and J. Garcia-Sucerquia, “Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform,” Appl. Opt. **49**(33), 6430–6435 (2010). [CrossRef] [PubMed]

#### 2.2.1 The Fresnel transform approach

*λ*=

_{c}*λ*and

*w*= 1:

*K*,

*L*) data points, generally (

*K*,

*L*)≥ (

*M*,

*N*). The pixel pitches of the reconstructed image in the

*x*and

*y*directions are given respectively by Δ

*η*=

_{x}*λd*/

*Lp*and Δ

_{x}*η*=

_{y}*λd*/

*Kp*, and depend on the wavelength. This may be a problem in digital color holography, as the reconstructed horizon (i.e. the calculated area) becomes different for each wavelength. The zero-padding approach [15

_{y}15. P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. **4**(1), 97–100 (2008). [CrossRef]

#### 2.2.2 The convolution approach

*FT*):where

*G*is the angular spectrum transfer function, and is given by (λ

_{c}= λ):

*u*

^{λ}_{0},

*v*

^{λ}_{0}) are the mean spatial frequencies localizing the reconstructed object at wavelength

*λ*[17

17. J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett. **34**(5), 572–574 (2009). [CrossRef] [PubMed]

21. P. Picart and P. Tankam, “Analysis and adaptation of convolution algorithms to reconstruct extended objects in digital holography,” Appl. Opt. **52**(1), A240–A253 (2013). [CrossRef] [PubMed]

22. P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A **25**(7), 1744–1761 (2008). [CrossRef] [PubMed]

*w*= 1 this algorithm is not suitable for the reconstruction of large objects [21

21. P. Picart and P. Tankam, “Analysis and adaptation of convolution algorithms to reconstruct extended objects in digital holography,” Appl. Opt. **52**(1), A240–A253 (2013). [CrossRef] [PubMed]

*w*≠1, one gets an adjustable magnification. If, instead of a plane reconstruction wave, the convolution approach is used with a spherical one, the reconstruction plane is now located at a distance 1/

*d*= 1/

_{r}*R*−1/

_{c}*d*

_{0}, and the transverse magnification γ of the object is now given by [3

3. P. Picart, P. Tankam, D. Mounier, Z. J. Peng, and J. C. Li, “Spatial bandwidth extended reconstruction for digital color Fresnel holograms,” Opt. Express **17**(11), 9145–9156 (2009). [CrossRef] [PubMed]

17. J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett. **34**(5), 572–574 (2009). [CrossRef] [PubMed]

21. P. Picart and P. Tankam, “Analysis and adaptation of convolution algorithms to reconstruct extended objects in digital holography,” Appl. Opt. **52**(1), A240–A253 (2013). [CrossRef] [PubMed]

#### 2.2.3 Case of extended objects

**52**(1), A240–A253 (2013). [CrossRef] [PubMed]

22. P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A **25**(7), 1744–1761 (2008). [CrossRef] [PubMed]

*λd*/

*p*. So the size of the set-up is directly proportional to the size of the object. For example, to study a 15 × 15cm

_{x}^{2}object using a wavelength at 532nm, with pixels 6.45μm

^{2}, the distance must be at least 4.849m [22

22. P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A **25**(7), 1744–1761 (2008). [CrossRef] [PubMed]

**35**(4), 977–982 (1996). [CrossRef]

23. J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. **49**(12), 125801 (2010). [CrossRef]

^{2}object could be located at 1.1m of the sensor, and its virtual image at less than 30cm and still respects the Shannon criteria.

## 3. Origin of chromatic aberrations

*p*’

*is taken as the reference position, there is a shift in the position of the other images (distance Δ*

_{R}*d*, cf Fig. 2(a)), which is given in Eq. (6), where

*f*’ is the focal of the lens for the red light, and

*ν*is the Abbe number [24]:As seen in section 2.2, the reconstruction distance is important in the reconstruction of digital holograms. It is therefore mandatory to correct the axial shifts of the different images. But these axial shifts will also induce a size difference Δ

*y’*between the red image and the other images, depending on the wavelength. This is expressed in Eq. (7), where

*y*’

*is the size of the red image, and where*

_{R}*γ*and Δ

_{opt}*γ*are respectively the optical magnification (provided by the lens or imaging system) and its variation [24]:An important parameter in Eq. (7) is the variation of the magnification Δ

_{opt}*γ*that must be experimentally measured.

_{opt}## 4. Total compensation of chromatic aberrations in digital color holography

### 4.1 Modified zero-padding algorithm

*x*-direction (a similar relation holds for the

*y*-direction) [25

25. P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. **29**(8), 854–856 (2004). [CrossRef] [PubMed]

26. P. Tankam and P. Picart, “Use of digital color holography for crack investigation in electronic components,” Opt. Lasers Eng. **49**(11), 1335–1342 (2011). [CrossRef]

*η*is the pixel pitch, depending on the wavelength

*λ*,

*d*is the numerical reconstruction distance used in the algorithm,

_{r}^{λ}*p*is the pixel pitch in the

_{x}*x*-direction and

*K*is the number of pixels of the discrete Fresnel transform. The zero-padding algorithm is based on the modification of the number of pixels

_{λ}*K*by adding rows and columns of “zeros” around the matrix formed by the image to be reconstructed, in order to fulfill Eq. (9). This principle can be modified to get the invariance of the pixel pitch as accurate as possible. This adaptation implies also to change slightly the reconstruction distance for every wavelength, and to find a pair of even integers fulfilling this equation:In order to keep these changes under a very small amount, some constraints to the condition in Eq. (10) are added. These constraints, summarized in Eq. (11), ensure working within the best achievable spatial resolution [26

_{λ}26. P. Tankam and P. Picart, “Use of digital color holography for crack investigation in electronic components,” Opt. Lasers Eng. **49**(11), 1335–1342 (2011). [CrossRef]

*d*

_{0}

^{λ}is the physical image distance due to the lens aberration. Equation (10) can now be rewritten as:There is little chance that a pair of even integers will satisfy Eq. (12) exactly. So, the integer pair (

*K**

_{λ}_{1},

*K**

_{λ}_{2}) has to be closest to an exact solution. Then, one can adjust the reconstruction distances, which are now calculated according to:If more than two wavelengths are used, their associated number of pixels and reconstruction distances are found using conditions similar to that detailed in Eq. (12). For example, these are the results for a third wavelength:

### 4.2 Correction parameters

*λ*). However, they are slightly laterally shifted and exhibit different sizes. The lateral shift can be estimated by measuring the center of the grid for each wavelength and will be compensated at the next step with the convolution algorithm. The size difference is more difficult to evaluate with good precision. One could easily measure the size of the grid, but the precision would be one pixel at best, which is not sufficient. A better precision is obtained by using the Hough transform [27]. In a set of polar coordinate axes, the Hough transform estimates every possible lines passing at each pixel of the image. Parameterization specifies a straight line with the angle of its normal (

*θ*) and its algebraic distance from the origin (

*ρ*). If a line is actually passing by a point in the image, it is automatically shown in the Hough transform by a clear intersection of all the possible lines into a real one, appearing through the polar coordinates of the intersection point (i.e. angle and position). Using the Hough transform, one has access to the equations of any straight line in the image. So, one gets an average value of the distances between each vertical and horizontal line of the grid, thus providing the measurement of the grid period. The blue color is considered to be the reference image to compensate for the red and green color. The ratio Γ(

*λ*) of the values of the estimated periods for the red and green images in regard of the blue one determines the transverse magnification that has to be applied to the green and red image to get the red, green, blue, images with the same size.

### 4.3 Convolution with adjustable magnification

**34**(5), 572–574 (2009). [CrossRef] [PubMed]

*λ*) between colors is used to get the same image sizes from the convolution algorithm by retrieving the new reconstruction distance

*d*:Finally, the mean spatial frequency along each color is slightly modified to account for the lateral shift, so that the useful spatial bandwidth may be localized at the suitable spectral region [17

^{’}_{r}**34**(5), 572–574 (2009). [CrossRef] [PubMed]

*u*’

^{λ}_{0},

*v*’

^{λ}_{0}) for the spatial frequencies of the angular spectrum transfer window are given by [17

**34**(5), 572–574 (2009). [CrossRef] [PubMed]

*X*,Δ

*Y*) for each wavelength:

## 5. Experimental validation

### 5.1 Retrieving the correction parameters

^{2}grid containing clearly marked parallel lines was used; three laser wavelengths in the red, green and blue domains (respectively 660nm, 532nm, 457nm) were used, as well as a 3-CCD recording device (pixel pitch at

*p*=

_{x}*p*= 6.45μm). The grid was located at 1450mm of the recording device, and the focal length of the negative lens was −250mm. Table 1 gives the parameters of the zero-padding algorithm, retrieved using Eqs. (12) and (13).

_{y}*ρ*,

*θ*). One can see the intersection points corresponding to the 22 lines seen in the reconstructed image of the grid (11 verticals for

*θ*= 90°, 11 horizontals for

*θ*= 0°), within the white squares on the center and on the left of Fig. 7.

*ρ*,

*θ)*of the points located inside the white squares in Fig. 7, corresponding to the real lines in the reconstructed image, one can measure the distance between each consecutive line of the reference object in the two directions of space. Using this method, the magnification for any wavelength to be applied into the convolution algorithm can be deduced, by measuring the ratio between the average period for the reference wavelength (with a magnification Γ = 1), and the average period for the other wavelengths. The blue image was used as the reference wavelength in our experiment, as its reconstructed image is the smallest, and the retrieved magnifications for the red and green wavelengths, as well as the retrieved average periods, are summarized in Table 2.

### 5.2 Application to three color holographic imaging

## 6. Conclusion

## 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. | C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express |

3. | P. Picart, P. Tankam, D. Mounier, Z. J. Peng, and J. C. Li, “Spatial bandwidth extended reconstruction for digital color Fresnel holograms,” Opt. Express |

4. | P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. |

5. | J. Garcia-Sucerquia, “Color lensless digital holographic microscopy with micrometer resolution,” Opt. Lett. |

6. | Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol. |

7. | A. Kowalczyk, M. Bieda, M. Makowski, M. Sypek, and A. Kolodziejczyk, “Fiber-based real-time color digital in-line holography,” Appl. Opt. |

8. | M. K. Kim, “Full color natural light holographic camera,” Opt. Express |

9. | R. Kingslake, |

10. | P. Tankam, Q. Song, M. Karray, J. C. Li, J.-M. Desse, and P. Picart, “Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry,” Opt. Lett. |

11. | U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. |

12. | A. Stadelmaier and J. H. Massig, “Compensation of lens aberrations in digital holography,” Opt. Lett. |

13. | T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A |

14. | S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. |

15. | P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. |

16. | T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. |

17. | J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett. |

18. | S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng. |

19. | F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. |

20. | J. F. Restrepo and J. Garcia-Sucerquia, “Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform,” Appl. Opt. |

21. | P. Picart and P. Tankam, “Analysis and adaptation of convolution algorithms to reconstruct extended objects in digital holography,” Appl. Opt. |

22. | P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A |

23. | J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. |

24. | F. A. Jenkins and H. E. White, |

25. | P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. |

26. | P. Tankam and P. Picart, “Use of digital color holography for crack investigation in electronic components,” Opt. Lasers Eng. |

27. | P. V. C. Hough, |

**OCIS Codes**

(090.0090) Holography : Holography

(090.1760) Holography : Computer holography

(100.3010) Image processing : Image reconstruction techniques

(090.1705) Holography : Color holography

(090.1995) Holography : Digital holography

**ToC Category:**

Holography

**History**

Original Manuscript: July 24, 2013

Revised Manuscript: September 17, 2013

Manuscript Accepted: September 26, 2013

Published: October 28, 2013

**Citation**

Mathieu Leclercq and Pascal Picart, "Method for chromatic error compensation in digital color holographic imaging," Opt. Express **21**, 26456-26467 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26456

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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]
- C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express16(13), 9753–9764 (2008). [CrossRef] [PubMed]
- P. Picart, P. Tankam, D. Mounier, Z. J. Peng, and J. C. Li, “Spatial bandwidth extended reconstruction for digital color Fresnel holograms,” Opt. Express17(11), 9145–9156 (2009). [CrossRef] [PubMed]
- P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt.50(34), H177–H182 (2011). [CrossRef] [PubMed]
- J. Garcia-Sucerquia, “Color lensless digital holographic microscopy with micrometer resolution,” Opt. Lett.37(10), 1724–1726 (2012). [CrossRef] [PubMed]
- Y. Ito, Y. Shimozato, P. Xia, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Four-wavelength color digital holography,” J. Disp. Technol.8(10), 570–576 (2012). [CrossRef]
- A. Kowalczyk, M. Bieda, M. Makowski, M. Sypek, and A. Kolodziejczyk, “Fiber-based real-time color digital in-line holography,” Appl. Opt.52(19), 4743–4748 (2013). [CrossRef] [PubMed]
- M. K. Kim, “Full color natural light holographic camera,” Opt. Express21(8), 9636–9642 (2013). [CrossRef] [PubMed]
- R. Kingslake, Lens Design Fundamentals, (Academic Pr, 1978).
- P. Tankam, Q. Song, M. Karray, J. C. Li, J.-M. Desse, and P. Picart, “Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry,” Opt. Lett.35(12), 2055–2057 (2010). [CrossRef] [PubMed]
- U. Schnars, T. M. Kreis, and W. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng.35(4), 977–982 (1996). [CrossRef]
- A. Stadelmaier and J. H. Massig, “Compensation of lens aberrations in digital holography,” Opt. Lett.25(22), 1630–1632 (2000). [CrossRef] [PubMed]
- T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A23(12), 3177–3190 (2006). [CrossRef] [PubMed]
- S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett.30(20), 2706–2708 (2005). [CrossRef] [PubMed]
- P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol.4(1), 97–100 (2008). [CrossRef]
- T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng.41(4), 771–778 (2002). [CrossRef]
- J. C. Li, P. Tankam, Z. J. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett.34(5), 572–574 (2009). [CrossRef] [PubMed]
- S. Seebacher, W. Osten, T. Baumbach, and W. Juptner, “The determination of material parameters of microcomponents using digital holography,” Opt. Lasers Eng.36(2), 103–126 (2001). [CrossRef]
- F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett.29(14), 1668–1670 (2004). [CrossRef] [PubMed]
- J. F. Restrepo and J. Garcia-Sucerquia, “Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform,” Appl. Opt.49(33), 6430–6435 (2010). [CrossRef] [PubMed]
- P. Picart and P. Tankam, “Analysis and adaptation of convolution algorithms to reconstruct extended objects in digital holography,” Appl. Opt.52(1), A240–A253 (2013). [CrossRef] [PubMed]
- P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A25(7), 1744–1761 (2008). [CrossRef] [PubMed]
- J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng.49(12), 125801 (2010). [CrossRef]
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