Phase retrieval method for digital holography with two cameras in particle measurement

Yohsuke Tanaka; Shunsuke Tani; Shigeru Murata

doi:10.1364/OE.24.025233

Phase retrieval method for digital holography with two cameras in particle measurement

Yohsuke Tanaka, Shunsuke Tani, and Shigeru Murata

Optics Express
Vol. 24,
Issue 22,
pp. 25233-25241
(2016)
•https://doi.org/10.1364/OE.24.025233

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Yohsuke Tanaka, Shunsuke Tani, and Shigeru Murata, "Phase retrieval method for digital holography with two cameras in particle measurement," Opt. Express 24, 25233-25241 (2016)

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- Holography
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Holography (090.0090)
- Digital holography (090.1995)
- Phase retrieval (100.5070)

About this Article
History
- Original Manuscript: September 6, 2016
- Revised Manuscript: October 16, 2016
- Manuscript Accepted: October 16, 2016
- Published: October 19, 2016

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Abstract

This paper presents a phase retrieval method for digital holography with two high-speed cameras in particle measurement. The conditions for recording two holograms are derived theoretically. We focus in particular on the distance between the two holograms. The relative misalignment of the two holograms is also evaluated by numerical simulations. Finally, we experimentally compared settling particles reconstructed by the presented method and the Gabor method.

1. Introduction

In-line digital holography, known as “Gabor holography” [1], is widely used in particle measurement (e.g., dispersed micro particles [2], plankton [3], snow crystals [4], and fuel droplets [5]) because of its simple setup and insensitivity to vibration. However, the method has a twin image problem [6] that occurs when an obstacle between in-focus objects and out-of-focus objects at the in-focus plane in the reconstructed hologram. The problem is caused by a lack of recorded phase information in the hologram.

Several approaches have been developed for recording the information using the phase-shifting method [7, 8]. However, it is diﬃcult to observe objects moving at high speed because the method requires at least two holograms recorded at diﬀerent times. To overcome this diﬃculty, a phase-shifting array device was developed for recording multiple holograms simultaneously [9–11]. However, the phase-shifting method is limited by having to be implemented on a vibration-isolation table because of its sensitivity to vibration.

The phase retrieval method [12, 13] solves such problems by using in-line holography to record two or more holograms at diﬀerent positions. This iterative-propagation approach is based on the Gerchberg-Saxton algorithm [14]. The intensity of the hologram corresponds to modulus constraint, and the propagation is carried out by using Fresnel-Kirchhoﬀ diﬀraction theory. However, this method has been used to observe only static objects because of the requirement of two or more holograms; it has not yet been applied to the measurement of moving particles at high speed.

In this paper, we use two high-speed camera to apply the phase retrieval method to particle measurement. The condition for recording two holograms is derived theoretically. We focus in particular on the distance between two holograms, and we use numerical simulations to evaluate their relative misalignment. Finally, the misalignment calibration is demonstrated experimentally. We also compare settling particles reconstructed by the present method and the Gabor method.

2. Phase retrieval method with two cameras in digital holography

2.1 Digital holography in particle measurement

We consider the case in which a particle is illuminated by a unit plane wave of wavelength λ. The complex amplitude $ψ_{z_{1}} (x_{1}, y_{1})$ at the recording plane a distance z₁ away is given by

ψ_{z_{1}} (x_{1}, y_{1}) = \frac{\exp (j k z_{1})}{j λ z_{1}} {\int \int}_{- \infty}^{\infty} [1 - p (x_{0}, y_{0})] exp {\frac{j k}{2 z_{1}} [{(x_{1} - x_{0})}^{2} + {(y_{1} - y_{0})}^{2}]} d x_{0} d y_{0},

where k = 2π/λ is the wave number of the plane wave. The diffracting aperture p(x₀, y₀) for a particle, is defined as the amplitude transmittance function,

p (x_{0}, y_{0}) = {\begin{matrix} 1, \sqrt{x_{0}^{2} + y_{0}^{2}} \leq {(d_{p} / 2)}^{2} \\ 0, \sqrt{x_{0}^{2} + y_{0}^{2}} > {(d_{p} / 2)}^{2} \end{matrix}

where d_p is the diameter of the particle. This aperture has circular symmetry, and under the far-field condition, d_p²/λ z₁. Performing the integration yields the intensity distribution [15]

I (r) = {| ψ_{z_{1}} (r) |}^{2} = 1 - \frac{π d_{p}^{2}}{2 λ z_{1}} sin (\frac{π r^{2}}{λ z_{1}}) \frac{2 J_{1} (π d_{p} r / (λ z_{1}))}{π d_{p} r / (λ z_{1})} + {(\frac{π d_{p}^{2}}{4 λ z_{1}})}^{2} {[\frac{2 J_{1} (π d_{p} r / (λ z_{1}))}{π d_{p} r / (λ z_{1})}]}^{2},

where J₁ denotes the first-order Bessel function. Figure 1 shows the intensity distribution of a particle with a diameter of 70 µm.

Fig. 1 Hologram intensity log₁₀I(r) of a particle against r derived from Eq. (3) for z₁ = 100mm, d_p = 70 µm and λ = 632.8 nm.

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The sine term in the right-hand side of Eq. (3) determines the fringe pattern of the signal. We obtain the difference between the nth and (n + 1)th fringe being 2π [16],

r_{n + 1}^{2} - r_{n}^{2} \approx 2 r Δ r = 2 λ z .

Here, we derive

r_{n}^{2} = 2 λ z n

(n = 1, 2,..., n

\in

N). Because of the low spatial frequency of charge-coupled devices (CCDs), the available particle information is contained in the first lobe [17]. The position r₀ of the end of the first lobe corresponds to the first zero-crossing position of the Bessel function:

r^{'} = \frac{1.22 λ z}{d_{p}} .

Thus, the recording distance of a particle is limited to the range

\frac{d_{p}^{2}}{λ} < z_{1} < \frac{d_{p} L / 2}{1.22 λ},

where L/2 is the half width of the CCD elements. In this equation, the left-hand side is based on the Fraunhofer condition and the right-hand side is derived from Eq. (5) with r₀ = L/2.

From Eqs. (4) and (5), the fringe spacing is Δr = d_p/1.22. Therefore, the spatial resolution Δx of the CCD is expressed as

Δ x < \frac{d_{p}}{2.44} = \frac{Δ r}{2} .

We find that the resolution depends on only the particle diameter, not on depth or wavelength.

The twin-image problem [18] occurs in the recording process of a hologram without phase information. For discussing this problem, we introduce the convolution kernel [19] defined as

h_{z 1} (x_{1}, y_{1}) \equiv \frac{1}{λ z_{1}} exp [j \frac{k}{z_{1}} (x_{1}^{2} + y_{1}^{2})] .

With this kernel, Eq. (1) can be expressed more compactly as the two-dimensional convolution

ψ_{z_{1}} = \exp (j k z_{1}) [1 - p (x_{0}, y_{0})] * h_{z_{1}} .

The hologram intensity,

I_{z_{1}}

, is recorded on a hologram as

\begin{matrix} I_{z_{_{1}}} = ψ_{z_{_{1}}} * ψ^{*}_{z_{_{1}}} = {| 1 - p * h_{z_{_{1}}} |}^{2} \\ = 1 - p^{*} * h_{z_{_{1}}}^{*} - p * h_{z_{_{1}}} + {| p * h_{z_{_{1}}} |}^{2} \\ \approx 1 - p^{*} * h_{z_{_{1}}}^{*} - p * h_{z_{_{1}}} \end{matrix}

Equation (10) is based on the assumption that the amplitude of the nonlinear term

{| p * h_{z_{_{1}}} |}^{2}

is much smaller than that of the diﬀracted particle wave.

In reconstruction, the pattern is illuminated for reconstructing particles with $h_{- z_{1}}$ , and the complex amplitude $ψ_{z_{0}}$ is reconstructed as

ψ_{z 0} = I_{z_{1}} * h_{- z_{1}} = 1 - p^{*} * h_{- 2 z_{1}} - p * h_{z_{1}} .

The first term on the right-hand side of Eq. (11) leads to a uniform component, and the second and third terms lead to the real and virtual images, respectively, of the particles. The suppression of the in-focus and out-of-focus particles causes the out-of-focus image in the intensity

I_{z_{0}} = ψ_{z_{0}} * ψ_{z_{0}}^{*}

of reconstructed particles. If we know the phase information of the hologram, the in-focus particles are reconstructed as

ψ_{z_{0}} = ψ_{z_{1}} * h_{- z_{1}} = 1 - p .

Therefore the phase information resolves the twin image problem in the recording process of in-line holography.

2.2 Phase retrieval method in digital holography

The information can be retrieved by using a phase retrieval (P.R.) method based on the Gerchberg–Saxton algorithm [14] which requires two holograms for use with holography [13,20]. The method consists of four steps between two holograms as shown in Fig. 2(a): (Step 1) reconstruct the complex amplitude $ψ_{z_{1} k}$ of the first hologram I₁ in the second hologram I₂ with the distance Δz between two holograms; (Step 2) replace the absolute value of the resulting complex amplitude with the square root of the second hologram I₂; (Step 3) back-reconstruct the new complex amplitude $ψ_{z_{2} k}^{'}$ to the first hologram; (Step 4) replace the absolute value of the reconstructed complex amplitude $ψ_{z_{1} k}$ with the square root of the first hologram I₁. These steps are formulated for the k th iteration as follows:

{ψ'}_{z_{2} k} = \exp (j Δ z) ψ_{z_{1} k} * h_{Δ z} = | {ψ'}_{z_{2} k}^{} | \exp (j ϕ_{2}^{'})

ψ_{z_{2} k} = \sqrt{I_{2}} \exp (j ϕ_{2}^{'})

ψ'_{z_{1} k}^{} = \exp (- j Δ z) ψ_{z_{2 k}} * h_{- Δ z} = | ψ'_{z_{1} k}^{} | \exp (j ϕ_{1}^{'})

ψ_{z_{1} k} = \sqrt{I_{1}} exp (j ϕ_{1}^{'})

where

ϕ_{1}^{'}

and

ϕ_{2}^{'}

are the retrieved phases in the first and second hologram, respectively. The program exits from its iterative loop when the mode of the image intensity reconstructed at z₀ by the retrieved complex amplitude of Eq. (16) becomes the maximum value. This mode corresponds to the background intensity because the area of the background is wider than the area of particles in the focused plane. The mode increases as the phase approaches the retrieved phase. Simulated and reconstructed holograms of Figs. 2(b) and 2(c) show that the eﬀect of the twin image has been removed by using the phase retrieval method.

Fig. 2 (a) Phase retrieval method for two holograms; comparison of a simulated and reconstructed hologram between (b) phase retrieval method and (c) Gabor method. The holograms in (b) and (c) were recorded at z₁ = 50 mm and z₂ = 100 mm, respectively. The wavelength is 632.8 nm. We randomly dispersed 500 particles with a diameter of 70 µm in the same plane with a 512 pixel × 512 pixel area (pixel size: 10 µm × 10 µm).

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In this retrieval process, the two recorded holograms must satisfy the range of Eq. (6) and the resolution of Eq. (7). However the distance Δz has not been given the attention it deserves in the recording procedure. From Eq. (9), the complex amplitude at z₁ is composed of two phases, namely the particle of $ϕ_{1}$ and the reference wave of kz₁;

ψ_{z_{1}} = \sqrt{I_{1}} \exp (j ϕ_{1}) \exp (j k z_{1}) .

The retrieved complex amplitude of Eq. (16) is also composed of the two retrieved phases as

ψ_{z_{1}} = \sqrt{I_{1}} \exp (j ϕ_{1}^{''}) \exp (j k m Δ z),

where

ϕ_{1}^{''}

and

k m

are the retrieved phase of a particle and reference wave obtained by the distance

Δ z

multiplied the integer m. If the retrieved phase has the relationship

ϕ_{1} \approx ϕ_{1}^{''}

, the distance Δz is derived from Eqs. (17) and (18) as

Δ z = \frac{z_{1}}{m} (m = 1, 2, .., m \in N) .

We have begun to verify this relationship using the holograms of Fig. 2(b). The position of hologram I₁ is fixed at z₁ that of the hologram I₂ is varied in the z direction. Figure 3(a) shows the signal-to-noise ratio (SNR) has peaks where m in Eq. (19) takes an integer value. When $m \geq 6$ , the peak shape becomes unstable in this condition. The SNR is reduced for $m \geq 10$ . This is why Δz is smaller than the far-field condition, 7.74 mm = $d_{p}^{2} / λ ≪ Δ z$ . The number of iterations N_it can be approximated as a linear function of m as shown in Fig. 3(b). The phase of the reference wave is retrieved quickly in the case of small m. These results indicate that the phase retrieval method needs to retrieve not only the phase of the particles, but also the phase of the reference wave.

Fig. 3 Influence of m in Eq. (19) on (a) the signal-to-noise ratio (SNR) and (b) the number of iterations N_it. The SNR is defined as $SNR = 10 {log}_{10} (σ_{p}^{2} / σ_{b}^{2})$ , where $σ_{p}$ and $σ_{b}$ are the standard deviations of the particles and background, respectively, of the intensity at z₀. The distance Δz is varied from 0.001 mm to 150 mm in increments of 0.001 mm.

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2.3 Evaluation of relative misalignment between two holograms

A relative misalignment between the two holograms is evaluated numerically as the SNR of the reconstructed amplitude in the xy plane and the z direction. The relative misalignment in the x direction is evaluated for a rotation and a shift in the xy plane. Figure 4 shows that the SNR of the phase retrieval method is lower than that of the Gabor method when the relative misalignment $ϵ_{x}$ in the x direction is more than two pixels. Reconstructed particles are also blurred by misaligned particles. Phase information has to be retrieved from the pixel in the same xy position or the misalignment may be up to one-third of the particle diameter. Relative to the results in Fig. 4, the eﬀect of the relative misalignment $ϵ_{Δ z}$ in the z direction is lower than that of $ϵ_{x}$ as shown in Fig. 5. If there is no misalignment in the x direction, as is also shown in Fig. 3(a), the SNR is greater than that of the Gabor method at all Δz. It is found that calibration of $ϵ_{x}$ is sensitive, but that of $ϵ_{Δ z}$ is not sensitive.

Fig. 4 SNR versus relative misalignment $ϵ_{x}$ in the x direction and reconstructed planes. Holograms of particles shown in Fig. 2 are recorded at z₁ = 50 mm and Δz = 50 mm. Hologram I₂ is shifted in the x direction with respect to hologram I₁.

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Fig. 5 SNR versus relative misalignment $ϵ_{Δ z}$ in the z direction. Holograms of Fig. 2 are recorded at z₁ = 50 mm and Δz = 50 mm. Hologram, I₂ is shifted in the z direction with respect to hologram I₁. This condition corresponds to m = 1 in Fig. 3(a).

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3. Experimental results

Two holograms of particles were recorded for the phase retrieval method by using two high-speed cameras without lenses and a He-Ne laser (wave length: 632.8 nm), as illustrated schematically in Fig. 6. Particles with an average diameter of 70 µm were settling from a particle feeder at a height of H = 150 mm. An area of 5.12 × 5.12 mm² was observed by the two high-speed cameras (FASTCAM Mini UX100, Photron, frame rate: 4,000 fps, image size: 1024 × 1024 pixel², cell size: 10 µm × 10 µm) located at two positions z₁ = 150 mm and z₂ = z₁ + Δz = 200 mm for the case of m = 3. Because the phase retrieval method is insensitive to vibration, none of the experiments were conducted on a vibration-isolation table.

Fig. 6 Optical arrangement for recording two in-line holograms with two high-speed cameras for phase retrieval method.

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As mentioned in Sec. 2.3, a relative misalignment between the two holograms must be corrected in the phase retrieval method with two cameras. First of all, the misalignment of a rotation and a shift in the xy plane was calibrated by the image distortion correction [21]. The vector field of Fig. 7(c) for the correction was calculated using particle image velocimetry [22] with the two reconstructed holograms of Figs. 7(a) and 7(b).

Fig. 7 Optical image distortion correction: (a, b) reconstructed holograms of particles; (c) vector field for image distortion correction.

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In order to calibrate the misalignment for the target distance Δz = 50 mm in the z direction, the installation distance between the two cameras was detected by changing the numerical condition of Δz at each iterative loop of the phase retrieval method, as shown in Fig. 8. The distance was obtained as Δz = 49.34 mm as the maximum value. The misalignment between the target and the installation distance was calibrated using an xyz stage.

Fig. 8 Mode of image intensity reconstructed at z₀ by the retrieved complex amplitude.

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Figure 9 shows a comparison of reconstructed experimental holograms of the settling particles using the phase retrieval method with two cameras and the Gabor method. The characteristic parts of the reconstructed holograms are magnified in the central part of each panel.

Fig. 9 Experimental holograms of settling particles reconstructed by the phase retrieval method with two high-speed cameras (left) and the Gabor method (right). Each hologram contains particles with an average diameter of 70 µm that were settling from the upper edge of the hologram at approximately terminal velocity.

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In the example of a low concentration of particles in Fig. 9(a), in the phase retrieval method compared to the Gabor method, the particle shape is more clearly visible on the reconstructed plane, and a clearer fringe pattern is also observed because of twin-image elimination. However, in the example of a high concentration of particles in Fig. 9(b), clusters of particles are also more clearly observed using the presented method.

4. Conclusion

In this paper, we derived the conditions for recording a particle using the phase retrieval method with two holograms. The signal-to-noise ratio of the reconstructed hologram and the number of iterations are especially dependent on the distance between the two holograms. Moreover, the signal-to-noise ratio is strongly aﬀected by the relative misalignment between the two holograms in the xy plane as compared to the z direction. The calibration procedure for this misalignment was also experimentally demonstrated. We conducted the experiments to observe the settling particles without the need for a vibration-isolation table. Fringe patterns and reconstructed particles were clearly observed by two high-speed cameras at 4,000 fps under both high and low particle concentrations. Therefore, we conclude that the phase retrieval method with two high-speed cameras could be used more widely in particle measurement because of its twin-image elimination, insensitivity to vibration, and simplicity of optical setup.

Funding

Ministry of Education, Culture, Sports, Science and Technology of Japan (16K06080).

References and links

1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948). [CrossRef] [PubMed]

2. S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Lasers Eng. 32(7–8), 567–574 (2000). [CrossRef]

3. J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, and A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U.S.A. 104(44), 17512–17517 (2007). [CrossRef] [PubMed]

4. P. Amsler, O. Stetzer, M. Schnaiter, E. Hesse, S. Benz, O. Moehler, and U. Lohmann, “Ice crystal habits from cloud chamber studies obtained by in-line holographic microscopy related to depolarization measurements,” Appl. Opt. 48(30), 5811–5822 (2009). [CrossRef] [PubMed]

5. D. Nguyen, D. Honnery, and J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Exp. Fluids 50(4), 949–959 (2011). [CrossRef]

6. J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010). [CrossRef]

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

8. S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48(9S2), 09LB01 (2009). [CrossRef]

9. Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004). [CrossRef]

10. Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006). [CrossRef] [PubMed]

11. Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), D183–D189 (2008). [CrossRef] [PubMed]

12. G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4(1), 159–165 (1987). [CrossRef]

13. Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, “Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm,” Opt. Express 11(24), 3234–3241 (2003). [CrossRef] [PubMed]

14. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diﬀraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

15. G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” J. Mod. Opt. 23(9), 685–700 (1976).

16. C. S. Vikram, “Particle Field Holography,” in Cambridge Studies in Modern optics (Cambridge University Press, 1992).

17. Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50(34), H22–H29 (2011). [CrossRef] [PubMed]

18. T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007). [CrossRef] [PubMed]

19. L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987). [CrossRef]

20. L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005). [CrossRef]

21. J. C. Russ, The Image Processing Handbook (CRC Press, 2016).

22. C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991). [CrossRef]

References

View by:
Article Order
|
Year
|
Author
|
Publication

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]
S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Lasers Eng. 32(7–8), 567–574 (2000).
[Crossref]
J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, and A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U.S.A. 104(44), 17512–17517 (2007).
[Crossref] [PubMed]
P. Amsler, O. Stetzer, M. Schnaiter, E. Hesse, S. Benz, O. Moehler, and U. Lohmann, “Ice crystal habits from cloud chamber studies obtained by in-line holographic microscopy related to depolarization measurements,” Appl. Opt. 48(30), 5811–5822 (2009).
[Crossref] [PubMed]
D. Nguyen, D. Honnery, and J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Exp. Fluids 50(4), 949–959 (2011).
[Crossref]
J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]
I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[Crossref] [PubMed]
S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48(9S2), 09LB01 (2009).
[Crossref]
Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]
Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[Crossref] [PubMed]
Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), D183–D189 (2008).
[Crossref] [PubMed]
G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4(1), 159–165 (1987).
[Crossref]
Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, “Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm,” Opt. Express 11(24), 3234–3241 (2003).
[Crossref] [PubMed]
R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diﬀraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” J. Mod. Opt. 23(9), 685–700 (1976).
C. S. Vikram, “Particle Field Holography,” in Cambridge Studies in Modern optics (Cambridge University Press, 1992).
Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50(34), H22–H29 (2011).
[Crossref] [PubMed]
T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]
L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]
L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005).
[Crossref]
J. C. Russ, The Image Processing Handbook (CRC Press, 2016).
C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

2011 (2)

D. Nguyen, D. Honnery, and J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Exp. Fluids 50(4), 949–959 (2011).
[Crossref]

Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50(34), H22–H29 (2011).
[Crossref] [PubMed]

2010 (1)

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

2009 (2)

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48(9S2), 09LB01 (2009).
[Crossref]

P. Amsler, O. Stetzer, M. Schnaiter, E. Hesse, S. Benz, O. Moehler, and U. Lohmann, “Ice crystal habits from cloud chamber studies obtained by in-line holographic microscopy related to depolarization measurements,” Appl. Opt. 48(30), 5811–5822 (2009).
[Crossref] [PubMed]

2008 (1)

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), D183–D189 (2008).
[Crossref] [PubMed]

2007 (2)

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, and A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U.S.A. 104(44), 17512–17517 (2007).
[Crossref] [PubMed]

2006 (1)

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[Crossref] [PubMed]

2005 (1)

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005).
[Crossref]

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

2003 (1)

Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, “Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm,” Opt. Express 11(24), 3234–3241 (2003).
[Crossref] [PubMed]

2000 (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Lasers Eng. 32(7–8), 567–574 (2000).
[Crossref]

1997 (1)

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

1991 (1)

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

1987 (2)

G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4(1), 159–165 (1987).
[Crossref]

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

1976 (1)

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” J. Mod. Opt. 23(9), 685–700 (1976).

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diﬀraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Adolf, J.

Amsler, P.

Awatsuji, Y.

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[Crossref] [PubMed]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Belas, R.

Benz, S.

Cen, K.

Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50(34), H22–H29 (2011).
[Crossref] [PubMed]

Chen, L.

Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50(34), H22–H29 (2011).
[Crossref] [PubMed]

Denis, L.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005).
[Crossref]

Ducottet, C.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005).
[Crossref]

Fink, H. W.

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Fournel, T.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005).
[Crossref]

Fournier, C.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005).
[Crossref]

Fujii, A.

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[Crossref] [PubMed]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diﬀraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Gharib, M.

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

Harada, D.

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48(9S2), 09LB01 (2009).
[Crossref]

Hesse, E.

Honnery, D.

D. Nguyen, D. Honnery, and J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Exp. Fluids 50(4), 949–959 (2011).
[Crossref]

Kaneko, A.

Katz, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

Koyama, T.

Kubota, T.

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[Crossref] [PubMed]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Latychevskaia, T.

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Liu, G.

G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4(1), 159–165 (1987).
[Crossref]

Lohmann, U.

Malkiel, E.

Matoba, O.

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[Crossref] [PubMed]

Moehler, O.

Murata, S.

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48(9S2), 09LB01 (2009).
[Crossref]

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Lasers Eng. 32(7–8), 567–574 (2000).
[Crossref]

Nguyen, D.

D. Nguyen, D. Honnery, and J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Exp. Fluids 50(4), 949–959 (2011).
[Crossref]

Nishio, K.

Onural, L.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

Osten, W.

Pedrini, G.

Place, A. R.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diﬀraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Schnaiter, M.

Scott, P. D.

G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4(1), 159–165 (1987).
[Crossref]

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

Sheng, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

Soria, J.

D. Nguyen, D. Honnery, and J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Exp. Fluids 50(4), 949–959 (2011).
[Crossref]

Stetzer, O.

Tahara, T.

Tanaka, Y.

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48(9S2), 09LB01 (2009).
[Crossref]

Thompson, B. J.

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” J. Mod. Opt. 23(9), 685–700 (1976).

Tiziani, H.

Tyler, G. A.

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” J. Mod. Opt. 23(9), 685–700 (1976).

Ura, S.

Wang, Z.

Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50(34), H22–H29 (2011).
[Crossref] [PubMed]

Willert, C. E.

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

Yasuda, N.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Lasers Eng. 32(7–8), 567–574 (2000).
[Crossref]

Zhang, T.

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

Zhang, Y.

Annu. Rev. Fluid Mech. (1)

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

Appl. Opt. (4)

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[Crossref] [PubMed]

Y. Wu, X. Wu, Z. Wang, L. Chen, and K. Cen, “Coal powder measurement by digital holography with expanded measurement area,” Appl. Opt. 50(34), H22–H29 (2011).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Exp. Fluids (2)

D. Nguyen, D. Honnery, and J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Exp. Fluids 50(4), 949–959 (2011).
[Crossref]

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10(4), 181–193 (1991).
[Crossref]

J. Mod. Opt. (1)

G. A. Tyler and B. J. Thompson, “Fraunhofer holography applied to particle size analysis a reassessment,” J. Mod. Opt. 23(9), 685–700 (1976).

J. Opt. Soc. Am. A (1)

G. Liu and P. D. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A 4(1), 159–165 (1987).
[Crossref]

Jpn. J. Appl. Phys. (1)

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48(9S2), 09LB01 (2009).
[Crossref]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Opt. Eng. (1)

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Lasers Eng. 32(7–8), 567–574 (2000).
[Crossref]

Opt. Lett. (1)

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

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diﬀraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Phys. Rev. Lett. (1)

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

Proc. SPIE (1)

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148–161 (2005).
[Crossref]

Other (2)

J. C. Russ, The Image Processing Handbook (CRC Press, 2016).

C. S. Vikram, “Particle Field Holography,” in Cambridge Studies in Modern optics (Cambridge University Press, 1992).

Cited By

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Fig. 1 Hologram intensity log₁₀I(r) of a particle against r derived from Eq. (3) for z₁ = 100mm, d_p = 70 µm and λ = 632.8 nm.

View in Article | Download Full Size | PPT Slide | PDF

View in Article | Download Full Size | PPT Slide | PDF

Fig. 3 Influence of m in Eq. (19) on (a) the signal-to-noise ratio (SNR) and (b) the number of iterations N_it. The SNR is defined as

SNR = 10 {log}_{10} (σ_{p}^{2} / σ_{b}^{2})

, where

σ_{p}

and

σ_{b}

are the standard deviations of the particles and background, respectively, of the intensity at z₀. The distance Δz is varied from 0.001 mm to 150 mm in increments of 0.001 mm.

View in Article | Download Full Size | PPT Slide | PDF

Fig. 4 SNR versus relative misalignment

ϵ_{x}

in the x direction and reconstructed planes. Holograms of particles shown in Fig. 2 are recorded at z₁ = 50 mm and Δz = 50 mm. Hologram I₂ is shifted in the x direction with respect to hologram I₁.

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Fig. 5 SNR versus relative misalignment

ϵ_{Δ z}

in the z direction. Holograms of Fig. 2 are recorded at z₁ = 50 mm and Δz = 50 mm. Hologram, I₂ is shifted in the z direction with respect to hologram I₁. This condition corresponds to m = 1 in Fig. 3(a).

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Fig. 6 Optical arrangement for recording two in-line holograms with two high-speed cameras for phase retrieval method.

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Fig. 7 Optical image distortion correction: (a, b) reconstructed holograms of particles; (c) vector field for image distortion correction.

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Fig. 8 Mode of image intensity reconstructed at z₀ by the retrieved complex amplitude.

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Equations (19)

Equations on this page are rendered with MathJax. Learn more.

ψ_{z_{1}} (x_{1}, y_{1}) = \frac{\exp (j k z_{1})}{j λ z_{1}} {\int \int}_{- \infty}^{\infty} [1 - p (x_{0}, y_{0})] exp {\frac{j k}{2 z_{1}} [{(x_{1} - x_{0})}^{2} + {(y_{1} - y_{0})}^{2}]} d x_{0} d y_{0},

p (x_{0}, y_{0}) = {\begin{matrix} 1, \sqrt{x_{0}^{2} + y_{0}^{2}} \leq {(d_{p} / 2)}^{2} \\ 0, \sqrt{x_{0}^{2} + y_{0}^{2}} > {(d_{p} / 2)}^{2} \end{matrix}

I (r) = {| ψ_{z_{1}} (r) |}^{2} = 1 - \frac{π d_{p}^{2}}{2 λ z_{1}} sin (\frac{π r^{2}}{λ z_{1}}) \frac{2 J_{1} (π d_{p} r / (λ z_{1}))}{π d_{p} r / (λ z_{1})} + {(\frac{π d_{p}^{2}}{4 λ z_{1}})}^{2} {[\frac{2 J_{1} (π d_{p} r / (λ z_{1}))}{π d_{p} r / (λ z_{1})}]}^{2},

r_{n + 1}^{2} - r_{n}^{2} \approx 2 r Δ r = 2 λ z .

r^{'} = \frac{1.22 λ z}{d_{p}} .

\frac{d_{p}^{2}}{λ} < z_{1} < \frac{d_{p} L / 2}{1.22 λ},

Δ x < \frac{d_{p}}{2.44} = \frac{Δ r}{2} .

h_{z 1} (x_{1}, y_{1}) \equiv \frac{1}{λ z_{1}} exp [j \frac{k}{z_{1}} (x_{1}^{2} + y_{1}^{2})] .

ψ_{z_{1}} = \exp (j k z_{1}) [1 - p (x_{0}, y_{0})] * h_{z_{1}} .

\begin{matrix} I_{z_{_{1}}} = ψ_{z_{_{1}}} * ψ^{*}_{z_{_{1}}} = {| 1 - p * h_{z_{_{1}}} |}^{2} \\ = 1 - p^{*} * h_{z_{_{1}}}^{*} - p * h_{z_{_{1}}} + {| p * h_{z_{_{1}}} |}^{2} \\ \approx 1 - p^{*} * h_{z_{_{1}}}^{*} - p * h_{z_{_{1}}} \end{matrix}

ψ_{z 0} = I_{z_{1}} * h_{- z_{1}} = 1 - p^{*} * h_{- 2 z_{1}} - p * h_{z_{1}} .

ψ_{z_{0}} = ψ_{z_{1}} * h_{- z_{1}} = 1 - p .

{ψ'}_{z_{2} k} = \exp (j Δ z) ψ_{z_{1} k} * h_{Δ z} = | {ψ'}_{z_{2} k}^{} | \exp (j ϕ_{2}^{'})

ψ_{z_{2} k} = \sqrt{I_{2}} \exp (j ϕ_{2}^{'})

ψ'_{z_{1} k}^{} = \exp (- j Δ z) ψ_{z_{2 k}} * h_{- Δ z} = | ψ'_{z_{1} k}^{} | \exp (j ϕ_{1}^{'})

ψ_{z_{1} k} = \sqrt{I_{1}} exp (j ϕ_{1}^{'})

ψ_{z_{1}} = \sqrt{I_{1}} \exp (j ϕ_{1}) \exp (j k z_{1}) .

ψ_{z_{1}} = \sqrt{I_{1}} \exp (j ϕ_{1}^{''}) \exp (j k m Δ z),

Δ z = \frac{z_{1}}{m} (m = 1, 2, .., m \in N) .

Abstract

1. Introduction

2. Phase retrieval method with two cameras in digital holography

2.1 Digital holography in particle measurement

2.2 Phase retrieval method in digital holography

2.3 Evaluation of relative misalignment between two holograms

3. Experimental results

4. Conclusion

Funding

References and links

References

2011 (2)

2010 (1)

2009 (2)

2008 (1)

2007 (2)

2006 (1)

2005 (1)

2004 (1)

2003 (1)

2000 (1)

1997 (1)

1991 (1)

1987 (2)

1976 (1)

1972 (1)

1948 (1)

Adolf, J.

Amsler, P.

Awatsuji, Y.

Belas, R.

Benz, S.

Cen, K.

Chen, L.

Denis, L.

Ducottet, C.

Fink, H. W.

Fournel, T.

Fournier, C.

Fujii, A.

Gabor, D.

Gerchberg, R. W.

Gharib, M.

Harada, D.

Hesse, E.

Honnery, D.

Kaneko, A.

Katz, J.

Koyama, T.

Kubota, T.

Latychevskaia, T.

Liu, G.

Lohmann, U.

Malkiel, E.

Matoba, O.

Moehler, O.

Murata, S.

Nguyen, D.

Nishio, K.

Onural, L.

Osten, W.

Pedrini, G.

Place, A. R.

Sasada, M.

Saxton, W. O.

Schnaiter, M.

Scott, P. D.

Sheng, J.

Soria, J.

Stetzer, O.

Tahara, T.

Tanaka, Y.

Thompson, B. J.

Tiziani, H.

Tyler, G. A.

Ura, S.

Wang, Z.

Willert, C. E.

Wu, X.

Wu, Y.