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Enhancement of spatial resolution in digital holographic microscopy using the spatial correlation properties of speckle patterns

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Abstract

In this study, we demonstrate enhancement of the spatial resolution in digital holographic microscopy (DHM) using the spatial correlation properties of speckle patterns. In this method, the spatial correlation coefficients of speckle intensity are controlled by illuminating a diffuser, such as a ground glass plate, with an illumination spot with intensity profiles of a ring shape produced by an amplitude-modulated aperture. These speckle patterns are incident on an object to achieve a higher numerical aperture of the illumination system in DHM. The theoretical predictions and experimental results show that higher spatial resolution in DHM can be realized by adjusting the spatial correlation properties of speckle patterns.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Digital holography is a useful technique for recording and reconstructing the complex amplitude of an optical field [1,2]. In this technique, an interference pattern of two coherent wavefronts is detected and digitized using an image sensor such as a charge-coupled device (CCD) or complementary metal–oxide–semiconductor camera and is called a digital hologram. Digital holograms are saved on a computer, and the optical field is reconstructed from them through numerical calculation. One of the main applications of the digital holographic technique is digital holographic microscopy (DHM) [37], which is actively investigated in the field of bio-imaging as a quantitative phase microscopy method [812]. In DHM, enhancement of the spatial resolution is a critical issue owing to the limitation of the number of pixels and the pixel pitch of an image sensor, and therefore, it has been investigated by several research groups [1317]. It can be realized by using a shorter wavelength in an optical source [13], by synthesizing a larger hologram [14] or a higher numerical aperture in off-axis illuminations [15], and by using structured illumination with a periodic pattern [16].

In recent years, enhancement of the spatial resolution in DHM using speckle patterns, which are regarded as random structured illumination, has been reported [1820]. Park et al. and Zheng et al. reported the enhancement of the spatial resolution in DHM using speckle illuminations [18,19]. Funamizu et al. investigated the estimation of spectral transmittance curves from RGB images in color DHM using speckle illuminations and discussed its spatial resolution [20]. In these methods, the enhancement of the spatial resolution is realized by increasing the numerical aperture of the illumination system in DHM. The numerical aperture of an illumination system that uses speckle patterns is inversely proportional to the average size of speckle intensity, which is called speckle size. Therefore, the spatial resolution in DHM can be enhanced by decreasing the speckle size. The speckle size is determined by the spatial correlation coefficient of speckle intensity, which obeys the square modulus of the Fourier transform of the intensity distribution incident on the diffuser [21]. The typical methods for reducing the speckle size include decreasing the propagation distance of speckle patterns and increasing the size of the intensity profile incident on the diffuser. The other method for adjusting the speckle size involves changing the function of the intensity profile incident on the diffuser, such as circular and Gaussian shapes.

In the field of laser speckles, peculiar types of speckle patterns have been reported [2225]. In some of these patterns, speckle grains form clusters, which suggest the existence of a longer spatial correlation beyond the speckle size [2225]. In speckles generated by illuminating the intensity profile of a ring aperture on a diffuser, the spatial correlation is longer in the longitudinal direction; these are called propagation-invariant, diffraction-free or nondiffracting speckles [22,23] after propagation-invariant, diffraction-free or nondiffracting beams [26]. Nondiffracting speckles have two notable properties, which are propagation-invariance and a sharper spatial correlation coefficient in the lateral direction compared with those of other speckles, and we will investigate the latter property in detail.

In this paper, we report the enhancement of the spatial resolution in DHM by controlling the spatial correlation properties of speckle patterns, in which we use nondiffracting speckle patterns generated from a ring aperture. This method is realized using the property that the spatial correlation coefficient of the intensity of a nondiffracting speckle is smaller in the lateral direction. To the best of our knowledge, this paper is the first report on the enhancement of the spatial resolution in DHM focused on the profile of the spatial correlation coefficient of speckle patterns.

2. Principle of enhancement of the spatial resolution using speckle patterns

Figure 1 shows the schematic of the enhancement of the spatial resolution in DHM using speckle illuminations. The lateral resolution in DHM can be determined by the optical geometry between an object and an image sensor, and the average size of speckle intensity distributions incident on the object. The numerical aperture $NA_{g}$ of the optical geometry between the object and the image sensor is given by the objective lens, whereas the numerical aperture $NA_{s}$ related to speckles is determined by the spatial correlation coefficients of speckle intensities [27]. It is known that the spatial correlation coefficient of speckle amplitude is expressed by the Fourier transform of the intensity transmittance of an intensity profile incident on a diffuser, and the spatial correlation coefficient of speckle intensity is given by the square modulus of the amplitude correlation coefficient [21]. It can be written as

$$\mu_{I}(\Delta x) = \frac{\left|\displaystyle \int I_{p}(x)\exp\left(-j \displaystyle \frac{2\pi}{\lambda z_{s}} x \Delta x\right)dx\right|^2}{|\int I_{p}(x)dx|^2},$$
where $I_{p}(x)$ is the intensity profile incident on a diffuser, which is called an illumination spot and is produced by an amplitude-modulated aperture, $\lambda$ is the wavelength of the optical source, $\Delta x$ is the difference between the distances in the Cartesian coordinate, and $z_s$ is the propagation distance of speckle patterns between the diffuser and the object. For simplicity, we use one-dimensional representation, and constant terms and the integral regions that span from $-\infty$ to $\infty$ are omitted.

 figure: Fig. 1.

Fig. 1. Schematic of the enhancement of the spatial resolution in DHM using speckle patterns. BS: Beam splitter; $z_s$: Propagation distance of speckle patterns between the diffuser and the object.

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As the illumination spot is produced by a ring function, the spatial correlation coefficient of speckle intensities is given by [23]

$$\mu_{I}(\Delta \rho) = \frac{1}{( r_o^2 - r_i^2 )^2} \Bigg[\frac{ 2r_oJ_{1}(r_o\Delta\rho)}{\Delta\rho} - \frac{2r_iJ_{1}(r_i\Delta\rho)}{\Delta\rho} \Bigg]^2,$$
where $J_{1}(\cdot )$ is the first-order Bessel function of the first kind, $r_o$ and $r_i$ are the outer and inner radii of the ring aperture, respectively, $\Delta \rho = 2\pi \Delta r/\lambda z_{s}$, and $\Delta r$ is the difference between the radii in the polar coordinate. Now, we consider the two limits for the illumination spot in Eq. (2). In the case of $r_i \to 0$, the illumination spot becomes a circular aperture, and its spatial correlation coefficient of speckle intensity is reduced to
$$\mu_{I}(\Delta \rho) = \left| 2\frac{J_{1}(r_{o}\Delta\rho)}{r_{o}\Delta\rho} \right|^2.$$
In the case of $r_i \to r_o$, which may be called a ring-slit aperture, the spatial correlation coefficient of speckle intensity is expressed as
$$\mu_{I}(\Delta \rho) = J^{2}_{0}(r_{o}\Delta\rho),$$
where $J_{0}(\cdot )$ is the zeroth-order Bessel function of the first kind. In the limit case in Eq. (4), the speckle fields are called propagation-invariant, diffraction-free or nondiffracting speckles.

Figure 2 (a) shows the spatial correlation coefficient for the intensity distributions of speckle patterns generated from a circular aperture and a ring aperture, which are calculated from Eq. (2) and (3), respectively. In Fig. 2 (a), the radius of the circular aperture is set to 0.5 mm. In the case of the ring aperture, the inner radius is set to be $r_{i}/r_{o}=$ 0.5 and 0.95 whereas the outer radius is set to the same value as the radius of the circular aperture. The other parameters in Fig. 2 are the same in these cases for $\lambda$=632.8 nm and $z_s$=20 mm, which are set to the experimental condition as explained later. It can be observed from this figure that the width of the main lobe of the spatial correlation coefficients decreases with an increase in the inner radius of the ring aperture, which indicates that the speckle intensity involves the interference patterns with a higher weight in the higher-spatial-frequency components as $r_{i}/r_{o}$ increases.

 figure: Fig. 2.

Fig. 2. Spatial correlation coefficients and power spectra of the intensity distributions of speckle patterns generated from a circular aperture and a ring aperture. (a) Spatial correlation coefficients. (b) Power spectra. The horizontal axis of (a) is $\Delta \rho = 2\pi \Delta r/\lambda z_{s}$, and $\Delta r$ is the difference between the radii in the polar coordinate. The horizontal axis of (b) is the radial coordinate of the spatial-frequency region.

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Based on the concept of angular spectrum [28], speckle fields can be regarded as the superposition of plane waves with random illumination directions, which correspond to the spatial frequency of plane waves. Each plane wave shifts the higher-spatial-frequency components of an object to the lower-spatial-frequency regions. The higher spatial frequencies of the object can pass through the limited aperture of the objective lens, and therefore, the numerical aperture can be increased using the illumination pattern with the higher-spatial-frequency components [18,19]. Using $NA_{g}$ and $NA_{s}$, the lateral resolution in DHM using speckle illuminations is determined by [1820]

$$\delta x = 0.61\frac{\lambda}{(NA_{g}+NA_{s})}=0.61\frac{\lambda}{(NA_{g}+\sin\phi)},$$
where $\phi$ is the incident angle of the plane waves involved in speckle patterns to the object. As is seen from Eq. (5), the spatial resolution in DHM can be enhanced by the numerical aperture $NA_s$ related to the speckle illuminations, whereas $NA_s$ is zero in the conventional DHM for the on-axis plane wave illumination. Therefore, in comparison with the conventional DHM in coherent imaging systems, the resolution enhancement is realized using the speckle illuminations under the condition of $0 < NA_s \leq NA_g$. The maximum of the resolution enhancement in DHM using speckle illuminations is the same as incoherent imaging systems while coherent imaging systems are used [1720], and therefore the spatial resolving power of this DHM is twice higher than that of the conventional DHM. DHM using speckle illuminations also has an advantage that the degree of the resolution enhancement of DHM can be controlled by the spatial correlation coefficient of speckle illuminations.

From Eq. (5), the enhancement of the spatial resolution in this method is determined by the spatial frequency components and the weights of interference patterns involved in the speckle intensities, i.e., the power spectrum of speckle intensity. It is given by the Fourier transform of the spatial correlation coefficient of speckle intensity [21]. The power spectrum of the speckle intensity distributions generated from the ring aperture is expressed as

$$\mathcal{G}(\nu) = \frac{2}{\pi(\nu_o^2-\nu_i^2)}Re \left\{ \nu_o^2[ K_1(\nu) - K_2(\nu) ] - \nu_i^2[ K_3(\nu) - K_4(\nu) ] \right\},$$
where $\nu$ is the radial coordinate of the spatial-frequency region, and $\nu _o=r_o/\lambda z_s$ and $\nu _i=r_i/\lambda z_s$ are the spatial frequencies of the outer and inner radii of the ring aperture, respectively. $Re\{\cdot \}$ represents the real part. In this equation, $K_1(\nu )$$K_4(\nu )$ are given by
$$K_1(\nu) = \arccos{\Big(\frac{\nu}{2\nu_o}\Big)} - \frac{\nu}{2\nu_o}\sqrt{ 1 - \Big(\frac{\nu}{2\nu_o}\Big)^2},$$
$$K_2(\nu) = \arccos{\Big(\frac{\nu_p}{2\nu_o}\Big)} -\frac{\nu_p}{2\nu_o}\sqrt{ 1 -\Big (\frac{\nu_p}{2\nu_o}\Big)^2},$$
$$K_3(\nu) = \arccos{\Big(-\frac{\nu}{2\nu_i}\Big)} +\frac{\nu}{2\nu_i}\sqrt{ 1 - \Big(\frac{\nu}{2\nu_i}\Big)^2},$$
$$K_4(\nu) = \arccos{\Big(\frac{ \nu_q}{2\nu_i}\Big)} - \frac{\nu_q}{2\nu_i}\sqrt{ 1 - \Big(\frac{\nu_q}{2\nu_i}\Big)^2},$$
where $\nu _p=(\nu _o^2 - \nu _i^2 +\nu ^2)/\nu$, $\nu _q=(\nu _o^2 - \nu _i^2 -\nu ^2)/\nu$. In the case of $r_i \to 0$, which corresponds to the circular aperture, Eq. (6) is reduced to [28]
$$\mathcal{G}(\nu) = \frac{2}{\pi} \Bigg[ \arccos{\Big(\frac{\nu}{2\nu_o}\Big)} - \frac{\nu}{2\nu_o}\sqrt{ 1 - \Big(\frac{\nu}{2\nu_o}\Big)^2} \Bigg].$$
In the case of $r_i \to r_o$, which is the nondiffracting speckles, Eq. (6) becomes
$$\mathcal{G}(\nu) = \delta(\nu),$$
where $\delta (\cdot )$ is the Dirac delta function. Rigorously speaking, the spatial resolution in DHM cannot be enhanced using the nondiffracting speckles as shown in Eq. (12) theoretically, because the power spectrum only has the DC term and is the same as the illumination of the plane wave vertical to an object. However, as the illumination spots with a ring shape for producing the nondiffracting speckle have a finite width in the practical case, the enhancement of the spatial resolution in DHM can be realized using the proposed method.

Figure 2 (b) shows the power spectrum of the speckle intensity distributions in the case of the circular and ring apertures, which is calculated using Eq. (6) and Eq. (11). It can be observed from this figure that the power spectrum has a higher weight in the high-spatial-frequency region with an increase in the inner radius $r_i$, whereas the weight is suppressed in other regions. This indicates that the higher-spatial-frequency components of the object are downshifted by plane waves with the higher-spatial-frequency components in the speckle patterns generated from the ring aperture. Notably, the power spectrum has moderate weights around the maximum of the spatial frequency in the speckle patterns generated from the ring aperture whereas it is zero in the case of the circular aperture. Therefore, the spatial resolution in DHM can be enhanced by the speckle illuminations generated from the ring aperture, and thus, it can be controlled using the spatial correlation coefficient of the speckle intensity distributions.

3. Experiment and results

Figure 3 shows the experimental setup for the enhancement of the spatial resolution in DHM using speckle illuminations. In this setup, we use a Mach–Zehnder interferometer in off-axis configuration. A He-Ne laser (NEC corporation GLG5410, 632.8 $nm$, 20 $mW$) is used as an optical source. Coherent light field emitted from the laser is split using a beam splitter BS$_{1}$. One of the split light beams is expanded by the objective lens OB$_{1}$ ($\times 40$) and then collimated by the lens L$_1$, which is used as the reference wave. The other is expanded by an objective lens OB$_{2}$ ($\times$5), collimated by a lens L$_{2}$, and incident on an aperture and a holographic diffuser (Edmund, #47-676), where a speckle pattern is generated. The speckle pattern is used as the illumination of the object, and the transmitted light is incident on the objective lens OB$_{3}$ ($\times$2, $NA_{g}$=0.06), for which we choose a low numerical aperture to demonstrate the proposed method. The object and reference waves are coupled by the BS$_3$ again, they interfere with each other, and they are detected using a monochrome CCD camera (AVT, Guppy F-146B) having 1392 $\times$ 1040 pixels with a pixel pitch of 4.65 $\times$ 4.65 $\mu m^2$. To separate and remove DC terms and a twin image from an object image in the reconstruction plane, digital holograms with a spatial carrier are obtained by adjusting the angle of BS$_3$ in the recording process. In the reconstruction process, we apply the angular spectrum method [3] and the spatial filtering method [29] to the holograms.

 figure: Fig. 3.

Fig. 3. Experimental setup of DHM using speckle patterns. M : Mirror; BS : Beam splitter; ND : Neutral density filter; OB : Objective lens; L : Lens.

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To control the spatial correlation coefficient of the speckle intensity and to demonstrate the enhancement of the spatial resolution in the proposed method, the amplitude-modulated apertures are placed immediately in front of the diffuser. We used the apertures with circular and ring shapes as the illumination spots incident on the diffuser. The radius of the circular aperture is set to $r_o$= 0.50 mm. The outer radius of the ring aperture is the same as that of the circular aperture, and the inner radius is set to $r_i$=0.95$r_o$. We use two types of test targets with amplitude and phase distributions: a star target (Edmund, #58-833) for intensity modulations and a quantitative phase microscopy target (QPMT, Benchmark technologies) for phase modulations. The QPMT has the refractive index $n_o$=1.52 and the star targets with seven heights. We use the star target with the height 350 nm, and then the phase modulation is 0.58$\pi$ radian. The distance $z_s$ between the diffuser and the target is 20.0 mm in the case of the star target and 13.5 mm in the case of the QPMT. At these distances, the spatial resolution in DHM is more enhanced in the case of the target with the phase modulations because the propagation distance of the speckle patterns is shorter and the speckle size becomes smaller. The reason for the difference in the propagation distances of the star target and the QPMT is that it is difficult to confirm the enhancement of the spatial resolution from the reconstructed image in the case of the QPMT for $z_s$=20 mm because the spatial resolution in DHM is enhanced in the area of concentric circles without the radial fringe patterns in the QPMT, which is shown in Figs. 6 (d)–(f). The field of view of DHM is 0.24 $\times$ 0.24 mm$^2$ and the magnification power is 20.0 times.

Figure 4 shows the reconstruction process of digital holograms in DHM using speckle illuminations. The complex amplitude of the reconstructed images of the object is modulated by illuminating speckle fields. Therefore, in the recording process, we acquire digital holograms with and without the object, which are called object and reference holograms, respectively. As the reference hologram has information on the complex amplitude of the speckle fields used as the illumination, it is used for removing the random modulations from the object holograms. As speckle patterns are changed by moving the diffuser in the in-plane direction, 25 holograms are sequentially recorded for the object and reference holograms using the CCD camera. The diffuser is shifted at an interval of 1.0 mm, which is the same as the diameter of the circular aperture and the outer diameter of the ring aperture, and therefore, these speckles are statistically independent of each other. Subsequently, the reconstruction process shown in Fig. 4 is applied to these holograms. In the reconstruction process, digital holograms are reconstructed using the angular spectrum method and the spatial filtering method. The fast Fourier transform (FFT) is applied to the digital hologram and its Fourier spectrum is calculated. By performing the spatial filtering method using a circular filter, the Fourier spectrum of the object image is obtained, whereas the DC terms and the twin image are removed. The object image is reconstructed by multiplying the filtered Fourier spectrum by the spatial-frequency transfer function in the wave propagation phenomena and then performing the inverse FFT. After applying these methods to multiple holograms, the intensity and phase distributions of the reconstructed images are averaged. The intensity distributions $I_{o}$ and $I_{r}$ of the reconstructed images of the object holograms and reference holograms, respectively, are averaged separately, and then the averaged intensity $I_{a}$ is given by $I_{a}=I_{o}/I_{r}$. In the phase distributions, after calculating the phase difference maps $\Phi _{d}$ of the reconstructed images of the object hologram and reference hologram, the averaged phase difference map $\Phi _{a}$ is obtained as [30]

$$\Phi_{a}=\arctan\Bigg( \frac{\Sigma_{i=1}^{n}\sin\Phi_{d, i}}{\Sigma_{i=1}^{n}\cos\Phi_{d, i}} \Bigg),$$
where $n$ is the number of holograms. There are two reasons for applying the averaging process to the reconstructed images [18]. The first reason is to suppress the effect of the singular point owing to the phase singularity in the speckle patterns on the intensity and phase distributions. The second reason is to reduce the degradation of the image quality owing to the inherent fixed pattern noise generated from the diffraction from scatterers in the optical path.

 figure: Fig. 4.

Fig. 4. Reconstruction process of digital holograms.

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Figures 5 (a) and (b) show the experimental results of the intensity distributions of the speckle patterns generated from the circular and ring apertures for $z_s$=20 mm. In these figures, the maximum intensity is normalized to 1.0. It can be observed from these figures that the speckle grains in the ring aperture form snake-like clusters whereas they are distributed uniformly in the circular aperture. The peculiar appearance of the speckle pattern depends on the spatial correlation coefficient with the sharp main lobe and the long tails consisting of ringing side lobes [23]. Figure 5 (c) shows the spatial correlation coefficients of the speckle intensities calculated from the images shown in Figs. 5 (a) and (b). It can be observed from this figure that the main lobe of the spatial correlation coefficient in the ring aperture becomes sharper in comparison with that of the circular aperture, which is consistent with the theoretical prediction in Fig. 2 (a) and can be used as the illumination for the enhancement of the spatial resolution.

 figure: Fig. 5.

Fig. 5. Experimental results of the speckle patterns in (a) the circular aperture and (b) the ring aperture for $r_{i}/r_{o}$=0.95. (c) shows the spatial correlation coefficients of the speckle intensities of (a) and (b).

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Figures 6 (a)–(f) show the intensity and phase distributions of the reconstructed images of the star target and the QPMT. Figures 6 (a)–(c) show the intensity distributions of the reconstructed images of the star target. Figures 6 (d)–(f) show the phase distributions of the reconstructed images of the QPMT. Figures 6 (a) and (d) correspond to the case of Gaussian-shaped illumination, and are obtained from the hologram without a diffuser and an aperture in the experimental setup shown in Fig. 3. Figures 6 (b) and (e) show the reconstructed images in the case of speckle illuminations using the circular aperture. Figures 6 (c) and (f) show the results of speckle illuminations using the ring aperture. In the case of speckle illuminations, the reconstructed images are averaged using 25 holograms on the basis of intensity or phase. In Figs. 6 (a)–(c), the maximum intensity of the reconstructed images is normalized to 1.0, and the white circle at the center of the reconstructed images is an unresolved region, in which there are no radial fringe patterns. The radial fringe pattern with higher spatial frequency can be observed around the center of the star target and around the second circle from the outside of the reconstructed image of the QPMT in the case of the ring aperture in comparison with the Gaussian-shaped illumination and the circular aperture, showing the enhancement of the spatial resolution in DHM using speckle illuminations generated from the ring aperture. It can also be observed from these figures that the speckle noise owing to the use of a laser light is suppressed in the reconstructed images obtained from the speckle illuminations generated from the circular aperture and ring aperture in comparison with the Gaussian-shaped illumination because of the averaging process using multiple holograms. It can also be observed in Figs. 6 (b), (c), (e) and (f) that the reconstructed images for the ring aperture have higher noise than those for the circular aperture, whereas the spatial resolution in DHM is more enhanced in the case of the ring aperture. There are two reasons for the high noise level in the case of the ring aperture. The first reason is that the speckle patterns with a higher value in the side lobe of speckle correlations, such as the speckle patterns generated from the ring aperture, nondiffracting speckles, and fractal speckles [2325], retain higher speckle contrast in the averaging process [31,32]. The second reason is that the noise with the higher-spatial-frequency components is also enhanced as the proposed method is a kind of enhancement of the higher-spatial-frequency components.

 figure: Fig. 6.

Fig. 6. Intensity and phase distributions of the reconstructed images of the star target and the QPMT. (a)–(c) show the intensity distributions of the reconstructed images of the star target. (d)–(f) show the phase distributions of the reconstructed images of the QPMT. (a) and (d) correspond to the case of Gaussian-shaped illumination. (b) and (e) correspond to the case of speckle illuminations using the circular aperture. (c) and (f) show the results of speckle illuminations using the ring aperture.

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Figures 7 (a) and (b) show the evaluation of the suppression of speckle noise in the reconstructed images against the number of holograms. Figure 7 (a) shows the results of the speckle contrast of intensity distributions shown in Figs. 6 (a)–(c). The speckle contrast of intensity distributions is evaluated as $C_I(n)=\sigma _I(n)/m_I(n)$, where $\sigma _I(n)$ and $m_I(n)$ are the standard deviation and mean of the speckle intensity, respectively, considering the number of holograms. These parameters are calculated using the square area of 200 $\times$ 200 pixels around the center of the reconstructed image, which is in the circular unresolved region of the star target. In the case of speckle illumination, the speckle contrast for a hologram is extremely high because of the singular point owing to the phase singularity in speckle patterns as explained in the previous part, and therefore, it is not shown to demonstrate the results clearly. Figure 7 (b) shows the standard deviation of the speckle patterns of phase distributions of the reconstructed images against the number of holograms. In this case, the suppression of speckle noises is evaluated using the standard deviation of the phase distributions, which is calculated from the square area of 60 $\times$ 60 pixels in the largest black area at the bottom right of the reconstructed image shown in Figs. 6 (d)–(f). In Figs. 7 (a) and (b), the yellow line represents the result of the Gaussian-shaped illumination, which is shown by a constant value over the horizontal axis owing to the reconstruction from a hologram. It can be observed from these figures that the speckle contrast of the intensity distributions and the standard deviation of the phase distributions decrease with an increase in the number of holograms, which shows that larger fluctuations of intensity and phase distributions are reduced by the averaging process and the image quality of the reconstructed images is improved quantitatively. It is also observed that the evaluation functions in the speckle illumination become lower than that in the Gaussian-shaped illumination around four holograms.

 figure: Fig. 7.

Fig. 7. Speckle contrasts of the intensity distributions and standard deviations of the phase distributions of the reconstructed images against the number of holograms. (a) Speckle contrasts. (b) Standard deviations.

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Figs. 8 (a) and (b) show the signal-to-noise ratio (SNR) in the reconstructed images against the number of holograms. Figure 8 (a) shows the results of intensity distributions shown in Figs. 6 (a)–(c). The SNR in the intensity distributions is given by $20\log _{10}[m_I(n)/\sigma _I(n)]$ because the reciprocal number of the speckle contrast corresponds to the SNR of speckle patterns [21]. Figure 8 (b) shows the SNR of phase distributions of the reconstructed images against the number of holograms. In this case, speckle noises are evaluated using the red square area of 10 $\times$ 10 pixels in the reconstructed image shown in the bottom right of Figs. 6 (d)–(f). The SNR of the phase distributions are also calculated by $20\log _{10}[m_\Phi (n)/\sigma _\Phi (n)]$, where $m_\Phi (n)$ and $\sigma _\Phi (n)$ are the mean and standard deviation of the phase distributions in the red square area. It can be observed in these figures that the SNR increases with an increase in the number of holograms, as expected in Figs. 7 (a) and (b), and therefore we also confirmed the improvement of the image quality by the SNR in the intensity and phase distributions of the reconstructed images. To reduce speckle noises and the inherent fixed pattern noises generated from the scattering in the optical path, several methods using multiple holograms have been proposed such as changing wavelengths [33], polarizations [34], illumination angles [35] and a movement of a diffuser in the lateral direction [36], and focal positions using electrically focus tunable lens [37]. As the noise reduction method in this study corresponds to the movement of the diffuser in the lateral direction and has the property of incoherent imaging systems, the degree of the noise reduction is higher than the others. However, the main restriction in this method is the acquisition rate of digital holograms. It can be improved using the scanning of the diffuser with the illumination spots by means of a galvanometer mirror [18] or the generation of speckle illuminations using a spatial light modulator [19]. Meanwhile, the noise reduction using electrically focus tunable lens is the simple, low cost and practial method with the higher acquisition rate of multiple holograms and the similar degree of the noise reduction to that in the case of [3335].

 figure: Fig. 8.

Fig. 8. SNR of the intensity and phase distributions of the reconstructed images against the number of holograms. (a) Intensity. (b) Phase.

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To confirm the enhancement of the spatial resolution quantitatively, we applied the analytical process shown in Fig. 9. First, the center of the targets is placed at the upper left in the reconstruction plane and digital holograms are recorded. Subsequently, the coordinate transformation from the Cartesian coordinate to the polar coordinate is applied to the reconstructed image. Each row of the reconstructed image in the polar coordinate is Fourier-transformed and the power spectrum is calculated by performing the square modulus of the Fourier spectrum. From the power spectrum, the contrast and SNR of the fringe pattern of each row are calculated. The contrast of the fringe pattern of each row is calculated from the division of the first peak value by the zeroth peak value. The SNR is given from $10\log _{10}(P_s/P_n)$, where $P_s$ and $P_n$ are the signal components, which correspond to the first peak value, and the noise components in the power spectrum as shown in the bottom left of Fig. 9. In the phase distributions of the reconstructed images shown in Figs. 6 (d)–(f), the analytical process is performed after adding $\pi$ to the phase values of the reconstructed images for producing the zeroth peak in the power spectrum.

 figure: Fig. 9.

Fig. 9. Analytical process of the spatial resolution using the contrast and SNR of the fringe patterns.

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Figure 10 shows the results of the transformation from the Cartesian coordinate to the polar coordinate applied to the reconstructed images, in which the arrangement of these figures corresponds to the reconstructed images shown in Figs. 6 (a)–(f). In Figs. 10 (a)–(c), the range of 0 to 210 pixels in the vertical axis corresponds to the unresolved region of the star target, which is shown by the white circles in the center of the reconstructed images shown in Figs. 6 (a)–(c). In Figs. 10 (d)–(f), the black lines around 427 and 217 pixels in the vertical axis correspond to the first and second circles from outside in the reconstructed image shown in Figs. 6 (d)–(f), respectively. It can be observed from these figures that the fringe patterns extend toward the origin of the vertical axis in the order of the Gaussian-shaped illumination, speckle illuminations generated from the circular aperture, and those generated from the ring aperture, which shows the enhancement of spatial resolution in DHM using speckle patterns generated from the ring aperture as shown in Figs. 6 (a)–(f).

 figure: Fig. 10.

Fig. 10. Reconstructed images after transforming from the Cartesian coordinate to the polar coordinate. The arrangement of these figures corresponds to the reconstructed images shown in Figs. 6 (a)–(f).

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Figures 11 (a) and (b) and Figs. 12 (a) and (b) show the results of the contrast in the analytical process shown in Fig. 9 and the magnified images in the region of interest. In Fig. 12 (a), the valley around 427 pixels is due to the first circle from outside in the reconstructed image shown in Figs. 6 (d)–(f), whereas the second circle from outside is represented by the valley around 217 pixels. It is observed in Fig. 11 and Fig. 12 that the result for the ring aperture retains the higher contrast of the fringe patterns than that in the Gaussian-shaped illuminations and in the circular aperture around the range 300 to 450 pixels for the intensity distributions and the range 180 to 260 pixels for the phase distributions as predicted in Figs. 6 (a)–(f) and Figs. 10 (a)–(f). In the case of the QPMT, particularly in Fig. 12 (b), the valley around 217 pixels can be observed in the case of the ring aperture whereas it is not observed in the case of the circular aperture, which indicates the enhancement of the spatial resolution in DHM using the speckle pattern generated from the ring aperture in comparison with that generated from the circular aperture. Figures 13 (a) and (b) show the results of the SNR in the analytical process shown in Fig. 9 and correspond to the results of the intensity and phase distributions, respectively. In these figures, the vertical axis is set to the range from -35 to 35 dB to show the results clearly. From these figures, the enhancement of the spatial resolution in the ring aperture can be clearly observed in the range pointed out in Fig. 11 and Fig. 12, even if these figures are not enlarged as Fig. 11 (b) and Fig. 12 (b). While the improvement of the SNR using speckle illuminations is observed in the intensity distributions, it is smaller in the phase distributions. This is because the speckle noise in the phase distributions becomes lower in the case of the Gaussian-shaped illumination owing to the low phase modulation of the QPMT in this experimental condition. Although the improvement of the SNR using speckle illuminations seems to be lower in the phase distributions, it is important in the phase unwrapping process, in which the phase distributions with the lower noise level is required. It is difficult to directly compare the values of the SNR in Fig. 8 and Fig. 13, because the different evaluation functions in the SNR are used. The evaluation function of the SNR in Fig. 8 is based on the speckle contrast in the area with a constant amplitude or phase value in reconstructed images, whereas the power spectrum of the fringe patterns is used in the SNR in Fig. 13. However, the SNR in both cases is useful for evaluating the degree of image quality improvement and resolution enhancement and for the possibility of the image restorations. Finally, in Figs. 14 (a) and (b), we show the one-dimensional plots of the intensity and phase distributions of the reconstructed images in 366 and 206 pixels in Figs. 10 (a)–(c) and (d)–(f). As predicted, the fringe pattern has a higher contrast in the case of the ring aperture whereas noisy patterns are observed in the case of the Gaussian-shaped illumination.

 figure: Fig. 11.

Fig. 11. Results of the application of the analysis in Fig. 9 to the reconstructed images of the star target. (a) Contrast of the fringe patterns in the reconstructed image of the star target. (b) Magnified image of (a).

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 figure: Fig. 12.

Fig. 12. Results of the application of the analysis in Fig. 9 to the reconstructed image of the QPMT. (a) Contrast of the fringe patterns in the reconstructed image of the quantitative phase microscopy target. (b) Magnified image of (a).

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 figure: Fig. 13.

Fig. 13. Results of SNR of the analysis in Fig. 9. (a) Intensity. (b) Phase.

Download Full Size | PPT Slide | PDF

 figure: Fig. 14.

Fig. 14. One-dimensional plots of the fringe patterns in the reconstructed images. (a) Fringe patterns of the intensity distributions of the reconstructed images in 366 pixels shown in Figs. 10 (a)–(c). (b) Fringe patterns of the phase distributions of the reconstructed images in 206 pixels shown in Figs. 10 (d)–(f).

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Whereas the enhancement of the spatial resolution is realized in the proposed method, the contrasts of fringe patterns in speckle illuminations decrease in the middle range 450 to 800 pixels for the intensity distributions and 250 to 550 pixels for the phase distributions as shown in Fig. 11 and Fig. 12. Although this drawback can be acceptable in the two-point resolution, it is crucial issue in the acquisition of the quantitative phase information because of the reduction of the phase modulation. However, it is important to note that the reconstructed images obtained from speckle illuminations still retain the modarate SNR in fringe patterns with the higher-spatial-frequency components, which implies the contrast of fringe patterns can be recovered or corrected using the several methods, such as the deconvolution and the iterative methods of complex amplitudes [19,38,39].

4. Conclusions

In the present paper, we reported the enhancement of the spatial resolution in DHM using speckle patterns generated from a ring aperture. In this method, the enhancement of the spatial resolution was realized using the property that the spatial correlation coefficient of the intensity distribution of a nondiffracting speckle pattern is shorter than that of other speckle patterns in the lateral direction. We provided the theoretical background of the lateral resolution in DHM using speckle illuminations and showed that the numerical aperture of the illumination system using speckle patterns generated from the ring aperture can be enhanced in comparison with that of the circular aperture under the condition of the same radius. In the experiment, we used amplitude- and phase-modulated targets as test objects. To evaluate the spatial resolution in DHM, we applied the transformation from the Cartesian coordinate to the polar coordinate to the reconstructed images and the Fourier analysis to each row of the reconstructed image after the transformation. We experimentally demonstrated the enhancement of the spatial resolution and improvement of image quality using the amplitude- and phase-modulated test targets. The main issue in the proposed method is an acquisition time of multiple holograms for different speckle patterns, which restricts the application of the proposed method to the area of bio-imaging. In the practical application to the bio-imaging, we need to optimize optical systems for a fast acquisition of multiple holograms in future work, such as the scanning of the diffuser with the illumination spots by means of a galvanometer mirror or the generation of speckle illuminations using a spatial light modulator. In conclusion, it is believed that this method can be useful for applications in the field of bio-imaging and an optical inspection of micro devices.

Funding

Japan Society for the Promotion of Science (JSPS) (JP15K06098, JP18K04159).

Acknowledgments

This work was supported by the JSPS KAKENHI Grant Numbers JP15K06098 and JP18K04159.

References

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

2. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

3. M. K. Kim, Digital Holographic Microscopy (Springer, 2011).

4. T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23(15), 1221–1223 (1998). [CrossRef]  

5. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007). [CrossRef]  

6. B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008). [CrossRef]  

7. M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010). [CrossRef]  

8. I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008). [CrossRef]  

9. P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, “On the holographic 3d tracking of in vitro cells characterized by a highly-morphological change,” Opt. Express 20(27), 28485–28493 (2012). [CrossRef]  

10. K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013). [CrossRef]  

11. J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014). [CrossRef]  

12. Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018). [CrossRef]  

13. A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express 18(13), 14159–14164 (2010). [CrossRef]  

14. F. L. Clerc, M. Gross, and L. Collot, “Synthetic-aperture experiment in the visible with on-axis digital heterodyne holography,” Opt. Lett. 26(20), 1550–1552 (2001). [CrossRef]  

15. V. Mico, Z. Zalevsky, and J. Garcia, “Superresolution optical system by common-path interferometry,” Opt. Express 14(12), 5168–5177 (2006). [CrossRef]  

16. J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014). [CrossRef]  

17. V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019). [CrossRef]  

18. Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009). [CrossRef]  

19. J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015). [CrossRef]  

20. H. Funamizu, Y. Tokuno, and Y. Aizu, “Estimation of spectral transmittance curves from rgb images in color digital holographic microscopy using speckle illuminations,” Opt. Rev. 23(3), 535–543 (2016). [CrossRef]  

21. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co, 2006).

22. J. Turunen, A. Vasara, and A. T. Friberg, “Propagation invariance and self-imaging in variable-coherence optics,” J. Opt. Soc. Am. A 8(2), 282–289 (1991). [CrossRef]  

23. K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun. 114(3-4), 203–210 (1995). [CrossRef]  

24. J. Uozumi, M. Ibrahim, and T. Asakura, “Fractal speckles,” Opt. Commun. 156(4-6), 350–358 (1998). [CrossRef]  

25. H. Funamizu and J. Uozumi, “Generation of fractal speckles by means of a spatial light modulator,” Opt. Express 15(12), 7415–7422 (2007). [CrossRef]  

26. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef]  

27. J. García, Z. Zalevsky, and D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13(16), 6073–6078 (2005). [CrossRef]  

28. J. W. Goodman, Introduction to Fourier optics, 3rd ed. (Roberts & Company, 2005).

29. 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]  

30. T. Baumbach, E. Kolenović, V. Kebbel, and W. Jüptner, “Improvement of accuracy in digital holography by use of multiple holograms,” Appl. Opt. 45(24), 6077–6085 (2006). [CrossRef]  

31. K. Uno, J. Uozumi, and T. Asakura, “Texture analysis of speckles due to random koch fractals by lacunarity,” Waves in Random Media 5(2), 253–263 (1995). [CrossRef]  

32. H. Funamizu and J. Uozumi, “Scaling reduction of the contrast of fractal speckles detected with a finite aperture,” Opt. Commun. 281(4), 543–549 (2008). [CrossRef]  

33. T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Image quality improvement of digital holography by superposition of reconstructed images obtained by multiple wavelengths,” Appl. Opt. 47(19), D38–D43 (2008). [CrossRef]  

34. L. Rong, W. Xiao, F. Pan, S. Liu, and R. Li, “Speckle noise reduction in digital holography by use of multiple polarization holograms,” Chin. Opt. Lett. 8(7), 653–655 (2010). [CrossRef]  

35. X. Kang, “An effective method for reducing speckle noise in digital holography,” Chin. Opt. Lett. 6(2), 100–103 (2008). [CrossRef]  

36. D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34(23), 3610–3612 (2009). [CrossRef]  

37. R. Schubert, A. Vollmer, S. Ketelhut, and B. Kemper, “Enhanced quantitative phase imaging in self-interference digital holographic microscopy using an electrically focus tunable lens,” Biomed. Opt. Express 5(12), 4213–4222 (2014). [CrossRef]  

38. Y. Cotte, M. F. Toy, N. Pavillon, and C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields,” Opt. Express 18(19), 19462–19478 (2010). [CrossRef]  

39. X.-J. Lai, H.-Y. Tu, C.-H. Wu, Y.-C. Lin, and C.-J. Cheng, “Resolution enhancement of spectrum normalization in synthetic aperture digital holographic microscopy,” Appl. Opt. 54(1), A51–A58 (2015). [CrossRef]  

References

  • View by:

  1. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
    [Crossref]
  2. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
  3. M. K. Kim, Digital Holographic Microscopy (Springer, 2011).
  4. T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23(15), 1221–1223 (1998).
    [Crossref]
  5. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007).
    [Crossref]
  6. B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008).
    [Crossref]
  7. M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
    [Crossref]
  8. I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008).
    [Crossref]
  9. P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, “On the holographic 3d tracking of in vitro cells characterized by a highly-morphological change,” Opt. Express 20(27), 28485–28493 (2012).
    [Crossref]
  10. K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
    [Crossref]
  11. J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014).
    [Crossref]
  12. Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
    [Crossref]
  13. A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express 18(13), 14159–14164 (2010).
    [Crossref]
  14. F. L. Clerc, M. Gross, and L. Collot, “Synthetic-aperture experiment in the visible with on-axis digital heterodyne holography,” Opt. Lett. 26(20), 1550–1552 (2001).
    [Crossref]
  15. V. Mico, Z. Zalevsky, and J. Garcia, “Superresolution optical system by common-path interferometry,” Opt. Express 14(12), 5168–5177 (2006).
    [Crossref]
  16. J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
    [Crossref]
  17. V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019).
    [Crossref]
  18. Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009).
    [Crossref]
  19. J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
    [Crossref]
  20. H. Funamizu, Y. Tokuno, and Y. Aizu, “Estimation of spectral transmittance curves from rgb images in color digital holographic microscopy using speckle illuminations,” Opt. Rev. 23(3), 535–543 (2016).
    [Crossref]
  21. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co, 2006).
  22. J. Turunen, A. Vasara, and A. T. Friberg, “Propagation invariance and self-imaging in variable-coherence optics,” J. Opt. Soc. Am. A 8(2), 282–289 (1991).
    [Crossref]
  23. K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun. 114(3-4), 203–210 (1995).
    [Crossref]
  24. J. Uozumi, M. Ibrahim, and T. Asakura, “Fractal speckles,” Opt. Commun. 156(4-6), 350–358 (1998).
    [Crossref]
  25. H. Funamizu and J. Uozumi, “Generation of fractal speckles by means of a spatial light modulator,” Opt. Express 15(12), 7415–7422 (2007).
    [Crossref]
  26. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [Crossref]
  27. J. García, Z. Zalevsky, and D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13(16), 6073–6078 (2005).
    [Crossref]
  28. J. W. Goodman, Introduction to Fourier optics, 3rd ed. (Roberts & Company, 2005).
  29. 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]
  30. T. Baumbach, E. Kolenović, V. Kebbel, and W. Jüptner, “Improvement of accuracy in digital holography by use of multiple holograms,” Appl. Opt. 45(24), 6077–6085 (2006).
    [Crossref]
  31. K. Uno, J. Uozumi, and T. Asakura, “Texture analysis of speckles due to random koch fractals by lacunarity,” Waves in Random Media 5(2), 253–263 (1995).
    [Crossref]
  32. H. Funamizu and J. Uozumi, “Scaling reduction of the contrast of fractal speckles detected with a finite aperture,” Opt. Commun. 281(4), 543–549 (2008).
    [Crossref]
  33. T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Image quality improvement of digital holography by superposition of reconstructed images obtained by multiple wavelengths,” Appl. Opt. 47(19), D38–D43 (2008).
    [Crossref]
  34. L. Rong, W. Xiao, F. Pan, S. Liu, and R. Li, “Speckle noise reduction in digital holography by use of multiple polarization holograms,” Chin. Opt. Lett. 8(7), 653–655 (2010).
    [Crossref]
  35. X. Kang, “An effective method for reducing speckle noise in digital holography,” Chin. Opt. Lett. 6(2), 100–103 (2008).
    [Crossref]
  36. D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, “Twin removal in digital holography using diffuse illumination,” Opt. Lett. 34(23), 3610–3612 (2009).
    [Crossref]
  37. R. Schubert, A. Vollmer, S. Ketelhut, and B. Kemper, “Enhanced quantitative phase imaging in self-interference digital holographic microscopy using an electrically focus tunable lens,” Biomed. Opt. Express 5(12), 4213–4222 (2014).
    [Crossref]
  38. Y. Cotte, M. F. Toy, N. Pavillon, and C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields,” Opt. Express 18(19), 19462–19478 (2010).
    [Crossref]
  39. X.-J. Lai, H.-Y. Tu, C.-H. Wu, Y.-C. Lin, and C.-J. Cheng, “Resolution enhancement of spectrum normalization in synthetic aperture digital holographic microscopy,” Appl. Opt. 54(1), A51–A58 (2015).
    [Crossref]

2019 (1)

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019).
[Crossref]

2018 (1)

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

2016 (1)

H. Funamizu, Y. Tokuno, and Y. Aizu, “Estimation of spectral transmittance curves from rgb images in color digital holographic microscopy using speckle illuminations,” Opt. Rev. 23(3), 535–543 (2016).
[Crossref]

2015 (2)

J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
[Crossref]

X.-J. Lai, H.-Y. Tu, C.-H. Wu, Y.-C. Lin, and C.-J. Cheng, “Resolution enhancement of spectrum normalization in synthetic aperture digital holographic microscopy,” Appl. Opt. 54(1), A51–A58 (2015).
[Crossref]

2014 (3)

2013 (1)

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

2012 (1)

2010 (4)

2009 (2)

2008 (5)

I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008).
[Crossref]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008).
[Crossref]

X. Kang, “An effective method for reducing speckle noise in digital holography,” Chin. Opt. Lett. 6(2), 100–103 (2008).
[Crossref]

H. Funamizu and J. Uozumi, “Scaling reduction of the contrast of fractal speckles detected with a finite aperture,” Opt. Commun. 281(4), 543–549 (2008).
[Crossref]

T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Image quality improvement of digital holography by superposition of reconstructed images obtained by multiple wavelengths,” Appl. Opt. 47(19), D38–D43 (2008).
[Crossref]

2007 (2)

2006 (2)

2005 (1)

2001 (1)

2000 (1)

1998 (2)

1995 (2)

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun. 114(3-4), 203–210 (1995).
[Crossref]

K. Uno, J. Uozumi, and T. Asakura, “Texture analysis of speckles due to random koch fractals by lacunarity,” Waves in Random Media 5(2), 253–263 (1995).
[Crossref]

1991 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

1967 (1)

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

Aizu, Y.

H. Funamizu, Y. Tokuno, and Y. Aizu, “Estimation of spectral transmittance curves from rgb images in color digital holographic microscopy using speckle illuminations,” Opt. Rev. 23(3), 535–543 (2016).
[Crossref]

Asakura, T.

J. Uozumi, M. Ibrahim, and T. Asakura, “Fractal speckles,” Opt. Commun. 156(4-6), 350–358 (1998).
[Crossref]

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun. 114(3-4), 203–210 (1995).
[Crossref]

K. Uno, J. Uozumi, and T. Asakura, “Texture analysis of speckles due to random koch fractals by lacunarity,” Waves in Random Media 5(2), 253–263 (1995).
[Crossref]

Badizadegan, K.

Baumbach, T.

Bernhardt, I.

I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008).
[Crossref]

Chang, G.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Charrière, F.

Cheng, C.-J.

Cho, S.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Choi, W.

Clerc, F. L.

Collot, L.

Colomb, T.

Cotte, Y.

Cuche, E.

Dan, D.

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Dasari, R.

Depeursinge, C.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Eigenthaler, U.

Emery, Y.

Faridian, A.

Feld, M. S.

Ferraro, P.

Finizio, A.

Fixler, D.

Friberg, A. T.

Funamizu, H.

H. Funamizu, Y. Tokuno, and Y. Aizu, “Estimation of spectral transmittance curves from rgb images in color digital holographic microscopy using speckle illuminations,” Opt. Rev. 23(3), 535–543 (2016).
[Crossref]

H. Funamizu and J. Uozumi, “Scaling reduction of the contrast of fractal speckles detected with a finite aperture,” Opt. Commun. 281(4), 543–549 (2008).
[Crossref]

H. Funamizu and J. Uozumi, “Generation of fractal speckles by means of a spatial light modulator,” Opt. Express 15(12), 7415–7422 (2007).
[Crossref]

Gao, P.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019).
[Crossref]

J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
[Crossref]

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Garcia, J.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019).
[Crossref]

V. Mico, Z. Zalevsky, and J. Garcia, “Superresolution optical system by common-path interferometry,” Opt. Express 14(12), 5168–5177 (2006).
[Crossref]

García, J.

Goodman, J. W.

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, 3rd ed. (Roberts & Company, 2005).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co, 2006).

Gross, M.

Hennelly, B. M.

Heo, J.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Hirscher, M.

Hopp, D.

Iannone, M.

Ibrahim, M.

J. Uozumi, M. Ibrahim, and T. Asakura, “Fractal speckles,” Opt. Commun. 156(4-6), 350–358 (1998).
[Crossref]

Ivanova, L.

I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008).
[Crossref]

Jo, Y.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Jung, J.

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Jüptner, W.

Kang, X.

Kebbel, V.

Kelly, D. P.

Kemper, B.

Ketelhut, S.

Kim, K.

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Kim, M. K.

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
[Crossref]

M. K. Kim, Digital Holographic Microscopy (Springer, 2011).

Kolenovic, E.

Kühn, J.

Lai, X.-J.

Langehanenberg, P.

I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008).
[Crossref]

Lawrence, R. W.

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

Lee, K.

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Lee, S.

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Lei, M.

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Li, R.

Lin, Y.-C.

Liu, S.

Marquet, P.

Memmolo, P.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Mico, V.

Micó, V.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019).
[Crossref]

Min, J.

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Monaghan, D. S.

Montfort, F.

Nahm, S.

Netti, P. A.

Nitanai, E.

Nomura, T.

Numata, T.

Okamura, M.

Osten, W.

J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
[Crossref]

A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express 18(13), 14159–14164 (2010).
[Crossref]

Pan, F.

Pandey, N.

Park, H.

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Park, Y.

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy,” Appl. Opt. 53(27), G111–G122 (2014).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009).
[Crossref]

Paturzo, M.

Pavillon, N.

Pedrini, G.

J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
[Crossref]

A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express 18(13), 14159–14164 (2010).
[Crossref]

Popescu, G.

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

Rong, L.

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Schubert, R.

Tokuno, Y.

H. Funamizu, Y. Tokuno, and Y. Aizu, “Estimation of spectral transmittance curves from rgb images in color digital holographic microscopy using speckle illuminations,” Opt. Rev. 23(3), 535–543 (2016).
[Crossref]

Toy, M. F.

Tu, H.-Y.

Turunen, J.

Uno, K.

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun. 114(3-4), 203–210 (1995).
[Crossref]

K. Uno, J. Uozumi, and T. Asakura, “Texture analysis of speckles due to random koch fractals by lacunarity,” Waves in Random Media 5(2), 253–263 (1995).
[Crossref]

Uozumi, J.

H. Funamizu and J. Uozumi, “Scaling reduction of the contrast of fractal speckles detected with a finite aperture,” Opt. Commun. 281(4), 543–549 (2008).
[Crossref]

H. Funamizu and J. Uozumi, “Generation of fractal speckles by means of a spatial light modulator,” Opt. Express 15(12), 7415–7422 (2007).
[Crossref]

J. Uozumi, M. Ibrahim, and T. Asakura, “Fractal speckles,” Opt. Commun. 156(4-6), 350–358 (1998).
[Crossref]

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun. 114(3-4), 203–210 (1995).
[Crossref]

K. Uno, J. Uozumi, and T. Asakura, “Texture analysis of speckles due to random koch fractals by lacunarity,” Waves in Random Media 5(2), 253–263 (1995).
[Crossref]

Vasara, A.

Ventre, M.

Vollmer, A.

von Bally, G.

I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008).
[Crossref]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008).
[Crossref]

Wu, C.-H.

Xiao, W.

Yamaguchi, I.

Yan, S.

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Yang, Y.

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Yao, B.

J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
[Crossref]

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Yaqoob, Z.

Ye, T.

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Yu, H.

Zalevsky, Z.

Zhang, T.

Zheng, J.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019).
[Crossref]

J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
[Crossref]

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Adv. Opt. Photonics (1)

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135–214 (2019).
[Crossref]

Appl. Opt. (6)

Appl. Phys. Lett. (1)

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

Bioelectrochemistry (1)

I. Bernhardt, L. Ivanova, P. Langehanenberg, B. Kemper, and G. von Bally, “Application of digital holographic microscopy to investigate the sedimentation of intact red blood cells and their interaction with artificial surfaces,” Bioelectrochemistry 73(2), 92–96 (2008).
[Crossref]

Biomed. Opt. Express (1)

Chin. Opt. Lett. (2)

J. Opt. (1)

J. Zheng, G. Pedrini, P. Gao, B. Yao, and W. Osten, “Autofocusing and resolution enhancement in digital holographic microscopy by using speckle-illumination,” J. Opt. 17(8), 085301 (2015).
[Crossref]

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

Nat. Photonics (1)

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

Opt. Commun. (3)

K. Uno, J. Uozumi, and T. Asakura, “Speckle clustering in diffraction patterns of random objects under ring-slit illumination,” Opt. Commun. 114(3-4), 203–210 (1995).
[Crossref]

J. Uozumi, M. Ibrahim, and T. Asakura, “Fractal speckles,” Opt. Commun. 156(4-6), 350–358 (1998).
[Crossref]

H. Funamizu and J. Uozumi, “Scaling reduction of the contrast of fractal speckles detected with a finite aperture,” Opt. Commun. 281(4), 543–549 (2008).
[Crossref]

Opt. Express (8)

H. Funamizu and J. Uozumi, “Generation of fractal speckles by means of a spatial light modulator,” Opt. Express 15(12), 7415–7422 (2007).
[Crossref]

J. García, Z. Zalevsky, and D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13(16), 6073–6078 (2005).
[Crossref]

Y. Cotte, M. F. Toy, N. Pavillon, and C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields,” Opt. Express 18(19), 19462–19478 (2010).
[Crossref]

A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express 18(13), 14159–14164 (2010).
[Crossref]

Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009).
[Crossref]

V. Mico, Z. Zalevsky, and J. Garcia, “Superresolution optical system by common-path interferometry,” Opt. Express 14(12), 5168–5177 (2006).
[Crossref]

P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, “On the holographic 3d tracking of in vitro cells characterized by a highly-morphological change,” Opt. Express 20(27), 28485–28493 (2012).
[Crossref]

J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007).
[Crossref]

Opt. Lett. (3)

Opt. Rev. (1)

H. Funamizu, Y. Tokuno, and Y. Aizu, “Estimation of spectral transmittance curves from rgb images in color digital holographic microscopy using speckle illuminations,” Opt. Rev. 23(3), 535–543 (2016).
[Crossref]

Photonics Res. (1)

J. Zheng, P. Gao, B. Yao, T. Ye, M. Lei, J. Min, D. Dan, Y. Yang, and S. Yan, “Digital holographic microscopy with phase-shift-free structured illumination,” Photonics Res. 2(3), 87–91 (2014).
[Crossref]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Sensors (1)

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: From principles to applications,” Sensors 13(4), 4170–4191 (2013).
[Crossref]

SPIE Rev. (1)

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
[Crossref]

Waves in Random Media (1)

K. Uno, J. Uozumi, and T. Asakura, “Texture analysis of speckles due to random koch fractals by lacunarity,” Waves in Random Media 5(2), 253–263 (1995).
[Crossref]

Other (4)

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Co, 2006).

J. W. Goodman, Introduction to Fourier optics, 3rd ed. (Roberts & Company, 2005).

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

M. K. Kim, Digital Holographic Microscopy (Springer, 2011).

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Figures (14)

Fig. 1.
Fig. 1. Schematic of the enhancement of the spatial resolution in DHM using speckle patterns. BS: Beam splitter; $z_s$: Propagation distance of speckle patterns between the diffuser and the object.
Fig. 2.
Fig. 2. Spatial correlation coefficients and power spectra of the intensity distributions of speckle patterns generated from a circular aperture and a ring aperture. (a) Spatial correlation coefficients. (b) Power spectra. The horizontal axis of (a) is $\Delta \rho = 2\pi \Delta r/\lambda z_{s}$, and $\Delta r$ is the difference between the radii in the polar coordinate. The horizontal axis of (b) is the radial coordinate of the spatial-frequency region.
Fig. 3.
Fig. 3. Experimental setup of DHM using speckle patterns. M : Mirror; BS : Beam splitter; ND : Neutral density filter; OB : Objective lens; L : Lens.
Fig. 4.
Fig. 4. Reconstruction process of digital holograms.
Fig. 5.
Fig. 5. Experimental results of the speckle patterns in (a) the circular aperture and (b) the ring aperture for $r_{i}/r_{o}$=0.95. (c) shows the spatial correlation coefficients of the speckle intensities of (a) and (b).
Fig. 6.
Fig. 6. Intensity and phase distributions of the reconstructed images of the star target and the QPMT. (a)–(c) show the intensity distributions of the reconstructed images of the star target. (d)–(f) show the phase distributions of the reconstructed images of the QPMT. (a) and (d) correspond to the case of Gaussian-shaped illumination. (b) and (e) correspond to the case of speckle illuminations using the circular aperture. (c) and (f) show the results of speckle illuminations using the ring aperture.
Fig. 7.
Fig. 7. Speckle contrasts of the intensity distributions and standard deviations of the phase distributions of the reconstructed images against the number of holograms. (a) Speckle contrasts. (b) Standard deviations.
Fig. 8.
Fig. 8. SNR of the intensity and phase distributions of the reconstructed images against the number of holograms. (a) Intensity. (b) Phase.
Fig. 9.
Fig. 9. Analytical process of the spatial resolution using the contrast and SNR of the fringe patterns.
Fig. 10.
Fig. 10. Reconstructed images after transforming from the Cartesian coordinate to the polar coordinate. The arrangement of these figures corresponds to the reconstructed images shown in Figs. 6 (a)–(f).
Fig. 11.
Fig. 11. Results of the application of the analysis in Fig. 9 to the reconstructed images of the star target. (a) Contrast of the fringe patterns in the reconstructed image of the star target. (b) Magnified image of (a).
Fig. 12.
Fig. 12. Results of the application of the analysis in Fig. 9 to the reconstructed image of the QPMT. (a) Contrast of the fringe patterns in the reconstructed image of the quantitative phase microscopy target. (b) Magnified image of (a).
Fig. 13.
Fig. 13. Results of SNR of the analysis in Fig. 9. (a) Intensity. (b) Phase.
Fig. 14.
Fig. 14. One-dimensional plots of the fringe patterns in the reconstructed images. (a) Fringe patterns of the intensity distributions of the reconstructed images in 366 pixels shown in Figs. 10 (a)–(c). (b) Fringe patterns of the phase distributions of the reconstructed images in 206 pixels shown in Figs. 10 (d)–(f).

Equations (13)

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μ I ( Δ x ) = | I p ( x ) exp ( j 2 π λ z s x Δ x ) d x | 2 | I p ( x ) d x | 2 ,
μ I ( Δ ρ ) = 1 ( r o 2 r i 2 ) 2 [ 2 r o J 1 ( r o Δ ρ ) Δ ρ 2 r i J 1 ( r i Δ ρ ) Δ ρ ] 2 ,
μ I ( Δ ρ ) = | 2 J 1 ( r o Δ ρ ) r o Δ ρ | 2 .
μ I ( Δ ρ ) = J 0 2 ( r o Δ ρ ) ,
δ x = 0.61 λ ( N A g + N A s ) = 0.61 λ ( N A g + sin ϕ ) ,
G ( ν ) = 2 π ( ν o 2 ν i 2 ) R e { ν o 2 [ K 1 ( ν ) K 2 ( ν ) ] ν i 2 [ K 3 ( ν ) K 4 ( ν ) ] } ,
K 1 ( ν ) = arccos ( ν 2 ν o ) ν 2 ν o 1 ( ν 2 ν o ) 2 ,
K 2 ( ν ) = arccos ( ν p 2 ν o ) ν p 2 ν o 1 ( ν p 2 ν o ) 2 ,
K 3 ( ν ) = arccos ( ν 2 ν i ) + ν 2 ν i 1 ( ν 2 ν i ) 2 ,
K 4 ( ν ) = arccos ( ν q 2 ν i ) ν q 2 ν i 1 ( ν q 2 ν i ) 2 ,
G ( ν ) = 2 π [ arccos ( ν 2 ν o ) ν 2 ν o 1 ( ν 2 ν o ) 2 ] .
G ( ν ) = δ ( ν ) ,
Φ a = arctan ( Σ i = 1 n sin Φ d , i Σ i = 1 n cos Φ d , i ) ,
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