Abstract

Optical imaging through diffusive or scattering media has attracted a great deal of attention. Lensless digital holography is used to reconstruct the intensity and phase of an object located behind a diffuser. For this study, we propose a method of reconstructing the object's intensity by compensating the complex amplitude of the diffuser by lensless digital holography. A priori information is necessary to obtain the complex amplitude of the diffuser, and we investigated the image quality of reconstructed images through diffusers. Our method does not use approximations to describe the propagation of the object light and the wavefronts disturbed by diffusers, and thus provides a more rigorous description of lightwave propagation. The image quality of the reconstructed images was dependent on the distance between the diffuser and the image sensor or between the diffuser and the sample. We investigated the image contrast of reconstructed images under different conditions.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Imaging through diffusers or scattering media has been widely investigated [14]. Retrieving information about objects through diffusers or scattering media has a vast range of applications. For example, when observing a biological specimen using a microscope, the image to be observed at a certain depth is deteriorated by the scattering and refractive index fluctuations. If the disturbed wavefronts can be corrected, it is possible to obtain a clearer image at a certain depth. In this sense, techniques for imaging through scatterers are essentially similar to the real-time adaptive optics techniques used for astronomical observations. Adaptive optics techniques require deformable mirrors or spatial phase modulators for phase correction. In contrast, holographic techniques have the advantage that the scattering imaging system can be constructed using only general-purpose optical elements. Methods for imaging through scattering media using holography were reported in the 1960s [59]. With the advent of digital holography, studies on techniques using digital holography to reconstruct the complex amplitude of an object placed behind a diffuser or scattering medium have been reported [1016]. Among these techniques, a single-shot imaging technique through a scattering medium by digital in-line hologram has been reported [16]. The technique utilizes the autocorrelation of speckle intensity and needs two diffusers, one in the object beam and one in the reference beam. Imaging through a scattering medium by combining digital holography and imaging optics has been reported using off-axis digital holography [10] and in-line phase-shift digital holography [15]. In those studies, the scattering medium is placed after a beam splitter to combine an object beam and a reference beam. The object beam passing through the object and the reference beam form interference fringes on the scattering medium. Therefore, the common random phase due to the scattering medium is canceled in the holographic recording process. Optical phase conjugation can be achieved by digital holography. The complex field from a point source after passing through a scattering medium is recorded, and the object's lightwave passing through a diffuser is reconstructed by digital holography [14,17]. Lensless digital holography [13] has been used to reconstruct objects through a diffuser plate. In this technique, the diffuser is placed only in the object path. In addition, lensless holography can reconstruct images without the use of any focusing lenses, offering the advantages of a large field of view, high resolution, cost-effectiveness, and depth-resolved three-dimensional (3D) imaging. In the method described in Ref. [13], object light and light from the diffuser are treated as independent waves with approximation. We have previously presented a rigorous reconstruction method to retrieve phase and intensity information of an object behind diffusive glass [18,19] or holographic diffusers [20] by digital holography. Our method measured the transmittance and phase of the diffuser in advance. By a priori measurement of the complex amplitude of the diffuser, the complex amplitude of an object through the diffusive glass is reconstructed by digital correction of the transmittance and phase changes due to the diffuser. The object intensity and phase at an arbitrary distance can be reconstructed by optical back propagation.

In the work described here, we investigate reconstruction of the complex amplitude of an object through a diffuser by changing two different distances, i.e., the distance between the object and the diffuser and the distance between the diffuser and a camera. The image quality of the reconstructed images was dependent on these two distances.

2. Reconstruction of complex amplitude of an object

In order to estimate complex amplitude of an object located behind a diffuser, our method is based on a lensless digital holographic imaging technique [18,19]. Figure 1 shows the concept and a diagram of the setup for reconstruction of an object image. We assume that the light intensity incident on an object is uniform and has a value of unity. When we denote the amplitude and phase of the object as ${A_{\textrm{obj}}}$ and ${\phi _{obj}}$, respectively, the complex amplitude of the light at the object plane is thus ${A_{obj}}\exp ({i{\phi_{obj}}} )$. Then, the light propagates from the object to the diffuser and reaches the diffuser. The complex amplitude of the object light is ${{{\cal P}}_{obj \to d}}[{{A_{obj}}\exp ({i{\phi_{obj}}} )} ]$, where ${{{\cal P}}_{obj \to d}}\; $represents the beam propagation from the object plane to the diffuser plane. When passing through the diffuser plate, the amplitude is reduced by the transmittance of the diffuser, and the phase is modulated by the diffuser. Assuming that the amplitude transmittance due to transmission through the diffuser is ${t_d}$ and that the phase change is ${\phi _d}$, the complex amplitude of the object light transmitted through the diffuser at the diffuser plate is ${{{\cal P}}_{obj \to d}}[{{A_{obj}}\exp ({i{\phi_{obj}}} )} ]\times {t_d}\exp ({i{\phi_d}} )$. Finally, the beam propagates from the diffuser to the sensor plane, and the complex amplitude at the sensor plane, ${{{\cal P}}_{d \to sensor}}[{{{{\cal P}}_{obj \to d}}[{{A_{obj}}\exp ({i{\phi_{obj}}} )} ]\times {t_d}\exp ({i{\phi_d}} )} ]$, can be obtained, where ${{{\cal P}}_{d \to sensor}}$ indicates the beam propagation from the diffuser plane to the sensor plane. From the diffuser to the sensor, light propagates the same optical path with/without the object (Fig. 1). When the complex amplitude of the diffuser plate at the diffuser plane is known in advance, the effects of the diffuser (transmittance, ${t_d},$ and phase modulation, ${\phi _d}$) can be compensated. We only obtain the complex amplitude of the diffuser on a senor plane by digital holography (Left panel in Fig. 1). Then, optical back propagation enables us to obtain the complex amplitude of the diffuser plate at the diffuser plane. We can eliminate the effect of amplitude/phase modulation by the diffuser at diffuser plane by dividing two kinds of complex amplitude at the diffuser plane. With this correction, the light wave from the object propagates as if it was not affected by the diffuser plate and propagates to the sensor plane.

 figure: Fig. 1.

Fig. 1. Concept and diagram for reconstruction of object image. BP denotes back beam propagation.

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The procedure for reconstructing the intensity and phase of the object is as follows, with reference to Fig. 1, which presents a schematic diagram showing reconstruction of the complex amplitude of an object through a diffuser: (1) First, the complex amplitude of the diffuser on the sensor plane is obtained without insertion of an object (left panel in Fig. 1). In order to obtain the complex amplitude at the sensor plane, an intensity image and phase image are required. The intensity is captured by blocking the reference beam. The phase image is obtained from digital holograms. (2) We reconstruct the complex amplitude of the diffuser at the diffuser plane by calculation with optical back propagation. Then, a priori information of the complex amplitude of the diffuser is obtained. (3) Then, an object is inserted, and the complex amplitude of the object through the diffuser at the sensor plane is acquired by digital holography. (4) The complex amplitudes of both the object and diffuser at the diffuser plane are obtained by optical back propagation. (5) Thereafter, the complex amplitude of the diffuser at the diffuser plane is compensated by dividing the complex amplitude obtained in step (4) by the complex amplitude obtained in step (2). (6) Furthermore, the complex amplitude of only the object is propagated back to the object plane, and the complex amplitude at the object plane is reconstructed. The object intensity and phase at an arbitrary distance are reconstructed by optical back propagation.

3. Experimental setup

The digital holographic imaging technique using the diffuser is based on phase-shifting lensless digital holographic imaging [21,22]. A schematic diagram is presented in Fig. 2. A He-Ne laser light source with a wavelength of 632.8 nm was used. The laser light beam is focused by a 10 × microscope objective lenses through a pinhole for spatial filtering. The beam was collimated using a lens (200 mm focal length). Then, the laser beam was truncated by a circular aperture with a diameter of 1.0 cm. The beam from the light source was separated by a beam splitter (2 cm cube-type) into two beams: a reference beam and a beam passing through the sample, i.e., the object beam. Two beams from a reference and object were spatially overlapped through a beam splitter (2 cm cube-type). Then, holograms were obtained using four-step phase shifting [23,24]. Phase shifting was performed using a piezo-transducer (PZT) (P-752.21C; PI Polytec Inc.). The phase was retrieved from four digital holograms. A CMOS camera (ORCA2.0; Hamamatsu Photonics K.K.) having 1920×1440 image pixels and a 3.63 μm pixel size was used. The 12-bit gray-level digital output was sent to a personal computer. Separately, the intensity information of only the object beam was recorded by blocking the reference beam. Using this process, one can record amplitude and phase information of the object at the sensor plane. The object intensity and phase are obtainable at an arbitrary distance using back beam propagation. We reconstructed the amplitude and phase of the object by using the angular spectrum approach [22]. 1951 United States Air Force (USAF) resolution targets (Positive type) (Edmund, 38-257) were used as samples. A holographic diffuser was inserted into the object beam side as a diffuser. The diffusion angle of the holographic diffuser was 1 degree with thickens of 0.78 mm (Edmund, # 47-993). The holographic diffuser diffusion angle is defined by the full width at half maximum of the angle from the center of the diffused light. Compared to frosted glass or opal diffusers, holographic diffusers have better transmittance, at 85%.

 figure: Fig. 2.

Fig. 2. Schematic diagram of experimental setup for imaging through diffuser with lensless phase-shift digital holography. BS: Beam Splitter, PZT: Piezoelectric transducer.

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The reconstructed image obtained from the experiment was evaluated by using the image contrast [13,14]. The following equation was used to calculate the averaged contrast m:

$$m\, = \,\frac{{\mu {\; _{max}}\textrm{-}{\mu _{min}}}}{{{\mu _{max}} + {\mu _{min}}}},$$
where ${\mu _{max}}$ and ${\mu _{min}}$ are the maximum and minimum averaged intensity values.

4. Experimental results

4.1 Reconstruction of object image

First, we set the distance between the diffuser and the sample, a, to 2.0 cm and the distance between the image sensor and the diffuser, b, to 9.5 cm. Figure 3(a) shows an intensity image of the test target through the diffuser captured by the camera. We attempted to reconstruct the object intensity merely by calculating the backward beam propagation from the camera to the test chart without considering the diffuser effect. From Fig. 3(b), it was not possible to reconstruct the intensity of the test target merely by performing backward propagation calculations from the camera to the test target. On the other hand, the proposed algorithm can reconstruct the object [Fig. 3(c)]. Note that the proposed method needs to acquire the intensity and phase of the diffuser a priori, as described in the previous section. In comparison, we reconstructed the intensity image of the test target without placing the diffuser in the system. Four interference images were acquired by the phase shifting method, and a phase image at the sensor plane was obtained. The complex amplitude at the object plane was calculated by performing the optical back propagation using the acquired intensity and phase images at the camera plane. Figure 3(d) shows a reconstructed intensity image of the test target without the diffuser in place. Comparing Figs. 3(b) and 3(d), the object behind the diffuser could not be reconstructed by back propagation with lensless holography. Comparing Figs. 3(c) and 3(d), visualization of the object behind the diffuser was possible by the proposed method, although the image quality through the diffuser degraded [Fig. 3(c)]. The experimental results show the feasibility of our method in reconstructing the intensity distribution of the object behind the diffuser.

 figure: Fig. 3.

Fig. 3. (a) Intensity image of 1951USAF test target through a diffuser, captured by the camera. The distance between the diffuser and the sample, a, was 2.0 cm and the distance between the image sensor and the diffuser, b, was 9.5 cm. (b) Reconstructed intensity image of the test target through the diffuser by directly performing back propagation from the image sensor to the sample without considering a diffuser. (c) Reconstructed intensity image obtained by our proposed method. (d) Reconstructed intensity image without diffuser by performing back propagation from image sensor to sample when diffuser was not inserted.

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We investigated the image quality of reconstructed images of the object behind the diffuser. In the experiments, the distance between the diffuser and the sample, a, was 2.0 cm and the distance between the image sensor and the diffuser, b, was 9.5 cm. To reconstruct an intensity image of the test target, we used the procedure described in the previous section. In the reconstruction algorithm, we need to optimize the parameters a and b. Figure 4 shows the reconstructed intensity images with various values of these parameters. First, we optimized the distance between the image sensor and the diffuser, b, because the parameter b was more critical for obtaining clear images. Then, we optimized the distance between the diffuser and the sample, a.

 figure: Fig. 4.

Fig. 4. Reconstructed intensity images of the 1951USAF test target. The distance between the diffuser and the test chart and the distance between the image sensor and the diffuser were changed in the reconstruction algorithm. In the experiments, the distance between the diffuser and the sample, a, was 2.0 cm and the distance between the image sensor and the diffuser, b, was 9.5 cm.

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4.2 Different distances

We investigated the image quality of reconstructed images of the object behind the diffuser when changing the distance between the diffuser and the object, a. We set the distance between the image sensor and the diffuser, b, to 9.5 cm. Images of the intensity distribution at the sample plane are presented in Fig. 5. The image quality of the reproduced images deteriorated as the object distance from the diffuser increased. The image contrast was calculated for the group 2, element 3 on the test target. The spatial resolution of this part was 5.04 (line pairs/mm).

 figure: Fig. 5.

Fig. 5. Reconstructed intensity image at different distances between the diffuser and object, a. The distance between the diffuser and the test chart was varied from 2.0 cm to 8.0 cm, while the distance between the image sensor and the diffuser was kept fixed at 9.5 cm. The image contrast was calculated for group 2, element 3 on the test target (indicated by yellow square).

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Next, we set the distance between the diffuser and the object a, to 5.0 cm, and the effect on the reconstructed image due to the change in the distance from the sensor plane to the diffuser, b, was investigated. Reconstructed images of the intensity distribution on the object plane are presented in Fig. 6 at b = 10.0 cm, 12.0 cm, and 14.0 cm. The image quality of the reproduced images deteriorated as the object distance from the diffuser increased. From Figs. 5 and 6, the image contrast of the reproduced images decreased as the distance between the diffuser and the object, a, increased and as the distance from the sensor plane to the diffuser, b, increased.

 figure: Fig. 6.

Fig. 6. Reconstructed intensity at different distances between the image sensor and the diffuser, b. The distance between the image sensor and the diffuser was varied from 10.0 cm to 14.0 cm, while the distance between the diffuser and the sample was kept fixed at 5.0 cm. The image contrast was calculated for group 2, element 3 on the test target (indicated by yellow square).

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4.3 Discussion

We examined the effect of the light intensity ratio of the object light and the reference light on the reconstruction results. We investigated intensity ratios of 1:1, 1:5, and 5:1 for the object and reference intensities. It was confirmed that the light intensity ratio did not affect the reconstruction results.

We investigated the quality of the reconstructed intensity information of the object behind the diffuser by using diffusers with different diffusion angles. The intensity distribution was reproduced by using diffusers with diffusion angles of 1°, 5°, and 10°. Here, we investigated the image contrast of group 1, element 4 (spatial frequency: 2.83 line pair/mm) and element 5 (spatial frequency: 3.17 line pair/mm). In the case of group 1, element 4, the contrast was 0.393 when the diffusion angle of the diffuser was 1°, 0.217 when it was 5°, and 0.177 when it was 10°. In the case of group 1 and element 5, the contrast was 0.385 when the diffusion angle of the diffuser was 1°, 0.199 when the diffusion angle was 5°, and 0.174 when the diffusion angle was 10°. These experimental results show that the smaller the diffusion angle of the diffuser plate, the higher the contrast and the more accurate the reproduction result. At a greater diffusion angle, the reconstructed image quality was degraded.

5. Conclusion

We demonstrated reconstruction of the intensity information of an object behind a diffuser by lensless digital holography. We presented a rigorous reconstruction method to retrieve phase and intensity information of an object behind holographic diffusers. In our method, the transmittance and phase of the diffuser were measured in advance. By a priori measurement of the complex amplitude of the diffuser, the complex amplitude of an object through diffuser was reconstructed by digital correction of the transmittance and phase change of the diffuser without any approximations. Digital holography was used to cancel the phase of the diffuser, and the intensity of a USAF test target located behind the diffuser was reconstructed. The image quality of the reconstructed images was dependent on the distance between the diffuser and the image sensor or the distance between the diffuser and the object. Dynamic imaging was not possible due to acquisition of two-types of the complex amplitude by phase-shifting method; however, the experimental results verified the validity of our method under static conditions.

Funding

Japan Society for the Promotion of Science (17K05083).

Acknowledgments

The authors thank A. Igarashi from Ritsumeikan University for assistance with the initial concept and experiments, and F. Araki from Ritsumeikan University for assistance with the experiments.

Disclosures

The authors declare no conflicts of interest.

References

1. A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017). [CrossRef]  

2. S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018). [CrossRef]  

3. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012). [CrossRef]  

4. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012). [CrossRef]  

5. J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966). [CrossRef]  

6. H. Kogelnik and K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58(2), 273–274 (1968). [CrossRef]  

7. H. Caulfield, “Holographic imaging through scatterers,” J. Opt. Soc. Am. 58(2), 276–277 (1968). [CrossRef]  

8. J. Gaskill, “Imaging through a randomly inhomogeneous medium by wavefront reconstruction,” J. Opt. Soc. Am. 58(5), 600–608 (1968). [CrossRef]  

9. E. Leith, C. Chen, H. Chen, Y. Chen, D. Dilworth, J. Lopez, J. Rudd, P. Sun, J. Valdmanis, and G. Vossler, “Imaging through scattering media with holography,” J. Opt. Soc. Am. A 9(7), 1148–1153 (1992). [CrossRef]  

10. Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013). [CrossRef]  

11. A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Looking through a diffuser and around an opaque surface: A holographic approach,” Opt. Express 22(7), 7694–7701 (2014). [CrossRef]  

12. S. Li and J. Zhong, “Dynamic imaging through turbid media based on digital holography,” J. Opt. Soc. Am. A 31(3), 480–486 (2014). [CrossRef]  

13. W. Harm, C. Roider, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Lensless imaging through thin diffusive media,” Opt. Express 22(18), 22146–24156 (2014). [CrossRef]  

14. R. Li, T. Peng, M. Zhou, X. Yu, P. Gao, J. Min, Y. Yang, M. Lei, B. Yao, C. Zhang, and T. Ye, “Rapid wide-field imaging through scattering media by digital holographic wavefront correction,” Appl. Opt. 58(11), 2845–2853 (2019). [CrossRef]  

15. S. Kodama, M. Ohta, K. Ikeda, Y. Kano, Y. Miyamoto, W. Osten, M. Takeda, and E. Watanabe, “Three-dimensional microscopic imaging through scattering media based on in-line phase-shift digital holography,” Appl. Opt. 58(34), G345 (2019). [CrossRef]  

16. R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019). [CrossRef]  

17. C. L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18(20), 20723–20731 (2010). [CrossRef]  

18. A. Igarashi, H. Arimoto, and W. Watanabe, “Reconstruction of complex amplitude by lensless phase-shift digital holography through an opaque glass plate,” Proc. SPIE 10711, 1071118 (2018). [CrossRef]  

19. W. Watanabe, S. Tabata, F. Araki, and H. Arimoto, “Looking through diffusive glass by digital amplitude/phase correction,” JSAP-OSA Joint Symposia 2019 Abstracts OSA Technical Digest (Optical Society of America, 2019), paper 18a_E215_1.

20. S. Tabata, F. Araki, H. Arimoto, and W. Watanabe, “Reconstruction quality of digital holographic images using a holographic diffuser with different distances,” BISC2020, BISCp-03 (Yokohama, Japan, 2020).

21. M. K. Kim, “Principles and techniques of digital holographic microscopy,” J. Photonics Energy 1, 018005 (2010). [CrossRef]  

22. T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography: With Matlab (Cambridge University Press, 2014).

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

24. A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017). [CrossRef]  

References

  • View by:

  1. A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017).
    [Crossref]
  2. S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
    [Crossref]
  3. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
    [Crossref]
  4. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
    [Crossref]
  5. J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966).
    [Crossref]
  6. H. Kogelnik and K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58(2), 273–274 (1968).
    [Crossref]
  7. H. Caulfield, “Holographic imaging through scatterers,” J. Opt. Soc. Am. 58(2), 276–277 (1968).
    [Crossref]
  8. J. Gaskill, “Imaging through a randomly inhomogeneous medium by wavefront reconstruction,” J. Opt. Soc. Am. 58(5), 600–608 (1968).
    [Crossref]
  9. E. Leith, C. Chen, H. Chen, Y. Chen, D. Dilworth, J. Lopez, J. Rudd, P. Sun, J. Valdmanis, and G. Vossler, “Imaging through scattering media with holography,” J. Opt. Soc. Am. A 9(7), 1148–1153 (1992).
    [Crossref]
  10. Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
    [Crossref]
  11. A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Looking through a diffuser and around an opaque surface: A holographic approach,” Opt. Express 22(7), 7694–7701 (2014).
    [Crossref]
  12. S. Li and J. Zhong, “Dynamic imaging through turbid media based on digital holography,” J. Opt. Soc. Am. A 31(3), 480–486 (2014).
    [Crossref]
  13. W. Harm, C. Roider, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Lensless imaging through thin diffusive media,” Opt. Express 22(18), 22146–24156 (2014).
    [Crossref]
  14. R. Li, T. Peng, M. Zhou, X. Yu, P. Gao, J. Min, Y. Yang, M. Lei, B. Yao, C. Zhang, and T. Ye, “Rapid wide-field imaging through scattering media by digital holographic wavefront correction,” Appl. Opt. 58(11), 2845–2853 (2019).
    [Crossref]
  15. S. Kodama, M. Ohta, K. Ikeda, Y. Kano, Y. Miyamoto, W. Osten, M. Takeda, and E. Watanabe, “Three-dimensional microscopic imaging through scattering media based on in-line phase-shift digital holography,” Appl. Opt. 58(34), G345 (2019).
    [Crossref]
  16. R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019).
    [Crossref]
  17. C. L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18(20), 20723–20731 (2010).
    [Crossref]
  18. A. Igarashi, H. Arimoto, and W. Watanabe, “Reconstruction of complex amplitude by lensless phase-shift digital holography through an opaque glass plate,” Proc. SPIE 10711, 1071118 (2018).
    [Crossref]
  19. W. Watanabe, S. Tabata, F. Araki, and H. Arimoto, “Looking through diffusive glass by digital amplitude/phase correction,” JSAP-OSA Joint Symposia 2019 Abstracts OSA Technical Digest (Optical Society of America, 2019), paper 18a_E215_1.
  20. S. Tabata, F. Araki, H. Arimoto, and W. Watanabe, “Reconstruction quality of digital holographic images using a holographic diffuser with different distances,” BISC2020, BISCp-03 (Yokohama, Japan, 2020).
  21. M. K. Kim, “Principles and techniques of digital holographic microscopy,” J. Photonics Energy 1, 018005 (2010).
    [Crossref]
  22. T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography: With Matlab (Cambridge University Press, 2014).
  23. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [Crossref]
  24. A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
    [Crossref]

2019 (3)

2018 (2)

A. Igarashi, H. Arimoto, and W. Watanabe, “Reconstruction of complex amplitude by lensless phase-shift digital holography through an opaque glass plate,” Proc. SPIE 10711, 1071118 (2018).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

2017 (2)

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017).
[Crossref]

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

2014 (3)

2013 (1)

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

2012 (2)

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

2010 (2)

1997 (1)

1992 (1)

1968 (3)

1966 (1)

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966).
[Crossref]

Araki, F.

W. Watanabe, S. Tabata, F. Araki, and H. Arimoto, “Looking through diffusive glass by digital amplitude/phase correction,” JSAP-OSA Joint Symposia 2019 Abstracts OSA Technical Digest (Optical Society of America, 2019), paper 18a_E215_1.

S. Tabata, F. Araki, H. Arimoto, and W. Watanabe, “Reconstruction quality of digital holographic images using a holographic diffuser with different distances,” BISC2020, BISCp-03 (Yokohama, Japan, 2020).

Arimoto, H.

A. Igarashi, H. Arimoto, and W. Watanabe, “Reconstruction of complex amplitude by lensless phase-shift digital holography through an opaque glass plate,” Proc. SPIE 10711, 1071118 (2018).
[Crossref]

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

S. Tabata, F. Araki, H. Arimoto, and W. Watanabe, “Reconstruction quality of digital holographic images using a holographic diffuser with different distances,” BISC2020, BISCp-03 (Yokohama, Japan, 2020).

W. Watanabe, S. Tabata, F. Araki, and H. Arimoto, “Looking through diffusive glass by digital amplitude/phase correction,” JSAP-OSA Joint Symposia 2019 Abstracts OSA Technical Digest (Optical Society of America, 2019), paper 18a_E215_1.

Barbastathis, G.

Bernet, S.

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Caulfield, H.

Chen, C.

Chen, H.

Chen, Y.

Deng, M.

Dilworth, D.

Fukuda, T.

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

Gao, P.

Gaskill, J.

Goodman, J. W.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966).
[Crossref]

Grange, R.

Harm, W.

Hsieh, C. L.

Huntley, W. H.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966).
[Crossref]

Igarashi, A.

A. Igarashi, H. Arimoto, and W. Watanabe, “Reconstruction of complex amplitude by lensless phase-shift digital holography through an opaque glass plate,” Proc. SPIE 10711, 1071118 (2018).
[Crossref]

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

Ikeda, K.

Jackson, D. W.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966).
[Crossref]

Javidi, B.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Jesacher, A.

Kano, Y.

Katz, O.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Kim, K.

R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019).
[Crossref]

Kim, M. K.

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

Kodama, S.

Kogelnik, H.

Komori, T.

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Laporte, G.

Lee, J.

Lehmann, M.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966).
[Crossref]

Lei, M.

Leith, E.

Li, R.

Li, S.

Liu, J.-P.

T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography: With Matlab (Cambridge University Press, 2014).

Lopez, J.

Min, J.

Miyamoto, Y.

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Naik, D. N.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017).
[Crossref]

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Looking through a diffuser and around an opaque surface: A holographic approach,” Opt. Express 22(7), 7694–7701 (2014).
[Crossref]

Ohta, M.

Osten, W.

S. Kodama, M. Ohta, K. Ikeda, Y. Kano, Y. Miyamoto, W. Osten, M. Takeda, and E. Watanabe, “Three-dimensional microscopic imaging through scattering media based on in-line phase-shift digital holography,” Appl. Opt. 58(34), G345 (2019).
[Crossref]

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017).
[Crossref]

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Looking through a diffuser and around an opaque surface: A holographic approach,” Opt. Express 22(7), 7694–7701 (2014).
[Crossref]

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Park, Y.-K.

R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019).
[Crossref]

Pedrini, G.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017).
[Crossref]

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Looking through a diffuser and around an opaque surface: A holographic approach,” Opt. Express 22(7), 7694–7701 (2014).
[Crossref]

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Peng, T.

Pennington, K. S.

Poon, T.-C.

T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography: With Matlab (Cambridge University Press, 2014).

Psaltis, D.

Pu, Y.

Ritsch-Marte, M.

Roider, C.

Rudd, J.

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Singh, A. K.

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017).
[Crossref]

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Looking through a diffuser and around an opaque surface: A holographic approach,” Opt. Express 22(7), 7694–7701 (2014).
[Crossref]

Singh, R. K.

R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019).
[Crossref]

Sinha, A.

Situ, G.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Somkuwar, A. S.

R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019).
[Crossref]

Sun, P.

Tabata, S.

S. Tabata, F. Araki, H. Arimoto, and W. Watanabe, “Reconstruction quality of digital holographic images using a holographic diffuser with different distances,” BISC2020, BISCp-03 (Yokohama, Japan, 2020).

W. Watanabe, S. Tabata, F. Araki, and H. Arimoto, “Looking through diffusive glass by digital amplitude/phase correction,” JSAP-OSA Joint Symposia 2019 Abstracts OSA Technical Digest (Optical Society of America, 2019), paper 18a_E215_1.

Takeda, M.

Tamaki, T.

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

Valdmanis, J.

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Vinu, R. V.

R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019).
[Crossref]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Vossler, G.

Wang, D.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Watanabe, E.

Watanabe, W.

A. Igarashi, H. Arimoto, and W. Watanabe, “Reconstruction of complex amplitude by lensless phase-shift digital holography through an opaque glass plate,” Proc. SPIE 10711, 1071118 (2018).
[Crossref]

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

W. Watanabe, S. Tabata, F. Araki, and H. Arimoto, “Looking through diffusive glass by digital amplitude/phase correction,” JSAP-OSA Joint Symposia 2019 Abstracts OSA Technical Digest (Optical Society of America, 2019), paper 18a_E215_1.

S. Tabata, F. Araki, H. Arimoto, and W. Watanabe, “Reconstruction quality of digital holographic images using a holographic diffuser with different distances,” BISC2020, BISCp-03 (Yokohama, Japan, 2020).

Yamaguchi, I.

Yang, Y.

Yao, B.

Ye, T.

Yu, X.

Zhang, C.

Zhang, T.

Zhang, Y.

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

Zhong, J.

Zhou, M.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8(12), 311–313 (1966).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

J. Photonics Energy (1)

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

Light: Sci. Appl. (1)

A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Exploiting scattering media for exploring 3D objects,” Light: Sci. Appl. 6(2), e16219 (2017).
[Crossref]

Nat. Photonics (1)

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Opt. Commun. (2)

Y. Zhang, G. Situ, G. Pedrini, D. Wang, B. Javidi, and W. Osten, “Application of short-coherence lensless Fourier transform digital holography in imaging through diffusive medium,” Opt. Commun. 286, 56–59 (2013).
[Crossref]

R. V. Vinu, K. Kim, A. S. Somkuwar, Y.-K. Park, and R. K. Singh, “Imaging through scattering media using digital holography,” Opt. Commun. 439, 218–223 (2019).
[Crossref]

Opt. Eng. (1)

A. Igarashi, T. Komori, T. Tamaki, H. Arimoto, T. Fukuda, and W. Watanabe, “Phase measurement of structural modifications created by femtosecond laser pulses in glass with phase-shifting digital holographic microscopy,” Opt. Eng. 56(11), 111702 (2017).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optica (1)

Proc. SPIE (1)

A. Igarashi, H. Arimoto, and W. Watanabe, “Reconstruction of complex amplitude by lensless phase-shift digital holography through an opaque glass plate,” Proc. SPIE 10711, 1071118 (2018).
[Crossref]

Other (3)

W. Watanabe, S. Tabata, F. Araki, and H. Arimoto, “Looking through diffusive glass by digital amplitude/phase correction,” JSAP-OSA Joint Symposia 2019 Abstracts OSA Technical Digest (Optical Society of America, 2019), paper 18a_E215_1.

S. Tabata, F. Araki, H. Arimoto, and W. Watanabe, “Reconstruction quality of digital holographic images using a holographic diffuser with different distances,” BISC2020, BISCp-03 (Yokohama, Japan, 2020).

T.-C. Poon and J.-P. Liu, Introduction to Modern Digital Holography: With Matlab (Cambridge University Press, 2014).

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Figures (6)

Fig. 1.
Fig. 1. Concept and diagram for reconstruction of object image. BP denotes back beam propagation.
Fig. 2.
Fig. 2. Schematic diagram of experimental setup for imaging through diffuser with lensless phase-shift digital holography. BS: Beam Splitter, PZT: Piezoelectric transducer.
Fig. 3.
Fig. 3. (a) Intensity image of 1951USAF test target through a diffuser, captured by the camera. The distance between the diffuser and the sample, a, was 2.0 cm and the distance between the image sensor and the diffuser, b, was 9.5 cm. (b) Reconstructed intensity image of the test target through the diffuser by directly performing back propagation from the image sensor to the sample without considering a diffuser. (c) Reconstructed intensity image obtained by our proposed method. (d) Reconstructed intensity image without diffuser by performing back propagation from image sensor to sample when diffuser was not inserted.
Fig. 4.
Fig. 4. Reconstructed intensity images of the 1951USAF test target. The distance between the diffuser and the test chart and the distance between the image sensor and the diffuser were changed in the reconstruction algorithm. In the experiments, the distance between the diffuser and the sample, a, was 2.0 cm and the distance between the image sensor and the diffuser, b, was 9.5 cm.
Fig. 5.
Fig. 5. Reconstructed intensity image at different distances between the diffuser and object, a. The distance between the diffuser and the test chart was varied from 2.0 cm to 8.0 cm, while the distance between the image sensor and the diffuser was kept fixed at 9.5 cm. The image contrast was calculated for group 2, element 3 on the test target (indicated by yellow square).
Fig. 6.
Fig. 6. Reconstructed intensity at different distances between the image sensor and the diffuser, b. The distance between the image sensor and the diffuser was varied from 10.0 cm to 14.0 cm, while the distance between the diffuser and the sample was kept fixed at 5.0 cm. The image contrast was calculated for group 2, element 3 on the test target (indicated by yellow square).

Equations (1)

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m = μ m a x - μ m i n μ m a x + μ m i n ,

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