1. Introduction

Imaging phase objects has always been a challenge in microscopy due to the lack of sufficient absorption by the sample resulting in low contrast amplitude images. There have been several attempts to translate the phase change of light as it traverses the sample into a change of amplitude, leading to phase-contrast microscopy [1] and differential interference microscopy [2]. Shearing interferometry is another method used to achieve phase-contrast imaging. In lateral shearing interferometry, a wedge plate or grating is often used to create interference between a laser beam and a shifted copy of itself. Phase gradients in the direction of the shear are measured and integration along the shear directions then makes it possible to extract full quantitative phase maps from the shifted shearograms. This has recently been applied to the imaging of biological specimens using white light illumination [3]. Shearing interferometry is also used for investigating wavefronts or testing beam collimation [4, 5], with a collimated beam resulting in linear fringes whereas a converging or diverging beam results in tilted fringes. Similar setups have been used for investigating laser produced plasmas in the context of material processing [6, 7].

Another method to directly record the quantitative phase of the object is through digital holographic microscopy (DHM). By using coherent light and combining a reference and an object wave, the phase of the object under investigation is encoded in the fringe pattern. It can then be extracted via appropriate numerical processing of the hologram [8, 9]. Digital holographic phase retrieval implementing a digital version of lateral shearing interferometry has been used to eliminate the defocus aberration by the microscope objective [10]. In this paper, we use a lateral shearing interferometer using a glass plate to achieve direct holographic imaging of microorganisms. We demonstrate high phase stability of the common-path setup through an evaluation of phase fluctuations over time and apply this method to the imaging of algae in a microfluidic channel, as well as red blood cells. In contrast to previously published works, we understand our system as a highly stable, digital holographic microscope for the imaging of biological specimens which stands apart from the cited studies.

The proposed lateral shearing interferometer for holographic imaging can be regarded as a form of a self-interference phase contrast microscope. Several variants of such setups have been presented in the literature. Popescu et al. [11] used the output of an inverted microscope and created the reference beam by spatially filtering the first order of diffraction of a grating in the path of the light. Jang et al. [12] presented a setup which they have specifically designed for use in conjunction with microfluidic devices. They use a beam splitter and a microscope objective in one of the subsequent light paths to invert the location of the sample and background images and create interference by reflecting the two light paths back and superimposing them. Digital lensless holographic imaging in conjunction with microfluidics has also been investigated by Bishara et al. [13]. Kemper et al. [14] used a similar setup but without the second microscope objective in an off-axis configuration. Most recently, this setup was further developed by Shaked [15] who implemented a spatial filtering similar to the one used by Popescu et al. by putting a pinhole on a mirror after the beam splitter and thus creating the reference beam. It should also be mentioned that Coppola et al. [16] proposed a digital self-referencing method. Our approach differs from the mentioned techniques in its simplicity of using a glass plate for achieving the large shear and, thus, producing spatially separated images, which makes the technique common-path, compact and cost effective.

2. Optical setup and image reconstruction

2.1. Optical setup

The setup that we propose is depicted in Fig. 1(a) . As a light source, we employ a HeNe-Laser (λ = 632.8 nm). The beam is directed towards the sample and subsequently magnified by a microscope objective. The shearing of the beams is achieved by a 3mm thick glass plate which is oriented at an angle of approximately 45 degrees to the light beam. Interference occurs between the portion of the beam that is reflected from the front and the back surface of this glass plate. Figure 1(b) shows the interference pattern without an object. Given that the size of the object is smaller than the shear and the beam is large enough, the portion of the beam that contains object information and the unperturbed part can interfere forming a hologram. As this happens both for the front and the back surface of the glass plate, we can observe two holograms on the camera (Prosilica EC 1600, 8-bit, pixel pitch: 4.4 μm) which is kept 9cm from the shearing plate. Figure 1(c) shows the interference pattern for a glass bead of 20 μm diameter. Of course, it is also possible to increase the amount of the shear so that only one object is imaged onto the camera. This setup can easily be mounted onto an inverted microscope which would greatly enhance its capabilities.

 

Fig. 1 Lateral shearing digital holographic microscope. (a) Experimental setup. (b) Fringe pattern without object. (c) Lateral shearing hologram of glass bead. Spatially separated phase distributions due to the front and back surface of the shearing plate can be seen.

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2.2. Image reconstruction

The processing of the recorded interferograms is similar to processing off-axis digital holograms [17]. The fringes represent a carrier frequency that shifts the spectral content of the real and virtual image from the origin in the Fourier domain. We can then spatially filter the real image in the Fourier domain by employing an appropriate mask. The filtered content is then shifted to the origin and, thus, the complex object wave of the sample can be retrieved after an inverse Fourier transform. In all the measurements presented in this paper, we first recorded the background without the object. This fringe pattern was then processed in the same way as the holograms of the samples and the resulting phase was subtracted from the recovered object phase in order to remove most of the aberrations of the system. The phase was then unwrapped using Goldstein’s branch cut method [18].

3. Experiments

3.1. Imaging of microspheres

In order to test the performance of the system, we first imaged glass microspheres with a mean diameter of 17.3 ± 1.4 μm and a refractive index of n_o = 1.56 (SPI Supplies).These beads were spread on a thin glass slide immersed in oil (refractive index n_m = 1.518) and covered by another glass slide. A 60 × microscope objective with NA = 0.85 was used for magnification. The holograms were recorded in the image plane and the complex amplitude of the wavefront was recovered by spatial filtering in the frequency domain as described above [17]. This allows us to directly access the phase of the wavefront. Figure 1(c) shows the recorded shearing hologram for a single glass bead. Note how the bending of the fringes of the left interferogram of the bead is opposite to that of the right. Figure 2(a) shows the wrapped phase distribution of the reconstructed image. After unwrapping the phase, the thickness can be calculated as $d=\Phi \lambda /(2\pi \Delta \text{n})$ where Φ denotes the unwrapped phase, λ is the wavelength of the light source used and Δn stands for the difference in refractive index between the sample and the surrounding medium. The result is presented in Fig. 2(b). Figure 2(c) shows the 3D profile of the thickness variation of the image of the bead on the right in Fig. 2(b). The cross-sectional thickness profile of the glass bead along the line in Fig. 2(b) is shown in the inset of Fig. 2(c). We measured the diameter of 51 glass beads and the computed mean diameter was 17.92 ± 1.91 μm, which is close to the value specified by the manufacturer. As our setup is common-path, it exhibits very good temporal stability. In order to test this, we imaged the fringe pattern of a coverslip without an object and recorded a series of 1200 holograms (total duration 8 minutes at 2.5 Hz) over an area of 512 × 512 pixels (37.5μm × 37.5μm). Phase distributions for all the holograms were computed, and the path length change was calculated by comparing the reconstructed phase distributions to a previously recorded reference background. It should be noted that the optical table was not isolated against vibrations during these measurements. We picked 1024 random points in the field of view and calculated the standard deviations of the fluctuations at these points. Figure 3 shows the histogram of these fluctuations indicating a mean fluctuation of less than 1 nm. This is highly beneficial for conducting studies of dynamics of microorganisms or cells which we intend to do in the future.

 

Fig. 2 (a) Wrapped phase profile of bead after reconstruction. (b) Thickness distribution of investigated bead. (c) 3D rendering of thickness profile on right side in Fig. 2(b). Inset shows 1D thickness profile along line in Fig. 2(b).

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Fig. 3 Histogram of standard deviations of fluctuations of 1024 randomly selected pixels within the field of view over the time of 8 minutes at a frame rate of 2.5 Hz. Inset shows variation of a representative point over time.

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3.2. Imaging of microorganisms and red blood cells

We envision the setup to be used in conjunction with a microfluidic channel in order to image, e.g., small microorganisms or red blood cells (RBCs) for comparison and identification. One possible application is the imaging of microorganisms in a microfluidic channel which we used instead of the object in the setup in Fig. 1. By adjusting the pressure gradient between source and sink we could adjust the speed of the flow in the channel [19].

Chilomonas protozoa which are about 20 – 40 μm in size were passed through the channel. In Fig. 4(a) , the hologram recorded at the image plane using a 25 × microscope objective (NA = 0.4) can be seen and Fig. 4(b) shows its reconstructed phase. Figure 4(c) shows the phase distribution of the reconstruction on the left after unwrapping and its 3D representation is shown in Fig. 4(d). Figures 4(e)-4(f) demonstrate experimental results obtained with red blood cells. Here we used a 532nm diode laser as source, an 8-bit CMOS sensor with 5.2μm pixel pitch and a 4mm thick fused silica glass plate for shearing. A thin blood smear on a glass plate was used as the object. Figure 4(e) shows a portion of the recorded hologram using a 45 × microscope objective (NA = 0.65). The reconstructed phase distribution before unwrapping is shown in Fig. 4(f) and its unwrapped 3D reconstruction in Fig. 4(g). The thickness distribution was determined using constant refractive indices of 1.42 and 1.34 for the cell and plasma, respectively [20]. The inset in Fig. 4(g) shows the unwrapped thickness profile along the line in Fig. 4(f). Both the algae and RBCs were measured at room temperature. It shall be noted that the two holograms of the organism correspond to slightly different focal planes due to the finite thickness of the glass plate. In our measurements, we brought one of the holograms into focus and neglected the other one.

 

Fig. 4 (a) Hologram showing a Chilomonas protozoa. (b) Phase image after reconstruction of a). Note that the two phase images are conjugates of each other. (c) Optical path length of left reconstructed phase image. (d) 3D rendering of phase in Fig. 4(c). (e) Experimental result of imaging RBCs with diode laser. (f) Reconstruced phase of highlighted RBC in (e). (g) 3D rendering of thickness distribution. Inset shows profile along line in (f).

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4. Discussion

Like in the work of Jang et al. [12], we currently use only half of the imaging sensor. This is why we also plan to use the device in conjunction with small samples or microfluidic channels in order to control the space that is covered by the objects under investigation. It is important to use the highest fringe frequency possible as this determines the amount of the object spectrum that can be filtered and, hence, the amount of detail that can be recovered. The fringe frequency can be increased by increasing the thickness of the glass plate. This has the additional benefit of increasing the distance between the sheared images. In order to describe the spatial frequency of the fringes, we can follow Shukla and Malacara [21] who state it as $f_s=S/r\lambda$. $S$ denotes the lateral shift induced by the glass plate, $\lambda$ the wavelength of the source and $r$ stands for the radius of curvature of the wavefront at the CCD. The shift $S$is given by Malacara [22] as $S/t=\sin (2\beta ){(n^2-{\sin }^2\beta )}^{-1/2}$ where $t$ is the thickness of the glass plate, $n$ the refractive index of the glass and $\beta$ is the angle of incidence on the glass plate. The glass plate that is used for creating the shear leads to a loss of about 90% of light power. This can be an issue for highly absorbing samples. A glass plate with reflection coatings on the front and back surfaces could be used in such cases. However, in our experiments we did not encounter any problems in this respect. In order to have more control about the angle and frequency of the fringes, we would like to use an air-wedge in the future [6, 7]. Yet, this adds complexity to the system and needs to be carefully engineered and assembled in order to be highly stable.

By reducing the width of the glass plate so far that the induced shift is a fraction of the size of the object, a standard shearing interferometer can be implemented that allows for the recovery of the gradient of the phase in the shear direction. It should be noted that we recently implemented such a shearing interferometer and used the gradient of the phase in the shearing direction for classification of red blood cells [23].

The main advantage of our setup when compared to the cited works on self-referencing phase microscopes and shearing interferometers is its simplicity, good temporal stability and its potential low cost. The temporal stability will allow for the investigation of dynamics of microorganisms or cells. Replacing the He-Ne laser with a laser diode, using a glass plate for the shearing and a webcam sensor to record the hologram, we envision the system to cost just around 50 USD. As has been shown, it can be easily combined with microfluidic devices, which makes this a very powerful, cheap sensing device that can be easily engineered to be portable and cost effective. We think that it, thus, has great potential for being used in remote and rural areas for screening of diseases.