1. Introduction

Digital holographic microscopy (DHM) is a well-developed interferometric technique for 3D imaging or visualizing transparent objects [1,2]. In this method, a laser beam is separated in two beams, one called object beam and going through the object to be imaged and one called reference beam. The two beams are then recombined with a slight angle to form an interferometric pattern, so-called off-axis hologram, recorded on a digital camera. The latter hologram is then processed with well-known algorithms to extract the phase and amplitude of the sample [2–4]. When applied to microscopy, it is often used to image transparent biological material and quantify the optical thickness of cells [5–12], since a quantitative measurement of the phase is accessible. Diverse implementations have been presented such as an add-on for a widefield microscope [13,14], a color DHM [15], autofocus [16] and stand-alone DHM in transmission and reflection configuration [17]. Reconstruction can be done in different depth planes which allows DHM to track elements in a 3D volume [11,18,19]. Tomography has also been investigated by rotating the sample and recording several holograms [20,21].

Compact versions of off-axis DHMs have been implemented [22–24]. For example, an implementation makes use of a beam splitter to obtain two beams, object and reference, from one light source [22,25]. An objective is added in front of the sample to increase the resolution. This type of design only works in reflection. Another proposed scheme is made of a set of different lenses to image in transmission [23]. The two paths are created by using only a part of a collimated beam for each beam (object and reference). Finally, other holographic techniques have been utilized, such as self-interference design [24,25] and shearing interferometry [26], to achieve this goal. All those implementations either include lenses or only work in reflection.

The same kind of device using a beam splitter has been presented for lensless imaging [27], i.e. without an objective in front of the sample, which makes it more compact but works only in reflection. Inline digital holography is another well studied technique that allows fabrication of ultra-compact devices [28,29] but it needs several digital inline holograms obtained by either changing the illumination wavelength, the angle illumination or a combination of both in order to extract the phase. Specific algorithms which are computationally intensive [28] are needed to retrieve the phase of the sample. This contrasts with off-axis holography which requires only one hologram to extract the phase. A comparison between inline and off-axis holography algorithms is presented in [4].

In this paper, we present a compact off-axis lensless transmission digital holographic microscope using side illumination to produce two collimated illumination beams with one source. The device is used to record holograms of different phase samples. In section 2, the device is described. The reconstruction process is presented in section 3. And the experimental results are presented in section 4.

2. Compact setup for lensless off-axis digital holography

The illumination is composed of a vertical cavity surface emitting laser (VCSEL, Vixar 680S, single mode, 0.75mW typical output power, 673nm wavelength, 100MHz linewidth) disposed in front of one side of a K9 prism. On the opposite side, a BAYFOL®HX photopolymer film of 70μm thickness from Covestro is laminated. Two analog volume hologram gratings are recorded separately in the photopolymer at two positions. The total diffracted light represents ~3.5% of the incident source light. This has not been optimized. This value is enough to use the camera with the smallest exposure time available. The recording process is detailed in [28]. The two gratings are designed to diffract the diverging light from the VCSEL inside the prism into two collimated beams separated by a 5.8° angle, as shown in Fig. 1. The angle between the beams is chosen to respect the Nyquist criterion necessary to resolve the interference fringes on the camera (The Imaging Source 27UJ003-ML, 1.67μm pixel size, similar to mobile phone camera).

 

Fig. 1 2D sketch of the compact digital holographic microscope. A VCSEL illuminates two spatially multiplexed volume analog holograms recorded on a photopolymer laminated on a prism. One diffracted beam goes through the sample and the other is used as reference. Both interfere on a camera.

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During the recording process of a digital hologram, a sample is inserted in one of the two diffracted beams. At ~4cm from the prism, the beams recombine in the camera plane where a digital hologram is recorded. The FOV is 12mm².

For ease of use and portability, a box has been designed and 3D printed to contain all the elements of the proposed system. Figure 2 shows a picture of the device in the proposed housing next to a typical smartphone.

 

Fig. 2 Picture of the device in the proposed 3D printed housing. The smartphone is shown for size comparison.

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The box size is: 6.5cmx4.2cmx7cm.

3. Numerical reconstruction

The hologram H is the interference between the reference beam R and the object beam O that went through the sample. The hologram can be written as:

The interference terms $R{O}^{*}$and $O{R}^{*}$contain the virtual and real images.

We first record a reference hologram without a sample in the beams. Then the sample is inserted in one of the two beams creating a diffraction pattern containing the sample information. This new hologram is recorded. The reference hologram is used to provide a reference phase background of 0 to be able to evaluate the quantitative phase of the object. In off-axis holography, we use the angle between the object beam and the reference beam to create a carrier frequency for the object diffraction information. That is why the Fourier transform of the hologram is composed of three features: the DC terms and the two images terms. The features are separated according to the angle between the two beams and the pixel size of the camera. During the reconstruction process only one of the two is selected in the Fourier plane. Amplitude and phase of the sample are then retrieved through backpropagation [2,3].

The reconstruction process is performed using KOALA software from LynceeTec.

4. Experimental results and discussion

A digital hologram of a homemade phase 1951 USAF test target (etched) was obtained using the proposed device and the phase and amplitude image was then reconstructed. The hologram, spectrum and phase images are shown in Figs. 3(a)-3(c). For comparison, the same sample was also imaged using a commercial DHM (LynceeTec DHM T1000 Fluo) with a 5x objective and the results are shown in Figs. 3(d)-3(f).

 

Fig. 3 (a) Hologram recorded with the proposed device. (b) Spectrum of hologram (a) with the mask selecting only one image. (c) Reconstructed phase with the proposed device of the full FOV. (d) Hologram recorded with the commercial DHM. (b) Spectrum of hologram (d) with the mask selecting only one image. (f) Reconstructed phase with a commercial DHM (full FOV). The elliptical filtering in (b) is due to the fact that the angles in both directions between the reference and object beams were not equal meaning that the center of the spectrum of the real image is not exactly in the diagonal of the spectrum passing by the DC term.

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The etching depth of the sample is measured in the reconstructed phase image with the proposed device and then compared with the phase image obtained with the commercial DHM. The results are shown in Fig. 4. Excellent quantitative agreement is found. Both measurements show a ~180nm etching depth showing that the proposed device allows obtaining accurate quantitative phase measurements.

 

Fig. 4 (a) Zoom on the red square of reconstructed phase Fig. 3(a) (crop of 0.9x0.9mm). (b) Reconstructed phase with a commercial DHM (full FOV).

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The temporal noise of the setup was measured by taking the value of the average phase of 5 pixels over the FOV during 10s. The presented setup has a temporal noise of ~9nm and the commercial DHM ~0.55nm. This noise level can be explained by vibrations in the setup due to the fact that all the elements were not on the same holder. This noise is reduced to 2nm when successive images at the camera rate are taken. The second origin of the background noise is the fact that the diffracted beams themselves are not perfectly spatially uniform, especially because of the substrate of the photopolymer used to fabricate the gratings. Upon lateral vibration, the spatial phase non uniformity translates to phase noise. Finally, the noise due to coherence can be removed by digitally filtering the specific unwanted frequencies that can be seen in the spectrum.

The lateral resolution obtained with the device is 3.91μm over a FOV of ~12mm², which corresponds to ~40% of the camera chip. The resolution is limited by the pixel size and the maximum size of the selected area in the Fourier space during reconstruction. Note that the commercial DHM has a FOV more than 6 times smaller for a resolution of ~3.1μm.

A similar experiment was made with human epithelial cells on a microscope slide. The result is shown in Fig. 5(a) along with the reconstruction from DHM image Fig. 5(b).

 

Fig. 5 Reconstructed phase of a hologram of human epithelial cells taken with the proposed device (a) and with a commercial DHM (b).

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The camera sensor area is larger than the presented FOV. The size of the FOV is related to the size of the diffracted beams from the analog gratings. Indeed, if the size of the diffracted beams is increased, the distance between the two analog gratings must be increased (to have separated beams) which induces a longer distance for the recombination of the two beams, i.e. a less compact device. To have two separated beams and a compact device, the choice was made to have a limited FOV of ~12mm², which is already more than 6 times larger than the one obtain with a 5x objective and similar resolution.

The presented device is cheap and simple in construction, which makes it possible to use for educational purposes for example. Indeed, if important volumes are considered, the photopolymer, prism and VCSEL do not exceed few US dollars. A mobile phone camera can be used as sensor.

5. Conclusion

In this paper we presented a compact off-axis lensless transmission digital holographic microscope. An illumination composed of a VCSEL, a prism and volume hologram gratings was built to obtain a 5cm height quantitative phase microscope, which has a one order of magnitude larger FOV than other off-axis compact DHM and is more than one order of magnitude more compact than other off-axis transmission compact DHM.

To demonstrate the phase retrieval ability of the presented device, digital holograms of a 1951 USAF phase test target and human epithelial cells were recorded. Phase images of the samples were reconstructed. To verify that the retrieved phase is quantitative, control phase images from a DHM were taken. The computed heights were similar in both measurements, proving the ability of the presented device to do quantitative phase retrieval.

The microscope has a free visual access to the sample from the top which allows for different imaging modalities at the same time, for example fluorescence imaging with a standard widefield microscope.