1. Introduction

In recent years, digital holography has been developed as a useful technique to image small particles ~10 $\text{μm}$in situ and potentially in near real-time. In particular, the characterization of small aerosol particles is possible with such techniques and has important potential applications, including climate change studies, imaging and tracking, and life sciences [1–10]. The objective of this article is to introduce a digital holographic microscopy (DHM) concept that uses a particle’s backscattered wave, rather than the forward, or side-scattered, wave that is typically used. Here, the backscattered wave interferes with a reference wave across a sensor-array, which results in an interference pattern that is the backscattered hologram. This hologram then yields an image of the particle once processed using the computational reconstruction routine described in [6]. This DHM arrangement is especially well suited for imaging optically opaque particle types [7].

2. Background

In our set up, a pellicle beam splitter is used to split a laser beam into two parts; one part undergoes transmission and illuminates the particle, while the other acts as the reference wave. The illumination wave backscatters from the particle and interferes with the reference before arriving at a two-dimensional optoelectronic sensor such as a digital camera. During this process both the reference and backscattered waves can be represented by their amplitudes as:

In Eq. (4), the first two terms are due to the interference between the unscattered and backscattered wave whereas the last term is due to the backscattered wave only. In principle, an image of the particle can be reconstructed from this pattern. In this work the particles block only a small fraction of the illuminating light, and consequently, the intensity of the reference wave dominates the intensity of the backscattered wave. Thus, the last term in Eq. (4) can be neglected, leaving

By subtracting the reference intensity leading to Eq. (4), imperfections in the incident beam profile are greatly suppressed [5]. The key characteristic of $I^{\text{con}}$ is its linear dependence on the amplitude of the backscattered wave, i.e., the wave phase is encoded in this detected intensity distribution. Equation (5) can then be used with the reconstruction algorithm described in [6] to render an image of the particle.

We note that in the conventional digital in-line holographic arrangement, i.e., that using the forward scattered light, the particle image is accompanied by its out-of-focus twin upon reconstruction [11–13]. This twin image is also present in the backscattered arrangement and can potentially degrade its imaging capability. However, the twin can be largely suppressed using the method of subtracting the average value of the hologram intensity from Eq. (4) as described in [6] for a forward scattering arrangement.

3. Experiment

The experimental setup of our backscatter digital holographic (BDH) arrangement is shown in Fig. 1. The arrangement is initially established by constructing a Michelson interferometer so that proper alignment of the beamsplitter (BS) can be achieved. The purpose of this step is to align the two beams (reference and illumination) such that they interfere constructively at the detector when no particle is present.

 

Fig. 1 Diagram of the experimental arrangement used to demonstrate BDH imaging of microparticles. Note that this arrangement shows the beam dump placed in front of M2 following the beam alignment step described below.

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The light source used in the experiment is a Q-Switched Nd:YLF laser, frequency doubled to 527 nm. At a distance of 5 cm from the laser is an iris to remove stray light from the laser head, and then at 9 cm from the iris we place an achromatic-doublet lens (L1) of focal length 4 cm. Next, at the focus of the lens we use a pin-hole (PH) of diameter 25$\text{μm,}$which produces the circular diffraction pattern. Using another iris, the central diffraction peak is selected and followed by another lens (L2) of focal length 40 cm, which collimates the central diffraction peak. The purpose of this step is to produce a clean transverse beam-profile. Next a pellicle BS of diameter 5.08 cm with a reflection-to-transmission ratio of 45%:55% is used to split the beam into the reference and illumination waves. This BS is 38 cm from L2 and is mounted on a translation stage to ease its alignment. Then, silver mirrors M1 and M2 are each placed at 50 cm from the BS. Here M1 is fixed and M2 is on a linear translation stage. We then adjust the position of M2 until an interference maximum is seen on the detector, which is a CCD camera (Finger Lakes Instrument, Model ML0081909) at a distance of 4 cm from the BS, see Fig. 1.

Following this alignment step, we remove mirror M2 and place a beam dump (BD) at 150 cm from the BS. We then place a glass window (W) on a xyz-translation stage, and another BD in front of M1. Later, this window will hold the particles under investigation. The intensity of the backscattered light from the (particle-free) window is recorded, which provides an estimate for the amount of light scattered by the bare glass. Next, we place a particle on the window, remove the BD from in front of M1, and record the backscattered hologram. By subtracting the particle-free and particle-loaded intensity patterns at the detector, we get the contrast backscattered hologram of Eq. (4).

4. Particle-image reconstruction

To render an image of the particle, we apply the reconstruction algorithm described in [2] and [6] to $I^{\text{con}}$ using the commercial software Mathematica. This process is essentially an application of the Fresnel-Kirchhoff diffraction theory to the backscattered hologram. An image is generated by simulating the diffraction of light through the hologram as though it were a transmission diffraction. The result is a reconstruction of the particle’s backscattered wave amplitude in a plane parallel to the hologram. The absolute-value squared of the wave in this plane, which is called the reconstruction plane, yields a particle image. However, this particle image will be out-of-focus unless the (computational) distance between the hologram and reconstruction planes is selected properly. We determine this distance by incrementally adjusting it until an in-focus image is obtained.

Once an in-focus image is generated, it is then necessary to calibrate the length scales in the reconstructed images. This is done using an optical fiber (Newport Corporation, F-SMF-28) of diameter 245$\text{μm}$as a calibration “particle” with known size. The fiber is placed on the same glass window described in Sec. 3. A backscatter hologram is then recorded, from which the image is reconstructed. Then, the same window, containing the optical fiber, is imaged with a traditional optical microscope to verify that the image reconstruction procedure can adequately render particle-size and shape. Figure 2 presents this microscope/holographic image comparison for the same optical fiber.

 

Fig. 2 Comparison between a traditional microscope image (a) of an optical-fiber and the corresponding image (b) of the same fiber reconstructed from its backscattered hologram. The optical arrangement used is that shown in Fig. 1. Note that white lines have been drawn in (b) to delineate the (low contrast) edges of the fiber.

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Next, we use the same optical arrangement to image a variety of microparticles from backscattered holograms. These particles, which include ragweed pollen spores (~10 $\text{μm}$ dia.), borosilicate glass microspheres (10 $\text{μm}$ dia.), and Aspergillus flavus (~5-25$\text{μm}$) spores are deposited on the glass window in Fig. 1. The holographic images of these particles are shown in Fig. 3. One can see from the reconstructed images in Fig. 3 that the resolution is insufficient to image individual ragweed and Aspergillus flavus spore particles, which occur here in many-particle clusters, but can resolve individual microspheres. There are many techniques that could be employed to improve this image resolution, and such is the intent of future work, see e.g., see [2, 7, 14].

 

Fig. 3 These images show the backscatter contrast hologram (left column) measured for various particles along with the reconstructed particle-images (right column). The particles include ragweed pollen spores (a, b), borosilicate glass microspheres (c, d), and Aspergillus flavus spores (e, f).

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5. Comments

One motivation for this work relates to imaging opaque particles. In the traditional in-line holographic microscope arrangement, i.e., that using the forward-scattered light, an opaque particle yields only its silhouette after image reconstruction. Thus, the particle surface characteristics are obscured. Using backscattered light, however, it may be possible to discern surface textures, or structural features, that are sufficiently larger than the diffraction limit. In this spirit, recent work in [7] achieves backscattered-light holographic microscopy, but is unable to resolve such surface characteristics and the particles under investigation are immobilized at short distances from the (CMOS) sensor array using a slide or microfluidic channel. What our work shows is that the concept in [7] can be extended to investigate particles that cannot be confined to a microfluidic channel or microscope slide, such as would be useful for in situ studies of aerosol particles.

6. Conclusion

This work explores the feasibility of imaging microparticles with digital holography using the backscattered light rather than the more commonly used forward scattered light. We show successful imaging of an optical fiber, ragweed pollen spore-cluster, glass microspheres, and Aspergillus flavus spore-clusters. While the resolution of the imaging technique can be improved, our results demonstrate that backscattered light holographic imaging may be useful for studies of opaque micrometer-sized particles that must be examined in a contact-free manner, such as aerosols.