1. Introduction

Digital holographic interference microscopy (DHIM) is a three-dimensional (3D) imaging modality based on interferometric principles that allows for recording of both quantitative phase and amplitude information [1,2]. Being both label-free and noninvasive, DHIM has become an attractive option for cell visualization, analysis, and identification [3–12]. Furthermore, DHIM allows for numerical focusing after acquisition [1] and is capable of video rate acquisition which enables analysis of spatiotemporal cellular behaviors [7,8]. Given these powerful capabilities, DHIM remains an actively growing research area.

Strategies for resolution enhancement of DHIM are at the forefront of research interests. Common strategies for resolution enhancement in DHIM include oblique and structured illumination [12–14]. These methods leverage the shifting of the numerical aperture cone to record higher spatial frequencies which may be synthesized to provide a resolution-enhanced image. The disadvantages of these techniques are the requirements of complex optical systems and multiple acquisition frames. Recently, microsphere-assisted microscopy [15–18] has emerged as a powerful single-shot super-resolution technique. Microsphere-assisted microscopy has found success in fluorescence imaging and digital holographic imaging alike [15,16].

In microsphere-assisted microscopy, resolution is enhanced due the photonic nanonet formed by the presence of a microsphere which redirects high frequency content that normally lies beyond the systems resolution limit into the imaging cone of the optical system [15–19]. This enables a simple method for imaging beyond the Abbe diffraction limit of λ/(2NA) [15,17]. By simply placing a glass microsphere between the sample and microscope objective lens of the imaging system, a magnified high-resolution image is formed and can be recorded after appropriate refocusing of the system. The effect of the microsphere will be determined by its size and refractive index, as well as the refractive index of the surrounding media [18], and the displacement distance between the microsphere and the sample [16,17]. Generally, smaller microspheres with higher refractive indices result in better resolution and greater magnification factors. These variables can be tailored based on the intended task [15–18].

In this paper, we present a compact and field portable implementation of microsphere-assisted digital holographic interference microscopy using a 3D-printed Mach-Zehnder interferometer. Several works have previously examined field-portable digital holographic devices [7,11,12,20–22]. These systems typically follow common-path geometries which use a portion of the object beam to act as the reference beam. To accomplish this goal these systems may require more expensive optical components, complex geometries, or place limits on either the usable field-of view or sparsity of the sample. Using a two-beam configuration such as the Mach-Zehnder may reduce the complexity or cost of the system, or otherwise alleviate limitations such as a reduced field-of-view or sparse sample requirement but will result in lower overall stability as the two arms may experience uncorrelated phase changes [9,22]. Despite this, we find our 3D-printed two-beam digital holographic microscope maintains suitable temporal stability for most imaging applications. Microspheres are placed in contact with samples under investigation for generation of resolution enhanced holograms. Resolution enhancement using the system is verified by imaging of a compact disc (CD) wherein the periodic structure of the CD is beyond the resolution capabilities of the native system without a microsphere present. Furthermore, the system is demonstrated to provide suitable cell imaging and identification properties through classification of animal red blood cells. Moreover, the field-portability of the system is established through temporal stability testing and fringe visibility analysis in various locations. The proposed system provides a low-cost and easy to implement system for superresolution digital holographic microscopy without requiring a complex configuration or multiple acquisition frames. To the best of our knowledge, this is the first report of a compact and field portable Mach-Zehnder interferometer for microsphere-assisted DHIM.

2. System design

For a low-cost system, the bulk of the instrument is 3D-printed and complimented by a few commonly used optical components. The 3D-printed system is composed with two mirrors (Newport, $\$ 26$ each), two one-inch cube beam splitters with cages (Thorlabs, $\$ 365$ each), two 10x (0.25 NA) objectives (Newport, $\$ 146$ each), a z-axis translation stage (Newport, $\$ 183$), a CMOS sensor (Basler acA3800-14um, $\$ 584$) and a 632.8 nm He-Ne source (Thorlabs, $\$ 943$). The total cost of the system using the was $\$ 2884$. This can be further reduced significantly through the use of laser diodes, and more cost-effective imaging devices. The system follows a Mach-Zehnder configuration wherein the source beam is split into an object and reference arm by the first beam splitter (BS1), mirrors are used to direct the beam paths through the two microscope objectives before passing through the second beam splitter (BS2) which causes the interference of the two beams at the sensor plane. The schematic diagram and 3D-printed system are shown by Fig. 1(a) and 1(b) respectively. In the object arm of the interferometer, the sample is placed on a z-axis translation stage to allow for focusing of the sample. We place borosilicate beads (n = 1.48) directly on top of the sample under inspection, wherein the microspheres used here had an average diameter of 230 µm. By placing a microsphere in direct contact with the sample under inspection, high spatial frequencies normally uncaptured by the imaging system may be collected by the microsphere-assisted system [17]. The 10x (0.25NA) objectives were chosen such that we could illustrate the resolution improvement by imaging of a compact disc as a test object. The principle design used here could be used with various objective lenses and microsphere sizes according to the desired imaging task. Care should be taken to carefully consider that the size of the microsphere is appropriate for the specimen under inspection and that the objective lens is suitable for the size of the microsphere chosen. Furthermore, considerations should be made with respect to the size and refractive index of the chosen microsphere as well as the ratio of refractive indices between the microsphere and background, as each plays an important role in the imaging performance of a microsphere-assisted system [15–18].

 

Fig. 1. (a) Schematic diagram of the optical system. (b) 3D printed compact and field portable microscope. Inset of (a) shows magnified section containing the microsphere and displaying the geometry for the wave vector analysis. The parallel and perpendicular components of the wave incident at P are given as u′ and w′. h is the height of displacement between the incident point P and the sample, and θ is the angle between centerline C and component w′.

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This process of enabling higher frequency information to enter the imaging system can be explained by considering the refraction for a plane wave incident upon the microsphere [19]. For the general case, wherein a wave vector, $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over k} = u\hat{x} + w\hat{z}$, is incident on the microsphere at point P, separated from the centerline C by an angle θ as shown by the inset of Fig. 1(a), the electromagnetic wave at point P is given as $E\left( {x,z = h} \right)\textrm{ } = \varepsilon \left( u \right){e^{j(ux + wh)}},$ where ɛ(u) is the amplitude, and only the (x, z) plane is considered due to the symmetry of the sphere. $\hat{x},\hat{z}$ represent unit vectors in the x, and z directions, respectively. The parallel component at P inside the microsphere, $(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over u} ^{\prime})$ will be equivalent to that outside the microsphere $(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over u} )$ due to the continuity equation (i.e. $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over u} ^{\prime} = \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over u} = u\cos \theta \hat{x} + w\sin \theta \hat{y}$) and for a propagating wave to exist inside the microsphere, the components of the wave vector inside the microsphere must satisfy $u^{\prime2} + w^{\prime2} = \textrm{ }{({{k_0}n} )^2}$. From these observations, it is deduced that waves normally uncaptured by the system in air will be collected by the system if they satisfy the relation ${u^2}co{s^2}\theta - {|w |^2}si{n^2}\theta \textrm{ } \le {k_0}^2{n^2}$[19]. The geometry for this example is illustrated by the inset of Fig. 1(a). By this explanation, it may be possible for a microsphere-assisted system to capture evanescent waves [see 15, 17, 19].

However, it should be noted that as θ increases, the height between sample and the microsphere (h) also increases, and the evanescent waves will decay on the order of e^-|w|h prior to reaching the microsphere surface [19]. Thus, the capture of evanescent waves may be restricted to areas of direct contact between the sample and microsphere.

The magnification factor from the microsphere can be calculated as M_MS= f/(f-s) where f is the focal length of the microsphere, and s is the distance from the center of the microsphere to the object [17]. When in direct contact, s is equivalent to the radius of the microsphere. Given the diameter (D) and refractive index (n), the focal length of a microsphere can be calculated as f = nD/4(n-1). From the previous two equations, a 230 µm microsphere with refractive index 1.48 will have a focal length of approximately 177 µm and an approximate additional magnification factor of 2.85×.

Given the Mach-Zehnder configuration, the system acts as an off-axis holographic system and allows for easy separation of the real and conjugate images by spectral filtering in the Fourier Domain [22]. The inverse transform of the recovered object spectrum provides the complex amplitude of the object, ($\tilde{U}$ (x, y)), and the object phase is given as Ф=tan^-1[Im{$\tilde{U}$}/Re{$\tilde{U}$}], where Im {·} and Re {·} represent the real and imaginary functions, respectively. Goldstein’s branch-cut method is used to retrieve the unwrapped phase distribution [23].

3. Experimental results and discussions

In this section, we present the results and discussions pertaining to the presented imaging system. First, the resolution enhancement of the system is confirmed by imaging of a periodic structure that is not resolvable in the absence of a microsphere. Next, we provide a quantitative analysis for the temporal stability and fringe visibility of the 3D-printed system recorded at various testing locations to assess the field-portability of the presented system. Lastly, we exhibit the capabilities of such a system for cell identification through examination of various classes of animal red blood cells.

3.1 Resolution enhancement of the microsphere-assisted system

To confirm the expected resolution enhancement has been obtained by the system, we image a compact disc (CD) using the proposed microsphere-assisted 3D-printed DHIM system. The CD has a periodic structure with a period of 1.6 µm. By the grating equation, d sin θ_g = λ where d is the period of the grating, and θ_g is the angle of the diffracted rays, a CD illuminated by a source of wavelength λ = 632.8×10⁻⁹ requires a numerical aperture of sin θ_g = 0.3955 to observe its periodic structure. This is beyond the native numerical aperture of the system (0.25 NA) when no microsphere is placed on the sample. In our case, a microsphere is placed on the sample under inspection, then a hologram is recorded, and numerical reconstruction is performed using the angular spectrum propagation approach. After reconstruction, the periodic structure of the sample is clearly recovered as shown by the recovered phase profile in Fig. 2(a). Also apparent, is the effect of the spherical aberration imposed by the presence of the microsphere.

 

Fig. 2. (a) Reconstructed phase profile of the compact disc in the microsphere-assisted imaging system. (b) Estimated spherical phase contribution of the microsphere calculated by surface fitting to the reconstructed phase in (a). (c) Recovered object phase after removal of the spherical phase contribution. (d) Amplitude image and (e) line profile across the line in (d) for the compact disc.

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To remove the spherical aberration imposed by the microsphere, we estimate the spherical phase contribution using a surface-fitting procedure [17]. The estimated spherical phase contribution and the recovered object phase after removal of the spherical aberration term are shown by Fig. 2(b) and 2(c) respectively. The line profile along the recovered amplitude image confirms the periodic structure of the CD has been recovered [see Fig. 2(e)]. Vertical gridlines for Fig. 2(e) each represent a distance of 1 µm, providing consistent results with the calculated magnification factor. These results confirm the microsphere has provided resolution enhancement and the microsphere assisted system has an effective numerical aperture of roughly 0.4 with total magnification factor of approximately 28.5×.

3.2 Field-portability assessment

In this section, we describe the procedures and results pertaining to assessing the field-portability of the proposed system. First, we consider the temporal stability of the system, then we provide analysis of the fringe visibility at varied imaging locations.

3.2.1 Temporal stability of the 3D-printed microscope

To assess the system’s field portability, we consider measurements of the temporal stability and fringe visibility. The temporal stability analysis provides a quantitative measure of the temporal noise and is measured by recording the path length changes for a blank glass slide over time. Here, we measured the temporal stability by recording video holograms of a blank glass slide without sample or microsphere for 20 seconds at 30 Hz for a 512 × 512 pixel-area. The recorded fringe pattern is then reconstructed, and optical path length difference at each pixel location is computed in comparison to a reference frame. The pixel-wise standard deviation of the path length differences is then computed, and the mean value defines the temporal stability of the system. The system was tested in various testing locations with and without a vibration isolation sheet. The tested locations include a floating optical table, a non-floating optical table, and a standard wooden table. These results are provided by Fig. 3.

 

Fig. 3. Results of temporal stability testing for various imaging locations. w/ vibration iso indicates the use of Sorbothane vibration isolation sheet.

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The best performance is achieved when the system is placed on the optical floating table having a mean of 11.75 nm, however, the system maintains stability under 25 nm for all tested conditions. The non-floating optical table and wooden table had mean values of 23.45 nm and 21.23 nm, respectively. With the addition of the vibration isolation sheet, these values decreased to 20.05 and 16.97 nm, respectively. No microsphere was used during these measurements such that a large pixel region could be used and to ensure consistency across trials by using the same region of the sensor. No visible effects on the stability were observed with the addition of the microsphere, and in a similar experiment using a 256 × 256 pixel region inside the microsphere for data taken on a floating optical table, we found the mean standard deviation to be 10.13 nm which is consistent with those results taken without a microsphere. These results indicate the system provides suitable temporal stability for most applications.

3.2.2 Fringe visibility

In addition to measuring the temporal stability, we also consider the fringe visibility (V_f) as a metric for hologram quality [24]. The fringe visibility is directly related to the fringe contrast and be calculated in the Fourier domain as twice the maximum of the absolute value of the real object term divided by the maximum of the absolute value of the DC term. That is, V_f = 2×max{|Û(C_x-S_x,C_yS_y)|}/max{|Û(C_x,C_y)|}, where Û (·) denotes complex amplitude in the Fourier domain, C_x, C_y represent the center of the Fourier Space (i.e. the DC term), S_x, S_y represent the shift to the +1 term containing object information, and max {·} is the maximum operator. The values for this metric range from 0 to 1 with 1 representing maximum contrast of the fringe pattern and 0 representing no observable fringe pattern. Intuitively, fringe visibility will relate to the quality of the recorded hologram, where more visible fringes lead to better reconstruction quality. We have calculated the fringe visibility for a reference frame taken at each location tested. As with the temporal stability testing, the data for fringe visibility was analyzed without the presence of a microsphere to avoid the variability of different microspheres affecting the results at each location and to allow for the same region of the sensor to be considered in each case. In our analysis, we find the system has the best fringe visibility (V_f = .864) when placed on the floating optical bench as should be expected. We also find that the system maintains good fringe visibility at all the tested locations, with only a 5.78% decrease from the results of the floating optical table to the lowest recorded visibility. Moreover, the fringe visibility was calculated as 0.836, 0.831, 0.814, and 0.836 for the non-floating optical table without vibration isolation sheet, non-floating optical table with vibration isolation sheet, wooden table without vibration isolation sheet, and wooden table with vibration isolation sheet, respectively. These results provide additional evidence of a field-portable system.

3.3 Cell identification using MS-assisted digital holographic microscopy

The proposed system is further presented for cell visualization and identification. Given, the improved resolution of the system, a microsphere-assisted system may be better equipped for visualization of small biological samples such as cells. Furthermore, the higher effective resolution may enable extraction of high-resolution features not normally resolvable in a system without a microsphere which could improve the discrimination abilities. Here, we classify between Goat and Cow red blood cells (RBCs) where both have similar shape and morphology, but the Goat RBC is slightly smaller by comparison. Figure 4 shows the visualization of example cells from each class both with and without a microsphere. Note, a randomly selected cell is chosen for each reconstruction in Fig. 4. Since the microspheres are placed directly onto the sample, we do not have the capabilities to directly compare the same cell with and without a microsphere present.

 

Fig. 4. (a) Reconstructed phase profiles for (a) a goat RBC without a microsphere in the system, (b) a goat RBC with a microsphere in the system, (c) a cow RBC without a microsphere in the system, and (d) a cow RBC with a microsphere in the system. RBC: Red blood cell.

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From these reconstructions, we can see the benefits of increased resolution and a more apparent central indentation of the RBCs in the microsphere-assisted reconstructions.

Fifty holograms for both the goat and cow RBCs were recorded using the microsphere-assisted digital holographic interference microscopy system. Following reconstruction of the phase profiles for each cell, morphological features were extracted for use in cell identification. The morphological features extracted included the mean optical path length, coefficient of variation of optical path length distribution, optical volume, projected cell area, cell thickness kurtosis, and cell thickness skewness [11]. A random forest model was trained on 50% of the data and the remaining data was used for testing [25]. A confusion matrix for the classification can be seen by Table 1 which indicates the system was 94% accurate in classifying between cow and goat RBCs.

Table 1. Confusion matrix for classification of segmented RBCs

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4. Conclusions

In summary, we have presented a compact and field portable 3D-printed system for microsphere-assisted digital holographic interference microscopy. The system is based on the Mach-Zehnder interferometer configuration and places microspheres directly on top of the sample to capture high frequency information and for ease of implementation. Following the recording of a hologram, a resolution enhanced image can be reconstructed. Surface fitting is applied for aberration correction to remove the spherical phase contribution of the microsphere. The system was tested and shown to have high temporal stability and good fringe contrast in various testing locations indicating its suitability as a field portable instrument. Lastly, the device was illustrated to show improved capabilities for biological cell visualization, and to perform highly accurate cell identification. To the best of our knowledge this is the first report of a field-portable device for microsphere-assisted digital holographic interference microscopy. The form factor and cost of the system can be further reduced by using compact sources such as laser diodes. We believe such a system can be useful for high resolution field applications. Future work includes investigation of high-resolution cell features for improved classification in diagnostic applications [26-27].