TY - JOUR
AU1 - Ling, Hangjian
AU2 - Sridhar, Kaushik
AU3 - Gollapudi, Sumanth
AU4 - Kumar, Jyoti
AU5 - Ohgami, Robert S
AB - Abstract The measurement of the volume of blood cells is important for clinical diagnosis and patient management. While digital holography microscopy has been used to obtain such information, previous off-axis setups usually involve a separated reference beam and are thus not very easy to implement. Here, we use the simple in-line Gabor setup without separation of a reference beam to measure the shape and volume of cells mounted on glass slides. Inherent to the in-line holograms, the reconstructed phase of the object is affected by the virtual image noise, producing errors in the cell volume measurement. We optimized our approach to use a single hologram without phase retrieval, increasing distance between cell and hologram plane to reduce the measurement error of cell volume to less than 6% in some instances. Therefore, the in-line Gabor setup can be a useful and simple tool to obtain volumetric and morphologic cellular information. digital holography, CMOS, cell volume, microscopy Introduction The measurement of the shape and volume of blood cells, such as red blood cells (RBCs), white blood cells (WBCs) and platelets, has been routinely used in clinical setting to guide diagnoses [1–3]. The measured shape provides important biophysical parameters [4–6] including two-dimensional (2D) morphology, thickness, size and volume, which can vary and be diagnostic in some pathological conditions, such as cancer, metabolic disorders and infections [7,8]. Various types of technologies including blood cell counter, phase contrast microscopy and digital holography have been implemented to obtain such information. Among them, digital holographic microscopy (DHM) is a unique method due to its advantages of low cost, ease of use, real-time feedback, label-free approach and wide field of view [9–13]. DHM is based on recording an interference (i.e. a hologram) between reference and object waves. A coherent or partially coherent light is used as the light source. The three-dimensional (3D) optical field (including both intensity and phase) is numerically reconstructed from the recorded hologram. The reconstructed intensities are typically used when using DHM to detect opaque particles [14] and to measure fluid velocities [15]. While using DHM to measure transparent objects such as blood cells, the reconstructed phases are typically used since they are proportional to the thickness of the object. Depending on whether the reference and object waves are in-line or not, there are two types of optical setups in DHM: the in-line and off-axis setups. The advantage of off-axis setup is that the reconstructed 3D field is free of twin image noise, and the reconstructed phase truly represents the cell thickness [16–19]. But it has smaller interference finger spacing on the holograms, which adds higher requirements to the digital sensor [20], for example, requiring a charge-coupled device with smaller pixel size. In addition, it requires a separated reference beam, which complicates the optical setup. The in-line setup is another widely used configuration to record the holograms of cells [21–23]. It has larger fringe patterns and is easier to implement in experiments. The disadvantage is that the reconstructed images include twin image noise, which can cause errors in phase and cell thickness [24]. Several types of solutions have been developed to address the twin image problem. First, one can immerse the object into a media with a comparable refractive index to minimize the phase shift. Jericho et al. [23] applied this method to estimate the thickness of various types of cells and showed good concordance. When the objects have strong phase shift, one can remove virtual images by applying the phase-shifting digital holography [25,26] and the iterative phase retrieval method [27,28]. In phase-shifting digital holography, multiple holograms are recorded where the phase of a separated reference beam is shifted. This method also requires a separated reference beam, similar to the off-axis DHM. In the iterative phase retrieval method, the wave is propagated back and forth among multiple planes with constraints applied on the object [29,30] or hologram planes [31,32]. This method is very attractive since it can be implemented in the simplest Gabor setup, where no additional optical elements are inserted to split the light beam. Other approaches such as the polarization-based method [33] and knife-edge aperture method [34] have also been developed to eliminate the virtual image but require additional optical components compared to the simple Gabor setup. In this paper, we focus on the in-line DHM without separation of reference beam due to the simple optical setup. Our aim is to implement this simple imaging system to evaluate volume of cells mounted on glass slides. Due to the in-line setup, the reconstructed phase is affected by virtual image noise. By increasing distance between cell and hologram plane, we show that the virtual image signal becomes weaker and the measurement error is reduced to less than 10%. In addition, we test the iterative phase retrieval method to remove the virtual images. However, the result shows that this method does not improve the measurement quality due to persistence of background noise on the raw holograms caused by debris and scratches on the slides affecting the light path. Experimental technologies The optical setup of in-line DHM is shown in Fig. 1. A Helium-Neon (HeNe) laser with a wavelength of 633 nm (Newport Corporation) is used to illuminate the sample volume. The laser beam passes a spatial filter (Newport 900, 25 μm pinhole, 10× objective) and a collimating lens (focal length 50.2 mm) before illuminating the sample. The scattered light by objects (object wave) and the undisturbed light (reference wave) form interference patterns, i.e. the holograms. The hologram is magnified by a 40× microscope objective (Olympus, NA = 0.65, infinity corrected), transmitted by a 1× tube lens (focal length 180 mm), and then recorded on a complementary metal-oxide semiconductor (CMOS) camera (FLIR, Grasshopper, GS3-U3-41C6M-C, pixel size 5.5 μm). The microscopy glass slide where RBCs are mounted seats on a transition stage, which allows us to vary the separation distance between the microscope objective and the glass slide within an accuracy of 10 μm. The imaging system has a resolution of 0.14 μm/pixel. All the optical components are aligned along the horizontal direction and seated on an optical rail. Fig. 1. Open in new tabDownload slide Schematic of digital in-line holography set up that includes (i) laser light source; (ii) spatial filter; (iii) collimator lens; (iv) tissue sample on microscopy glass slide of dimensions 25 × 75 mm; (v) microscopy objective; (vi) tube lens and (vii) CMOS camera of area 2048 × 2048 pixels, pixel size 5.5 μm. The location of the hologram plane is defined at z = 0. Fig. 1. Open in new tabDownload slide Schematic of digital in-line holography set up that includes (i) laser light source; (ii) spatial filter; (iii) collimator lens; (iv) tissue sample on microscopy glass slide of dimensions 25 × 75 mm; (v) microscopy objective; (vi) tube lens and (vii) CMOS camera of area 2048 × 2048 pixels, pixel size 5.5 μm. The location of the hologram plane is defined at z = 0. We use a Cartesian coordinate system (x, y, z), where x and y denote the two directions perpendicular to the optical axis and z represents the direction of the light beam. We define the hologram plane at z = 0. Note, this hologram plane coincides with the focal plane of the microscopy objective. We use zcell to denote the distance between the hologram plane and object plane where the cells are located. The magnitude of zcell is not a prior known parameter. We will show later that zcell can be obtained by reconstructing the hologram at various z and comparing the focal parameters consisting of image sharpness. The intensity distributions of the hologram are described by the equation below as $$\begin{equation}I\left( {x,y;z = 0} \right){\ } = {\ }{\left| {R + O} \right|^2} = {\left| R \right|^2} + {\ }{\left| O \right|^2} + R{O^*} + {R^*}O\end{equation}$$(1) where R and O represent the complex amplitudes of reference and object waves at plane |$z = 0$|⁠, respectively, and superscript * denotes conjugate. The complex optical field (including both amplitude and phase) at the object plane |$z = {z_{cell}}$| can be reconstructed from hologram I as follows: $$\begin{equation}U(x,y;z = {z_{cell}}){\ } = I \otimes h\left( {x,y,z = {z_{cell}}} \right)\end{equation}$$(2) where ⊗ represents convolution and |$h\left( {x,{\ }y,{\ }z} \right)$| is a diffraction kernel. We choose the Rayleigh–Sommerfeld diffraction formula, |$h = z/i\lambda {\left( {{x^2} + {y^2} + {z^2}} \right)^{0.5}} \exp\{ ik{\left( {{x^2} + {y^2} + {z^2}} \right)^{0.5}}$|} [35], where λ is the wavelength of the light, and |$k = 2\pi /\lambda $| is the wavenumber. Then, the phase distribution on the object plane can be calculated as follows: $$\begin{equation}\Delta \theta ^\prime\left( {x,y} \right){\ } = \rm{{\ }atan{\ }\left( {Im{\ }\left\{ U \right\}/Re{\ }\{ U\} } \right){\ }(mod{\ }2\pi )}\end{equation}$$(3) Inherent to the in-line setup, the reconstructed optical field is affected by virtual image noise. The in-focal real image and in-focal virtual image are located symmetrically on two sides of the hologram plane. The in-focal virtual image propagates in 3D space and creates the out-focal virtual image noise on the object plane (i.e. the in-focal real image plane). Thus, the reconstructed phase at the object plane has errors due to the out-focal virtual image noise. As the out-focal virtual image propagates further away from its origin (or source), the signal becomes weaker. Thus, we expect that the error caused by the out-focal virtual image noise reduces with increasing zcell, as will be demonstrated later in the simulations. Moreover, the reconstructed phase at the object plane could have negative values due to the effect of the virtual image. In reality, the phase shift caused by the sample should always be positive, given that the sample has a larger refractive index than that of the surrounding medium. To avoid false negative phase values in the reconstruction, we modify the phase obtained from Eq. (3) by $$\begin{equation}\Delta \theta \left( {x,y} \right){\ } = \Delta \theta ^\prime{\ }-{\ }{\rm{min}}{\ }(\Delta \theta ^\prime).\end{equation}$$(4) Note, Eq. (4) is simply a shift of the phase such that there is no negative value. This equation does not totally remove the effect of virtual image. Yet, as will be demonstrated later, this approach allows us to estimate the average phase value (and thus the volume) of the object when the magnitude of zcell is properly selected. The physical thickness of cell is given by $$\begin{equation}d\left( {x,y} \right) = \lambda (\Delta \theta /2\pi )/({n_{cell}}-{n_{med}})\end{equation}$$(5) where λ is the wavelength, and ncell and nmed are the refractive index of the cell and the surrounding medium of cell, respectively. To make a blood smear slide, a drop of blood was placed on a slide and extended with a cover slip at a 45° angle. After drying at room temperature for 15–20 min, the cells on the slide were fixed with methanol and stained with Wright Giemsa; a glass coverslip was then applied using mounting media. The refractive indices of RBCs and the mounting media are ncell = 1.4, and nmed = 1.33 [16]. Normally, before using Eqs. (4) and (5), a phase unwrapping algorithm needs to be performed to remove the ∼2π discontinuities in the spatial distribution of the phase. While in the current study, considering the small difference between ncell and nmed, as well as the small thickness of the cell (<2 μm), the maximal phase shift caused by the RBCs is less than 1π. Therefore, there is no need to perform phase unwrapping. Note, in our experiment, we use the raw holograms for the reconstruction and analysis of cell thickness. The raw hologram contains fringe patterns generated by debris and scratches on the slide where the cells are mounted. If the cells are free to move, e.g. immersed in a container, an image containing only background noise can be calculated by recording a series of images and then taking the mean of these images. Subsequently, a hologram without background noise can be obtained by subtracting or dividing this background image. In the current study, however, the cells are fixed on the slide. As a result, we are unable to separate the signals from the holograms generated by background noise and cells. Because of the background noise, the iterative phase retrieval methods [27] fail to remove the virtual image and do not improve the quality of the reconstructed phase image. Under this situation, one needs to select a relatively large distance between sample and hologram plane (zcell) such that the virtual image signal is weaker. Interestingly, without removing the virtual image, the error of reconstructed phase is less than 10% when the zcell is sufficiently large, as will be demonstrated later. Numerical test We first numerically test the phase reconstruction from a single hologram, and study the distance at which the effect of a virtual image can be ignored. The object in our simulation is a 2D disk having a transmission function t(x, y) as follows: $$\begin{equation}t\left( {x,y} \right) = \begin{cases} \exp \left( {1i} \right)\!,& \left( {x - {x_c}} \right)^2 + \left( {y - {y_c}} \right)^2 \leq {D^2}/4\\ 1\!,& \left( {x - {x_c}} \right)^2 + \left( {y - {y_c}} \right)^2 \gt D^2/4 \end{cases}\end{equation}$$(6) where (xc, yc) denotes the centroid of the object on the hologram, and D denotes the diameter of the object. Thus, a uniform phase shift (here, one wavelength of light) is applied to a region within the object. The intensity of the light remains the same after passing through the object. The reason for applying only one wavelength phase shift is to simulate weak phase-shift objects (i.e. those having similar refractive index with the surrounding medium). However, this method may not be applicable for strong phase-shift objects. The phase distribution for an object with D = 7 μm is shown in Fig. 2(a). Fig. 2. Open in new tabDownload slide Numerical test of phase reconstruction in in-line hologram without removing virtual image: (a) the original phase distribution of object; (b–d) the reconstructed phase distribution for object located at zcell = 3, 7 and 14D; (e) phase distributions across the center of the original object and the reconstructed image for zcell = 7D and (f) error of the reconstructed phase. The relevant parameters in the simulation are λ = 633 nm, image pixel size 5.5 μm/40 = 0.14 μm, image size 600 pixels and cell diameter D = 7 μm. Fig. 2. Open in new tabDownload slide Numerical test of phase reconstruction in in-line hologram without removing virtual image: (a) the original phase distribution of object; (b–d) the reconstructed phase distribution for object located at zcell = 3, 7 and 14D; (e) phase distributions across the center of the original object and the reconstructed image for zcell = 7D and (f) error of the reconstructed phase. The relevant parameters in the simulation are λ = 633 nm, image pixel size 5.5 μm/40 = 0.14 μm, image size 600 pixels and cell diameter D = 7 μm. Then, following the procedures as previously described [36], the synthetic hologram I(x, y) is generated based on diffraction theory: $$\begin{equation}I(x,y){\ } = |t(x,y) \otimes h\left( {x,y,z = {z_{cell}}} \right){|^2}.\end{equation}$$(7) The synthetic hologram is then reconstructed to the location of the original object (i.e. object plane) by Eq. (2). The reconstructed phase distribution is obtained by Eq. (3). We simulate holograms for objects at various distances to the hologram plane ranging from zcell = D to zcell = 15D. Each hologram is reconstructed to the object plane to calculate the phase distributions. Figure 2b and d shows the reconstructed phases for objects located at zcell = 3D, 7D and 14D. Clearly, the reconstructed images demonstrate the original object shape in the center of the image, but with the addition of background noise due to the effects of the virtual image. The magnitude of reconstructed phase for the object is also very similar to the original one, as shown in Fig. 2e. We also calculate the average phase value, denoted as Δθmeasured, within the reconstructed object, and compare it to the ground truth value, denoted as Δθtruth (here, Δθtruth = 1). As shown in Fig. 2f, the error defined as (Δθmeasured − Δθtruth)/Δθtruth is reduced from 30 to about 10% with increasing zcell from 1D to 10D. Yet, further increasing zcell introduces additional error due to the cutoff of fringe patter by the finite sensor size. Since the average phase value within the reconstructed object corresponds to the average thickness of the object, we expect that the error of using this method for the measurement of cell volume can be reduce to 10% when choosing a reasonable zcell in the range of 5D < zcell < 10D. For RBCs, the typically cell diameter is about D = 7 μm. As will be demonstrated in the next section, we use zcell = 50 μm ≈ 7.1D to measure the volume of RBCs and find that the error of cell volume is less than 10%. Since this paper focuses on the cell volume, a discussion on the error of phase distributions within the object is for future study. Experimental results Before calculating the phase and thickness of the sample, the parameter zcell, i.e. the distance between the sample and the hologram plane, must be known. However, this parameter is not a previously known variable in our experiment. To determine zcell, we reconstruct the hologram to various distances z and compare the image sharpness of the reconstructed phase. As shown in Fig. 3, the phase distribution has the sharpest edges near the cell boundaries when z = zcell. To calculate the focal parameter, denoted as F(z), in Fig. 3c, we first calculate the spatial gradient of the phase. Then, these spatial gradients near the cell boundaries are sum up to obtained F’(z). The focal parameter is defined as F(z) = F’(z)/max{F’(z)}. We also attempted to determine the focal plane based on the plane of minimal amplitude [37]. However, the minimal amplitude does not have a sharp peak compared to the phase, likely due to background noise. Fig. 3. Open in new tabDownload slide Determining the focal plane of the cell: (a) reconstructed phase distribution at different z locations near zcell; (b) the gradient of the phase distribution corresponding to (a) and (c) the focal parameter obtained based on the image sharpness (i.e. the gradient of the phase image near the cell edges). The inset in (c) is the original hologram of the cell to generate the phases in (a). Fig. 3. Open in new tabDownload slide Determining the focal plane of the cell: (a) reconstructed phase distribution at different z locations near zcell; (b) the gradient of the phase distribution corresponding to (a) and (c) the focal parameter obtained based on the image sharpness (i.e. the gradient of the phase image near the cell edges). The inset in (c) is the original hologram of the cell to generate the phases in (a). As shown in the simulation, due to the effect of virtual image noise, the reconstructed phase may not represent the original thickness of the sample. The error of the reconstructed phase reduces with increasing zcell. In our experiment, we move the slide along the optical path and record several holograms of the same cells at various zcell. We reconstruct each hologram to the object plane and compare the resulting phase distribution. As shown in Fig. 4, as zcell increases, the reconstructed phase shows higher sharpness due to the weaker signal of the virtual image. We utilize holograms recorded at zcell = 50 μm for the analysis of cell thickness and volume. RBCs typically have biconcave disc shape. Thus, the phase distribution of RBCs is expected to have lower phase value in the middle of the cell. However, in Fig. 4, some cells have lower phase values in the cell center, while others have similar phase value across the entire cell. The reasons may be due to the inherent variation of RBCs shape in the prepared sample, and the noise due to the background fringes and virtual images. Fig. 4. Open in new tabDownload slide (a) Holograms and (b) the corresponding phase reconstructions. The cells locate at distances from the hologram plane zcell = 4, 17 and 50 μm. Fig. 4. Open in new tabDownload slide (a) Holograms and (b) the corresponding phase reconstructions. The cells locate at distances from the hologram plane zcell = 4, 17 and 50 μm. Then, we estimate the cell volume V from the reconstructed phase at the focal plane z = zcell since the volume data provide clinically relevant information. Currently, a manual image segmentation is used to detect the regions that belong to the cells. The area of each segmented region can be calculated, and we denote it as S. Then, using Eq. (4), the thickness of the selected region is evaluated. The average thickness of the selected cell is calculated by accounting for variations over the cell surface and is denoted as dcell. Finally, the cell volume can be estimated as V = Sdcell. Using this procedure, we capture and analyze three holograms (denoted as Sample #1, #2 and #3), each corresponding to a different peripheral blood smear slide. All the blood smear slides contain only RBCs, and no WBCs are involved in this study. Since the hologram has a size of 2048 × 2048 pixels much larger than the size of individual cells, Sample #1, #2 and #3 contain 36, 36 and 25 RBCs (a total of 97 cells), respectively. The resulting volumetric information is compared to the mean corpuscular volume (MCV) data obtained from automated hematology analyzers (DxH 900, Beckman Coulter). Hematology analyzers are routinely used in the clinical setting and considered the gold standard for generating complete blood count (CBC) laboratory results [38,39]. A one-sample t-test at a confidence interval of 99% was performed to compare the DHM experimental data to the MCV values from the hematology analyzer. There was no statistically significant difference observed between the CMOS-derived volumetric data and the hematology analyzer, as shown in Fig. 5. Fig. 5. Open in new tabDownload slide Data analysis of volumetric information from hologram reconstruction and MCV values from the blood counter: (a) Sample #1 (n = 36 cells) shows a standard error (SE) of 5.23% and a discrepancy of 5.96 compared to MCV values; (b) Sample #2 (n = 36 cells) shows an SE of 9.72% and a discrepancy of 8.35 compared to MCV values and (c) Sample #3 (n = 25 cells) shows an SE of 6.50% and a discrepancy of 6.50 compared to MCV. ns, not significant. Fig. 5. Open in new tabDownload slide Data analysis of volumetric information from hologram reconstruction and MCV values from the blood counter: (a) Sample #1 (n = 36 cells) shows a standard error (SE) of 5.23% and a discrepancy of 5.96 compared to MCV values; (b) Sample #2 (n = 36 cells) shows an SE of 9.72% and a discrepancy of 8.35 compared to MCV values and (c) Sample #3 (n = 25 cells) shows an SE of 6.50% and a discrepancy of 6.50 compared to MCV. ns, not significant. It should be noted that Fig. 5 compares the averaged volume of a large number of cells. The measurement errors of the volumes of individual cells could be larger than 10%. Due to the difficulty of isolating individual cells, we do not quantify the errors for individual cells. By averaging for a large number of cells, the measurement error is reduced. For clinical diagnostics where the average volume of a large number of cells is of interests, the current method provides a comparable solution to a CBC analyzer. While for scientific research where accurately measuring the information of a single cell is important, the current method may not be informative. The phase retrieval method has been successfully implemented in previous studies to remove the virtual image and improve the accuracy of phase reconstruction. This method is based on the estimation of the missing phase information on the hologram plane. In most of these studies, the holograms are free of background noise. Here, we test whether the phase retrieval method can be implemented to the raw holograms containing background noise. We used the two holograms shown in Fig. 4 that were recorded for the same sample located at zcell = 17 μm and zcell = 50 μm. We applied the Gerchberg–Saxton iterative phase retrieval algorithm to estimate the phase distribution on both hologram planes. This method involves the propagation of light field back and forth between the two hologram planes. After obtaining the complex amplitudes at both hologram planes, we reconstructed them to the object plane to obtain phase distribution of the cells. The result is compared with the one obtained from direct reconstruction of a single hologram. As shown in Fig. 6, the phase retrieval method does not improve the quality of reconstructed phase distributions. Fig. 6. Open in new tabDownload slide Comparison of the phase distribution obtained from two methods: reconstructing a single hologram (a) without phase retrieval and (b) with phase retrieval based on two holograms. Fig. 6. Open in new tabDownload slide Comparison of the phase distribution obtained from two methods: reconstructing a single hologram (a) without phase retrieval and (b) with phase retrieval based on two holograms. Discussion and conclusion Here, a simple in-line DHM setup was used to extract volume information from peripheral blood smear slides in the absence of phase retrieval methods. The resulting volumetric information derived was compared with the currently accepted gold standard technique, a hematology analyzer and no significant difference was observed. Pathology slide preparation processing has been shown to affect cellular shape but preserve the volume of cells as mass and density of the cells is not affected (volume = cell mass/density) [40]. An optimized distance between the sample and hologram plane of 50 μm (zcell ≈ 7D) was also used to reduce the virtual image noise artifacts without the use of a separated reference beam. It is possible to further reduce the virtual noise in future versions of the imaging system by implementing an autofocusing algorithm that identifies the sharpest features in the reconstructed images based on the intensity variations [41]. Given the simplicity of the setup, it would also be possible to integrate convolutional neural networks pipelines [42] along with data reconstruction to identify features in various disease pathologies. One major issue that limits the accuracy of the current method is the background noise on the raw holograms due to the debris and scratches on the physical slides. Future research is required to separate between the signals generated by the cells and background noise. For example, modification of cell sample preparation procedures by placing the cells in a small container or using flow channel where the cells can move can allow for the development of noise-free holograms. Afterward, the virtual images can be completely removed by applying the phase retrieval methods. Moreover, the upper bounds of the cell density and object size that can be measured using the current paradigm have not been formally evaluated. If the cell density or cell size becomes too large, a separated reference beam may be required. The current method has only been tested for relatively small phase-shifting cells. For cells with large thickness and strong phase-shifting properties, a phase unwrapping algorithm should be added to the current data analysis procedure. The accuracy of the current method depends on the magnitude of zcell/D (i.e. ratio of the defocusing distance of the sample to the cell diameter). When implementing the current method for cells with different sizes, a different defocusing distance (zcell ≈ 7D) should be used. It should be noted that the current simple inline setup is limited to estimating the thickness and volume of relatively simple objects that have nearly uniform phase distribution (or thickness). Due to the inline setup, the virtual image is not totally removed even with an optimized hologram distance and creates errors in the phase reconstruction. 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Published by Oxford University Press on behalf of The Japanese Society of Microscopy. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - Measurement of cell volume using in-line digital holography
JF - Microscopy
DO - 10.1093/jmicro/dfaa077
DA - 2020-12-29
UR - https://www.deepdyve.com/lp/oxford-university-press/measurement-of-cell-volume-using-in-line-digital-holography-f0m0AMFPvY
SP - 1
EP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -