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Curr. Opt. Photon. 2022; 6(6): 598-607

Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.598

Copyright © Optical Society of Korea.

## Diagnosis of Unstained Biological Blood Cells Using a Phase Hologram Displayed by a Phase-only Spatial Light Modulator and Reconstructed by a Fourier Lens

Dahi Ghareab Abdelslam Ibrahim

Engineering and Surface Metrology Lab., National Institute of Standards, El haram, El Giza 12211, Egypt

Corresponding author: *dahi.abdelsalam@nis.sci.eg, ORCID 0000-0002-4429-5096

Received: April 18, 2022; Revised: June 28, 2022; Accepted: July 18, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this paper, a simple nondestructive technology is used to investigate unstained biological blood cells in three dimensions (3D). The technology employs a reflective phase-only spatial light modulator (SLM) for displaying the phase hologram of the object being tested, and a Fourier lens for its reconstruction. The phase hologram is generated via superposing a digital random phase on the 2D image of the object. The phase hologram is then displayed by the SLM with 256 grayscale levels, and reconstructed by a Fourier lens to present the object in 3D. Since noise is the main problem in this method, the windowed Fourier filtering (WFF) method is applied to suppress the noise of the reconstructed object. The quality of the reconstructed object is refined and the noise level suppressed by approximately 40%. The technique is applied to objects: the National Institute of Standards (NIS) logo, and a film of unstained peripheral blood. Experimental results show that the proposed technique can be used for rapid investigation of unstained biological blood cells in 3D for disease diagnosis. Moreover, it can be used for viewing unstained white blood cells, which is still challenging with an optical microscope, even at large magnification.

Keywords: 3D reconstruction, Cell analysis, Noise reduction, Phase hologram, Spatial light modulator

OCIS codes: (070.0070) Fourier optics and signal processing; (090.0090) Holography; (100.0100) Image processing; (240.0240) Optics at surfaces

Blood plays an important role in the body’s homeostasis, the circulation of nutrients and removal of waste, the distribution of hormones, and the elimination of excess heat [1]. Blood consists of several components, including red blood cells (RBCs), platelets, plasma, and white blood cells (WBCs). The characterization of RBCs and WBCs is crucial for disease diagnosis. The characterization of RBCs is important for understanding the pathophysiology of many diseases, including anemia and heart diseases [2]. The characterization of WBCs is important for the detection of different diseases such as lymphoma, COVID-19, and cancer [3, 4]. WBCs play various roles in defending the host from invaders and abnormal cells [5, 6]. WBCs are classified into different types according to their morphologies and functions in the immune system. Viewing a two-dimension (2D) image of WBCs clearly under an optical microscope requires special stains. Such stains require chemical fixation procedures, which limit live-cell analysis. Confocal fluorescence microscopy enables the three dimension (3D) structural images of living WBCs [7], but with chemical staining procedures that inevitably present significant drawbacks, such as phototoxicity and photobleaching. A different approach by measuring 3D refractive-index maps of the WBCs was proposed [6], but the technique is based on the separation of a specific type of WBCs from RBCs. In this paper, a simple nondestructive technology for viewing unstained WBCs clearly in 3D is presented. The technology includes an spatial light modulator (SLM), which displays the phase hologram of the object being investigated. The phase hologram is generated by superposing a random phase upon the object being investigated. There are typically three types of computer-generated holograms (CGHs) [8, 9]: phase-only, where the material modulates only the phase of an incoming wavefront, and the transmittance amplitude is unity; amplitude-only, where the material modulates only the amplitude of an incoming wavefront, and the transmittance phase is constant; and complex-amplitude, where the material modulates both phase and amplitude of an incoming wavefront. The detour-phase hologram has the capability to encode the amplitude and phase of the complex hologram [10]. The drawback of the detour method is that the diffraction efficiency is low. For this reason we used the phase-only CGH technique [11], which has a higher diffraction efficiency than the detour method. The only drawback of the phase-only CGH technique is that the reconstructed object is noisy. We overcome the problem of noise by using the windowed Fourier filtering (WFF) algorithm. The effectiveness of the proposed method is proved by simulations and real experiments.

In this paper, two objects are studied: The first is a simulated National Institute of Standards (NIS) logo, and the second is unstained peripheral-blood film (PBF). The PBF includes both RBCs and WBCs taken from the eye vein of a male albino rat. All guidelines for the care and use of animals are followed and approved by the Institutional Animal Care and Use Committee (CU-IACUC) of Cairo University (approval number CUIFC3220). The preparation of the PBF is carried out following the Brown procedures [12]. The PBF is photographed using an automatic image contour analysis system (SAMICA) (ELBEK GmbH, Siegen, Germany) with a magnification of 1200X. The phase hologram is then generated by superposing a random phase on the 2D image being investigated. The phase hologram is then displayed by the SLM and reconstructed by the Fourier Lens (FL). The reconstructed image is then enhanced against noise using the WFF algorithm. Experimental results show that unstained WBCs on the surface of the PBF can be viewed clearly in 3D. Moreover, the quality of the reconstructed object is good, since the noise level is suppressed by approximately 40% using the WFF method. The proposed method does not require the separation of WBCs from RBCs to see the WBCs clearly. Moreover, it does not require direct handling of the sample, just a 2D photograph of the sample by a high-magnification microscope. To the best of our knowledge, this is the first time that reconstruction by FL and SLM with filtration by WFF is used to view unstained WBCs clearly.

### 2.1. Phase-only Computer-generated Hologram

In the phase-only CGH, for a typical object a random phase pattern can be superposed without affecting the irradiance distribution. If tpq denotes the transmittance of the cell corresponding to the Fourier coefficient |hpq| and phase ϕpq, then

tpq=hpqexpjϕpqexpjϕpq

where |hpq| denotes the amplitude of the Fourier transform, and ϕpq denotes its phase. Therefore, the reconstructed object has the following form:

Obj=x,y1expjϕ pq

where ℑx,y−1 denotes the operator for the inverse 2D Fourier transform. A typical algorithm for the phase-only technique is shown in Fig. 1.

Figure 1.Flowchart for the phase-only computer-generated hologram (CGH) method.

### 2.2. Windowed Fourier Filtering

WFF gives a filtered image. The output of WFF is usually a complex field, and its real part should be used [13–15]. Since the reconstructed object is noisy, it is necessary to suppress the noise to see the reconstructed object clearly. A great number of approaches have been developed to overcome the problem of noise in the reconstruction process [16, 17], each with its own merits and demerits. In this study, WFF is selected to enhance the image because it does not require dark and flat images, like the flat-fielding approach does.

The reconstructed object Obj expressed in Eq. 2 is convolved with the windowed Fourier transform (WFT), the equation for which can be expressed as:

WFTfx,fy=+ + Obj x,yr x,ydxdy,

where r(x, y) = exp[−x2 / 2σx2y2 / 2σy2] is the Gabor transform, which is a Gaussian function, and the symbol * denotes complex conjugation. Here σx = 10 and σy = 10 are the standard deviations of the Gaussian function in the x and y directions respectively. By shifting the central position of the Gaussian window point by point and computing the WFT of the signal, the fundamental spectral component of each local signal can be extracted. Then, by integrating all of these spectral components, a universal spectral component can be retrieved as:

+ + WFT f0,f0 dxdy=F f0,f0

Finally, applying the inverse Fourier transform to the universal spectral component, a complex image is obtained. The real values of the complex image are taken to provide a filtered image, which is free from noise.

Using this algorithm, the phase holograms of two objects are generated. The first object is a simulated NIS logo, and the second object is an unstained PBF. Figure 2(a) shows a simulated 2D image of the NIS logo.

Figure 2.Simulation for illustration. (a) A simulated National Institute of Standards (NIS) logo. (b) Phase spectrum. (c) Amplitude spectrum. (d) Digitally reconstructed image from the phase hologram. (e) A filtered image of (d) using windowed Fourier filtering (WFF) at threshold = 100. (f) Intensity profiles along the red and blue lines of (d) and (e).

Figure 2(b) shows the phase hologram generated after superposing a digital random phase [rand (x, y)] on the 2D image of Fig. 2(a). Figure 2(c) shows the amplitude spectrum of Fig. 2(a). Figure 2(d) shows the numerical reconstruction of Fig. 2(b). As seen in Fig. 2(d), the reconstructed image is noisy. As mentioned in the introduction, the phase-only technique has a higher diffraction efficiency than the detour method, but the reconstructed object is noisy. The WFF technique is used to reduce this noise as much as possible. To calculate the significance of using the WFF in terms of noise reduction, we used the standard-deviation function (std2) in MATLAB to quantify the noise. Std2(A) computes the standard deviation of all values in array A. std2 (also called σ) for Fig. 2(d) is calculated to be 61.39. Figure 2(e) shows the filtered image of Fig. 2(d) using the WFF technique. Its value of σ is calculated to be 35.70. The profiles along the red and blue lines of Figs. 2(d) and 2(e) are extracted and plotted in Fig. 2(f). The time taken to extract the filtered image is around three seconds, using a personal computer with 8 GB of RAM and a 2.9-GHz processor. The unit of the extracted intensity is arbitrary (a.u.). Figure 3(a) shows the difference between Figs. 2(d) and 2(e). The difference in σ is calculated in MATLAB as STD2(diff), and the value is calculated to be 25.69, which means that the noise level is suppressed by approximately 42% at a threshold of 100. The value of threshold is selected by trying many values in the WFT algorithm until a filtered image is obtained. Figure 3(b) shows the intensity profile along the black line of Fig. 3(a).

Figure 3.Noise estimation. (a) Difference between Figs. 2(d) and 2(e). (b) Intensity profile along the black line of (a).

The simulation and numerical reconstruction of Fig. 2 are supposed to be free from the effects of flat-field correction and pixel crosstalk in the SLM. The effects of flat-field correction and pixel crosstalk are explained in detail in references [16–19]. Experimentally, these effects should be accounted for via calibration of the SLM. Here we proposed a simple method for calibration, employing a half-wave plate fixed at the fast axis and a polarizer fixed at 180°.

### 2.3. Calibration of the SLM

Figure 4(a) shows a schematic diagram of the optical setup proposed for calibration of the SLM [20].

Figure 4.Spatial light modulator (SLM) calibration. (a) Schematic diagram of the optical setup for spatial light modulator (SLM) calibration. (b) Obtained results: experimental (red) and simulated (blue) profiles.

A light-emitting diode (LED) source emits a beam of light at 635 nm. The beam is expanded to illuminate the SLM window. A half-wave plate (λ/2) fixed at the fast axis is placed prior to the SLM, and a uniform sheet of grayscale levels from 0 to 255 is displayed on the window of the SLM. We generated 14 intensity images from 0 to 252 levels in steps of 18 intervals. The generated images are captured by the charge-coupled device (CCD) camera. At the center of each captured image, the average intensity of an array of 15 × 15 pixels is measured. The obtained intensity values are plotted against the corresponding phase (in radians), and the result is the experimental wave that characterizes the intensity recorded by the CCD camera due to a change in the grayscale values displayed on the SLM. The experimental wave is simulated to compensate for the noise. Figure 4(b) shows the obtained experimental profile (in red), which looks noisy. To quantify this noise, a simulated profile (in blue) is generated to compensate for the noise attached to the experimental profile. The simulated profile equation is generated as I = 9 sin (1.35x + 3.09) + 30, where x is a linear spaced vector defined in Matlab as linspace (0, 2π, 1,000) with 1,000 generated points. As seen in Fig. 4(b), the results of the first half (from 0 to π) of the profile are rather matching, while in the second half of the profile (from π to 2π) the results deviate a bit, as seen in the black dashed arrows. Such deviations may come from instability of the laser light. We claim that such deviations may be reduced by using the WFF method.

### III. EXPERIMENTAL RESULTS

The proposed holographic projection system is depicted in Fig. 5(a). It utilizes a laser diode (LD) with a wavelength of λ = 635 nm, which is expanded and collimated by a beam expander (BE) to illuminate the SLM window (resolution 1,920 × 1,080 pixels, pixel pitch 8 µm, model Pluto; Photonics AG, Berlin, Germany).

Figure 5.Experiment of the holographic projection system (a) Schematic diagram. (b) Reconstruction illustration of the computer-generated hologram.

The SLM is placed at the front focal plane of a Fourier lens (FL = 120 mm). A polarizer (P) and analyzer (A) are placed before and after the SLM, to select the correct polarization state with respect to the SLM’s slow axis. A CCD camera is placed at the back focal plane of the FL, to capture the reconstructed object.

Here we experimentally investigate two samples: the NIS logo, and a PBF image that includes unstained white and RBCs. For the first example, the phase hologram of Fig. 2(b) is displayed on the window of a reflection SLM. The reconstructed object from one phase hologram is shown in Fig. 6(a). The reconstructed object has been corrected by WFF and the image filtered at a threshold of 240 is shown in Fig. 6(b). Figure 6(c) shows the 3D pseudocolor of Fig. 6(b).

Figure 6.Reconstruction of the simulated National Institute of Standards (NIS). (a) Reconstructed object of one phase hologram of Fig. 2(b) using spatial light modulator (SLM) and Fourier lens. (b) A filtered image of (a), using windowed Fourier filtering (WFF) at threshold = 240. (c) 3D pseudocolor of (b).

As seen in Fig. 6(a), σ is found to be 18.77, while σ for Fig. 6(b) is 4.16. The difference in σ is 18.77− 4.16 = 14.61, which means that the noise level is suppressed by approximately 39%. Figure 7(a) shows the difference between Figs. 6(a) and 6(b), and Figure 7(b) shows the intensity profile along the black line of Fig. 7(a). Figure 8(a) shows the reconstructed NIS object from an average of ten phase holograms using SLM and FL. Figure 8(b) shows the filtered image of Fig. 8(a) using the WFF method. The 3D pseudocolor of Fig. 8(b) is shown in Fig. 8(c). The profiles along the red and blue lines of Figs. 8(a) and 8(b) are extracted and plotted as shown in Fig. 8(d). As seen in Fig. 8(a), σ is found to be 10.72, while σ for Fig. 8(b) is 6.52. The difference in σ is 10.72 − 6.52 = 4.20, which means that the noise level is suppressed by approximately 39%.

Figure 7.Noise estimation. (a) Difference between Figs. 6(a) and 6(b). (b) Intensity profile along the black line of (a).

Figure 8.Reconstruction of National Institute of Standards (NIS) from average of ten phase holograms. (a) Reconstructed object from an average of ten phase holograms using spatial light modulator (SLM) and Fourier lens. (b) A filtered image of (a) using WFF at threshold = 240. (c) 3D pseudocolor of (b). (d) Intensity profiles along the red and blue lines of (a) and (b).

Figure 9(a) shows the difference between Figs. 8(a) and 8(b). Figure 9(b) shows the intensity profile along the black line of Fig. 9(a).

Figure 9.Noise estimation. (a) Difference between Figs. 8(a) and 8(b). (b) Intensity profile along the black line of (a).

The second sample is a peripheral blood film (PBF) image, which includes unstained white and RBCs. PBF is a valuable diagnostic and monitoring tool that is commonly used in the characterization of many clinical diseases, and in assessing their progression [4]. In this study the PBF is prepared and then photographed using an automatic image contour analysis system (SAMICA) (ELBEK GmbH). The system is provided with an electronic camera connected to a computer through a built-in interface card, and the image can be magnified up to 1200× and displayed by the computer. The blood sample is collected and taken from a male albino rat (age about 2 months and average weight ≈150 g). All guidelines for the care and use of animals are followed and approved by the Institutional Animal Care and Use Committee (CU-IACUC) of Cairo University (approval number CUIFC3220).

The rat is anesthetized with ether, and then a blood sample is collected from the eye vein by heparinized capillary tubes to view unstained WBCs and RBCs. Figure 10(a) shows a magnified image of the PBF, which includes RBCs and WBCs. The size of the image in Fig. 10(b) is 550 × 560 pixels. As seen in Fig. 10(a), the RBCs appear clearly, while the WBCs cannot be viewed. As seen in Fig. 10(b), both the RBCs and WBCs are clearly viewed in 3D, with no contrast agents added to the PBF sample. Figure 11(a) shows the phase hologram of the 2D image of Fig. 10(a). As seen in the hologram, the phase range is from 0 to 255, which matches the phase range of the SLM. Figure 11(b) shows the optical reconstruction of Fig. 11(a) using the FL. As seen in Fig. 11(b), the reconstructed image is noisy, which is the main drawback of using this method.

Figure 10.Diagnoses of unstained peripheral-blood film (PBF), photographed by an automatic image contour analysis system (ELBEK GmbH, Siegen, Germany) with a magnification of 1200×. (a) Captured 2D image (b) 3D pseudocolor intensity-distribution image of (a), after construction and filtration by the windowed Fourier filtering (WFF) method, threshold = 150.

Figure 11.Reconstruction before filtration with the windowed Fourier filtering (WFF) method (a) Typical phase hologram used for reconstruction of the 2D image of Fig. 10(a). (b) Optical reconstruction of (a).

We overcome this problem by using the WFF method. To see the performance of the WFF method in suppressing the noise, two cells (one WBC and one RBC) are studied before and after applying the WFF. The WBC is within the white solid rectangles of Figs. 10(b) and 11(b), and the RBC is within the white dashed rectangles. Figure 12(a) shows the selected solid rectangle of Fig. 10(b), before filtering with WFF.

Figure 12.Noise estimation. (a) 3D pseudocolor of the solid white rectangle of Fig. 10(b), before correction with windowed Fourier filtering (WFF). (b) A filtered image of (a) using WFF. (c) 3D pseudocolor of the dashed white rectangle of Fig. 10(b), before correction with WFF. (d) A filtered image of (c) using WFF.

Figure 12(b) shows the filtered image of Fig. 12(a). Figure 12(c) shows the selected dashed rectangle of Fig. 10(b), before correction with WFF. Figure 12(d) shows the filtered image of Fig. 12(c). The threshold value for both Figs. 12(b) and 12(d) is 150. Figure 13(a) shows the difference between Figs. 12(a) and 12(b). The difference in σ is calculated in MATLAB as STD2(diff), and the value is found to be 18.67, which means that the noise level is suppressed by approximately 50% at a threshold value of 150. Figure 13(b) shows the difference between Figs. 12(c) and 12(d). The difference in σ is calculated to be 17.13, which means that the noise level is suppressed by approximately 40% at the threshold value of 150.

Figure 13.Noise estimation. (a) Difference between Figs. 12(a) and 12(b). (b) Intensity profile along the black line of (a).

The 10% difference between Figs. 13(a) and 13(b) is just due to the fact that the WBC is bigger in area than the RBC. The area of Figs. 12(a) and 12(b) is 200 × 400 pixels, while the area of Figs. 12(c) and 12(d) is 120 × 190 pixels. As seen in Fig. 10(b), the cells in the PBF are viewed clearly in 3D with no contrast agents, and the PBF shows uniformity in the cell morphology [21]. The WBC in the white solid rectangle in Fig. 10(b) is bigger in area than the RBC in the white dashed rectangle, which confirms that the selected cell in the solid rectangle of Fig. 10(b) is reliably a WBC. The WBC in the solid white rectangle of Fig. 10(b) looks to be of the macrophage type. This type of cell has the ability to eliminate foreign substances by engulfing them and initiating an immune response [6]. The merit of the proposed nondestructive technology is that it can be used for viewing all types of WBCs, with no contrast agents. Moreover, the cells are viewed in 3D, which means more details about the images are obtained.

In conclusion, we have presented a simple optical setup based on phase-hologram generation, for the diagnosis of unstained blood cells. The optical setup included a phase-only SLM to display the generated phase hologram, and a FL for reconstruction. Since noise is the main problem in this method, we used the WFF method to mitigate the noise as much as possible. The WFF method reduced the level of noise in the reconstructed image by approximately 40%. The proposed optical system can be utilized to study WBCs in various disease conditions. The merit of the proposed technique is that it does not require the use of exogenous labeling agents or staining procedures. Moreover, it does not require one to separate the WBCs before visualization.

The author declares no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the author upon reasonable request.

This paper is based upon work supported by Science, Technology & Innovation Funding Authority (STDF) under a grant (40490).

Science, Technology & Innovation Funding Authority (STDF) under Grant no. (40490).

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### Article

#### Article

Curr. Opt. Photon. 2022; 6(6): 598-607

Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.598

Copyright © Optical Society of Korea.

## Diagnosis of Unstained Biological Blood Cells Using a Phase Hologram Displayed by a Phase-only Spatial Light Modulator and Reconstructed by a Fourier Lens

Dahi Ghareab Abdelslam Ibrahim

Engineering and Surface Metrology Lab., National Institute of Standards, El haram, El Giza 12211, Egypt

Correspondence to:*dahi.abdelsalam@nis.sci.eg, ORCID 0000-0002-4429-5096

Received: April 18, 2022; Revised: June 28, 2022; Accepted: July 18, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

In this paper, a simple nondestructive technology is used to investigate unstained biological blood cells in three dimensions (3D). The technology employs a reflective phase-only spatial light modulator (SLM) for displaying the phase hologram of the object being tested, and a Fourier lens for its reconstruction. The phase hologram is generated via superposing a digital random phase on the 2D image of the object. The phase hologram is then displayed by the SLM with 256 grayscale levels, and reconstructed by a Fourier lens to present the object in 3D. Since noise is the main problem in this method, the windowed Fourier filtering (WFF) method is applied to suppress the noise of the reconstructed object. The quality of the reconstructed object is refined and the noise level suppressed by approximately 40%. The technique is applied to objects: the National Institute of Standards (NIS) logo, and a film of unstained peripheral blood. Experimental results show that the proposed technique can be used for rapid investigation of unstained biological blood cells in 3D for disease diagnosis. Moreover, it can be used for viewing unstained white blood cells, which is still challenging with an optical microscope, even at large magnification.

Keywords: 3D reconstruction, Cell analysis, Noise reduction, Phase hologram, Spatial light modulator

### I. INTRODUCTION

Blood plays an important role in the body’s homeostasis, the circulation of nutrients and removal of waste, the distribution of hormones, and the elimination of excess heat [1]. Blood consists of several components, including red blood cells (RBCs), platelets, plasma, and white blood cells (WBCs). The characterization of RBCs and WBCs is crucial for disease diagnosis. The characterization of RBCs is important for understanding the pathophysiology of many diseases, including anemia and heart diseases [2]. The characterization of WBCs is important for the detection of different diseases such as lymphoma, COVID-19, and cancer [3, 4]. WBCs play various roles in defending the host from invaders and abnormal cells [5, 6]. WBCs are classified into different types according to their morphologies and functions in the immune system. Viewing a two-dimension (2D) image of WBCs clearly under an optical microscope requires special stains. Such stains require chemical fixation procedures, which limit live-cell analysis. Confocal fluorescence microscopy enables the three dimension (3D) structural images of living WBCs [7], but with chemical staining procedures that inevitably present significant drawbacks, such as phototoxicity and photobleaching. A different approach by measuring 3D refractive-index maps of the WBCs was proposed [6], but the technique is based on the separation of a specific type of WBCs from RBCs. In this paper, a simple nondestructive technology for viewing unstained WBCs clearly in 3D is presented. The technology includes an spatial light modulator (SLM), which displays the phase hologram of the object being investigated. The phase hologram is generated by superposing a random phase upon the object being investigated. There are typically three types of computer-generated holograms (CGHs) [8, 9]: phase-only, where the material modulates only the phase of an incoming wavefront, and the transmittance amplitude is unity; amplitude-only, where the material modulates only the amplitude of an incoming wavefront, and the transmittance phase is constant; and complex-amplitude, where the material modulates both phase and amplitude of an incoming wavefront. The detour-phase hologram has the capability to encode the amplitude and phase of the complex hologram [10]. The drawback of the detour method is that the diffraction efficiency is low. For this reason we used the phase-only CGH technique [11], which has a higher diffraction efficiency than the detour method. The only drawback of the phase-only CGH technique is that the reconstructed object is noisy. We overcome the problem of noise by using the windowed Fourier filtering (WFF) algorithm. The effectiveness of the proposed method is proved by simulations and real experiments.

In this paper, two objects are studied: The first is a simulated National Institute of Standards (NIS) logo, and the second is unstained peripheral-blood film (PBF). The PBF includes both RBCs and WBCs taken from the eye vein of a male albino rat. All guidelines for the care and use of animals are followed and approved by the Institutional Animal Care and Use Committee (CU-IACUC) of Cairo University (approval number CUIFC3220). The preparation of the PBF is carried out following the Brown procedures [12]. The PBF is photographed using an automatic image contour analysis system (SAMICA) (ELBEK GmbH, Siegen, Germany) with a magnification of 1200X. The phase hologram is then generated by superposing a random phase on the 2D image being investigated. The phase hologram is then displayed by the SLM and reconstructed by the Fourier Lens (FL). The reconstructed image is then enhanced against noise using the WFF algorithm. Experimental results show that unstained WBCs on the surface of the PBF can be viewed clearly in 3D. Moreover, the quality of the reconstructed object is good, since the noise level is suppressed by approximately 40% using the WFF method. The proposed method does not require the separation of WBCs from RBCs to see the WBCs clearly. Moreover, it does not require direct handling of the sample, just a 2D photograph of the sample by a high-magnification microscope. To the best of our knowledge, this is the first time that reconstruction by FL and SLM with filtration by WFF is used to view unstained WBCs clearly.

### 2.1. Phase-only Computer-generated Hologram

In the phase-only CGH, for a typical object a random phase pattern can be superposed without affecting the irradiance distribution. If tpq denotes the transmittance of the cell corresponding to the Fourier coefficient |hpq| and phase ϕpq, then

$tpq=hpqexpjϕpq≈expjϕpq$

where |hpq| denotes the amplitude of the Fourier transform, and ϕpq denotes its phase. Therefore, the reconstructed object has the following form:

$Obj=ℑx,y−1expjϕ pq$

where ℑx,y−1 denotes the operator for the inverse 2D Fourier transform. A typical algorithm for the phase-only technique is shown in Fig. 1.

Figure 1. Flowchart for the phase-only computer-generated hologram (CGH) method.

### 2.2. Windowed Fourier Filtering

WFF gives a filtered image. The output of WFF is usually a complex field, and its real part should be used [13–15]. Since the reconstructed object is noisy, it is necessary to suppress the noise to see the reconstructed object clearly. A great number of approaches have been developed to overcome the problem of noise in the reconstruction process [16, 17], each with its own merits and demerits. In this study, WFF is selected to enhance the image because it does not require dark and flat images, like the flat-fielding approach does.

The reconstructed object Obj expressed in Eq. 2 is convolved with the windowed Fourier transform (WFT), the equation for which can be expressed as:

$WFTfx,fy=∫−∞+∞ ∫ −∞ +∞ Obj x,yr∗ x,ydxdy,$

where r(x, y) = exp[−x2 / 2σx2y2 / 2σy2] is the Gabor transform, which is a Gaussian function, and the symbol * denotes complex conjugation. Here σx = 10 and σy = 10 are the standard deviations of the Gaussian function in the x and y directions respectively. By shifting the central position of the Gaussian window point by point and computing the WFT of the signal, the fundamental spectral component of each local signal can be extracted. Then, by integrating all of these spectral components, a universal spectral component can be retrieved as:

$∫−∞+∞ ∫ −∞ +∞ WFT f0,f0 dxdy=F f0,f0$

Finally, applying the inverse Fourier transform to the universal spectral component, a complex image is obtained. The real values of the complex image are taken to provide a filtered image, which is free from noise.

Using this algorithm, the phase holograms of two objects are generated. The first object is a simulated NIS logo, and the second object is an unstained PBF. Figure 2(a) shows a simulated 2D image of the NIS logo.

Figure 2. Simulation for illustration. (a) A simulated National Institute of Standards (NIS) logo. (b) Phase spectrum. (c) Amplitude spectrum. (d) Digitally reconstructed image from the phase hologram. (e) A filtered image of (d) using windowed Fourier filtering (WFF) at threshold = 100. (f) Intensity profiles along the red and blue lines of (d) and (e).

Figure 2(b) shows the phase hologram generated after superposing a digital random phase [rand (x, y)] on the 2D image of Fig. 2(a). Figure 2(c) shows the amplitude spectrum of Fig. 2(a). Figure 2(d) shows the numerical reconstruction of Fig. 2(b). As seen in Fig. 2(d), the reconstructed image is noisy. As mentioned in the introduction, the phase-only technique has a higher diffraction efficiency than the detour method, but the reconstructed object is noisy. The WFF technique is used to reduce this noise as much as possible. To calculate the significance of using the WFF in terms of noise reduction, we used the standard-deviation function (std2) in MATLAB to quantify the noise. Std2(A) computes the standard deviation of all values in array A. std2 (also called σ) for Fig. 2(d) is calculated to be 61.39. Figure 2(e) shows the filtered image of Fig. 2(d) using the WFF technique. Its value of σ is calculated to be 35.70. The profiles along the red and blue lines of Figs. 2(d) and 2(e) are extracted and plotted in Fig. 2(f). The time taken to extract the filtered image is around three seconds, using a personal computer with 8 GB of RAM and a 2.9-GHz processor. The unit of the extracted intensity is arbitrary (a.u.). Figure 3(a) shows the difference between Figs. 2(d) and 2(e). The difference in σ is calculated in MATLAB as STD2(diff), and the value is calculated to be 25.69, which means that the noise level is suppressed by approximately 42% at a threshold of 100. The value of threshold is selected by trying many values in the WFT algorithm until a filtered image is obtained. Figure 3(b) shows the intensity profile along the black line of Fig. 3(a).

Figure 3. Noise estimation. (a) Difference between Figs. 2(d) and 2(e). (b) Intensity profile along the black line of (a).

The simulation and numerical reconstruction of Fig. 2 are supposed to be free from the effects of flat-field correction and pixel crosstalk in the SLM. The effects of flat-field correction and pixel crosstalk are explained in detail in references [16–19]. Experimentally, these effects should be accounted for via calibration of the SLM. Here we proposed a simple method for calibration, employing a half-wave plate fixed at the fast axis and a polarizer fixed at 180°.

### 2.3. Calibration of the SLM

Figure 4(a) shows a schematic diagram of the optical setup proposed for calibration of the SLM [20].

Figure 4. Spatial light modulator (SLM) calibration. (a) Schematic diagram of the optical setup for spatial light modulator (SLM) calibration. (b) Obtained results: experimental (red) and simulated (blue) profiles.

A light-emitting diode (LED) source emits a beam of light at 635 nm. The beam is expanded to illuminate the SLM window. A half-wave plate (λ/2) fixed at the fast axis is placed prior to the SLM, and a uniform sheet of grayscale levels from 0 to 255 is displayed on the window of the SLM. We generated 14 intensity images from 0 to 252 levels in steps of 18 intervals. The generated images are captured by the charge-coupled device (CCD) camera. At the center of each captured image, the average intensity of an array of 15 × 15 pixels is measured. The obtained intensity values are plotted against the corresponding phase (in radians), and the result is the experimental wave that characterizes the intensity recorded by the CCD camera due to a change in the grayscale values displayed on the SLM. The experimental wave is simulated to compensate for the noise. Figure 4(b) shows the obtained experimental profile (in red), which looks noisy. To quantify this noise, a simulated profile (in blue) is generated to compensate for the noise attached to the experimental profile. The simulated profile equation is generated as I = 9 sin (1.35x + 3.09) + 30, where x is a linear spaced vector defined in Matlab as linspace (0, 2π, 1,000) with 1,000 generated points. As seen in Fig. 4(b), the results of the first half (from 0 to π) of the profile are rather matching, while in the second half of the profile (from π to 2π) the results deviate a bit, as seen in the black dashed arrows. Such deviations may come from instability of the laser light. We claim that such deviations may be reduced by using the WFF method.

### III. EXPERIMENTAL RESULTS

The proposed holographic projection system is depicted in Fig. 5(a). It utilizes a laser diode (LD) with a wavelength of λ = 635 nm, which is expanded and collimated by a beam expander (BE) to illuminate the SLM window (resolution 1,920 × 1,080 pixels, pixel pitch 8 µm, model Pluto; Photonics AG, Berlin, Germany).

Figure 5. Experiment of the holographic projection system (a) Schematic diagram. (b) Reconstruction illustration of the computer-generated hologram.

The SLM is placed at the front focal plane of a Fourier lens (FL = 120 mm). A polarizer (P) and analyzer (A) are placed before and after the SLM, to select the correct polarization state with respect to the SLM’s slow axis. A CCD camera is placed at the back focal plane of the FL, to capture the reconstructed object.

Here we experimentally investigate two samples: the NIS logo, and a PBF image that includes unstained white and RBCs. For the first example, the phase hologram of Fig. 2(b) is displayed on the window of a reflection SLM. The reconstructed object from one phase hologram is shown in Fig. 6(a). The reconstructed object has been corrected by WFF and the image filtered at a threshold of 240 is shown in Fig. 6(b). Figure 6(c) shows the 3D pseudocolor of Fig. 6(b).

Figure 6. Reconstruction of the simulated National Institute of Standards (NIS). (a) Reconstructed object of one phase hologram of Fig. 2(b) using spatial light modulator (SLM) and Fourier lens. (b) A filtered image of (a), using windowed Fourier filtering (WFF) at threshold = 240. (c) 3D pseudocolor of (b).

As seen in Fig. 6(a), σ is found to be 18.77, while σ for Fig. 6(b) is 4.16. The difference in σ is 18.77− 4.16 = 14.61, which means that the noise level is suppressed by approximately 39%. Figure 7(a) shows the difference between Figs. 6(a) and 6(b), and Figure 7(b) shows the intensity profile along the black line of Fig. 7(a). Figure 8(a) shows the reconstructed NIS object from an average of ten phase holograms using SLM and FL. Figure 8(b) shows the filtered image of Fig. 8(a) using the WFF method. The 3D pseudocolor of Fig. 8(b) is shown in Fig. 8(c). The profiles along the red and blue lines of Figs. 8(a) and 8(b) are extracted and plotted as shown in Fig. 8(d). As seen in Fig. 8(a), σ is found to be 10.72, while σ for Fig. 8(b) is 6.52. The difference in σ is 10.72 − 6.52 = 4.20, which means that the noise level is suppressed by approximately 39%.

Figure 7. Noise estimation. (a) Difference between Figs. 6(a) and 6(b). (b) Intensity profile along the black line of (a).

Figure 8. Reconstruction of National Institute of Standards (NIS) from average of ten phase holograms. (a) Reconstructed object from an average of ten phase holograms using spatial light modulator (SLM) and Fourier lens. (b) A filtered image of (a) using WFF at threshold = 240. (c) 3D pseudocolor of (b). (d) Intensity profiles along the red and blue lines of (a) and (b).

Figure 9(a) shows the difference between Figs. 8(a) and 8(b). Figure 9(b) shows the intensity profile along the black line of Fig. 9(a).

Figure 9. Noise estimation. (a) Difference between Figs. 8(a) and 8(b). (b) Intensity profile along the black line of (a).

The second sample is a peripheral blood film (PBF) image, which includes unstained white and RBCs. PBF is a valuable diagnostic and monitoring tool that is commonly used in the characterization of many clinical diseases, and in assessing their progression [4]. In this study the PBF is prepared and then photographed using an automatic image contour analysis system (SAMICA) (ELBEK GmbH). The system is provided with an electronic camera connected to a computer through a built-in interface card, and the image can be magnified up to 1200× and displayed by the computer. The blood sample is collected and taken from a male albino rat (age about 2 months and average weight ≈150 g). All guidelines for the care and use of animals are followed and approved by the Institutional Animal Care and Use Committee (CU-IACUC) of Cairo University (approval number CUIFC3220).

The rat is anesthetized with ether, and then a blood sample is collected from the eye vein by heparinized capillary tubes to view unstained WBCs and RBCs. Figure 10(a) shows a magnified image of the PBF, which includes RBCs and WBCs. The size of the image in Fig. 10(b) is 550 × 560 pixels. As seen in Fig. 10(a), the RBCs appear clearly, while the WBCs cannot be viewed. As seen in Fig. 10(b), both the RBCs and WBCs are clearly viewed in 3D, with no contrast agents added to the PBF sample. Figure 11(a) shows the phase hologram of the 2D image of Fig. 10(a). As seen in the hologram, the phase range is from 0 to 255, which matches the phase range of the SLM. Figure 11(b) shows the optical reconstruction of Fig. 11(a) using the FL. As seen in Fig. 11(b), the reconstructed image is noisy, which is the main drawback of using this method.

Figure 10. Diagnoses of unstained peripheral-blood film (PBF), photographed by an automatic image contour analysis system (ELBEK GmbH, Siegen, Germany) with a magnification of 1200×. (a) Captured 2D image (b) 3D pseudocolor intensity-distribution image of (a), after construction and filtration by the windowed Fourier filtering (WFF) method, threshold = 150.

Figure 11. Reconstruction before filtration with the windowed Fourier filtering (WFF) method (a) Typical phase hologram used for reconstruction of the 2D image of Fig. 10(a). (b) Optical reconstruction of (a).

We overcome this problem by using the WFF method. To see the performance of the WFF method in suppressing the noise, two cells (one WBC and one RBC) are studied before and after applying the WFF. The WBC is within the white solid rectangles of Figs. 10(b) and 11(b), and the RBC is within the white dashed rectangles. Figure 12(a) shows the selected solid rectangle of Fig. 10(b), before filtering with WFF.

Figure 12. Noise estimation. (a) 3D pseudocolor of the solid white rectangle of Fig. 10(b), before correction with windowed Fourier filtering (WFF). (b) A filtered image of (a) using WFF. (c) 3D pseudocolor of the dashed white rectangle of Fig. 10(b), before correction with WFF. (d) A filtered image of (c) using WFF.

Figure 12(b) shows the filtered image of Fig. 12(a). Figure 12(c) shows the selected dashed rectangle of Fig. 10(b), before correction with WFF. Figure 12(d) shows the filtered image of Fig. 12(c). The threshold value for both Figs. 12(b) and 12(d) is 150. Figure 13(a) shows the difference between Figs. 12(a) and 12(b). The difference in σ is calculated in MATLAB as STD2(diff), and the value is found to be 18.67, which means that the noise level is suppressed by approximately 50% at a threshold value of 150. Figure 13(b) shows the difference between Figs. 12(c) and 12(d). The difference in σ is calculated to be 17.13, which means that the noise level is suppressed by approximately 40% at the threshold value of 150.

Figure 13. Noise estimation. (a) Difference between Figs. 12(a) and 12(b). (b) Intensity profile along the black line of (a).

The 10% difference between Figs. 13(a) and 13(b) is just due to the fact that the WBC is bigger in area than the RBC. The area of Figs. 12(a) and 12(b) is 200 × 400 pixels, while the area of Figs. 12(c) and 12(d) is 120 × 190 pixels. As seen in Fig. 10(b), the cells in the PBF are viewed clearly in 3D with no contrast agents, and the PBF shows uniformity in the cell morphology [21]. The WBC in the white solid rectangle in Fig. 10(b) is bigger in area than the RBC in the white dashed rectangle, which confirms that the selected cell in the solid rectangle of Fig. 10(b) is reliably a WBC. The WBC in the solid white rectangle of Fig. 10(b) looks to be of the macrophage type. This type of cell has the ability to eliminate foreign substances by engulfing them and initiating an immune response [6]. The merit of the proposed nondestructive technology is that it can be used for viewing all types of WBCs, with no contrast agents. Moreover, the cells are viewed in 3D, which means more details about the images are obtained.

### IV. CONCLUSION

In conclusion, we have presented a simple optical setup based on phase-hologram generation, for the diagnosis of unstained blood cells. The optical setup included a phase-only SLM to display the generated phase hologram, and a FL for reconstruction. Since noise is the main problem in this method, we used the WFF method to mitigate the noise as much as possible. The WFF method reduced the level of noise in the reconstructed image by approximately 40%. The proposed optical system can be utilized to study WBCs in various disease conditions. The merit of the proposed technique is that it does not require the use of exogenous labeling agents or staining procedures. Moreover, it does not require one to separate the WBCs before visualization.

### DISCLOSURES

The author declares no conflicts of interest.

### DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the author upon reasonable request.

### ACKNOWLEDGMENT

This paper is based upon work supported by Science, Technology & Innovation Funding Authority (STDF) under a grant (40490).

### FUNDING

Science, Technology & Innovation Funding Authority (STDF) under Grant no. (40490).

### Fig 1.

Figure 1.Flowchart for the phase-only computer-generated hologram (CGH) method.
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 2.

Figure 2.Simulation for illustration. (a) A simulated National Institute of Standards (NIS) logo. (b) Phase spectrum. (c) Amplitude spectrum. (d) Digitally reconstructed image from the phase hologram. (e) A filtered image of (d) using windowed Fourier filtering (WFF) at threshold = 100. (f) Intensity profiles along the red and blue lines of (d) and (e).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 3.

Figure 3.Noise estimation. (a) Difference between Figs. 2(d) and 2(e). (b) Intensity profile along the black line of (a).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 4.

Figure 4.Spatial light modulator (SLM) calibration. (a) Schematic diagram of the optical setup for spatial light modulator (SLM) calibration. (b) Obtained results: experimental (red) and simulated (blue) profiles.
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 5.

Figure 5.Experiment of the holographic projection system (a) Schematic diagram. (b) Reconstruction illustration of the computer-generated hologram.
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 6.

Figure 6.Reconstruction of the simulated National Institute of Standards (NIS). (a) Reconstructed object of one phase hologram of Fig. 2(b) using spatial light modulator (SLM) and Fourier lens. (b) A filtered image of (a), using windowed Fourier filtering (WFF) at threshold = 240. (c) 3D pseudocolor of (b).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 7.

Figure 7.Noise estimation. (a) Difference between Figs. 6(a) and 6(b). (b) Intensity profile along the black line of (a).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 8.

Figure 8.Reconstruction of National Institute of Standards (NIS) from average of ten phase holograms. (a) Reconstructed object from an average of ten phase holograms using spatial light modulator (SLM) and Fourier lens. (b) A filtered image of (a) using WFF at threshold = 240. (c) 3D pseudocolor of (b). (d) Intensity profiles along the red and blue lines of (a) and (b).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 9.

Figure 9.Noise estimation. (a) Difference between Figs. 8(a) and 8(b). (b) Intensity profile along the black line of (a).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 10.

Figure 10.Diagnoses of unstained peripheral-blood film (PBF), photographed by an automatic image contour analysis system (ELBEK GmbH, Siegen, Germany) with a magnification of 1200×. (a) Captured 2D image (b) 3D pseudocolor intensity-distribution image of (a), after construction and filtration by the windowed Fourier filtering (WFF) method, threshold = 150.
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 11.

Figure 11.Reconstruction before filtration with the windowed Fourier filtering (WFF) method (a) Typical phase hologram used for reconstruction of the 2D image of Fig. 10(a). (b) Optical reconstruction of (a).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 12.

Figure 12.Noise estimation. (a) 3D pseudocolor of the solid white rectangle of Fig. 10(b), before correction with windowed Fourier filtering (WFF). (b) A filtered image of (a) using WFF. (c) 3D pseudocolor of the dashed white rectangle of Fig. 10(b), before correction with WFF. (d) A filtered image of (c) using WFF.
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

### Fig 13.

Figure 13.Noise estimation. (a) Difference between Figs. 12(a) and 12(b). (b) Intensity profile along the black line of (a).
Current Optics and Photonics 2022; 6: 598-607https://doi.org/10.3807/COPP.2022.6.6.598

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Wonshik Choi,
Editor-in-chief