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Abstract
Digital holographic microscopy (DHM) is a powerful quantitative phase imaging (QPI) technique that is capable of recording sample's phase information to enhance image contrast. In off-axis DHM, high-quality QPI images can be generated within a single recorded hologram, and the system stability can be enhanced by common-path configuration. Diffraction gratings are widely used components in common-path DHM systems; however, the presence of multiple diffraction beams leads to system power loss. Here, we propose and demonstrate implementation of a volume holographic grating (VHG) in common-path DHM, which provides single diffraction order. VHG in common-path DHM (i.e., VHG-DHM) helps in improving signal-to-noise ratio as compared to the conventional DHM. In addition, VHG, with inherently high angular selectivity, reduces image noise caused by stray light. With a simple fabrication process, it is convenient to utilize VHG to control the beam separation angle of DHM. Further, by using Bragg-matched wavelength degeneracy to avoid potential cell damaging effect in blue light, the VHG is designed for recording at a maximum sensitive wavelength of ∼488 nm, while our VHG-DHM is operated at the longer wavelength of red 632.8 nm for cell observation. Experimental results, measured by the VHG-DHM, show the measurement of target thickness ranging from 100 nm to 350 nm. In addition, stability of the system is quantitatively measured. High-contrast QPI images of human lung cancer cells are demonstrated.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the fields of biomedical imaging, to enhance image contrast of transparent samples is always a crucial concern. Transparent samples, for example living cells, under conventional brightfield microscopy, often suffer poor image contrast due to low index changes and minimal intensity variation. The common methods to enhance intensity contrast involve using specific chemical dyes to stain various parts of the sample, enabling samples to be visualized and distinguished under a microscope [1]. However, the staining process’s fixation, permeabilization steps, or phototoxicity are not suitable for observing living cells. It is important to note that when light passes through different thickness distributions within transparent samples, it can lead to varying optical path differences, consequently causing phase variations. Although phase variations for cell observation is hardly detected by conventional brightfield microscopy, standard phase contrast imaging is able to observe minimal phase changes [2,3]. However, phase contrast images offer only qualitative information, and lack of quantitative values. Quantitative phase imaging (QPI) provides an alternate solution and provides quantitative information of sample's phase map under label-free and non-invasive conditions, making it widely applicable in many living cell and cell growth studies [4,5].
Digital holographic microscopy (DHM) is one of the QPI techniques that utilize interferometry to generate holograms [6,7]. The hologram is formed by mutually interfering two beams. One beam carries sample information acting as the object beam, and the other with uniform wavefront acting as the reference beam. The hologram is then digitally recorded by the charge-coupled device (CCD) and reconstructed by digital processing [6]. In DHM, the hologram stores comprehensive wavefront information, including both amplitude and quantitative phase details. This enables reconstruction of propagation complex field by applying diffraction theory [8,9]. DHM has a wide range of applications including, surface profilometry [10,11], cell diagnosis [12–14], metrology [15,16], and biomedical imaging [17,18]. DHM with in-line configuration suffers from DC background term and twin images, leading to image quality degradation due to those undesired signals. DHM with off-axis configuration becomes the most common method since it separates the desired signal from the undesired background DC noise and twin images [8]. In the off-axis DHM, the hologram is modulated with the carrier frequency by setting the object beam and the reference beam with an offset angle. The conventional type of the off-axis DHM is based on the Mach-Zehnder interferometer [19] or Michelson-type interferometer [20] where two beams propagate along entirely independent paths, and thus fringe vibration from environmental fluctuations leads to noise error. To overcome this issue, off-axis DHM methods based on common-path setup have been proposed [21]. The common-path interferometer is based on the concept is to let two beams travel nearly the same optical path to make the system more stable and insensitive from environmental fluctuations.
The common-path DHM setups can be realized by various beam-splitting elements, such as, shear plate [22,23], Lloyd’s mirror [24], wedge plate [25], beam splitter [26], Fresnel biprism [27,28], Wollaston prism [29], and diffraction grating [30–33]. However, those components have certain drawbacks. For example, the glass plate used for the shear plate has low reflectivity, leading to a significant loss of laser power. Recently, the Fresnel biprism has been widely used in the common-path DHM setup because it can split light into equal halves with nearly no power loss. However, the inclination angle of beams makes the imaging plane not parallel with the camera plane, which may lead to aberrations and degradation in image quality. Also, the Wollaston prism needs additional polarization components for splitting the beam and generating interference patterns [29]. Diffraction phase microscopy is another classic type of common-path DHM setup that utilizes diffraction grating [30,31]. The zero-order and first-order grating diffraction beams are employed as the hologram's object and reference beams. However, conventional diffraction gratings suffer from significant power loss due to multiple diffraction orders. In order to eliminate multi-order diffraction and to improve diffraction efficiency, we propose the implementation of a volume holographic grating (VHG) in the common-path DHM setup.
VHG is essentially a thick grating, compared with multiple diffraction orders of the most common characteristics of thin gratings or Ronchi ruling grating [33]. VHGs exhibit high Bragg angular and spectral selectivity. With proper design and fabrication, only single beam is diffracted by the VHG with high diffraction efficiency [34,35] at specific angles and wavelengths that satisfy well-known Bragg condition [34]. With such unique diffraction characteristics, VHGs have been applied in a variety of biomedical imaging systems, including confocal microscopy [36], optical sectioning microscopy [37], light sheet microscopy [38], and beam shaping [34]. In this work, we incorporate the VHG in an off-axis DHM system with a simple common-path configuration. The zero-order term generated by the VHG is applied as an object beam, and the first-order term is applied as a reference beam after pinhole filtering. Without multiple undesired diffraction beams, our VHG-DHM and provide good system stability. Higher light intensity can enhance the signal-to-noise ratio of the captured hologram. In addition, flexible design process of the key component VHGs is convenient to fabricate any desired separate angle between two beams in common-path DHM. The quantitative phase imaging performance of our proposed system has been evaluated by measuring thickness of standard phase targets, as well as phase distribution of human lung cancer cells.
2. Volume holographic grating
To form the VHG for our common-path VHG-DHM, PQ-PMMA photosensitive material is prepared. Both PQ (phenanthrenequinone) and AIBN (2-methyl propionitrile) are first mixed with liquid MMA (methyl methacrylate) at a constant temperature of 40°C. Then mixed liquid is put into the oven at 50 °C and cured for 120 hours. After the heat-curing process, the PQ-PMMA with approximately 2.3 mm thickness are well prepared as VHG recording photo-sensitive material. After the recorded PQ-PMMA is dark diffusion and fixing, its material characteristics will be fixed and cannot be reused for the recording. However, as long as VHG is properly preserved, it can be utilized for a very long time. Also, the PQ-PMMA fabricated process is very simple and low-cost. Normally, an adequate amount of PQ-PMMA material can be manufactured in a single production cycle and preserved for later use. More details of the PQ-PMMA preparation procedure is described in our previous work [39].
In the VHG recording process, a 488 nm laser (Innova 304C, Coherent Inc.) is used to meet material-sensitive wavelength requirement. A K-sphere diagram for recording VHG is depicted in Fig. 1(a). The laser light source is collimated into plane waves and separated into two beams by the beam splitter. One beam is incident on the PQ-PMMA material at an oblique angle, while the other is with normal incidence. The two beams are interfered within overlapping region on the PQ-PMMA to form a VHG. The grating vectors ${\vec{K}_G}$ of the VHG can be expressed as
and the two recording beam’s wave vectors ${\vec{K}_{r,1}}$ and $\; {\vec{K}_{r,2}}$ is given by ${\theta _{r,1}}\; \textrm{and}\; {\theta _{r,2}}$ are the incident angles of the two recording beams, and the two angles are 0° and 16°, respectively. k is the wavenumber, which is equal to $\frac{{2\pi }}{{{\lambda _o}}}$, and ${\lambda _o}$ is the recording operation wavelength with 488 nm. After dark diffusion and fixing the recorded PQ-PMMA, the VHG is obtained. In the reconstruction, the probe beam is selected with wavelength ${\lambda _p}$ and incident angle ${\theta _p}$ to match the Bragg condition which is described as where $\varphi $ is the angle between the ${\vec{K}_G}$ and the z-axis, and n is the refraction index. As the Bragg condition is matched, the detuning parameter $\vartheta $ for Bragg mismatched condition is reduced to zero, and the diffracted signal beam provides high diffraction efficiency. The detuning parameter $\vartheta $ is described byIn this work, VHG is integrated in the common-path DHM to form VHG-DHM system. It is worth mentioning that the VHG is recorded at PQ-PMMA’s maximum sensitive wavelength at ∼488 nm. However, to avoid potential cell damaging effect in blue light, it is operated in our VHG-DHM system at the wavelength of ${\lambda _p}$= 632.8 nm for cell imaging, based on Bragg matched condition (Eq. (4)) as shown in Fig. 1(b). The diffraction efficiency is 73% for the first-order beam, and 17% for the zero-order beam. Both zero-order for and first-order diffraction beams are utilized in our VHG-DHM approach: the former is used as the object beam and the latter as the reference beam.
Fig. 1. The K-sphere diagram for both VHG recording and reconstruction. (a) VHG recorded on PQ-MMA in 488 nm wavelength. ${\vec{K}_{r,1}}$ and ${\vec{K}_{r,2}}$ are the wave vector of recording beams, and the ${\vec{K}_G}$ is the wave vector of the generated VHG. (b) VHG reconstruction at 632.8 nm wavelength, the ${\vec{K}_p}$ and ${\vec{K}_d}$ denotes the wave vector of probe and diffraction beams.
3. Principle of digital holographic microscopy
DHM digitally record the interference of two beams through a CCD. The complex fields of the object beam ($O$) and the reference beam ($R$) are described as
where ${A_o}({x,y} )$ and ${\phi _o}({x,y} )$ are the amplitude and phase distribution of the object beam, respectively. The reference beam ($R$) is a uniform plane wave, and the amplitude distribution of the reference beam ${A_r}$ is constant. In off-axis DHM setup, the reference beam is tilted with an offset angle ($\mathrm {\theta}$). In our case, the beam is tilted only in the x direction, and thus ${e^{i{\phi _r}}} = {e^{jksin (\mathrm {\theta} )x}}$. While the object beam and reference beam overlap on the CCD, the recorded hologram intensity distribution (${I_H}$) is described as4. Experimental setup
The system configuration of our proposed common-path VHG-DHM is shown in Fig. 2. A He-Ne laser with 632.8 nm wavelength is collimated into the plane wave by a spatial filter and a lens (L1). A sample is illuminated by the collimated He-Ne laser, and sample scattered beam is collected by an objective lens (MO, NA = 0.4). Subsequently, two relay systems are used. The first relay comprising lenses L2 (f = 50 mm) and L3 (f = 50 mm) is to convert the optical path from vertical to parallel with the optical table. In the second relay consisting of L4 (f = 33 mm) and L5 (f = 33 mm), the recorded VHG is inserted between two lenses (L4 and L5) to diffract light into zero and first order beams. A pinhole with a diameter of 25 µm is positioned at the Fourier plane of L5 to filter out the object information and becomes the uniform spherical wave. We then utilize filtered first-order beams as the reference beam, and the zero-order beams as object beams. Finally, after two beams pass through the tube lens (TL, f = 180 mm) the first-order and zero-order beams overlap, and interfered hologram is recorded digitally on the CCD sensor.
Fig. 2. The proposed schematic of the common-path VHG-DHM. SF: spatial filter; L: lens; M: mirror; MO: microscope objective lens; VHG: volume holographic grating; TL: tube lens; CCD: charge-coupled device.
5. Experimental results
To verify quantitative phase imaging ability of the VHG-DHM, a raw hologram of the USAF resolution phase target is captured by CCD. The hologram size is 1024 × 768 pixels, with a pixel pitch of 4.65 µm. The interference fringe is clearly seen in the hologram image as shown in Fig. 3(a). Due to the transparent property of the phase target, Fig. 3(a) shows low contrast in its intensity information. To extract phase information, the reconstruction procedure discussed above is applied. Hence, Fig. 3(b) shows the corresponding hologram spectrum after Fourier transformation. In the spectrum, due to the offset angle ($\mathrm {\theta} $) described in Eq. (9), there are the zero, first, and minus order components, which correspond to the hologram's DC, primary, and conjugate terms. The first order is selected as our desired signal. The circular filter is applied to filter out the first-order signal and center it to the baseband. After applying inverse Fourier transform, the reconstructed phase information of the target is obtained. However, the initial reconstructed phase imaging shown in Fig. 4(a) suffers the background noise distribution. To remove the background noise, the blank region hologram shown in Fig. 4(b) is recorded as the reference hologram for performing the phase compensation [31]. By subtracting the background noise, the quantitative phase image without background noise is obtained.
Fig. 3. The recorded digital hologram of the transparent phase target. (a) The raw hologram. (b) The corresponding 2D hologram spectrum of (a), the yellow dot circle denotes the filter region of the selected spectrum.
Fig. 4. Phase reconstruction images of our common-path VHG-DHM. (a) The reconstructed phase image of the target hologram without phase compensation. (b) Background phase obtained by the blank region’s hologram.
Figure 5 shows the reconstructed phase image of the resolution phase target with 200 nm and 350 nm. The resultant phase image shows high contrast information and the quantitative phase value is also obtained. The phase value represents phase difference distribution of the target, which is related to the target thickness and refractive index difference with the surrounding media. The sample thickness ($t$) is able to be calculated by the measured sample’s phase distribution ${\phi _o}({x,y} )$ using the following formula
where ${n_s}$ and ${n_r}$ are the refractive index of the target and the surrounding media respectively. The measured thickness of the target structured with theoretical thickness 200 nm is 182 nm, the percent error compared with theoretical is 9%. And the measured thickness of the sample structured with theoretical thickness 350 nm is 347.3 nm, the percent error compared with theoretical is about 1%. We also recorded quantitative phase images of the focused star phase target, as shown in Fig. 6. The measured thickness of the sample structured with a theoretical thickness of 100 nm is 102.9 nm, resulting in a percent error of approximately 2.9% when compared to the theoretical value. Similarly, for the sample structured with a theoretical thickness of 200 nm, the measured thickness is 213.8 nm, resulting in a percent error of about 6.9% when compared to the theoretical value.Fig. 5. Results of the resolution phase target with thicknesses equal to 200 nm and 350 nm. (a1, b1). The quantitative phase images are obtained from the target hologram with thicknesses of 200 nm and 350 nm. (a2, b2). The zoomed-in phase image of the highlighted blue square boxes in (a1) and (b1). (a3, b3) The thickness distribution of the gray dotted line in (a2, b2), the blue line is the measured thickness and the black dotted line is the theoretical thickness distribution.
Fig. 6. Results of the focused stars phase target with thicknesses equal to 100 nm and 200 nm. (a1, b1) The quantitative phase images obtained from the target hologram with thicknesses of 100 nm and 200 nm. (a2, b2) The thickness distribution of the gray dotted line in (a1, b1), the blue line is the measured thickness and the black dotted line is the theoretical thickness distribution.
The complex amplitude is obtained in the hologram reconstruction, which contains complete three-dimensional (3D) information recorded and is able to perform the depth reconstruction. To show depth reconstruction ability of VHG based common-path DHM system, the hologram of transmission USAF resolution target is recorded in defocus 0.4 mm. The complex field is obtained in the hologram reconstruction procedure. Figure 7(a) shows the amplitude distribution of the reconstructed complex filed at the initial hologram recording plane, the image shows blur due to the image is at the defocus portion. By using the angular spectrum method [9], we propagate the reconstructed complex filed to the focus portion, and the reconstructed image is clearly shown in Fig. 7(b).
Fig. 7. The amplitude reconstructed image of the transmission USAF target hologram which is recorded at defocus 0.4 mm portion. (a) The reconstructed amplitude image at the initial portion. (b) The reconstructed amplitude image propagated to the focus portion by using the angular spectrum method.
To measure temporal stability of the VHG-DHM, we conducted a series of measurements using holograms of a blank glass plate. The holograms are recorded for 10 frames/second for 15 seconds without any vibration isolation. Each hologram is reconstructed to obtain its phase map and compare the phase difference with the first frame. The standard deviation $\sigma $ of each pixel across all frames is computed, and the resulting standard deviation of temporal phase fluctuations for all image pixels is shown in Fig. 8(a). And Fig. 8(b) shows the histogram of the standard deviation value from Fig. 8(a). Average standard deviation value of the VHG-DHM is 0.048 radians which is closely matching with the other methods [27]. A small deviation in standard deviation arises due to the different experimental conditions of the two setups. Compared to the conventional Mach-Zender DHM setup, our system exhibits much higher temporal stability [27].
Fig. 8. Temporal stability measurement of system. (a) Standard deviation of temporal phase fluctuation of entire field of view. (b) The histogram of the standard deviation of phase difference obtained from (a).
Finally, to demonstrate potentials of our system for biomedical imaging, human lung cancer cells are imaged. The cells are fixed on a glass plate and immersed in the phosphate buffered saline. The phosphate buffered saline refractive index is about 1.335. Based on Eq. (11), the cell phase variation is related to the refractive index of the cell, the surrounding media and the cell thickness. In the experimental demonstration, the phase information of cells is directly obtained by the Fourier transform process. Due to the cell thickness distribution is over the 2π modulation, the phase calculated from Eq. (10) is wrapped in the region of 2π. To solve this problem, we have used the phase unwrapping algorithm [40] to let the cell phase image cover over the 2π region. Figure 9 shows the quantitative phase image of human lung cancer cell CLY1 which shows clear 3D distribution of the cells can be obtained with our method. The measured cell radius is about 27 µm. The phase variation range produced by cell thickness is approximately 5.95 radius.
Fig. 9. The quantitative phase image of human lung cancer cell CLY1. (a) 3D view of the phase distribution of human cells. (b) Zoomed-in phase image of the highlighted black square boxes, and (c) diagonal phase distribution of (b).
6. Discussion
In our common-path VHG-DHM approach, the VHG is designed for recording at maximum sensitive wavelength at ∼488 nm. To avoid potential cell damaging effect in blue light, based on Bragg-matched condition, our VHG-DHM is operated at longer wavelength of red 632.8 nm for cell observation. Compared with zero-order light, the first-order light of VHG has stronger diffraction efficiency. This allows the intensity of the reference beam to be equivalent to the intensity of the object beam after passing through the pinhole filter, and thus maintains the contrast of the holographic fringes. Also, the angular and spectral selectivity of the VHG enables the generation of single spectral efficiency diffraction light and can suppress scattered light and dispersion in DHM.
To discuss the maximum angle of the incident beam that passes through the VHG, measured the angular selectivity following the earlier procedure [35,39]. We first find tilt angle at which VHG can achieve the highest diffraction efficiency. The VHG is then rotated to test the intensity attenuation while the Bragg condition is mismatched. The measured angular selectivity is found to be $\mathrm{\Delta }\theta = 0.05^\circ $. In the VHG-DHM configuration, VHG acts as a specialized beam splitting component during imaging. The incident light on the VHG is a collimated beam that carries the sample information and acts as the probe beam to reconstruct the VHG. The reconstructed first-order diffracted beam of VHG is treated as the reference beam to pass through a pinhole to generate a point source. The probe beam is directly passing through the VHG, and it does not change the wave vector directions or high spatial frequency content and generates zero-order diffraction. Later, this zero-order diffraction acts as a signal for recording the digital hologram at the camera plane by interference with the reference beam obtained from the pinhole and the lens. We intentionally chose a zero-order beam as a signal beam to avoid any information loss during digital holographic recording process.
The angle between the signal and the reference for recording a digital hologram is decided by the size of the pixel on the CCD, and that is the limit that is the same for the VHG or any other method. In the case of the VHG, we have the freedom to choose the angle between the reference and the signal while recording, which is an advantage of the present method. As long as the Bragg matching condition is satisfied and the incident angle is within the angular selectivity range, diffraction will occur. We tried to compare the power efficiency of VHG with common-path DHM incorporating other optical components. In our case, the diffraction efficiency of VHG is around 90%, with 17% for the zero-order beam and 73% for the first-order beam, some of the power of the beam is still lost due to the surface reflection and the material property. However, optical components such as the glass plate contribute to a significant 90% power loss, as shown in Ref. [22]. The power usage can be very high for refractive optical components such as biprism, which can have approximately 99% power usage. We believe that our system’s power utilization can be improved by modifying the VHG recording material fabrication procedure. The reconstructed phase distribution also suffers some vibration and deviation, it might come from the laser speckle noise and insufficient sampling rate. This problem can be solved by applying the larger bandwidth of the DHM light source and CCD with a smaller pixel size.
It's important to highlight that our VHG-DHM system represents an innovative approach to incorporating volume holographic optical elements within the field of digital holography. In this work, VHG is employed as a highly efficient beam-splitting component in DHM, but its potential goes far beyond this application. In the future, VHG multiplexing capacity can be further investigated and integrated into a variety of DHM applications, such as multi-wavelength imaging and sectioning approaches [37]. VHG can also be integrated into the illumination side of structured light-illuminated DHM to generate incident light from different angles [41]. We can also record the aberration compensation phase on VHG to enhance the hologram quality.
7. Conclusion
In summary, we proposed the common-path VHG-DHM system. Unlike conventional thin diffraction grating with multiple order beams, the VHG characteristics of single diffraction order helps in avoiding unwanted diffraction orders. Both stray and diversion beams are suppressed by VHG narrow angular selectivity characteristics. In our VHG-DHM system, the object beam and the reference beam are generated by the zero and first-order diffraction beam of the VHG. The system is simple, and provide good temporally stability. In addition, the fabrication of the VHG is convenient to design the beam-splitting component for the common-path DHM setup. Our proposed system also shows the ability of nano-structure thickness measurement, the experimental results show that structure thicknesses can be measured within small error range. The depth reconstruction experiment shows the ability to refocus the out-of-focus images, and it can be applied in a variety of 3D imaging applications. Furthermore, our VHG-DHM shows high contrast of the quantitative phase images of cancer cells. The sample is no need for dyeing or more complicated processing, which helps us have more living cells applications.
Funding
National Health Research Institutes, Taiwan (NHRI-EX113-11327EI); National Science and Technology Council, Taiwan (NSTC 112-2221-E-002-055-MY3, NSTC 112-2221-E-002-212-MY3); National Taiwan University (NTU-CC-113L8507, NTU-113L891102).
Acknowledgments
The authors gratefully acknowledge financial support from Taiwanese National Science and Technology Council and National Taiwan University, and we thank Dr. Huei-Wen Chen for providing biological samples.
Disclosures
Authors have 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 authors upon reasonable request.
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