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Abstract
We propose single-path single-shot phase-shifting digital holographic microscopy (SSP-DHM) in which the quantitative phase information of an object wave is acquired without a laser light source. Multiple phase-shifted holograms are simultaneously obtained using a linear polarizer, a liquid crystal on a silicon spatial light modulator (LCoS-SLM), and a polarization-imaging camera. Complex amplitude imaging of a USAF1951 test target and phase imaging of transparent HeLa cells are performed to show its quantitative phase-imaging ability. We also conduct an experiment for the motion-picture imaging of transparent particles to highlight the single-shot imaging ability of SSP-DHM.
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Phase imaging is performed to measure the optical properties of transparent objects such as cells, glasses, and optical elements. The structure of a transparent object is visualized utilizing the refractive index difference between an object measured and its surrounding medium. Since the Zernike phase-contrast microscope [1] was invented, it has been applied to observing microscopic and transparent objects to date. However, it is difficult to conduct a quantitative measurement directly from a generated phase-contrast image. Optical imaging with digital signal processing has contributed to the visualization of three-dimensional (3D) and quantitative phase information without mechanical scanning. Digital holography (DH) [2,3] has been proposed as a promising computational and quantitative 3D imaging technique, based on holography and digital signal processing. Quantitative information is recorded with an image sensor as an interference fringe image called a digital hologram. 3D and quantitative phase images are reconstructed with a computer from the recorded hologram by calculations for the numerical model of holography. Digital holographic microscopy (DHM) is an application of DH and has been proposed for both 3D microscopy and quantitative phase microscopy (QPM) [4]. The optical thickness distribution of a sample has been quantitatively measured, and the 3D structure of the refractive index distribution has been obtained by the combination of DH and computed tomography [5]. However, DHM generally requires a coherent light source to form a digital hologram on the image sensor plane.
DH without a laser light source has been proposed with ingenuities of optical implementations and characteristic theories. There are two representative DH techniques with a commonly used light source, incoherent DH (IDH) [6–11] and self-reference DH (SRDH) [12–19]. IDH is a technique to obtain a digital hologram with spatially incoherent light and to analyze 3D information of incoherent light based on holography [6–11]. It is notable that IDH generates a digital hologram of spatially incoherent light such as self-luminous light [6,9,10], illumination light generated from lamps [7] and light-emitting diodes (LEDs) [9,10], thermal light [11], and sunlight [8]. In IDH, two object waves with different wavefront curvature radii are generated with a self-interference holography system [6–11]. The 3D position of each object point is encoded as a digital hologram, and the phase information of interference light contains quantitative 3D information of an object wave. Many groups including our research group have proposed single-shot phase-shifting (SSPS) IDH [20–26] and its microscopy application to single-shot quantitative 3D sensing of incoherent light in the microscopic field of view. Multiple phase-shifted incoherent holograms are simultaneously recorded with a single-shot exposure of an image sensor. However, it has been difficult to obtain the quantitative phase distribution of a transparent specimen with SSPS-IDH until now.
On the other hand, SRDH generates a reference wave from an object wave [12–16] and can be used for quantitative phase imaging (QPI) with a commonly used light source such as a halogen lamp [14,15] and an LED [16]. The main difference of SRDH from IDH is in generating a reference wave whose wave vector is unique. The reference wave acts as a spatially coherent or partially coherent light wave on the image sensor plane in SRDH. A self-reference holography system enables the measurement of quantitative phase information of a transparent specimen with an incoherent light source and the generated reference wave, and it is utilized for QPM [12–16]. SRDH is implemented with an arbitrary light source [17–19]. However, conventional QPM requires a Zernike phase-contrast microscope [13,15] or multiple exposures [12,14,16]. Here, if an SSPS holography technique without a laser light source is applied to SRDH with a wide-field optical microscope, a commonly used incoherent wide-field optical microscope can be converted into an incoherent holographic microscope to measure both intensity and quantitative phase images in 3D space. Furthermore, such a DH system is also potentially applicable to more general 2D imaging techniques as a novel holographic 3D measurement apparatus to measure both intensity and quantitative phase. In comparison with conventional QPM techniques, neither a Zernike phase-contrast microscope nor multiple exposures are required. From this perspective, advances in high-quality polarization-imaging cameras and high-power LEDs pave the way to realizing QPM with SSPS holography, which can be readily implemented in a wide-field optical microscope. In particular, an LED as small as 1 mm can provide interference fringes in DH [27]. This feature, as well as its simplicity and low cost, is advantageous for realizing single-shot incoherent QPM. Furthermore, the applicability of a single-path holography setup leads to a compact optical system.
In this article, we propose single-path single-shot phase-shifting digital holographic microscopy (SSP-DHM) without a laser light source and with a commonly used wide-field optical microscope. Single-shot QPI with LED light is performed using optical components such as a linear polarizer, a liquid crystal on a silicon spatial light modulator (LCoS-SLM), and a polarization-imaging camera. This time, we adopt a self-reference holography technique termed Fourier phase microscopy [12] to SSP-DHM to conduct QPI. QPI of transparent and microscopic specimens is experimentally demonstrated using optical devices and a wide-field optical microscope. We also conduct an experiment for the motion-picture imaging of transparent particles to highlight the effectiveness of single-shot imaging ability. Then, we discuss that SSP-DHM has the capability for simultaneous measurements of quantitative phase information and a self-luminous image.
2. Single-path single-shot phase-shifting digital holographic microscopy (SSP-DHM)
Figure 1 shows the schematic of SSP-DHM for QPI. SSP-DHM is the microscopy application of SSP-DH. SSP-DH is the combination of SSPS-DH [28–32] and SRDH. The proposed SSP-DHM consists of the combination of three optical systems: a wide-field optical microscope for intensity imaging, an SRDH system, and an SSPS-DH system. A wide-field optical microscope adopts a spatially and temporally low-coherence light source such as an LED. An incoherent light source such as a halogen lamp is also applicable by inserting an aperture, as demonstrated by Fourier phase microscopy with white light [14]. On the other hand, a high-power LED whose diameter is around 1 mm is currently available. In view of the relationship between the spatial coherence and visibility of interference fringes, such a small LED enables the production of interference fringes in our system. As a result, spatial filtering to improve spatial coherency is not always required when using such a small LED and the decrease in light intensity is avoided. The magnified image of transparent specimens O(x,y) is obtained through the output port of the wide-field microscope to the SSP-DH system. The polarization direction of the magnified image is aligned as linear polarization by a polarizer. After passing the polarizer, Fourier transformation (FT) of the magnified image FT[O(x,y)] is optically conducted by a lens, where FT[] denotes the FT. An FT pattern of the magnified image is formed on the back focal plane of the lens and an LCoS-SLM is set on the plane. Here, we illustrate polarization transitions to generate multiple phase-shifted holograms in Fig. 2. The transmittance axis of the polarizer and the working axis of the LCoS-SLM have the angle of 45 degrees with each other. On the FT plane, a plane-wave component of the magnified image is collected on a spot, and the component is utilized as a reference wave. Its mathematical expression is as follows.
Fig. 2. Polarization transitions to generate multiple phase-shifted incoherent holograms in the proposed SSP-DHM system. Diagrams of the systems (a) with and (b) without a quarter-wave plate.
Here, IFT[] denotes inverse FT, θ is a transmission axis of a micropolarizer in the polarization-imaging camera, γ (≤ 1, γ (0) = 1) is the function related to the visibility of the interference fringes and temporal coherency of light, and ΔL indicates the optical-path-length difference between the two light waves. Equation (4) denotes that intensity ratio is modulated by adjusting r. $IFT[b(\xi ,\eta )FT[O(x,y)]]$ becomes a plane wave when $b(\xi ,\eta )$ is the delta function. Spot size is based on the diffraction limit in the case where a coherent plane wave generated from a laser is Fourier-transformed. However, the spot size is enlarged on the FT plane using a spatially low-coherence light such as an LED. The intensity distribution of $IFT[b(\xi ,\eta )FT[O(x,y)]]$ is low to generate a digital hologram clearly when the value of r is small. Therefore, the value of r should be adjusted for the spot size of the light source on the FT plane. When the intensity ratio of $IFT[a(\xi ,\eta )FT[O(x,y)]]$ to $IFT[b(\xi ,\eta )FT[O(x,y)]]$ is small, r has a certain value, and the phase distribution of $IFT[b(\xi ,\eta )FT[O(x,y)]]$ becomes a quasi-plane wave. Next, note that the intensity of the second term for the right-hand side in Eq. (4) decreases as the optical-path-length difference increases between the two waves in DH. When the spectrum in the wavelength/wavenumber domain is based on the rectangle or Gauss function, γ (ΔL) is based on Sinc or the Gauss function. As the value of ΔL increases, γ (ΔL) decreases to zero and interference fringes disappear. ΔL should be less than the coherence length to obtain clear interference fringe patterns. However, the coherence length is more than 20 µm in the case where the central wavelength and the full width at half maximum are 625 nm and 18 nm, respectively. It is possible that ΔL can be set to be within several wavelengths using a single-path interferometer. The polarization-imaging camera has four transmission axes θ = 0, π/4, π/2, and 3π/4 with a polarizer array that is composed of four types of linear micropolarizer. Therefore, four phase-shifted incoherent digital holograms are simultaneously obtained on the basis of space-division multiplexing. In the image-reconstruction procedure, various algorithms proposed for SSPS-DH [28–31] can be applied. Four holograms are numerically generated from the recorded image in a computer. Then, phase-shifting interferometry is conducted and the complex amplitude image of the magnified image on the image sensor plane is obtained. Quantitative phase information of an object is contained in the complex amplitude image obtained on the basis of SRDH [16]. Numerical refocusing calculations such as diffraction integrals can be applied to the complex amplitude image, and intensity and quantitative phase images focused on arbitrary depths are reconstructed. Thus, image-reconstruction algorithms of SSPS-DH and SSPS-IDH can be simply applied to obtain both intensity and quantitative phase images. Note that depth resolution can be improved by using information science in the calculation of numerical refocusing [33,34].
3. Experiments
We have conducted experiments to show the effectiveness of SSP-DHM. We have constructed the QPM system shown in Fig. 1. A stage to put specimens, a magnification system, and a mirror were the components of a commercially available inverted optical microscope (IX-73, Olympus). An oil-immersion microscope objective whose magnification and numerical aperture were 60 and 1.42, respectively, was set. We used a red LED with a nominal wavelength of 625 nm as the spatially and temporally low-coherence light source, which was mounted in a four-wavelength LED head (LED4D201, Thorlabs). A polarizer was set as illustrated in Fig. 1. The magnified image of the specimens was introduced to an SSP-DHM system through the output port of the microscope. Lenses whose focal lengths were 180 and 360 mm were selected to obtain two magnifications in the SSP-DHM system, and the total magnification of the SSP-DHM system was 120. An LCoS-SLM (X10468-01, HAMAMATSU Photonics K.K.) was used and r was set as 300 µm. We put a USAF1951 test target as an amplitude specimen. The phase pattern shown in Fig. 1 was displayed on the LCoS-SLM. In this experiment, a quarter-wave plate was used to generate circularly polarized light, and the polarization transitions shown in Fig. 2(a) were adopted. Four types of phase-shifted incoherent digital hologram were simultaneously recorded using a red channel of a polarization-imaging camera (VP-PHX050S-Q, Lucid), as shown in Figs. 3(a)–3(e). The object wave was retrieved from the recorded single image. A diffraction integral was calculated to obtain the numerically focused image of the object. The complex amplitude distribution of the object wave was reconstructed as shown in Figs. 3(f) and 3(g). It is considered that the phase distribution of the term IFT[b(ξ,η)FT[O(x, y)]] contained a slightly spherical wave component on the plane wave component. It might cause a slight change in the numerical focusing distance. The degree of the shift in the depth direction for the reconstructed image due to a slightly spherical wave component is a future research topic. Experimental results indicate the complex amplitude imaging ability of SSP-DHM.
Fig. 3. Experimental results for an amplitude object. (a) Recorded image. Multiple phase-shifted holograms with the phase shifts of (b) 0, (c) π/2, (d) π, and (e) 3π/2, which are obtained from (a). (f) Intensity and (g) phase distributions of the reconstructed image. The numerical propagation distance for the magnified image of the object was 170 mm.
We conducted an experiment using fluorescence-stained HeLa cells to demonstrate QPI of transparent objects. The cells were stained and processed as described in [35] to investigate the relationship between fluorescence and quantitative phase images. Nuclei and cell cytoskeletons were stained with DAPI and Alexa 555 and their fluorescence light was generated with ultraviolet and green excitation light, respectively. Experimental conditions were the same as those in the previous experiment. The object wave was retrieved from a single image. Diffraction integrals were calculated for the retrieved object wave to obtain the complex amplitude distributions of the object wave on arbitrary planes. An intensity image on the image sensor plane, which corresponded to the hologram with 0 phase shift, was used as the intensity distribution of the object wave on the image sensor plane. The field of view of the constructed SSP-DHM system was 70.4 µm × 58.9 µm. Figure 4 shows the experimental results. We obtained fluorescence microscopy images of HeLa cells shown in Figs. 4(a)–4(c) using the excitation-light source and fluorescence-filter unit in the inverted optical microscope. The phase pattern of the LCoS-SLM was plane, and the color polarization-imaging camera in the SSP-DHM system captured fluorescence images. Nuclei, nucleoli in nuclei, cell cytoskeletons, and a particle in the cell body were clearly visualized. However, cell damage caused by the required staining and photobleaching are the problems. The particle in Fig. 4(c) had autofluorescence. The particle was excited by blue illumination light, and fluorescence light was obtained using a fluorescence mirror unit (U-BNA, Olympus). From the recorded image shown in Fig. 4(d), four phase-shifted incoherent holograms were numerically generated as shown in Figs. 4(e)–4(h). Intensity and phase images focused on different depths shown in Figs. 4(i)–4(l) were reconstructed successfully. SSP-DHM for QPI enabled us to record the digital holograms of cells with an LED and to conduct stain-free cell imaging with quantitative phase values at any depth. Nuclei were visualized, nucleoli in nuclei were also observed, and the localizations of the particle in 3D space were recognized. The QPI ability of the constructed SSP-DHM was confirmed experimentally.
Fig. 4. Experimental results for a phase object. Fluorescence images of (a) nuclei, (b) cell cytoskeletons, and (c) a particle in cell bodies and cell cytoskeletons. The focal plane of (a) is the same as that of (b) and is different from that of (c). (d) Recorded image that contains four-phase-shifted holograms based on space-division multiplexing. Multiple phase-shifted holograms with the phase shifts of (e) 0, (f) π/2, (g) π, and (h) 3π/2, which are obtained from (d). Intensity distributions of the reconstructed images in which the numerical propagation distances for the magnified specimens are (i) 7 and (j) 30 mm. Quantitative phase images in which the numerical propagation distances are (k) 7 and (l) 30 mm. Nucleoli are focused in (i) and (k). A particle is focused in (j) and (l). Blue and red arrows indicate nucleoli and a particle, respectively. White (255) and black (0) in phase images denote 1.26 and 0 radians, respectively.
We have conducted additional experiments for quantitative phase motion-picture imaging of multiple transparent specimens whose diameter and refractive index were known. A green LED with a nominal wavelength of 530 nm was used as the spatially incoherent light source, which was mounted in a four-wavelength LED head (LED4D201, Thorlabs). The polystyrene particles of 1 µm diameter were put into a water droplet on a slide glass, and the water droplet containing the particles was surrounded with oil. Then, the particles in water were sandwiched by the cover and slide glasses and were set as the phase objects. Brownian movements of the particles were recorded as holograms. In this experiment, a quarter-wave plate was removed, and circularly polarized light was generated using the LCoS-SLM. Four types of phase-shifted digital motion-picture hologram were simultaneously recorded using a green channel of a polarization-imaging camera (VP-PHX050S-Q, Lucid). The frame rate of the camera was 10 fps. Figure 5 shows the experimental results. Figures 5(a)–5(c) are intensity, quantitative phase, and 3D rendering of phase images, respectively. Figure 5(d) shows four phase-shifted holograms based on space-division multiplexing. Intensity and phase images shown in Figs. 5(e)–5(j) were reconstructed from the hologram. Figures 5(e)–5(j) show that the intensity and quantitative phase images of the particles placed at different depths were successfully reconstructed. Then, we obtained the phase plot along the line shown in Fig. 5(i). The full width at half maximum of the phase profile of the particle in Fig. 5(i) was 1.08 µm, which was derived from Fig. 5(k). Using the derived width and the peak of the phase value in Fig. 5(k), we calculated the refractive index of the particles as 1.585. The refractive index of a polystyrene particle is generally 1.59. This result means that the QPI of a 1-µm-order object has been successfully demonstrated. Visualization 1 shows the obtained quantitative phase motion-picture image of Brownian movements of several transparent particles. This result reveals the quantitative phase motion-picture sensing ability of SSP-DHM. Figure 6 shows the results of another experiment conducted to demonstrate the simultaneous complex amplitude motion-picture imaging of multiple transparent particles. The field of view of the reconstructed images was 59 µm × 59 µm, and the frame rate was 10 fps. Complex amplitude distributions on different depths were reconstructed, and different particles at different depths were numerically and successfully focused. Visualization 2 shows the 3D rendering of the motion-picture image of the reconstructed phase distribution. The ability for 3D motion-picture sensing of transparent specimens was indicated. From the results, the proposed SSP-DHM has enabled holographic motion-picture sensing with an LED light even for actively moving transparent specimens. Brownian movements of the multiple specimens were captured simultaneously. This experimental result indicated the simultaneous 3D tracking capability for moving transparent and microscopic specimens. Thus, the ability for quantitative phase motion-picture imaging was experimentally demonstrated.
Fig. 5. Experimental results for moving phase objects. (a) Intensity and (b) phase distributions of the objects. The numerical propagation distance for the magnified image of the objects was 31 mm. (c) 3D rendering of (b) using pseudo color. (d) A digital hologram of the area enclosed by the yellow rectangles in (a) and (b). Intensity distributions of the magnified images of the objects with numerical propagation distances of (e) 0, (f) 31, and (g) 53 mm. Phase distributions of the magnified images of the objects with numerical propagation distances of (h) 0, (i) 31, and (j) 53 mm. White (255) and black (0) in phase images denote 6.28 and 0 radians, respectively. (k) Plot of the phase profile for a particle shown in (i). The plot is obtained along the pink line. The motion-picture image of 3D rendering of the phase distribution is seen in Visualization 1. The area of Visualization 1 is inside the red rectangle shown in (b). The numerical propagation distance of Visualization 1 is 53 mm.
Fig. 6. Experimental results for moving multiple phase objects. (a), (b) Intensity distributions of objects. Arrows indicate the focused transparent particles. (c), (d) Quantitative phase distributions. White (255) and black (0) in phase images denote 6.28 and 0 radians, respectively. The numerical propagation distances to focus on the magnified particle image were (a), (c) 7 mm and (b), (d) −24 mm. (e) 3D rendering for one of the quantitative phase motion-picture images. The motion-picture image of 3D rendering of the phase distribution in (e) is seen in Visualization 2.
4. Discussions and conclusion
Self-reference holography has enabled the realization of QPM with an incoherent light source [13–16]. However, conventional QPM requires a Zernike phase-contrast microscope [13,15]. The main difference between SRDH with a Zernike phase-contrast microscope [13] and the proposed technique is in the type of wide-field optical microscope. It is difficult to obtain a bright fluorescence image by SRDH with a Zernike phase-contrast microscope. On the other hand, a fluorescence image is obtained using the proposed technique with a simple modification. Figure 7 illustrates an optical implementation for simultaneous recording of fluorescence and quantitative phase images with a single-shot exposure. Fluorescence light and an incoherent hologram are separated by a dichroic mirror. An image sensor and a polarization-imaging camera record the fluorescence light and the incoherent hologram, respectively. We term the dichroic mirror and an image sensor as a fluorescence image sensing unit in Fig. 7. It is notable that any wide-field optical microscope can be converted to a multifunctional 3D microscope by constructing an IDH system and introducing it to the wide-field optical microscope.
Fig. 7. Optical implementation for simultaneous recording of fluorescence and quantitative phase images with a single-shot exposure. Fluorescence light and an incoherent hologram are separated by a dichroic mirror.
The quality of the reconstructed images in SSP-DHM is related to the angular-spectrum distribution of the light diffracted from the specimen and the visibility of interference light. In Fig. 3, a negative USAF1951 test target was used. A plane-wave component is limited in the fine structures of the specimen. The intensity of the reference wave becomes lower than that of the object wave. On the other hand, in Figs. 4–6, the plane-wave component is dominant in the hologram. In this case, the intensity of the reference wave becomes higher than that of the object wave. The qualities of the hologram and the reconstructed images are decreased when the intensity ratio is large, as described in Ref. [16]. Furthermore, spatial and temporal coherencies are limited when using an LED as a light source. Visibility of interference light and available dynamic range to record a digital hologram in which interference fringes of each object point are incoherently superimposed are decreased by low coherencies. In comparison to the hologram generated when using a laser, a digital hologram with low visibility is generated. An image sensor with a high dynamic range is important to accurately record a digital hologram generated using an LED and to increase the accuracy for holographic measurement. This time we have used an image sensor with 12-bit. It is considered that the quality of the reconstructed images is affected in the experiments by the quantization of the hologram. The image quality will be improved using a modified phase pattern proposed in Ref. [16] and a polarization-imaging camera with higher dynamic range.
Spatial information such as the field of view and resolution is partially reduced by space-division multiplexing. However, the space-bandwidth product (SBWP) of SSP-DHM can be improved by applying SSPS with two phase shifts [36]. Two-step phase-shifting interferometry [37–40] can be applied to improving the pixel density of each phase-shifted hologram [36,26]. Two-step phase-shifting interferometry for IDH has been successfully developed [41], and resolution and/or field of view will be improved. Quadriwave lateral shearing interferometry is also proposed as another QPI system without a laser light source [42,43]. The main difference between the SSP-DH and the interferometry is the available SBWPs. The SBWPs available for recording an object wave in SSPS with two and four phase shifts are 4.5 and 2.25 times, respectively, of the SBWP in quadriwave lateral shearing interferometry. Besides quadriwave lateral shearing interferometry, QPI without a laser light source has been performed using diffraction phase microscopy (DPM) [44], lateral shearing interferometry [45], and a single-path shearing interferometer with a phase gradient [46]. Single-shot QPI has been performed with SSP-DHM and DPM. The main difference between SSP-DHM and DPM is their optical configurations. DPM is implemented with an off-axis configuration, a grating, and lenses. In DH SSPS-DH can generally obtain larger SBWP than off-axis DH. The decrease of the visibility of interference fringes due to an off-axis configuration when using temporally low-coherence light is suppressed with SSPS-DH by using an in-line DH configuration.
We have proposed SSP-DHM for QPI. Complex amplitude imaging of amplitude and phase objects was performed successfully and experimentally. Complex amplitude motion-picture imaging was experimentally demonstrated, owing to the single-shot imaging ability of SSP-DHM. The QPI ability was experimentally demonstrated using a transparent 1-µm-order object. An incoherent light source is used to obtain an incoherent hologram for the imaging of quantitative phase information of an object. SSPS-IDHM has already been used for single-shot full-color 3D imaging of incoherent light generated from a halogen lamp [23,26], and the proposed technique will be extended to the imaging of light from a lamp and other incoherent light sources. The proposed SSP-DHM will contribute to QPI for observations of actively moving transparent materials and reflective objects, label-free observations of dynamics in a living cell and interaction of cells, particle and flow measurements to clarify physical phenomena, multifunctional image measurement by inserting a fluorescence image sensing unit, and conversion of commonly used 2D imaging techniques and systems into a novel holographic 3D measurement apparatus to measure both intensity and quantitative phase.
Funding
Mitsubishi Foundation (202111007); Precursory Research for Embryonic Science and Technology (JPMJPR16P8); Cooperative Research Program of "Network Joint Research Center for Materials and Devices" (20211086); Japan Society for the Promotion of Science (JP18H01456).
Acknowledgement
We thank Atsushi Matsuda and Takako Koujin for providing HeLa cells used for the experiment in Fig. 4.
Disclosures
The authors declare 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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