1. Introduction

Computational imaging has realized multidimensional imaging from two-dimensional image(s). Light-wave information, such as three-dimensional (3D), multiwavelength, and polarization images, is reconstructed by exploiting both physics and mathematics. By numerical modeling of a physical phenomenon and signal processing with mathematics, researchers have presented various types of computational 3D microscopy without mechanical scanning. Digital holographic microscopy (DHM) [1,2] is a promising computational 3D microscopy imaging technique based on holography and digital signal processing. An image sensor records an interference fringe image called a digital hologram, and a computer processes the digital hologram numerically to obtain a 3D image by calculations for the numerical model of holography. On the basis of diffractive optics, a phase distribution of an interference light wave is utilized and successfully reconstructed with a simple numerical model. DHM is a microscopy application of digital holography (DH) [3,4] and many applications have emerged from DHM: quantitative phase imaging (QPI) and measurements [5], multidimensional image sensing [6], and real-time 3D motion-picture measurements [7]. However, DHM generally requires a coherent light source to record a digital hologram to obtain sufficient coherence for the generation of a digital hologram.

DH with an incoherent and low-coherence light source such as a light-emitting diode (LED) and sunlight, termed incoherent DH (IDH) [8–13] is a technique to obtain a digital hologram with incoherent or low-coherence light and to reconstruct the 3D information of multiple spatially incoherent objects based on holography. It is notable that this technique generates a digital hologram with incoherent or low-coherence light sources such as self-luminous objects [8], lamps [9], LED(s) [10], and sunlight [11]. This DH has also been successfully applied to the 3D measurement of thermal radiation [12] and improvements of point-spread and optical transfer functions with Fresnel incoherent correlation holography (FINCH) [13]. Two representative implementations have been adopted in IDH: self-interference DH [8–13] and self-reference. DH [5,14–18]. The former is effective particularly when recording a digital hologram of self-luminous light. The latter is a useful technique to conduct QPI with a common-path interferometer. The latter technique is implemented in laser DH [14,18], DH with coherent light [5], and DH with incoherent and low-coherence light [15–17]. In IDH for QPI [15–17], several types of optical systems have been proposed: the uses of a Zernike phase-contrast microscope and a single-path interferometer [15], the use of phase-shifting phase pinhole set on the Fourier plane [16] whose system has been proposed as Fourier phase microscopy [5], and an off-axis configuration with spatial filtering and grating [17]. In these optical systems, the optical system in which all the light diffracted from an object can be utilized to generate a digital hologram has not been implemented. This is because a polarizer, a beam splitter, and a grating are inserted between an object and an image sensor. The increase in the light-use efficiency is important particularly when a bright hologram is obtained, weak light should be introduced to a sample such as cells, and illumination-light intensity is limited.

In this article, we propose a QPI technique and its application to microscopy with IDH. Quantitative phase information of transparent specimens is recorded with a single-path interferometer and an LED. We require neither a two-arm interferometer nor a beam splitter and use a phase-only spatial light modulator (SLM) to generate a reference wave from the object wave. All the intensity of the light diffracted from the objects can be utilized to generate a spatially and temporally low-coherence digital hologram, and the intensity of light to illuminate objects can be reduced. A commercially available wide-field optical microscope is adopted to construct a quantitative phase microscopy (QPM) system. Phase-shifting interferometry (PSI) techniques [19–24] are applicable to the proposed QPI technique. The validity of the proposed QPI technique is demonstrated.

2. Single-path phase-shifting DH using an LED

Figure 1(a) illustrates an optical implementation of the proposed QPI technique applied to microscopy. The optical system is composed of a commercially available optical microscope with a polarized and spatially and temporally low-coherence light for illumination, two lenses for optical Fourier/inverse Fourier transforms (FTs), a polarization-sensitive phase-only SLM, an image sensor, and a computer to reconstruct a quantitative phase image from the recorded digital holograms. Polarized light generated from the light source of an optical microscope illuminates 3D specimens. A small LED whose size is around 1 mm or less is used. Light generated from such a light source is called as incoherent or low-coherence light. The size of the light source is related to the visibility of interference fringes [25]. As the size increases, the visibility decreases. However, an image sensor with a high dynamic range can capture a digital hologram of such light. The microscope outputs a magnified image of the 3D specimens near the intermediate image plane. One lens with a focal length of f₁ carries out to conduct an FT optically to the object wave of the magnified image. The SLM is set on the back focal plane of the lens. The SLM displays the phase patterns illustrated in Figs. 1(b) or 1(c) to generate a reference wave from the object wave. Light that is not modulated by the specimens preserves its plane wavefront component and is collected at the center spot in the FT plane. The unmodulated object wave is exploited as the reference wave. This is based on self-Ref. DH [5]. Its mathematical expression is as follows:

 

Fig. 1. Proposed QPM with spatially and temporally low-coherence DH. (a) Optical system. The QPM is based on self-reference DH with spatially and temporally low-coherence light. (b) Phase patterns displayed on the polarization-sensitive phase-only SLM. (c) Other types of phase pattern displayed.

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3. Experiments

We have constructed the QPM system shown in Fig. 1 to demonstrate its validity. A stage on which specimens are set, 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 in front of the LED to illuminate specimens with polarized light. The magnified image of the specimens was introduced to a DH system through the output port of the microscope. Lenses whose focal lengths were 180 and 360 mm were set to obtain two-fold magnification in the DH system, and the total magnification of the QPM system was 120. A liquid-crystal on silicon SLM (LCOS-SLM) (X10468-01, HAMAMATSU Photonics K.K.) was set and r was 300 μm. We set HeLa cells as the transparent specimens and the phase patterns shown in Fig. 1(c) on the LCOS-SLM. The cells were stained and processed under the conditions described in [19] 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. Four phase-shifted digital holograms were recorded sequentially using a scientific complementary metal oxide semiconductor (sCMOS) lensless camera (Andor Technology, Zyla 4.2 plus). Each exposure time was 40 ms. The object wave was retrieved from the recorded holograms, and the quantitative phase images of the specimens on the image sensor plane were reconstructed after the calculations of PSI. Then, a diffraction integral was calculated to obtain the complex amplitude distribution of the object wave on a plane. An intensity image on the image sensor plane was obtained by setting the phase of the SLM as the plane in this QPI with single-wavelength PSI and we used it as one of the holograms.

Figures 2(a)–2(i) show the experimental results. We cannot determine the shapes of cell cytoskeletons and nuclei accurately from the bright-field image shown in Fig. 2(a). We conducted fluorescence microscopy to obtain cell images shown in Figs. 2(b) and 2(c). However, cell damage caused by the required staining and photobleaching are the problems. We investigated the small dark particles in Fig. 2(a) and found that these particles in cell bodies have autofluorescence as shown in Fig. 2(d). These particles were excited by blue illumination light, and fluorescence light was obtained using a fluorescence mirror unit (U-BNA, Olympus). QPM with DH enabled us to record digital holograms of cells with an LED and to conduct stain-free cell imaging with quantitative phase values at any depth, as shown in Figs. 2(f)–2(i). Nuclei were visualized, and the localizations of the particles in 3D space were recognized. The validity of the constructed QPM system was confirmed experimentally.

 

Fig. 2. Experimental results. (a) Bright-field image of HeLa cells. Fluorescence images of (b) nuclei, (c) cell cytoskeletons, and (d) particles in cell bodies. (e) One of the recorded spatially and temporally low-coherence holograms. (f) Intensity and (g) reconstructed quantitative phase images on the image sensor plane. (h) Intensity and (i) quantitative phase images reconstructed by the calculation of a diffraction integral to focus on the particles in cells. White (255) and black (0) in-phase images denote 3π/2 and 2π/3 radians, respectively. Arrows in the figures indicate nucleoli in nuclei.

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An additional experiment was carried out to show quantitative phase measurement ability and to compare two types of phase mask shown in Figs. 1(b) and 1(c). We set an LED with nominal wavelength of 625 nm, which was contained in the four-wavelength LED head (LED4D201, Thorlabs). We adopted one of the four-step PSI techniques for the proposed QPM system. Each exposure time was 30 ms. Prepared specimens were transparent polystyrene beads whose diameter was 1 μm (YG Microspheres 1.00 μm, Polysciences). Figure 3 shows the experimental results. Numerical propagation distance was 50 mm from the image sensor plane to the magnified image plane. The results reveal that the focused intensity and quantitative phase images were obtained successfully using respective phase patterns as shown in Figs. 3(a)–3(d). However, the phase distributions of the background were unclear when using the phase pattern in Fig. 1(b), in comparison with using the phase patterns in Fig. 1(c), as shown in Figs. 3(b) and 3(d). This is because the plane wave component was not contained in the object wave when using the patterns in Fig. 1(b). Flatness of the phase distributions was compared, and Fig. 3(e) obviously indicated that phase information of the background was retrieved without noise by using the pattern in Fig. 1(c). Standard deviations of the plots of Figs. 3(b) and 3(d) were 1.92 and 0.196 radians, respectively. Using the patterns shown in Fig. 1(c), plane wave and quasi-plane wave components were contained in the object wave and such spatial frequency components were successfully retrieved. Thus, the phase patterns in Fig. 1(c) was effective for low spatial frequency components. Furthermore, the shapes of particles were visualized clearly as quantitative phase values. We plotted the phase values of a particle shown in Fig. 3(f) as Fig. 3(g). The plot in Fig. 3(g) indicated that optical thickness information was obtained for the particle with a constant refractive index of 1.59. The diameter of the particle was known. We calculated the refractive index using the phase values of the top and bottom of the particle and known diameter. The calculated refractive index was 1.586, which is close to the reference value. Therefore, quantitative phase-measurement ability was experimentally demonstrated.

 

Fig. 3. Experimental results for QPI and comparative evaluations of the phase patterns in Figs. 1(b) and 1(c). (a) Intensity and (b) phase distributions obtained with the pattern in Fig. 1(b). (c) Intensity and (d) phase distributions obtained with the pattern in Fig. 1(c). (e) Plots of the phase distributions along the lines shown in (b) and (d). (f) Magnified image inside of the circle shown in (d). (g) Phase plot along the pink line shown in (f).

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Self-interference DH obtains quantitative phase information of not an object wave but an interference light wave. As a result, relationship between the depth position of the object from the image sensor plane and numerical propagation distance Z becomes not proportional but nonlinear [26]. This relationship causes the considerable decrease of the depth resolution along the depth position of the object. On the other hand, self-reference DH can acquire a complex amplitude distribution of an object wave by generating a plane reference wave from the object wave. It is expected that the relationship between the depth position and the numerical propagation distance becomes proportional, as indicated for a two-arm laser holography system using a Mach-Zehnder interferometer. Therefore, we conducted additional experiments to show 3D sensing ability with the proportional relationship for the constructed system. A light source, a polarizer, an optical microscope, lenses, and an LCoS-SLM were the same as those used for the previously conducted experiments. The phase patterns shown in Fig. 1(c) was used and r was 200 μm. A CMOS camera (Andor Technology, Neo5.5) was used as the image sensor. Exposure time to record a phase-shifted hologram was 33 ms. A USAF1951 test target attached on a cover glass and oil was set as the specimen and put on the stage of the optical microscope. Four phase-shifted holograms were recorded, and the specimen was moved in the depth direction by using a micrometer of the optical microscope. Recording and moving were repeated sequentially. Regular shift of 14 μm in the depth direction was introduced for each movement. Figure 4 shows experimental results. Z were proportionally changed for each shift of the specimen. Complex amplitude images of the object wave were successfully reconstructed on the image sensor and reconstructed image planes even when the distance between the magnified image of the specimen and the image sensor plane was more than 500 mm. Figure 5 shows proportional relationship of the depths between the specimen on the object plane and the reconstructed image on the image plane. Refocusing distances against regular depth-position shifts in self-reference DH are obviously different from those in self-interference DH [26]. This is because a quasi-plane reference wave was successfully generated in the proposed self-reference DH system. Using the proposed DH, not only QPI but also 3D sensing ability different from that of self-interference DH were performed.

 

Fig. 4. Experimental results to show 3D sensing ability of the proposed technique. Z means the numerical propagation distance for the obtained complex amplitude distribution. White (255) and black (0) in-phase images denote 2π and 0 radians, respectively.

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Fig. 5. Relationship between the depths of the specimen on the object plane and the reconstructed image on the image plane.

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4. Conclusion

We have proposed a QPI technique with single-path phase-shifting DH and an LED. Stain-free QPI with an LED was demonstrated. Experimental results also showed quantitative cell-measurement capability and quantitative phase-measurement ability of this technique. The proposed QPM system can utilize all the intensity of the light diffracted from the specimens and can achieve QPI with weak light and short exposure time. Spatial coherence is improved using an aperture even for sunlight and it is considered that quantitative phase information of an outdoor scene can be obtained with an aperture. The proposed phase patterns in Fig. 1(c) are effective for an object wave that sufficiently contains a plane-wave component; their optimization is a future work. The proposed QPM system can be implemented with a commercially available wide-field optical microscope. The QPI technique will contribute to material and life sciences, industry, and our life by 3D sensing of weak-light-scattering and phase objects.