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Abstract
We propose a palm-sized single-shot phase-shifting incoherent digital holography (SSPS-IDH) system in which three-dimensional (3D) information of spatially incoherent light is recorded as a self-interference hologram. To implement this single-shot 3D recording system, we adopt thin optical elements and no refractive lens. 3D information is obtained with a single-shot exposure of a polarization image sensor. More than 3,800-fold downsizing in volume can be achieved in comparison with a conventional incoherent digital holography (DH) system. An SSPS-IDH system is constructed, and its single-shot 3D sensing ability is experimentally demonstrated.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Computational imaging has contributed to the recording of light-wave information such as three-dimensional (3D), multiwavelength, and polarization images by exploiting a mathematical method. Various 3D imaging techniques without a mechanical scan have been presented to date by numerical modeling of a physical phenomenon and signal processing with mathematics. Digital holography (DH) [1,2] is a promising computational 3D imaging technique based on holography and digital signal processing. Quantitative 3D information is recorded with an image sensor as an interference fringe image called a digital hologram and reconstructed with a computer by calculations for the numerical model of holography. On the basis of diffractive optics, a quantitative phase distribution of an interference light wave is utilized and successfully reconstructed with a simple numerical model. Digital holographic microscopy (DHM) is a microscopy application of DH [3,4], and many applications have emerged from DHM: quantitative phase imaging and measurements [5], multidimensional motion-picture image sensing [5], and simultaneous 3D motion-picture measurement of multiple specimens [6]. However, DH and DHM generally require a coherent light source to record a digital hologram because an interference fringe image should be generated on the image sensor plane.
Incoherent DH (IDH) [7–10] is a technique to obtain a digital hologram with spatially incoherent light and to observe the 3D information of multiple spatially incoherent light sources based on holography. It is notable that the technique generates a digital hologram of incoherent light such as self-luminous light [7,10] and sunlight [11] by using a self-interference holography system. In IDH, spatially incoherent light is regarded as a summation of spatially incoherent point-light sources, and each point-light source is encoded as each Gabor zone plate (GZP) pattern through a self-interference holography system. In each GZP pattern, 3D information of each point-light source is contained because the pitch and center of a GZP pattern correspond to information in depth and in-plane directions. Each GZP pattern superimposes on the image sensor plane incoherently and forms a digital hologram of a spatially incoherent light wave. To date, IDH has been applied successfully to fluorescence 3D microscopy [7], 3D imagery with a commercially available light source such as a light-emitting diode (LED) and a lamp [8–10], 3D measurement of thermal radiation [12], and improvements of point-spread and optical transfer functions with Fresnel incoherent correlation holography (FINCH) [10]. After many inventions in IDH, single-shot phase-shifting IDH (SSPS-IDH) [13–18] was proposed as a method for incoherent 3D imaging from a single in-line hologram with single-shot phase-shifting DH [19–21].
Downsizing is one of the important research themes in DH and incoherent 3D imaging techniques [22–28]. Compact incoherent 3D imaging systems using iteration and/or PSF engineering have been proposed to date, and a compact system is now required for IDH. The sizes of incoherent DH systems are increased particularly when using a reflective spatial light modulator (SLM) and a refractive lens and when applied to microscopy. As an example, conventional incoherent DHM systems adopt the combination of an ordinarily used 2D microscope and an IDH system [10,29–31]. Such IDH systems in DHM systems required dimensions of 600 mm × 400 mm × 250 mm. On the other hand, in SSPS-IDH, the use of a geometric phase lens successfully enabled downsizing [15,16]. Further improvement will allow a system of SSPS-IDH to be taken outdoors by hand.
In this article, to achieve downsizing for SSPS-IDH, we propose a palm-sized SSPS-IDH system. We adopt thin optical elements and no refractive lens to SSPS-IDH. In the constructed system, 3D information is obtained with a single-shot exposure of a polarization image sensor. An SSPS-IDH system with dimensions of 25 mm × 25 mm × 25 mm, including optical elements and a camera and excluding an illuminator, is constructed. Experiments were conducted.
2. Single-shot phase-shifting incoherent digital holography (SSPS-IDH) system
Figure 1 illustrates the basic concept of SSPS-IDH. An SSPS-IDH system consists of attached thin optical elements and a polarization image sensor. A specimen is illuminated by a spatially incoherent light source, and a light wave diffracted from the specimen is introduced to the system. In the system, a polarizer and geometric phase lenses are attached to each other, and they work to generate linear polarization and two orthogonally polarized circular light waves whose wavefront curvature radii are different, respectively. In Fig. 1, we set the transmission axis of the polarizer in the horizontal direction. Then, two light waves propagate to the image sensor plane. Here, we use single-shot phase-shifting holography [19–21] to implement a single-shot 3D imaging system with incoherent light. To realize a compact optical system, we adopt a polarization-based single-shot phase-shifting interferometer with a micropolarizer array and two orthogonally polarized circular light waves [13,15,16,18,20]. The two waves generate four phase-shifted incoherent holograms after passing a micropolarizer array, and the image sensor records four phase-shifted incoherent holograms simultaneously with a single-shot exposure. From the recorded incoherent hologram, we apply an image-reconstruction algorithm of single-shot phase-shifting digital holography [19–21,13], and multiple phase-shifted holograms are numerically generated in a computer. Then, phase-shifting interferometry is applied, and a complex amplitude distribution of an interference light is retrieved. Finally, diffraction integrals are calculated and then a 3D image of a specimen is reconstructed.
Figure 2 shows the schematic of the recording system. To describe the system theoretically, we set an object as a spatially incoherent point-light source, the distance between the specimen and attached optical elements as z1, the distance between the attached optical elements and the image sensor as z2, C1, C2, and C3 as coefficients, θ as a transmission axis of a micropolarizer, the transmission of a polarizer in front of geometric phase lenses as 0 degree, linear phase function as $L({r_o}) = \exp [{i2\pi ({x_o}x + {y_o}y)/\lambda } ]$, ${r_o} = ({x_o},{y_o})$, quadratic phase function as $Q(1/z) = \exp [{i\pi ({x^2} + {y^2})/(\lambda z)} ]$, an imaginary unit as $i = \sqrt { - 1}$, λ as a central wavelength, focal lengths of the first and second geometric phase lenses as ± f1 and ± f2, respectively, and * as convolution. A complex amplitude distribution of an interference light on the image sensor plane is expressed as
Finally, diffraction integrals are calculated to the point object and 2D intensity images at arbitrary planes are reconstructed. An incoherent object is regarded as the incoherent summation of spatially incoherent point-light sources; therefore, this theory can be extended to an incoherent 3D object. The occlusion problem is effectively solved when using information science [33,34].
Figure 3 illustrates the polarization transitions of the two waves to generate an image that contains multiple phase-shifted incoherent holograms. Light polarization and an image sensor with a micropolarizer array are utilized to generate phase-shifted holograms. Linear polarization of an incoherent object wave is extracted, and the two object waves whose circular polarization directions are orthogonal are separated by the first geometric phase lens. Phase functions of convergent and divergent lenses are introduced to the respective circularly polarized object waves. Then, phase functions of divergent and convergent lenses are introduced to the respective circularly polarized object waves by the second geometric phase lens. As a result, two object waves interfere with a small angle. Circularly polarized two light waves illuminate the polarization image sensor and four phase-shifted holograms are simultaneously recorded. Phase shifts at respective holograms are determined by the transmission axes of the micro-polarizer array θ.
3. Experimental results
We have constructed SSPS-IDH systems and conducted experiments to investigate their validity. Figure 4(a) shows a photograph of the constructed SSPS-IDH system. A commercially available polarization-imaging camera (Lucid, VP-PHX050S-Q) was used as the image sensor. A polarizer and two commercially available polarization-directed flat lenses whose focal lengths are ±45 mm and ±40 mm (Edmund Optics) were attached and fixed in front of the C-mount of the camera. An example of the diffraction efficiencies of lenses is described in [35]. The constructed SSPS-IDH system had dimensions of 30 mm × 35 mm × 50 mm, including the camera and excluding a light source. A white LED attached on a cell phone was used as a light source and exposure time was 9 ms. The Group 3, Line 3 area of a negative USAF1951 test target was set as a specimen, and its incoherent hologram was recorded by the light source and the SSPS-IDH system. Besides, we conducted additional recordings of holograms by changing the depth positions of the object to show 3D sensing ability. An image of the specimen was obtained from a single hologram at the green-color channel. For comparison, images were reconstructed from a single incoherent hologram without phase-shifting interferometry. Figures 4(b)–4(k) show the experimental results. As shown in Figs. 4(b)–4(f), multiple phase-shifted incoherent digital holograms were obtained with a single-shot exposure. Figures 4(g) and 4(h) show that, when using single-shot phase-shifting interferometry, no undesired diffraction waves were superimposed. Figures 4(i) and 4(j) were reconstructed images of the object after the object was moved in the depth direction from Fig. 4(h). Apertures whose widths were less than 50 μm were successfully and clearly resolved as shown in Figs. 4(h)–4(j). Figure 4(k) shows the results quantitatively. Thus, an experiment using the constructed SSPS-IDH system was successfully conducted.
Fig. 4. Constructed SSPS-IDH system and experimental results. (a) Photograph of SSPS-IDH system. (b) Recorded hologram with dimensions of 8.45 mm × 7.07 mm. De-mosaicked holograms at green-color channel with the phase shifts of (c) 0, (d) π/2, (e) π, and (f) 3π/2. (g) Image reconstructed with a single incoherent hologram without phase-shifting interferometry. (h)–(j) Images reconstructed by SSPS-IDH when the object was set on different depth positions. Line pairs of Group 3, Line 3 area of a USAF1951 test target are 10.10 lp/mm, and therefore, the width of the apertures is 49.5 μm. Numerical propagation distances were (h) 468 mm, (i) 444 mm, and (j) 434 mm. (k) Plots along yellow lines in (g) and (h).
We conducted an experiment for a reflective 3D object using the constructed SSPS-IDH system. Figure 5 shows the newly constructed SSPS-IDH system and its optical setup. Figure 5(a) shows that the optical elements for SSPS-IDH were attached to each other, and fifteen cover glasses, each of which had a thickness was 0.17 mm, were inserted to obtain the fixed z2 between the compact polarization image sensor (Lucid, VP-PHX050S-PNL) and the second geometric phase lens. This time we used multiple cover glasses to obtain the rigid value of z2 for this experimental demonstration. The use of multiple glasses causes multiple reflection between each boundary. The uses of antireflection coatings to respective optical components and a transparent plate with a designed thickness and/or phase lenses with designed sizes will lead to make a compact hologram sensing system, termed “Holosensor”, with high light-use efficiency. In the cases where the mounts with different sizes of phase lenses are used to construct compact 3D macroscopy and 3D microscopy systems with high light-use efficiency, a compact 3D sensing system with the designed minification/magnification is constructed by setting the second phase lens as thin/thick in comparison to the first phase lens. The distance between the image sensor and the second geometric phase lens was adjusted by inserting transparent optical element(s) such as cover glasses. By setting z1 and z2, we can adjust the magnification, which will open possibilities of applications of this system to 3D macroscopy and 3D microscopy. Figures 5(b) and 5(c) show that the size of the SSPS-IDH system in the x- and z-axis directions was 25 mm. The size in the y-axis direction was the same as that in the x-axis direction. A reflective 3D object had a white surface and a width of 7 mm as shown in Fig. 5(d). Figures 5(e) and 5(f) show that the SSPS-IDH system can come close to the object to record its 3D information. Light irradiated from a red LED (Thorlabs, M625L4) with a lens was introduced to the object from the top side of the object as shown in Fig. 5(g). The exposure time was 1 ms. To show 3D sensing ability of the system for a reflective object, the depth position of the object was changed once after recording a digital hologram. The depth position of the object was shifted 2 mm toward the back. Then, another digital hologram was captured. Images of the object at respective depth positions were reconstructed from the respective digital holograms. For comparison, focused object images were obtained, not only by SSPS-IDH but also with a single incoherent hologram without phase-shifting interferometry. Figure 6 shows the experimental results. Four phase-shifted holograms were obtained after de-mosaicking from a single image based on SSPS-IDH as shown in Figs. 6(a)–6(d). Figures 6(e)–6(h) show that the quality of the image reconstructed by SSPS-IDH was much higher than that obtained from a single incoherent hologram without phase-shifting interferometry. Focused and defocused object images were freely obtained after recording a single image as shown in Figs. 6(g) and 6(h). Figures 6(i)–6(l) were reconstructed images of the object after movement in the depth direction. Figure 6(k) shows that the numerical propagation distance was the same as that shown in Fig. 6(g), and a defocused image was obtained because the object was moved in the depth direction. A focused image of the object after movement was successfully obtained by changing the numerical propagation distance as shown in Fig. 6(l). These results indicate that the constructed SSPS-IDH system has the 3D sensing ability for a reflective 3D object. Diffraction patterns shown in Figs. 6(g), 6(h), 6(k), and 6(l) indicate higher-order waves generated by geometric phase lenses. Single-shot 3D sensing for a reflective 3D object was experimentally demonstrated.
Fig. 5. SSPS-IDH system and its optical setup. (a) Photograph of the constructed SSPS-IDH system. Side views with the scale to measure the size of the SSPS-IDH system in the (b) z- and (c) x-axis directions. (d) Photograph of a reflective 3D object. (e) Side and (f) top views of the optical setup. (g) Light source and geometry of the illumination for the object.
Fig. 6. Experimental results for a reflective 3D object. De-mosaicked holograms with the phase shifts of (a) 0, (b) π/2, (c) π, and (d) 3π/2. (e)–(h) Reconstructed images of the object before movement in the depth direction. (i)–(l) Reconstructed images of the object after movement. (e), (f), (i), (j) Images reconstructed with a single incoherent hologram without phase-shifting interferometry. (g), (h), (k), (l) Images reconstructed by SSPS-IDH. The numerical propagation distances were (e), (g), (i), (k) 187 mm and (f), (h), (j), (l) 193 mm.
4. Discussion and conclusion
The validity of the SSPS-IDH system was experimentally demonstrated, and in this section, we discuss the way to improve the resolution of SSPS-IDH. The resolution is severely affected by the pixel pitch of each phase-shifted hologram in the SSPS-IDH system. In the constructed SSPS-IDH system with a color image sensor, the pixel pitch of a phase-shifted incoherent hologram at red and blue channels was 13.8 μm, and then the resolution beyond the pixel pitch was difficult without the super-resolution of FINCH. However, an image sensor with a pixel pitch of less than 1 μm for a camera in a cell phone is now commercially available. The resolution will reach easily the 1 μm order by introducing such an image sensor to a polarization-imaging camera. At this time, results indicate the possibility of taking the DH and DHM systems outdoors by hand. Improvement of resolution with diffraction optics will also be achieved using an optical design based on FINCH.
We have proposed a palm-sized SSPS-IDH system by which 3D information of a 10-μm-order structure is obtained with a single-shot exposure of an image sensor. An experiment was conducted, and apertures whose width was less than 50 μm were focused and successfully resolved. A more compact SSPS-IDH system was constructed to record a digital hologram of a reflective 3D object. The constructed SSPS-IDH system had dimensions of 25 mm × 25 mm × 25 mm, and with an appropriate light source such as an LED and sunlight, it is easy to take it outdoors by hand. Macro 3D sensing ability was successfully demonstrated for a reflective 3D object. Field of view and resolution improvements are the next research themes, and the optical design will be further improved. SSPS-IDH will have various applications, such as portable 3D microscopy that can be taken outdoors by hand, telemedicine, on-chip 3D microscopy, and other portable 3D imaging applications.
Funding
Precursory Research for Embryonic Science and Technology (JPMJPR16P8); Japan Society for the Promotion of Science (JP18H01456); Cooperative Research Program of "Network Joint Research Center for Materials and Devices" (20211086).
Acknowledgement
We thank Yuichi Kozawa for helpful discussions.
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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