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We present phase-shifting interferometry techniques applied for multidimensional incoherent digital holography and toward ultimately low light-intensity sensing. Using incoherent holography with multiwavelength-multiplexed phaseshifting interferometry that is termed computational coherent superposition (CCS), full-color three-dimensional (3D) information of an incoherent object can be obtained from the recorded wavelength-multiplexed self-interference holograms. Furthermore, an optical setup of incoherent holography based on CCS is implemented as a palm-sized incoherent digital holographic sensing system, termed “Holosensor.” Using incoherent holography with single-shot phase-shifting holography, high-speed 3D motion-picture imaging has been demonstrated. Phase-shifting interferometry is also a powerful 3D sensing technique for ultimately low light-intensity conditions.

The use of phase-shifting interferometry (PSI) in the ultra-low-light region would open the way for important applications, such as imaging of phototoxic substances and sensing of ultrafast phenomena. In the ultra-low-light region, the statistical nature of photons can be a dominant source of noise compared with other noise caused by experimental instruments. Here we theoretically derive the precision limit determined by the statistical nature of photons for simultaneously measuring the transmittance and phase of a sample with PSI. We show that the precision of PSI depends on the phase and transmittance themselves. We also show a trade-off relation between transmittance and phase. Then we compare PSI with sequential optimal measurements in which the transmittance and phase of a sample are separately measured for each corresponding optimal measurement. We also discuss the case where the input number of photons fluctuates with a Poisson distribution and show that the fluctuation affects both the transmittance and phase precision for PSI.

Fresnel incoherent correlation holography (FINCH) was a milestone in incoherent holography. In this roadmap, two pathways, namely the development of FINCH and applications of FINCH explored by many prominent research groups, are discussed. The current state-of-the-art FINCH technology, challenges, and future perspectives of FINCH technology as recognized by a diverse group of researchers contributing to different facets of research in FINCH have been presented.

We present multidimensional information sensing using incoherent digital holography with phase-shifting interferometry. Spatially incoherent light is recorded as an incoherent hologram by incoherent holography and three-dimensional, wavelength, and temporal information is obtained by applying various phase-shifting interferometry techniques such as the computational coherent superposition scheme.

We present color fluorescence imaging using an incoherent digital holographic technique in which holographic multiplexing of multiple wavelengths is exploited. Self-interference incoherent digital holography with a single-path in-line configuration and the computational coherent superposition scheme are adopted to obtain color holographic three-dimensional information of self-luminous objects with a monochrome image sensor and no mechanical scanning. We perform not only simultaneous color three-dimensional sensing of multiple self-luminous objects but also color fluorescence imaging of stained biological samples. Color fluorescence imaging with an improved point spread function is also demonstrated experimentally by adopting a Fresnel incoherent correlation holography system.

We propose a phase-shifting interferometry technique using only two in-line phase-shifted self-interference holograms. There is no requirement for additional recording or estimation in the measurement. The proposed technique adopts a mathematical model for self-interference digital holography. The effectiveness of the proposed technique is demonstrated by experiments on incoherent digital holographic microscopy and color-multiplexed fluorescence digital holography with computational coherent superposition. Two-color-multiplexed four-step phase-shifting incoherent digital holography is realized for the first time, to the best of our knowledge, using the proposed technique.

We present an incoherent two-color digital holography system to record holograms with 2,048 x 2,048 pixels at 72 fps for fluorescence-stained cell imaging. We utilize single-shot wavelength-multiplexed incoherent digital holography with computational coherent superposition.

We present an incoherent digital holography system with 102 fps for simultaneous, holographic, and microscopic motion-picture sensing of multiple fluorescence nanoparticles. We utilize single-path single-shot phase-shifting incoherent digital holography with a birefringent material array.

Phase-shifting interferometry selectively extracting wavelength information has been proposed since 2013, which is called computational coherent superposition (CCS) of multiple wavelengths. In this proceeding, we apply CCS to self-interference incoherent holography and construct single-path, mechanical-motion-free, wavelength-multiplexed, incoherent multicolor digital holographic microscopy systems. Also, we numerically investigate quantum fluctuation in phase-shifting interferometry for the sensing of weak light such as natural light and nonlinear light. After that, we briefly discuss the difference between the digital holography systems with CCS and phase-shifting interferometry with a Bayer color image sensor.

We present approaches for simultaneous, holographic, and microscopic multicolor motion-picture sensing of multiple natural light sources. We utilize single-shot incoherent digital holography with a polarization-imaging sensor, phase-shifting interferometry, and computational coherent superposition (CCS) as approaches.

We present a multiwavelength incoherent digital holographic microscope with wavelength-multiplexed phase-shifted holograms and halogen lamp. A multicolor holographic image is obtained from spatially incoherent white light, using neither mechanical scanning nor a color image sensor.

We present an incoherent color digital holographic microscope for single-shot multicolor three-dimensional imaging of microscopic specimens. The system does not require any spatial light modulator and light-use efficiency is improved due to no beam splitter.

We propose multiwavelength in-line phase-shifting digital holography with a monochrome image sensor, single reference arm, and no mechanical scanning. We use phase-shifting interferometry selectively extracting wavelength information as a method to obtain multiwavelength object waves separately from wavelength-multiplexed phase-shifted holograms. By exploiting a liquid crystal on silicon spatial light modulator with a wide phase-modulation range as an electrically driven phase shifter in this interferometry, we remove mechanically moving parts during phase shifting. Its effectiveness is experimentally demonstrated.

For incoherent and coherent digital holography, the parallel phase-shifting technique has been used to reduce the number of exposures required for the phase-shifting technique which eliminates zero-order diffraction and conjugates image components. Although the parallel phase-shifting technique can decrease the hologram recording time, the image interpolations require additional calculation time. In this study, we propose a technique that reduces the calculation time for image interpolations; this technique is based on the convolution theorem. We experimentally verified the proposed technique and compared it with the conventional technique. The proposed technique is more effective for more precise interpolation algorithms because the calculation time does not depend on the size of interpolation kernels.

Computational holography, encompassing computer-generated holograms and digital holography, utilizes diffraction calculations based on complex-valued operations and complex Fourier transforms. However, for some holographic applications, only real-valued holograms or real-valued diffracted results are required. This study proposes a real-valued diffraction calculation that does not require any complex-valued operation. Instead of complex-valued Fourier transforms, we employ a pure real-valued transform. Among the several real-valued transformations that have been proposed, we employ the Hartley transformation. However, our proposed method is not limited to this transformation, as other real-valued transformations can be utilized.

We propose a quantitative phase imaging technique with single-path phase-shifting digital holography using a light-emitting diode (LED). A reference wave is generated from an object wave in the Fourier plane using a single-path interferometer, based on self-reference digital holography. The object wave interferes with the reference wave, and the quantitative phase information of the object wave is recorded as a digital hologram. Quantitative phase images of objects are obtained by applying a phase-shifting interferometry technique. All the light diffracted from the objects can be utilized to generate a digital hologram. Its validity is experimentally demonstrated by constructing an optical system with a wide-field optical microscope.

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.

We propose a novel algorithm that does not require any Fourier transform to extract multiple object waves in a single image recorded with spatial frequency-division multiplexing. Smoothing is utilized to extract the desired object-wave information from a spatially multiplexed image. Numerical and experimental results show its validity and applicability for image and Fresnel digital holography. Our investigations clarify the speeding up of both the object-wave extractions and multiple object–image reconstructions quantitatively.

We propose a dual-wavelength phase-shifting digital holography technique with four wavelength-multiplexed holograms based on phase-division multiplexing utilizing the 2π ambiguity and zeroth-order diffraction-image suppression. Zeroth-order wave suppression is implemented by introducing the averaging method. Its effectiveness is experimentally shown and numerically and quantitatively investigated. The numerical investigation demonstrates the tolerance of the proposed technique against incoherent light noise and changes in the reference wave intensity. The image quality in the proposed technique depends on the intensity ratio between the object and reference waves but does not degrade with constant changes in intensity. In contrast, a previously reported four-step dual-wavelength phase-shifting technique was affected by the factors described above.

We propose a multicolor lensless three-dimensional image-sensing technique with a full space-bandwidth product of an image sensor, seven wavelength-multiplexed holograms, a single reference arm, and no mechanical movements. Its effectiveness is experimentally demonstrated.

We present a digital holography using high dynamic range (HDR) imaging to improve quality of the reconstructed image of digital holography. The technique extends the dynamic range of the digitally recorded hologram using multiple holograms recorded with different exposures. We numerically and experimentally demonstrated the technique based on an off-axis digital holography system. In the numerical simulation and experiment, the quality of the reconstructed images by the proposed technique is higher than that by the conventional digital holography without HDR imaging.

We propose a digital holographic microscope for the single-shot multicolor three-dimensional (3D) image sensing of specimens illuminated by spatially and temporally incoherent white light. The proposed microscope exploits self-interference, single-shot phase-shifting incoherent digital holography, a polarization-imaging color image sensor, and static polarization-sensitive optical elements to generate two object waves with different curvature radii. The microscope does not require any spatial light modulator or a beam splitter, and can be constructed with a compact single-path optical setup. The color holographic 3D motion picture recording of spatially and temporally incoherent white light at a speed of 10 fps order is experimentally demonstrated with the proposed microscope.

We propose a holographic technique by which multiwavelength three-dimensional spatial information is obtained with both a single-shot exposure of a monochrome image sensor and an in-line holographic multiplexing scheme. We develop a specially designed monochrome image sensor with a wavelength-dependent phase-modulation array, which is used to obtain the holographic information required for the proposed technique. The proposed technique is applicable for not only laser holography but also spatially and temporally incoherent holography. Its validity is experimentally demonstrated by constructing a color-multiplexed fluorescence digital holographic microscope and a multicolor incoherent digital holography system with a white-light source.

In this Letter, we propose spatially incoherent multiwavelength three-dimensional (3D) microscopy that exploits holographic multiplexing and is based on computational coherent superposition (CCS). The proposed microscopy generates spatially incoherent wavelength-multiplexed self-interference holograms with a multiband-pass filter and spatially and temporally incoherent light diffracted from specimens. Selective extractions of 3D spatial information at multiple wavelengths from the holograms are realized using the CCS scheme. We constructed fully mechanical-motion-free holographic multiwavelength 3D microscopy systems and conducted experiments to demonstrate the microscopy.

We propose multiwavelength-multiplexed phase-shifting incoherent color digital holography. In this technique, a monochrome image sensor records wavelength-multiplexed, phase-shifted, and incoherent holograms, and a phase-shifting interferometry technique selectively extracts object waves at multiple wavelengths from the several recorded holograms. Spatially incoherent light that contains multiple wavelengths illuminates objects, and multiwavelength-incoherent object waves are simultaneously obtained without using any wavelength filters. Its effectiveness is experimentally demonstrated for transparent and reflective objects.

The quality of reconstructed images in relation to the bit depth of holograms formed by wavelength-selective phase-shifting digital holography was investigated. Wavelength-selective phase-shifting digital holography is a technique to obtain multiwavelength three-dimensional (3D) images with a full space-bandwidth product of an image sensor from wavelength-multiplexed phase-shifted holograms and has been proposed since 2013. The bit resolution required to obtain a multiwavelength holographic image was quantitatively and experimentally evaluated, and the relationship between wavelength resolution and dynamic range of an image sensor was numerically simulated. The results indicate that two-bit resolution per wavelength is required to conduct color 3D imaging.

Digital holography (DH) is a promising technique for modern three-dimensional (3D) imaging. Coherent holography records the complex amplitude of a 3D object holographically, giving speckle noise upon reconstruction and presenting a serious drawback inherent in coherent optical systems. On the other hand, incoherent holography records the intensity distribution of the object, allowing a higher signal-to-noise ratio as compared to its coherent counterpart. Currently there are two incoherent digital holographic techniques: optical scanning holography (OSH) and Fresnel incoherent correlation holography (FINCH). In this review, we first explain the principles of OSH and FINCH. We then compare, to some extent, the differences between OSH and FINCH. Finally, some of the recent applications of the two incoherent holographic techniques are reviewed. Published version

Single-shot multiwavelength digital holography using angular multiplexing and spatial bandwidth enhancement is proposed to extend the field of view without the superimposition of undesired images. Angular multiplexing is used to record multiple wavelength information with a single-shot exposure of a monochromatic image sensor. Enlargement of the field of view without the superimposition of undesired images is achieved by designing both the object-wave spectra and angle conditions to obtain wide spatial bandwidths in the respective wavelengths with a high signal-to-noise ratio. Theoretical analyses clarified that the field of view is 1.33 times extended in square by the proposed technique in the case of dual wavelengths. Single-shot, multiple wavelengths, and 3D image recording with both the extended field of view and no superimposition of the zeroth-order diffraction wave is experimentally demonstrated while the zeroth-order wave remains, and the color-synthesized image is degraded in the conventional technique. Experimental results agree well to the theoretical analysis.

We propose single-shot multiwavelength phase unwrapping using a single reference beam and a monochromatic image sensor. A single beam containing multiple wavelengths passes through a reference arm and acts as reference waves. Multiple-wavelength information is multiplexed in the space domain on the monochromatic image sensor and is separated in the spatial frequency domain by utilizing the spatial frequency difference of interference fringes at multiple wavelengths. From a single hologram, multiwavelength phase unwrapping is conducted and an unwrapped phase image is obtained. Both transmission and reflective single-shot multiwavelength digital holography systems using a monochromatic image sensor can be constructed with a simple optical setup employing the proposed technique. Single-shot multiwavelength phase unwrapping by the proposed technique is numerically simulated and experimentally demonstrated.

We propose multiwavelength in-line digital holography with wavelength-multiplexed phase-shifted holograms and arbitrary symmetric phase shifts. We use phase-shifting interferometry selectively extracting wavelength information to reconstruct multiwavelength object waves separately from wavelength-multiplexed monochromatic images. The proposed technique obtains systems of equations for real and imaginary parts of multiwavelength object waves from the holograms by introducing arbitrary symmetric phase shifts. Then, the technique derives each complex amplitude distribution of each object wave selectively and analytically by solving the two systems of equations. We formulate the algorithm in the case of an arbitrary number of wavelengths and confirm its validity numerically and experimentally in the cases where the number of wavelengths is two and three.

We propose three-wavelength phase-shifting interferometry selectively extracting wavelength information from wavelength-multiplexed images with arbitrary phase shifts. Wavelength information is multiplexed on the space and spatial frequency domains and is separated in the polar coordinate plane by utilizing the proposed phase-shifting interferometry. 0th-order diffraction waves and conjugate images are also removed from wavelength-multiplexed images when extracting wavelengths separately. As a result, a full spatial bandwidth of a monochromatic image sensor at each wavelength is available with a small number of images. Images required for three-wavelength three-dimensional imaging with a full spatial bandwidth of a monochromatic image sensor are decreased and speeding up of measurement is expected in comparison with a conventional technique. The validity of the proposed technique is numerically confirmed.

We propose three-wavelength digital holographic microscopy with seven wavelength-multiplexed holograms and arbitrary small phase shifts. Full space-bandwidth product of a monochromatic image sensor at each wavelength is available with a small number of images.

We propose a technique capable of obtaining spectral information and three-dimensional information of objects. This technique is based on digital holography and spectral estimation technique. In this technique, multiple lasers operating at different wavelengths, such as red, green, and blue, are used to record the complex amplitude of the object in digital holography, and multiple reconstructed monochrome images can be obtained by each wavelength. Spectral estimation technique is used to estimate the spectral reflectance distribution of the object from the multiple reconstructed monochrome images. Through the spectral estimation technique, the spectral reflectance distribution of object can be obtained. The effectiveness of the proposed method was confirmed by a numerical simulation and an experiment.

An A4-sized parallel phase-shifting digital holography system was constructed and experimentally demonstrated. Parallel phase-shifting digital holography is a technique being capable of instantaneous recording of three-dimensional (3-D) image of moving object. Aiming at a 3-D motion picture measurement of moving object system that can be carried on sites where the measurement system is needed, we improved a previous portable parallel phase-shifting digital holography system. The size and weight of the improved portable system are 300 mm × 210 mm × 160 mm and 6 kg, respectively. Also, we experimentally recorded a series of holograms of a moving object and reconstructed motion pictures, which show the same event but are focused at each depth, from the holograms. Thus, the 3-D motion picture recording and reconstruction capability of the constructed system were successfully demonstrated. A 3-D motion picture at 10 frames/s was obtained by the system.

We propose and demonstrate a multicolor single-pixel digital holography technique. The intensity and phase images of an object are simultaneously obtained from the time-sequence intensity data captured using a single-pixel photodetector. Moreover, phase-structured light and phase-shifting interferometry are implemented using only a spatial light modulator without any mechanical movements. The adopted configuration dramatically simplifies the optical setup by removing both imaging optics and the resultant chromatic aberration. The effectiveness of the proposed technique is demonstrated numerically and experimentally.

To improve the quality of reconstructed images, we apply bicubic interpolation and B-spline interpolation to parallel phase-shifting digital holography for the first time. The effectiveness of bilinear interpolation, bicubic interpolation, and B-spline interpolation in parallel phase-shifting digital holography is shown by a numerical simulation. In the simulation result, the application of bicubic interpolation and B-spline interpolation succeeded in decreasing the rootmean- square error of the reconstructed image by 12.6 and 11.9%, respectively.

Parallel phase-shifting digital holography (PPSDH) is a technique of single-shot phase-shifting digital holography. We found that there are two problems with this technique. (1) Some extraneous noises caused by the intensity unevenness of the reference wave become slightly superimposed on the object image. (2) The conjugate image cannot be completely removed. This is because the object wave causes the phase-shift error by illuminating an image sensor with a large incident angle. To solve these problems, we propose an algorithm for removing residual 0th-order diffraction and conjugate images in PPSDH. In the proposed algorithm, we modified phase-shifting interferometry in order to work through the unevenness of the intensity distribution and applied the Fourier transform technique to PPSDH to remove the residual conjugate image. The effectiveness of the proposed algorithm was experimentally verified.

We propose single-shot multiwavelength digital holography using a monochromatic image sensor and dual reference arms. Multiple wavelength information is multiplexed on the monochromatic image sensor plane in the space domain and is separated in the spatial frequency domain by utilizing the difference between the spatial frequencies of interference fringes at respective wavelengths. The recordable spatial bandwidth that is utilized for object waves is extended by using dual reference arms in comparison with that using a single reference arm. Both the three-dimensional and three-wavelength information of an object were recorded and reconstructed without the crosstalk between object waves with multiple wavelengths.

We propose multiwavelength digital holography based on phase-division multiplexing using arbitrary symmetric phase shifts to each wavelength. A monochromatic image sensor records wavelength-multiplexed phase-shifted holograms and wavelength information is separated in the polar coordinate plane.

We propose a single-shot phase unwrapping technique using a single wavelength and parallel phase-shifting interferometry. In the proposed technique, an object is illuminated by two laser beams, which are emitted from the same laser, and have different illumination angles and polarizations. Two types of object waves generated by the two beams are separately and simultaneously recorded by a polarization-imaging camera. In the path of the reference wave, an array of phase retarders is placed to implement the parallel phase-shifting technique. A highly accurate three-dimensional shape is reconstructed from a single hologram. We numerically simulated the proposed technique and conducted a preliminary experiment to verify its effectiveness. It was confirmed that millimeter-order height, which was several thousand times the wavelength of the laser, can be reconstructed by the proposed technique without wrapping.

We propose a color digital holography using four recording wavelengths to improve the color reproduction of three-dimensional imaging of objects. In conventional color digital holography, three-wavelength light beams corresponding to red, green, and blue are used for recording holograms. In this paper, a laser-emitting yellow light is added to the conventional color digital holography. Also spectral estimation technique is introduced to the four-wavelength recording technique to improve the color reproduction of color digital holography. The effectiveness of the proposed method was numerically confirmed. Also the proposed technique was experimentally demonstrated using four lasers operated at 473, 532, 561, and 633 nm, respectively. When Macbeth color chart consisting of 24 color patches was used as objects, in comparison to conventional technique, the average color differences between the objects and the reconstructed images by the proposed technique for the 24 colors are decreased from 7.88 to 6.24 in numerical simulation and from 10.02 to 8.63 in experiment, respectively.

We succeeded in 3-D motion-picture imaging for dynamic motion of biological objects swimming at different depths by parallel phase-shifting digital holographic microscopy (PPSDHM). PPSDHM is a technique for high-quality instantaneous 3-D imaging of specimens in the microscopic field of view by single-shot recording of multiple phase-shifted holograms. We constructed a PPSDHM for recording high-speed dynamic phenomena and then motions of biological objects in water were recorded at 20 000 and 150 000 frames/s, respectively, which is the fastest among the previous reports on 3-D imaging of biological objects.

We propose an in-line color digital holography that can suppress a 0th-order diffraction image and a conjugate image. This technique reconstructs the image of an object from two holograms that are formed at two different distances from the object for each primary color. We numerically simulated the proposed technique and confirmed that it enabled the reconstruction of higher-quality images of an object than the Fresnel transform alone, which is the simplest reconstruction algorithm in digital holography. The effectiveness of the proposed technique was also quantitatively shown by evaluating the reconstructed images using root-mean-square errors. Thus, it was confirmed that the proposed technique was capable of recording and reconstructing both three-dimensional information and color information of an object.

We comparatively analyzed and quantitatively evaluated the field of view and the viewing zone of single-shot phaseshifting digital holography that uses space-division multiplexing, for the first time. We formulated the sampling intervals in the techniques in which the phase of the reference wave is spatially divided into two and four steps, and numerically simulated the areas. It was clarified that each area of the spatial two-step phase-shifting technique was twice as wide as that of the spatial four-step phase-shifting technique. We also experimentally investigated the areas. The ghost appeared for the spatial four-step technique when the object was between the boundary of the field of view of the spatial two-step technique and that of the spatial four-step technique, but did not appear for the spatial two-step technique.