Evaluation of parallel phase-shifting digital holography by photon-counting method

We propose a parallel two-step phase-shifting digital holography technique capable of instantaneous measurement of three-dimensional objects, with a view toward measurement of dynamically moving objects. The technique is based on phase-shifting interferometry. The proposed technique carries out the two-step phase-shifting method at one time and can be optically implemented by using a phase-shifting array device located in the reference beam. The array device has a periodic two-step phase distribution, and its configuration is simplified compared with that required for three-step and four-step parallel phase-shifting digital holographies. Therefore the optical system of the proposed technique is more suitable for the realization of a parallel phase-shifting digital holography system. We conduct both a numerical simulation and a preliminary experiment in the proposed technique. The results of the simulation and the experiment agree well with those of sequential phase-shifting digital holography, and results are superior to those obtained by conventional digital holography using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.

We propose an algorithm that can improve the quality of the reconstructed image from the single hologram recorded by the optical system of the parallel four-step phase-shifting digital holography. The proposed algorithm applies the image-reconstruction algorithm of parallel two-step phase-shifting digital holography to the hologram so as to reduce errors in the reconstructed image and eliminate ghosts. We numerically and experimentally confirmed that the proposed algorithm decreased 25% in terms of root mean square error in amplitude, and eliminated the ghosts, respectively.

An encryption system that combines compressive sensing (CS) and two‐step parallel phase shifting digital holography (PPSDH) using double random phase encoding (DRPE) is presented in this paper. The two‐step PPSDH is a linear inline holographic scheme and is much suitable for encrypting the 2D/3D information in a single exposure. The distribution of random phase mask (RPM) in the DRPE is implemented using circular harmonic key which increases the security of the encryption process. In this system, the keys used to encrypt are spatial positions of the planes, wavelength, and rotation of the circular harmonics in RPMs, and CS acts as an additional key that makes the system more secure than the conventional optical encryption methods. At the transmission end, two‐step PPSDH is applied to encrypt the object information in single hologram. The digital mirror device (DMD) is placed between the object and a single‐pixel detector for acquiring fewer hologram measurements. At the receiver end, the single digital hologram is numerically recovered by using a CS optimization problem. The original complex object field is decrypted from the CS recovered holograms by the inversion of two‐step PPSDH process with the help of the correct keys. The numerical simulations are presented for complex 2D and 3D objects to test the feasibility of the proposed encryption and decryption system. The proposed method carried out intensity and phase reconstruction of the original object field using single‐pixel compressive imaging. The computer simulation results demonstrated that the encrypted information is highly secured with the rotation of the circular harmonic key. The sensitivity of the decrypted intensity and phase images is also studied with variations of the encrypted keys. The obtained results show that the proposed encryption scheme is feasible and has better security performance and robustness.

Sound field imaging techniques have been found very useful for acoustic designs. Building on this idea, innovative techniques are needed and presented in this paper, where we report on developed imaging of the sound field radiated from speakers by parallel phase-shifting digital holography. We adopted an ultrasonic wave radiated from a speaker for an object. The phase distribution of the light wave was modulated by the sound field radiated from the speaker. The modulated phase distribution was recorded in the form of multiplexed phase-shifted holograms at the frame rate of 100,000 fps. A 40,000 Hz sound field radiated from a speaker is used as an observation target. Our proposed method can implement the imaging of the sound field successfully. Also, in order to demonstrate the digital refocusing capability of digital holography, we set two speakers, whose difference in depth positions was 6.6 cm, as a long-depth object. We demonstrated the digital refocusing on the two speakers along with the capability of measuring the positions of the objects. Furthermore, we succeeded in imaging of 40,000 Hz and 41,000 Hz sound fields radiated from the two speakers. The presented experimental results showed that parallel phase-shifting digital holography is very useful and suitable for sound field imaging.

Parallel phase-shifting digital holography (PPSDH) has been introduced. Movies of high-speed 3-D imaging and those of high-speed phase imaging obtained by PPSDH using a high-speed camera will be demonstrated at the presentation. PPSDH will contribute for 3-D measurement of moving object in such the applications as biological microscope, particle and flow measurement, and so on. This study was partially supported by Next Generation World-Leading Researchers, Japan Society for the Promotion of Science (JSPS).

Parallel phase-shifting digital holography is a powerful technique for recording motion picture of holograms with an image sensor and numerically reconstructing the motion picture of the high-quality three-dimensional (3-D) images of the object in a computer. This technique provides high-quality images of light intensity and phase of the object at a time instant at arbitrary depth position. Therefore, the technique achieves 3-D motion-picture imaging of a dynamic object. The technique provides not only large depth of field and high temporal resolution at the same time but also a motion picture of an invisible object. It is difficult for other 3-D imaging techniques to achieve these features of parallel phase-shifting digital holography. The authors review two experiments demonstrating the 3-D imaging by the technique and the features of the technique. One experiment demonstrated the motion-picture 3-D imaging of a minute crystal, sinking down in solution, by refocusing the amplitude images of the crystal. The result was obtained for the first time, to the best of our knowledge. The other demonstrated the motion-picture 3-D imaging of refractive indices of dynamic invisible gas flow by applying the Abel inversion to the phase images of the flow obtained by the technique.

The authors review recent advances in high-speed imaging of dynamic object with parallel phase-shifting digital holography. 3-D imaging of temperature of the air surrounding a heated object was demonstrated as an example of the advances.

A superresolution method for interference fringes obtained by parallel four-step phase-shifting digital holography is proposed. A complex amplitude distribution of an object wave is derived from a recorded hologram by parallel phase-shifting interferometry using two pixels without any interpolation procedures. Multiple distributions are derived by changing one of the two pixels when conducting phase-shifting interferometry. The angular spectrum distribution of the object wave is obtained by both the Fourier transforms and synthesis of the spectrum distribution from the Fourier-transformed images in the spatial frequency domain. Available space bandwidth is extended to half of that of an image sensor.

Two-photon holographic microscopy (TPHM) is a powerful technique for stimulating biological cells three-dimensionally. TPHM requires an imaging technique to detect fluorescence lights from the three-dimensionally distributed cells. In this study, parallel phase-shifting incoherent digital holography is applied to TPHM. Owing to the parallel phase-shifting method, the lights from the cells are detected with the frame rate of an image sensor. The feasibility of the proposed method is experimentally verified.

Development of the Imaging System for the Curing Process in UV Curing Resin Using Parallel Phase-Shifting Digital Holography

We developed a camera having the image sensor on which the phase-shifting array device suitable for near-infrared light was attached, and succeeded in parallel phase-shifting digital holography using ultrashort laser pulses of 96 fs duration.

Using parallel phase-shifting digital holography with a high-speed camera, the authors succeeded in phase-shifting interferometry at the rate of 180,000 fraames/s. Motion pictures of three-dimensional image of dynamically moving objects were demonstrated.

Phase-shifting digital holography has been used for the study of vibrating objects. The time-averaged complex amplitude of Fresnel diffracted field due to a vibrating object was obtained by using a three-step phase-shifting algorithm. Taking the inverse Fresnel transform of the complex amplitude resulted in an image of the object superimposed with Bessel fringes. The Bessel fringes are contour map of the vibration amplitude. By sinusoidally modulating the phase of the reference beam at the vibration frequency, the brightest fringe could be shifted to points of interest, thus extending the measurable range of vibration amplitude.

This paper investigates anisoplanatic numerical wave simulation in the context of lucky look imaging. We demonstrate that numerical wave propagation can produce root mean square (RMS) wavefront distributions and probability of lucky look (PLL) statistics that are consistent with Kolmogorov theory. However, the simulated RMS statistics are sensitive to the sampling parameters used in the propagation window. To address this, we propose and validate a new sample spacing rule based on the point source bandwidth used in the propagation and the level of atmospheric turbulence. We use the tuned simulator to parameterize the wavefront RMS probability density function as a function of turbulence strength. The fully parameterized RMS distribution model is used to provide a way to accurately predict the PLL for a range of turbulence strengths. We also propose and validate a new parametric average lucky look optical transfer function (OTF) model that could be used to aid in image restoration. Our OTF model blends the theoretical diffraction-limited OTF and the average turbulence short exposure OTF. Finally, we show simulated images for several anisoplanatic imaging scenarios that reveal the spatially varying nature of the RMS values impacting local image quality.

Recently, it has become necessary to detect cracks in structures such as buildings and bridges. Phase-shifting digital holography is one valuable method that can be used to measure the strain distribution on the surface of an object. However, to simplify the optical measurement setup, more compact equipment is required. An interferometric trigger method with dual piezo actuators for phase shifting is proposed. This method is useful for designing a head discrete-type measurement system that uses phase-shifting digital holography with multiple imaging sensors. The ability to phase shift using the proposed trigger method was confirmed with the reconstruction of an object and an experiment that was performed to measure the displacement distribution.