Two-step Phase-shifting Digital Holography Research Articles

Robust Holographic Reconstruction by Deep Learning with One Frame

A robust method is proposed to reconstruct images with only one hologram in digital holography by introducing a deep learning (DL) network. The U-net neural network is designed according to DL principles and trained by the image data set collected using phase-shifting digital holography (PSDH). The training data set was established by collecting thousands of reconstructed images using PSDH. The proposed method can complete the holography reconstruction with only a single hologram and then benefits the space bandwidth product and relaxes the storage loads of PSDH. Compared with the results of PSDH, the results of deep learning are immune to most disturbances, including reference tilt, phase-shift errors, and speckle noise. Assisted by a GPU processor, the proposed reconstruction method can reduce the consumption time to almost one percent of the time needed by two-step PSDH. This method is expected to be capable of holography imaging with a single hologram, with high capacity, efficiently in the digital holography applications.

Super-Bandwidth Two-Step Phase-Shifting Off-Axis Digital Holography by Optimizing Two-Dimensional Spatial Frequency Sampling Scheme

The presence of the auto correlation and twin cross correlation noises restrict the available spatial bandwidth of the holographic microscopy to much less than the available bandwidth of the digital sensor. Therefore, in order to record the same image area as conventional 2D intensity imaging techniques, several images should be taken. We present two-step phase-shifting off-axis digital holography with maximum space-bandwidth product for three-dimensional (3D) digital holography. Removing the autocorrelation term using a two-step phase-shifting technique significantly increases the available bandwidth for off-axis interferometry. An optimizing super-diagonal two-dimensional (2D) spatial frequency sampling scheme at the sub-Nyquist frequency is employed for performing off-axis interferometry in the absence of the autocorrelation term. The spatial bandwidth of the proposed two-step phase-shifting technique is 400% of that in square scheme off-axis digital holography. Experimental results demonstrate the feasibility of this technique in extracting the 3D morphology of transparent microscopic objects with a larger bandwidth.

Proposal for Optical One-time Password Authentication Using Digital Holography

A new optical one-time password (OTP) authentication method using digital holography is proposed, which enhances security strength in the authentication system. A challenge-response optical OTP algorithm based on two-factor authentication is presented using two-step phase-shifting digital holography, and two-way authentication is also performed using challenge-response handshake in both directions. Identification (ID), password (PW), and OTP are encrypted with a shared key by applying phase-shifting digital holography, and these encrypted pieces of information are verified by each party by means of the shared key. The encrypted digital holograms are obtained by Fourier-transform holography and are recorded on a CCD with 256 quantized gray-level intensities. Because the intensity pattern of such an encrypted digital hologram is distributed randomly, it guards against a replay attack and results in higher security level. The proposed method has advantages, in that it does not require a time-synchronized OTP, and can be applied to various authentication applications. Computer experiments show that the proposed method is feasible for high-security OTP authentication.

랜덤 위상 마스크와 2-단계 위상 천이 디지털 홀로그래피를 이용한 이진 영상 이중 암호화

랜덤 위상 마스크와 2-단계 위상 천이 디지털 홀로그래피를 이용한 이진 영상 이중 암호화

Detection and correction of wavefront errors caused by slight reference tilt in two-step phase-shifting digital holography.

A simple and convenient method, without the need for any additional optical devices and measurements, is suggested to improve the quality of the reconstructed object wavefront in two-step phase-shifting digital holography by decreasing the errors caused by reference beam tilt, which often occurs in practice and subsequently introduces phase distortion in the reconstructed wave. The effects of reference beam tilt in two-step generalized interferometry is analyzed theoretically, showing that this tilt incurs no error either on the extracted phase shift or on the retrieved real object wave amplitude on the recording plane, but causes great deformation of the recovered object wavefront. A corresponding error detection and correction approach is proposed, and the formulas to calculate the tilt angle and correct the wavefront are deduced. A series of computer simulations to find and remove the wavefront errors caused by reference beam tilt demonstrate the effectiveness of this method.

Selective Interpolation Method for Two-Step Parallel Phase-Shifting Digital Holography

We propose the reconstruction algorithm for two-step parallel phase-shifting digital holography. Parallel phase-shifting digital holography records a single hologram and numerically extracts the multiple images needed for obtaining the complex amplitude in phase-shifting technique. During the reconstruction process, phase error and degradation of image occur due to the calculation error. The proposed algorithm interpolates into two steps that include the subpixel data to reduce the error, so the quality that a reconstructed image can be enhanced. Both numerical simulation and experiment are conducted to verify the effectiveness of the proposed algorithm.

Experimental Study of Two-step Phase-shifting Digital Holography based on the Calculated Intensity of a Reference Wave

Two-step quadrature phase-shifting digital holography based on the calculated intensity of a reference wave is proposed. In the Mach-Zehnder interferometer (MZI) architecture, the method only records two quadrature-phase holograms, without reference-wave intensity or object-wave intensity measurement, to perform object recoding and reconstruction. When the reference-wave intensity is calculated from the 2D correlation coefficient (CC) method that we presented, the clear reconstruction image can be obtained by some specific algorithm. Its feasibility and validity were verified by a series of experiments with 2D objects and 3D objects. The presented method will be widely used in real-time or dynamic digital holography applications.

基于相移量提取的两步相移数字全息术

基于相移量提取的两步相移数字全息术

Double images hiding by using joint transform correlator architecture adopting two-step phase-shifting digital holography

Based on the joint Fresnel transform correlator, a new system for double images hiding is presented. By this security system, the dual secret images are encrypted and recorded as intensity patterns employing phase-shifting interference technology. To improve the system security, a dual images hiding method is used. By digital means, the deduced encryption complex distribution is divided into two subparts. For each image, only one subpart is reserved and modulated by a phase factor. Then these modified results are combined together and embedded into the host image. With all correct keys, by inverse Fresnel transform, the secret images can be extracted. By the phase modulation, the cross talk caused by images superposition can be reduced for their spatial parallel separation. Theoretical analyses have shown the system's feasibility. Computer simulations are performed to show the encryption capacity of the proposed system. Numerical results are presented to verify the validity and the efficiency of the proposed method.

Algorithm for reconstructing wide space-bandwidth information in parallel two-step phase-shifting digital holography

We propose an image-reconstruction algorithm of parallel phase-shifting digital holography (PPSDH) which is a technique of single-shot phase-shifting interferometry. In the conventional algorithms in PPSDH, the residual 0th-order diffraction wave and the conjugate images cannot be removed completely and a part of space-bandwidth information is discarded. The proposed algorithm can remove these residual images by modifying the calculation of phase-shifting interferometry and by using Fourier transform technique, respectively. Then, several types of complex amplitudes are derived from a recorded hologram according to the directions in which the neighboring pixels used for carrying out the spatial phase-shifting interferometry are aligned. Several distributions are Fourier-transformed and wide space-bandwidth information of the object wave is obtained by selecting the spectrum among the Fourier-transformed images in each region of the spatial frequency domain and synthesizing a Fourier-transformed image from the spectrum.

一种在二步相移数字全息中实现准确相移的方法

The quality of reconstruction in phase-shifting digital holography was determined by the accuracy of phase shift.An approach to obtain accurate phase shift in two-step digital holography was proposed.This approach employed an ordinary open-loop controlled piezoelectric actuator,and a serial of phase shift holograms corrisponding to different phase shift angles would be obtained by means of changing the volgate exerted on the piezoelectric actuator continuously.Then the holograms could be used to reconstruct the object intensity on the CCD plane.The object intensity on the CCD plane that already recorded by CCD would be used as a criterion to evalutae the quality of the reconstuction.The correlation coefficients between the criterion and the same intensity reconstructed with different phase shift holograms were obtained.The correlation coefficient reached its maximum when the phase shift hologram is with the accurate phase shift angle.Simulation was carried out and thereafter the approach was employed in experiment.The quality of the reconstructed field by using the accurate value and the nominal value were compared.The feasibility of this method has been verified by both computer simulations and experiments.

Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography

We propose an algorithm for compensating the phase-shift error of polarization-based parallel two-step phase-shifting digital holography, which is a technique for recording a spatial two-step phase-shifted hologram. Although a polarization-based system of the technique has been experimentally demonstrated, there had been the problem that the phase difference of two phase-shifted holograms had been changed by the extinction ratio of the micropolarizer array attached to the image sensor used in the system. To improve the performance of the system, we established and formulated an algorithm for compensating the phase-shift error. Accurate spatial phase-shifting interferometry in the system can be conducted by the algorithm regardless of phase-shift error due to the extinction ratio. By the numerical simulation, the proposed algorithm was capable of reducing the root mean square errors of the reconstructed image by 1/4 and 1/5 in amplitude and phase, respectively. Also, the algorithm was experimentally demonstrated, and the experimental results showed that the system employing the proposed algorithm suppressed the conjugate image, which slightly appeared in the image reconstructed by the system not employing the algorithm, even when the extinction ratio was 10:1. Thus, the effectiveness of the proposed algorithm was numerically and experimentally verified.

Experimental demonstration of parallel two-step phase-shifting digital holography

Parallel two-step phase-shifting digital holography is a technique for single-shot implementation of phase-shifting interferometry and requires only the intensity distribution of the reference wave and spatial two phase-shifted holograms. We constructed a system of parallel two-step phase-shifting digital holography and experimentally demonstrated the technique, for the first time. The system uses an originally fabricated image sensor having an array of 2 × 1 micro polarizers. Each micro polarizer was attached on pixel by pixel. In the experiment, the unwanted images, the zero-order diffraction wave and the conjugate image, are removed from the reconstructed image of objects by the system, while the images superimpose on the image of objects reconstructed by Fresnel transform alone. Also the capability of single-shot and three-dimensional imaging is demonstrated by the system.

Parallel two-step phase-shifting digital holography using polarization

We propose an optical implementation of a parallel two-step phase-shifting digital holography that utilizes a polarization technique. The implementation uses a phase-shifting array device consisting of a retarder array attached to an image sensor, and does not require the optical system to image the phase-shifting array device onto the image sensor required for the previously reported optical implementation of the parallel two-step phase-shifting digital holography. Then, the proposed implementation is essentially simple to align and compose. A preliminary experiment showed that the parallel two-step phase-shifting digital holography based on the proposed implementation can remove the conjugate image clinging to the image reconstructed by Fresnel transform alone with DC term suppression. Also, when the reconstruction distance was changed, the qualities of the reconstructed images were quantitatively evaluated by using normalized root-mean-square error. It was clarified that the proposed implementation was superior to other parallel phase-shifting digital holographies and Fresnel transform alone. Thus, the validity of the proposed implementation was confirmed.

Image quality improvement of parallel four-step phase-shifting digital holography by using the algorithm of parallel two-step phase-shifting digital holography

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.

Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography

Phase-shifting digital holographic technique is a powerful tool for the measurement of various physical parameters, such as object deformation and liquid or cell’s refractive index change. However, for an accurate measurement, phase-shifting error in the reference wave path is still a major issue. In this paper, three novel and simple algorithms are proposed to quantitatively detect and correct phase-shifting error for a pure phase object in two-step phase-shifting digital holography. Influence of phase-shifting error is illustrated, and the effectiveness of the proposed algorithms is demonstrated by numerical simulation results.

Improving image quality of parallel phase-shifting digital holography

The authors propose parallel two-step phase-shifting digital holography to improve the image quality of parallel phase-shifting digital holography. The proposed technique can increase the effective number of pixels of hologram twice in comparison to the conventional parallel four-step technique. The increase of the number of pixels makes it possible to improve the image quality of the reconstructed image of the parallel phase-shifting digital holography. Numerical simulation and preliminary experiment of the proposed technique were conducted and the effectiveness of the technique was confirmed. The proposed technique is more practical than the conventional parallel phase-shifting digital holography, because the composition of the digital holographic system based on the proposed technique is simpler.

Parallel two-step phase-shifting digital holography

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.