Phase-only Information Research Articles

End-to-end design of metasurface-based complex-amplitude holograms by physics-driven deep neural networks

Abstract Holograms which reconstruct the transverse profile of light with complex-amplitude information have demonstrated more excellent performances with an improved signal-to-noise ratio compared with those containing amplitude-only and phase-only information. Metasurfaces have been widely utilized for complex-amplitude holograms owing to its capability of arbitrary light modulation at a subwavelength scale which conventional holographic devices cannot achieve. However, existing methods for metasurface-based complex-amplitude hologram design employ single back-diffraction propagation and rely on the artificial blocks which are able to independently and completely control both amplitude and phase. Here, we propose an unsupervised physics-driven deep neural network for the design of metasurface-based complex-amplitude holograms using artificial blocks with incomplete light modulation. This method integrates a neural network module with a forward physical propagation module and directly maps geometric parameters of the blocks to holographic images for end-to-end design. The perfect reconstruction of holographic images verified by numerical simulations has demonstrated that compared with the complete blocks, an efficient utilization, association and cooperation of the limited artificial blocks can achieve reconstruction performance as well. Furthermore, more restricted controls of the incident light are adopted for robustness test. The proposed method offers a real-time and robust way towards large-scale ideal holographic displays with subwavelength resolution.

Cryptanalysis of phase information based on a double random-phase encryption method

Phase-only information derived using a double random-phase encryption (DRPE) algorithm is not visually recognizable but can be authenticated using a nonlinear cross-correlation method. This can be considered to enhance DRPE security (which is vulnerable to a chosen-plaintext attack). Here, we show that phase-only images derived using the DRPE method remains vulnerable to such an attack; the at-risk images include full- and sparse-phase images and phase information with noise. We develop an encoder–decoder deep-learning method to decrypt phase-only images encrypted using the DRPE method. The deep-learning structure can be trained using only spare phase information from the encrypted image; experimentally, the trained model readily decrypted phase-only or partial-phase-encrypted images based on the DRPE algorithm.

Synthetic amplitude for improved reconstruction of noniterative phase holograms.

In this paper, we show how a specially designed synthetic amplitude can be used to obtain greatly improved reconstruction of objects only using the phase data of their Fourier or Fresnel transforms. The reconstruction of objects from phase-only information is of interest because phase modulation has much higher efficiency than amplitude modulation and can be achieved with a high degree of precision with current liquid-crystal-on-silicon spatial light modulators. However, direct reconstruction of an object from its phase information usually results in severely degraded outputs. Due to this issue, to achieve optimal reconstruction, the object information must be codified in a phase hologram by means of time-consuming algorithms. To avoid these kinds of algorithms, we propose using a synthetic amplitude, designed in such a way that, when multiplied with the phase information of the object, leads to high-quality reconstruction. This synthetic amplitude contains no information about the object and can be used to reconstruct a number of different inputs without further processing. We present experiments carried out in virtual and actual optical systems verifying the validity of our proposal for 2D, 3D, and dynamic scenes.

Optical image encryption system using nonlinear approach based on biometric authentication

A nonlinear image encryption scheme using phase-truncated Fourier transform (PTFT) and natural logarithms is proposed in this paper. With the help of the PTFT, the input image is truncated into phase and amplitude parts at the Fourier plane. The phase-only information is kept as the secret key for the decryption, and the amplitude distribution is modulated by adding an undercover amplitude random mask in the encryption process. Furthermore, the encrypted data is kept hidden inside the face biometric-based phase mask key using the base changing rule of logarithms for secure transmission. This phase mask is generated through principal component analysis. Numerical experiments show the feasibility and the validity of the proposed nonlinear scheme. The performance of the proposed scheme has been studied against the brute force attacks and the amplitude-phase retrieval attack. Simulation results are presented to illustrate the enhanced system performance with desired advantages in comparison to the linear cryptosystem.

Comparing of phase shifting method and one-dimensional continuous wavelet transform method for reconstruction using phase-only information

Comparing of phase shifting method and one-dimensional continuous wavelet transform method for reconstruction using phase-only information

An Iterative Fourier Transform Algorithm for digital hologram generation using phase-only information and its implementation in a fixed-point digital signal processor

An Iterative Fourier Transform Algorithm (IFTA) for digital hologram generation from a digital image using phase-only information is described in this paper. The algorithm is implemented in a Texas Instruments TMS320C64x fixed point digital signal processor (DSP). The holograms are reconstructed in real time using a liquid crystal display system and a He–Ne laser. The ideas described in this paper can be extended to digital hologram generation of three-dimensional objects and their reconstruction in real time using liquid crystal spatial light modulators, which could be a way for 3D-display systems.

Optical detection and measurement of living cell morphometric features with single-shot quantitative phase microscopy

We present a quadriwave lateral shearing interferometer used as a wavefront sensor and mounted on a commercial non-modified transmission white-light microscope as a quantitative phase imaging technique. The setup is designed to simultaneously make measurements with both quantitative transmission phase and fluorescence modes: phase enables enhanced contrasted visualization of the cell structure including intracellular organelles, while fluorescence allows a complete and precise identification of each component. After the characterization of the phase measurement reliability and sensitivity on calibrated samples, we use these two imaging modes to measure the characteristic optical path difference between subcellular elements (mitochondria, actin fibers, and vesicles) and cell medium, and demonstrate that phase-only information should be sufficient to identify some organelles without any labeling, like lysosomes. Proof of principle results show that the technique could be used either as a qualitative tool for the control of cells before an experiment, or for quantitative studies on morphology, behavior, and dynamics of cells or cellular components.

Symmetric Phase-Only Matched Filter (SPOMF) for Frequency-Domain Software GPS Receivers

The symmetric phase-only matched filter (SPOMF) is studied in this paper for processing GPS signals. The use of phase-only information is equivalent to equalizing the magnitude spectrum in contrast to the original spectrum that tapers off according to a sinc-function. This tends to accentuate the high frequency components corresponding to edges or transitions in the signals. As such, the SPOMF produces a much sharper peak (ideally a Dirac delta function) that is more accurate in timing and less sensitive to multipath. In addition, the same operation is applicable to both a binary phase shift keying (BPSK) modulated signal such as the GPS C/A-code and P(Y)-code and a binary offset carrier (BOC) modulation such as the GPS M-code and Galileo codes. More importantly, it only produces a single matching peak regardless of which modulation code is used.

Three-Dimensional Display System based on Digital Holography

A three-dimensional (3-D) display system based on digital holography is presented. Complex amplitude of 3-D object is calculated from digital holograms. Phase-only information can be used to reconstruct the 3-D object when the amplitude distribution is broad enough due to the speckle. We also demonstrate the complex amplitude processing to improve the image quality or manipulate the 3-D object.

Spectral Phase Based Medical Image Processing 1

To exploit the spectral phase characteristics of digital or digitized mammograms for early detection of microcalcifications, shape, and sizes of suspected lesions and to demonstrate its use for training radiologists to discriminate signal features in different spatially varying backgrounds. We propose two algorithms: in the phase-only image (POI) reconstruction algorithm the spectral phase of the digital mammogram is extracted from its Fourier spectrum. This is coupled with unit magnitude and inverse Fourier transformed to reconstruct the POI thus enhancing the features of interest such as microcalcifications, shape, and sizes of suspected lesions. In the algorithm for image reconstruction from a priori phase-only information, spectral phase is used to extract signal features of the digital mammogram and then this is combined with spectral magnitude that is extracted and averaged over an ensemble of unrelated digital mammograms. The results for several digital phantoms and mammograms show that POI reconstructs only high spatial frequencies related to the features such as microcalcifications, shape, and size of masses like cysts and tumors. The results on image reconstruction from a priori phase-only information demonstrate the changes in the visibility of signal features when buried in a wide variety of real world mammogram backgrounds with different densities. The POI can aid radiologists in early detection of microcalcifications, lesions, and other masses of interest in digital mammograms. This reconstruction method is self-adaptive to changes in the background. The image reconstruction from a priori phase-only information can help the radiologist as a training tool in his decision-making process. Preliminary experiments indicate the potential of the techniques for early diagnosis of breast cancer. Clinical studies on these algorithm procedures are in progress for application as a diagnostic CAD tool in digital mammography. These methods can in general be applied to other medical images such as CT and MRI images.

Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram.

A three-dimensional (3D) object reconstruction technique that uses only phase information of a phase-shifting digital hologram and a phase-only spatial-light modulator is proposed. It is well known that a digital hologram can store both amplitude and phase information of an optical electric field and can reconstruct the original 3D object in a computer. We demonstrate that it is possible to reconstruct optically 3D objects using only phase information of the optical field calculated from phase-shifting digital holograms. The use of phase-only information enables us to reduce the amount of data in the digital hologram and reconstruct optically the 3D objects using a liquid-crystal spatial light modulator without optical power loss. Numerical evaluation of the reconstructed 3D object is presented.

Phase-only photorefractive joint transform correlator

In this work we propose a method to improve the discrimination capability of joint transform correlators. The technique is mainly developed to apply in photorefractive joint transform correlators that use a liquid crystal spatial light modulator to display the input plane and a BSO crystal to record dynamically the joint transform plane. The discrimination capability of the system is increased by using a phase-encoded input in combination with the phase-only information of the reference. To this end we use the liquid crystal modulator working in a pure phase mode. We perform numerical simulations to show that the proposed method also improves the discrimination capability of correlators with conventional linear detection of the joint power spectrum. Experimental results obtained with our photorefractive correlator are shown.

Three-dimensional matching by use of phase-only holographic information and the Wigner distribution.

Matching of three-dimensional (3-D) objects is achieved by Wigner analysis of the correlation pattern between the phase-only holographic information of a reference object and that of a target object. First, holographic information on the reference object and on the target object is extracted by use of optical scanning holography as a form of electrical signal. This electrical information is then stored in a computer for digital processing. In the digital computer, the correlation between the phase-only information of the hologram of the reference object and that of the target object is calculated and analyzed by use of a Wigner distribution. The Wigner distribution yields a space-frequency map of the correlation pattern that indicates whether the 3-D image of the target object matches that of the reference object. When the 3-D image of the target object matches that of the reference object, the Wigner distribution gives a well-defined line that directly indicates the 3-D location of the matched target object. Optical experiments with digital processing are described to demonstrate the proposed matching technique.

Optimal reconstruction of images from localized phase

The importance of localized phase in signal representation is investigated. The convergence rate of the POCS algorithm (projection onto convex sets) used for image reconstruction from spectral phase is defined and analyzed, and the characteristics of images optimally reconstructed from phase-only information are presented. It is concluded that images of geometric form are most efficiently reconstructed from their spectral phase, whereas images of symmetric form have the poorest convergence characteristics. The transition between the two extremes is shown to be continuous. The results provide a new approach and analysis of the previously reported advantages of the localized phase representation over the global approach, and suggest possible compression schemes.

Performance of double phase encoding encryption technique using binarized encrypted images

We investigate the performance of an image encryption tech- nique that uses random-phase encoding in both the input plane and the Fourier plane, using partial information of the encrypted image. We first investigate the phase-only information of the encrypted data for decryp- tion. A binary version of the phase-only information is also considered for decryption. Binary images are well suited for optical display and practical implementation. Using partial information of the encrypted image, a re- constructed complex image is generated, which is used for decryption. Tests are performed for both gray-scale and binary images. We show that the phase information of the encrypted image is very important in the reconstruction of the decrypted image. Computer simulations show that for the images tested here, binarization of the encrypted image can re- cover the original image with low mean squared error. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)04302-5) noise. 3 The fault-tolerance properties of this technique were investigated in Ref. 4. In this paper, we evaluate the phase information of the encrypted image and investigate the ef- fect of its binarization on the recovered image. We give the reasons for the binarization of the encrypted image, and tackle the problems raised by it. It is shown that postpro- cessing of the decrypted image can improve the quality of the recovered images. We show, for the images tested here, that recovered images of very good quality can be obtained.

Extracting multiple frequencies from phase-only data

The problem of extracting multiple frequencies from phase-only data is addressed. Multiple frequency estimation is accomplished by reconstructing the Fourier transform of the complex-valued time signal and then finding peaks in the frequency domain. We present a set of conditions under which a discrete-time complex sequence can be completely specified by its phase-only information. Two candidate multiple frequency estimation schemes are introduced, one based on a closed-form least-squares inverse, the other an iterative reconstruction algorithm. The uniqueness of the closed-form solution and the convergence of the iterative scheme have been proven under certain conditions. Several examples are given, including the case where the phase is quantized as would happen in an analog-to-digital (A/D) converter. Extensions to the multidimensional case, and to the case of real-part only reconstruction are straightforward.

All-optical nonlinear joint Fourier transform correlator

We present the first all-optical nonlinear joint transform correlator based on a square-law receiver in the Fourier plane. Our device uses a photorefractive limiting quadratic processor. The compressional nonlinearity associated with the transfer function of the limiting quadratic processor enables the correlator to detect signals embedded in Gaussian and non-Gaussian noise. In the limiting region this device correlates the phase-only information of the input. This is the first time to our knowledge that photorefractives or real-time holography has been used in the correlation of the phase-only information. We demonstrate the operation of this device experimentally, and we evaluate its performance throughcomputer simulation for various forms of noise.

Analytic signal reconstruction from instantaneous phase

In this paper we use a set of results previously established on signal reconstruction from phase-only information in order to develop a new method around the notion of the analytic signal. Instead of using the phase (Fourier domain) of a sequence as the partial information, we develop an iterative algorithm (based on Gerchberg-Saxton's), which uses the concept of instantaneous phase for recovering all the sequence. Finally, an application of this numerical algorithm and its results are presented.