Two-step phase-shifting interferometry and its application in image encryption

Real-time millimeter wave holography with an arrayed detector

Millimeter and terahertz wave imaging has emerged as a powerful tool for applications such as security screening, biomedical imaging, and material analysis. However, intensity images alone are often insufficient for detecting variations in the dielectric constant of a sample, and extraction of material properties without additional phase information requires extensive prior knowledge of the sample. Digital holography provides a means for intensity-only detectors to reconstruct both amplitude and phase images. Here we utilize a commercially available source and detector array, both operating at room temperature, to perform digital holography in real-time for the first time in the mm-wave band (at 290 GHz). We compare the off-axis and phase-shifting approaches to digital holography and discuss their trade-offs and practical challenges in this regime. Owing to the low pixel count, we find phase-shifting holography to be the most practical and high fidelity approach for such commercial mm-wave cameras even under real-time operational requirements.

Quantitative phase imaging of living red blood cells combining digital holographic microscopy and deep learning

Digital holographic microscopy as a non-contacting, non-invasive, and highly accurate measurement technology, is becoming a valuable method for quantitatively investigating cells and tissues. Reconstruction of phases from a digital hologram is a key step in quantitative phase imaging for biological and biomedical research. This study proposes a two-stage deep convolutional neural network named VY-Net, to realize the effective and robust phase reconstruction of living red blood cells. The VY-Net can obtain the phase information of an object directly from a single-shot off-axis digital hologram. We also propose two new indices to evaluate the reconstructed phases. In experiments, the mean of the structural similarity index of reconstructed phases can reach 0.9309, and the mean of the accuracy of reconstructions of reconstructed phases is as high as 91.54%. An unseen phase map of a living human white blood cell is successfully reconstructed by the trained VY-Net, demonstrating its strong generality.

Synchronous Phase-Shifting Interference for High Precision Phase Imaging of Objects Using Common Optics

Quantitative phase imaging and measurement of surface topography and fluid dynamics for objects, especially for moving objects, is critical in various fields. Although effective, existing synchronous phase-shifting methods may introduce additional phase changes in the light field due to differences in optical paths or need specific optics to implement synchronous phase-shifting, such as the beamsplitter with additional anti-reflective coating and a micro-polarizer array. Therefore, we propose a synchronous phase-shifting method based on the Mach-Zehnder interferometer to tackle these issues in existing methods. The proposed method uses common optics to simultaneously acquire four phase-shifted digital holograms with equal optical paths for object and reference waves. Therefore, it can be used to reconstruct the phase distribution of static and dynamic objects with high precision and high resolution. In the experiment, the theoretical resolution of the proposed system was 1.064 µm while the actual resolution could achieve 1.381 µm, which was confirmed by measuring a phase-only resolution chart. Besides, the dynamic phase imaging of a moving standard object was completed to verify the proposed system's effectiveness. The experimental results show that our proposed method is suitable and promising in dynamic phase imaging and measurement of moving objects using phase-shifting digital holography.

Optical single-channel color image encryption based on chaotic fingerprint phase mask and diffractive imaging

An optical single-channel color image encryption scheme based on chaotic fingerprint phase mask and diffractive imaging is proposed. In this proposed encryption scheme, the fingerprint used to generate the random phase masks is served as a secret key directly. Additionally, the random phase masks generated by the fingerprint, chaotic Lozi map, and secure hash algorithm (SHA-256) are used only as interim variables. With the help of the chaotic fingerprint phase masks placed at different diffraction distances, the color image that is encoded into a grayscale pattern by the phase-truncation technique is encrypted into a noise-like diffraction pattern. For decryption, the color image can be retrieved from the noise-like diffraction pattern by using an iterative phase retrieval algorithm, fingerprint, and phase keys generated from the encryption process. Since the fingerprint key shared by the sender and authorized receiver is strongly linked with the user and does not need to be transmitted over the open network, the security of this proposed encryption scheme can be greatly improved. Additionally, the parameters of the chaotic Lozi map and Fresnel diffraction distances can also provide additional security to the proposed encryption scheme. Furthermore, compared with the encryption schemes based on digital holography, the implementation of this proposed encryption scheme is relatively simple. The numerical simulations and analysis verify the feasibility, security, and robustness of this proposed encryption scheme.

Multi-Party Cryptographic Key Distribution Protocol over a Public Network Based on a Quick-Response Code

In existing cryptographic key distribution (CKD) protocols based on computational ghost imaging (CGI), the interaction among multiple legitimate users is generally neglected, and the channel noise has a serious impact on the performance. To overcome these shortcomings, we propose a multi-party interactive CKD protocol over a public network, which takes advantage of the cascade ablation of fragment patterns (FPs). The server splits a quick-response (QR) code image into multiple FPs and embeds different “watermark” labels into these FPs. By using a CGI setup, the server will acquire a series of bucket value sequences with respect to different FPs and send them to multiple legitimate users through a public network. The users reconstruct the FPs and determine whether there is an attack in the public channel according to the content of the recovered “watermark” labels, so as to complete the self-authentication. Finally, these users can extract their cryptographic keys by scanning the QR code (the cascade ablation result of FPs) returned by an intermediary. Both simulation and experimental results have verified the feasibility of this protocol. The impacts of different attacks and the noise robustness have also been investigated.

Phase Retardation Analysis in a Rotated Plane-Parallel Plate for Phase-Shifting Digital Holography

In this paper, we detail a phase-shift implementation in a rotated plane-parallel plate (PPP). Considering the phase-shifting digital holography application, we provide a more precise phase-shift estimation based on PPP thickness, rotation, and mutual inclination of reference and object wavefronts. We show that phase retardation uncertainty implemented by the rotated PPP in a simple configuration is less than the uncertainty of a traditionally used piezoelectric translator. Physical experiments on a phase test target verify the high quality of phase reconstruction.

Single-path single-shot phase-shifting digital holographic microscopy without a laser light source

We propose single-path single-shot phase-shifting digital holographic microscopy (SSP-DHM) in which the quantitative phase information of an object wave is acquired without a laser light source. Multiple phase-shifted holograms are simultaneously obtained using a linear polarizer, a liquid crystal on a silicon spatial light modulator (LCoS-SLM), and a polarization-imaging camera. Complex amplitude imaging of a USAF1951 test target and phase imaging of transparent HeLa cells are performed to show its quantitative phase-imaging ability. We also conduct an experiment for the motion-picture imaging of transparent particles to highlight the single-shot imaging ability of SSP-DHM.

Asymmetric optical cryptosystem for multiple images based on devil's spiral Fresnel lens phase and random spiral transform in gyrator domain

An asymmetric cryptosystem is presented for encrypting multiple images in gyrator transform domains. In the encryption approach, the devil's spiral Fresnel lens variable pure phase mask is first designed for each image band to be encrypted by using devil' mask, random spiral phase and Fresnel mask, respectively. Subsequently, a novel random devil' spiral Fresnel transform in optical gyrator transform is implemented to achieved the intermediate output. Then, the intermediate data is divided into two masks by employing random modulus decomposition in the asymmetric process. Finally, a random permutation matrix is utilized to obtain the ciphertext of the intact algorithm. For the decryption approach, two divided masks (private key and ciphertext) need to be imported into the optical gyrator input plane simultaneously. Some numerical experiments are given to verify the effectiveness and capability of this asymmetric cryptosystem.

Image encryption scheme based on alternate quantum walks and discrete cosine transform

As an important information medium, the digital image exists widely on the Internet. Quantum walks have the property of encrypting information. For the eneryption problem of optical digital images, an encryption scheme based on discrete cosine transform (DCT) and alternate quantum walks (AQW) is proposed in this paper. First, we use AQW and XOR operation to preprocess images in the spatial domain. Then, AQW are used to generate two random phase masks which can operate the preprocessed image and the DCT image, respectively. Finally, the encrypted image is obtained by using discrete cosine inverse exchange. The control parameters of AQW can replace the random phase mask as the key in the encryption and decryption process, so it is convenient for key management and transmission. The experimental simulation carried out the analysis of the image pixel histogram, the correlation of adjacent pixels, the robustness against noise and the sensitivity of secret keys, the results show that the image encryption method has strong security.

Two-step phase-shifting interferometry for self-interference digital holography

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.

Random phase-shifting digital holography based on a self-calibrated system

Random phase-shifting digital holography based on a self-calibrated system is proposed. In the proposed method, the hologram and the calibration interference fringes can be recorded simultaneously in a single image based on the space-division-multiplexing technique. Three randomly phase-shifted holograms and corresponding interference fringes are recorded, and the phase-shifting amount between each two adjacent holograms is calculated by the sampling Moiré method from the calibration interference fringes. A reflective object is used to demonstrate the effectiveness of the proposed method in the numerical and experiment.

Three-dimensional measurement of a particle field using phase retrieval digital holography

Digital inline holography (DIH) has long been used to measure the three-dimensional (3D) distribution of micrometer particles in suspensions. However, DIH experiences a virtual image problem that limits the particle density and the placement of the hologram plane relative to the sample volume. Here, we apply virtual-image-free phase retrieval digital holography (PRDH) to detect opaque particles in 3D volumes that exceed $ 2000\;{\rm particles}/{{\rm mm}^3} $2000particles/mm³. PRDH is based on recording two holograms whose planes are displaced along the optical axis, and then reconstructing the complete optical waves estimated by the iterative phase retrieval algorithm. Both numerical and experimental tests are performed, and results show that PRDH recovers the original 3D particle distributions even when the hologram planes are within the particle suspensions. Moreover, compared to single-hologram-based DIH, PRDH is proved to have better particle detection qualities. The uncertainty in the localization of particle centers is reduced to less than one particle diameter.

High temporal and spatial resolution single-shot digital holography with Fresnel domain filtering using witch's hat illumination

High-resolution, single-shot on-axis digital holography is proposed. Generally, an on-axis configuration samples carrier fringes with higher spatial resolution compared to an off-axis configuration. However, the reconstructed image is obtained with unnecessary images of a conjugate image and a zero-order beam. The proposed method uses a phase-modulated illumination beam and image processing to eliminate these unnecessary images. Since time-division and parallel phase-shifting methods are not required, the proposed method has higher temporal and spatial resolutions. During image processing, the conjugate image is removed by filtering on the Fresnel domain while keeping most of the information of the object image intact. The usefulness of the proposed method is confirmed by a numerical simulation and an optical experiment.

Experimental demonstration of ghost-imaging-based authentication in scattering media

Optical imaging in scattering media and its applications are challenging and meaningful. In this paper, we propose and experimentally verify a new optical authentication method using structured-detection-based ghost imaging (GI) in scattering media. Object wave is disturbed by multiple diffusers, and then sequentially modulated by a series of random amplitude-only patterns embedded in a spatial light modulator (SLM). The modulated wave passes through another scattering medium, and its intensity is measured by using a single-pixel bucket detector without spatial resolution. During the decryption and authentication, a reference pattern is first retrieved by using all recorded single-pixel intensity signals. Subsequently, a small number of the recorded single-pixel intensity signals are further randomly selected, and a 1-bit compression operation is applied to these selected intensity signals to generate binary signals as ciphertext. The random amplitude-only patterns corresponding to the selected single-pixel intensity signals serve as principal security keys, and wavelength, axial distance and pixel size can serve as supplementary keys. Two strategies are further developed for the decryption and authentication. It is experimentally verified that the proposed method possesses high robustness and high discrimination capability. The proposed method established by using scattering media can significantly enrich optical security, and provides a promising approach for optical authentication.

Accurate and fast two-step phase shifting algorithm based on principle component analysis and Lissajous ellipse fitting with random phase shift and no pre-filtering

To achieve high measurement accuracy with less computational time-in-phase shifting interferometry, a random phase-shifting algorithm based on principal component analysis and Lissajous ellipse fitting (PCA&LEF) is proposed. It doesn't need pre-filtering and can obtain relatively accurate phase distribution with only two phase shifted interferograms and less computational time and is suitable for different background intensity, modulation amplitude distributions and noises. Moreover, it can obtain absolutely accurate result when the background intensity and modulation amplitude are perfect and can partly suppress the effect of imperfect background intensity and modulation amplitude. Last but not least, it removes the restriction that PCA needs more than three interferograms with well-distributed phase shifts to subtract relatively accurate mean. The simulations and experiments verify the correctness and feasibility of PCA&LEF.

Object wave retrieval using normalized holograms in three-step generalized phase-shifting digital holography

Phase-shifting methods using interferogram normalization are often applied to smooth objects, for which the requirements for the normalization approach, including zero-order term elimination and the norm approximation condition, are easily achieved. Here we propose a three-step generalized phase-shifting method using the normalization approach for diffuse objects. In the proposed method, the zero-order terms are sufficiently suppressed by mutual subtraction of the phase-shifted holograms. The norm approximation condition is satisfied, and the complex field of the object wave can be estimated by the normalization approach when the hologram satisfies the phase randomness condition. We present an object wave retrieval algorithm using three phase-shifted holograms, in which estimation of phase-shift values is unnecessary. The proposed method is verified through simulations and optical experiments.

Wavelength-Selective Phase-Shifting Digital Holography: Color Three-Dimensional Imaging Ability in Relation to Bit Depth of Wavelength-Multiplexed Holograms

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.

Three-step random phase retrieval approach based on difference map normalization and diamond diagonal vector normalization

To overcome the phase shift error in phase shifting interferometry, a three-step random phase retrieval approach based on difference map normalization and diamond diagonal vector normalization (DN&DDVN) is proposed. It does not need pre-filtering for the interferograms and can obtain relatively accurate phase distribution with a simple process and less computational time. This simulation and experiment verify the correctness and feasibility of DN&DDVN.

Simultaneous 2-step phase-shifting interferometry with a full-band interferometric signal being recovered

2-step phase-shifting interferometry (PSI) is an important technology for phase retrieval due to its outstanding performance in balancing detector bandwidth, temporal resolution, and quantitative quality. The most significant difficulty in this technology should ascribe to the distortion of low spatial frequencies in the retrieved interference signals, which is caused by the imperfect background intensity estimation. In this Letter, we overcome this key difficulty by iteratively recovering the lost spectrum of interferometric signals during spatial filtering and realize truly full space-bandwidth utilization in 2-step PSI. We also use this method to reduce the necessary number of spatially matched cameras in the quadrature simultaneous phase-shifting interferometer to significantly simplify its optical setup.

eHoloNet: a learning-based end-to-end approach for in-line digital holographic reconstruction

It is well known that in-line digital holography (DH) makes use of the full pixel count in forming the holographic imaging. But it usually requires phase-shifting or phase retrieval techniques to remove the zero-order and twin-image terms, resulting in the so-called two-step reconstruction process, i.e., phase recovery and focusing. Here, we propose a one-step end-to-end learning-based method for in-line holography reconstruction, namely, the eHoloNet, which can reconstruct the object wavefront directly from a single-shot in-line digital hologram. In addition, the proposed learning-based DH technique has strong robustness to the change of optical path difference between reference beam and object light and does not require the reference beam to be a plane or spherical wave.

Random two-step phase shifting interferometry based on Lissajous ellipse fitting and least squares technologies

To accurately obtain the phase distribution of an optical surface under test, the accurate phase extraction algorithm is essential. To overcome the phase shift error, a random two-step phase shifting algorithm, which can be used in the fluctuating and non-uniform background intensity and modulation amplitude, Lissajous ellipse fitting, and least squares iterative phase shifting algorithm (LEF&LSI PSA), is proposed; pre-filtering interferograms are not necessary, but they can get relatively accurate phase distribution and unknown phase shift value. The simulation and experiment verify the correctness and feasibility of the LEF & LSI PSA.

Nanometer-order thermal deformation measurement by a calibrated phase-shifting digital holography system

A thermal deformation measurement system based on calibrated phase-shifting digital holography is proposed. Two synchronized ordinary CMOS cameras are used in the calibrated phase-shifting digital holography system. One is to record the holograms including the object information, and the other is to record the interference fringes to evaluate phase-shifting errors. The calibrated phase-shifting digital holography can provide the high quality reconstructed images which are applied to calculate the thermal deformation of the object. Meanwhile, the thermal images of the object at different temperatures are recorded by a thermal camera. Nanometer-order thermal deformation measurement of an electronic device is achieved in a real experiment. Our measurement system could be useful for electric packaging materials development or the system design.

Five-step phase-shifting white-light interferometry for the measurement of fiber optic extrinsic Fabry-Perot interferometers

Five-step phase-shifting white-light interferometry is presented for interrogating the absolute cavity length of the fiber optic extrinsic Fabry-Perot interferometer (EFPI). It combines ideas of phase-shifting interferometry and white-light interferometry (WLI) to extend the measurement range of fiber optic WLI. Five sub-interferograms intercepted from the white-light optical spectrum are used to recover the optical path difference (OPD) of the EFPI. This method is demonstrated to interrogate a wider range of OPD. The experimental results show that the measurement resolution ranges from 0.5 μm to 5 μm with cavity length ranges from 16 μm to 12,402 μm, and it has a great advantage in measuring EFPIs with short cavity lengths.

Phase retrieval in two-shot phase-shifting interferometry based on phase shift estimation in a local mask

Fringe analysis in two-shot phase-shifting interferometry is important but meets challenges due to a limited number of images, corrupting noise, and background modulation. Here we propose an effective algorithm for phase retrieval from two interferograms with unknown phase shifts. The algorithm first evaluates the phase shift in a local mask through phase fitting and global optimization and then computes a full-field phase map using an arctangent function. Since the phase shift evaluation is performed within a local mask, the algorithm is fast compared with conventional optimization-based algorithms and typically needs tens of seconds to complete the processing. Computer simulation and experimental results show that the proposed algorithm has excellent performance compared with state-of-the-art algorithms. A complete software package of the algorithm in MATLAB is available at http://two-shot.sourceforge.io/.

Two-step phase shifting differential-recording digital holographic microscopy

We present two-step phase-shifting differential-recording digital holographic microscopy (TPD-DH in microscopy) for phase imaging of microscopic transparent elements. Two CCDs are employed to record two interferograms at two different defocusing distances. The interferograms on the two CCD cameras are shifted for a phase retarder 0 and π via an all-optics phase shifting unit. A novel algorithm is proposed to reconstruct both amplitude and phase distributions of the object wave from the recorded interferograms. This method has the same spectrum bandwidth and measurement accuracy with those of conventional four-step phase-shifting interferometry (FS-PSI), whereas it reduces the measurement time by half.

Optical cryptosystem based on single-pixel encoding using the modified Gerchberg-Saxton algorithm with a cascaded structure

In this paper, an optical cryptosystem is developed based on single-pixel encoding using the modified Gerchberg-Saxton algorithm with a cascaded structure. A series of random intensity-only patterns are pre-generated as principal security keys, and phase-only masks for optical encoding and decoding are generated by the modified Gerchberg-Saxton algorithm with a cascaded structure. Subsequently, a series of 1D intensity points, i.e., ciphertexts, are recorded by a single-pixel detector, which may provide a potential for establishing low-cost and compact security systems. The phase-mask generation process can be flexibly designed by modifying the Gerchberg-Saxton algorithm with a cascaded structure; hence high sensitivity and the large indirect space for phase can be guaranteed. It is also illustrated that compared with previous works, the higher eavesdropping percentage is requested to the attackers in the proposed single-pixel optical cryptosystem. The proposed method using a cascaded structure provides a novel strategy for single-pixel intensity-modulated optical security.

Threshold secret sharing scheme based on phase-shifting interferometry

We propose a new method for secret image sharing with the (3,N) threshold scheme based on phase-shifting interferometry. The secret image, which is multiplied with an encryption key in advance, is first encrypted by using Fourier transformation. Then, the encoded image is shared into N shadow images based on the recording principle of phase-shifting interferometry. Based on the reconstruction principle of phase-shifting interferometry, any three or more shadow images can retrieve the secret image, while any two or fewer shadow images cannot obtain any information of the secret image. Thus, a (3,N) threshold secret sharing scheme can be implemented. Compared with our previously reported method, the algorithm of this paper is suited for not only a binary image but also a gray-scale image. Moreover, the proposed algorithm can obtain a larger threshold value t. Simulation results are presented to demonstrate the feasibility of the proposed method.

Virtual interferogram-generation algorithm for robust complex amplitude measurement using two interferograms

We propose a virtual interferogram-generation algorithm using two interferograms. This algorithm can measure a complex amplitude of a signal beam with high accuracy even when its intensity is greater than the intensity of a reference beam. Unlike the conventional algorithm that uses two interferograms, our algorithm can compute measurements when the phase shift of interferograms in not equal to π/2. Our method generates two phase-shifted holograms in a computer by capturing the intensities of two signal beams, two reference beams, and two interferograms. The complex amplitude of a signal beam is calculated by four interference patterns, two holograms, and two interferograms. The proposed algorithm can drastically suppress the calculation error caused by the smaller value between the intensity of the reference beam and can choose the most suitable phase shift.

Two-step phase-shifting SPIDER

Comprehensive characterization of ultrafast optical field is critical for ultrashort pulse generation and its application. This paper combines two-step phase-shifting (TSPS) into the spectral phase interferometry for direct electric-field reconstruction (SPIDER) to improve the reconstruction of ultrafast optical-fields. This novel SPIDER can remove experimentally the dc portion occurring in traditional SPIDER method by recording two spectral interferograms with π phase-shifting. As a result, the reconstructed results are much less disturbed by the time delay between the test pulse replicas and the temporal widths of the filter window, thus more reliable. What is more, this SPIDER can work efficiently even the time delay is so small or the measured bandwidth is so narrow that strong overlap happens between the dc and ac portions, which allows it to be able to characterize the test pulses with complicated temporal/spectral structures or narrow bandwidths.

Single-shot and phase-shifting digital holographic microscopy using a 2-D grating

We demonstrate digital holographic microscopy that, while being based on phase-shifting interferometry, is capable of single-shot measurements. A two-dimensional (2-D) diffraction grating placed in a Fourier plane of a standard in-line holographic phase microscope generates multiple copies of a sample image on a camera sensor. The identical image copies are spatially separated with different overall phase shifts according to the diffraction orders. The overall phase shifts are adjusted by controlling the lateral position of the grating. These phase shifts are then set to be multiples of π/2. Interferograms composed of four image copies combined with a parallel reference beam are acquired in a single shot. The interferograms are processed through a phase-shifting algorithm to produce a single complex image. By taking advantage of the higher sampling capacity of the in-line holography, we can increase the imaging information density by a factor of 3 without compromising the imaging acquisition speed.

White-light quantitative phase imaging unit

We introduce the white-light quantitative phase imaging unit (WQPIU) as a practical realization of quantitative phase imaging (QPI) on standard microscope platforms. The WQPIU is a compact stand-alone unit which measures sample induced phase delay under white-light illumination. It does not require any modification of the microscope or additional accessories for its use. The principle of the WQPIU based on lateral shearing interferometry and phase shifting interferometry provides a cost-effective and user-friendly use of QPI. The validity and capacity of the presented method are demonstrated by measuring quantitative phase images of polystyrene beads, human red blood cells, HeLa cells and mouse white blood cells. With speckle-free imaging capability due to the use of white-light illumination, the WQPIU is expected to expand the scope of QPI in biological sciences as a powerful but simple imaging tool.

New method of attack and security enhancement on an asymmetric cryptosystem based on equal modulus decomposition

A recently proposed asymmetric cryptosystem based on coherent superposition and equal modulus decomposition has shown to be robust against a specific attack. In this paper, we have shown that it is vulnerable to a newly designed attack. With this attack, an intruder is able to access the exact private key and obtain precise attack results using a phase retrieval algorithm. In addition, we have also proposed a security-enhanced asymmetric cryptosystem using a random decomposition technique and a 4f optical system. In the proposed system, random decomposition is employed to create an effective trapdoor one-way function. As a result, it is able to avoid various types of attacks and maintain the asymmetric characteristics of the cryptosystem. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed method.

Multiple-wavelength double random phase encoding with CCD-plane sparse-phase multiplexing for optical information verification

A novel method is proposed by using multiple-wavelength double random phase encoding (MW-DRPE) with CCD-plane sparse-phase multiplexing for optical information verification. Two different strategies are applied to conduct sparse-phase multiplexing in the CCD plane. The results demonstrate that large capacity can be achieved for optical multiple-image verification. The proposed optical verification strategy is implemented based on optical encoding, and the keys generated by optical encryption can further guarantee the safety of the designed optical multiple-image verification system. The proposed method provides a novel alternative for DRPE-based optical information verification.

Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter

A common-path parallel-quadrature on-axis phase-shifting interferometry using a modified Michelson configuration with a polarizing cube beam splitter is proposed for quantitative phase measurement. The frequency spectrum of the circularly polarized object beam is split into two beams using a beam splitter. One beam is converted to a 45° linearly polarized beam to act as the object beam, and the other beam is low-filtered by a pinhole mirror to act as the reference beam. Two interferograms with quadrature phase shift can be simultaneously captured by combining the 45° linearly polarized object beam with the circularly polarized reference beam through a 45° tilted polarizing cube beam splitter, and the phase of a specimen can be then retrieved through a two-step phase-shifting algorithm. Experiments are carried out to demonstrate the validity and stability of the proposed method.

Two-channel algorithm for single-shot, high-resolution measurement of optical wavefronts using two image sensors

We propose a two-channel holographic diversity interferometer (2ch-HDI) system for single-shot and highly accurate measurements of complex amplitude fields with a simple optical setup. In this method, two phase-shifted interference patterns are generated, without requiring a phase-shifting device, by entering a circularly polarized reference beam into a polarizing beam splitter, and the resulting patterns are captured simultaneously using two image sensors. However, differences in the intensity distributions of the two image sensors may lead to serious measurement errors. Thus, we also develop a two-channel algorithm optimized for the 2ch-HDI to compensate for these differences. Simulation results show that this algorithm can compensate for such differences in the intensity distributions in the two image sensors. Experimental results confirm that the combination of the 2ch-HDI and the calculation algorithm significantly enhances measurement accuracy.

Triple-image encryption based on phase-truncated Fresnel transform and basic vector operation

A triple-image encryption method is proposed that is based on phase-truncated Fresnel transform (PTFT), basic vector composition, and XOR operation. In the encryption process, two random phase masks, with one each placed at the input plane and the transform plane, are generated by basic vector resolution operations over the first and the second plaintext images, and then a ciphered image in the input plane is fabricated by XOR encoding for the third plaintext image. When the cryptosystem is illuminated by an on-axis plane, assisted by PTFT, the ciphered image is finally encrypted into an amplitude-only noise-like image in the output plane. During decryption, possessing the correct private key, decryption keys, and the assistant geometrical parameter keys, and placing them at the corresponding correct positions, the original three plaintext images can be successfully decrypted by inverse PTFT, basic vector composition, and XOR decoding. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.

Group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform

A novel method of group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform is presented. The proposed method employs three different groups of multiple images. The color images of each group are individually segregated into R, G, and B channels. Each channel is first permutated by using a sequence of chaotic pairs generated with a system of two symmetrically coupled identical logistic maps and then gyrator transformed. The gyrator spectrum of each channel is multiplied together and then modulated by a random phase function to obtain a corresponding multiplex channel. The encoded multiplex image is restituted through a concatenation of R, G, and B multiplex channels. The phase and amplitude functions of the first, second, and third groups of encoded multiplex images are generated. The host image is a single-level 2D discrete wavelet transformed to decompose into LL, HL, LH, and HH subbands. HL, LH, and HH subbands are then replaced with phase functions of the first, second, and third groups, respectively. Finally, the resultant image is an inverse single-level 2D discrete wavelet transformed to construct a watermarked image. The three groups of multiple images are protected not only by the encryption algorithm but also visually by the host image. Thus, a high level of security can be achieved. Each group includes group decryption keys, and each image of the group comprises individual decryption keys beside parameters of coupled logistic maps and gyrator transform. As a result, the key space is very large. The decryption system can be realized by using an optoelectronic device. The numerical simulation results confirm the validity and security of the proposed scheme.

Compressive optical image encryption

An optical image encryption technique based on compressive sensing using fully optical means has been proposed. An object image is first encrypted to a white-sense stationary noise pattern using a double random phase encoding (DRPE) method in a Mach-Zehnder interferometer. Then, the encrypted image is highly compressed to a signal using single-pixel compressive holographic imaging in the optical domain. At the receiving terminal, the encrypted image is reconstructed well via compressive sensing theory, and the original image can be decrypted with three reconstructed holograms and the correct keys. The numerical simulations show that the method is effective and suitable for optical image security transmission in future all-optical networks because of the ability of completely optical implementation and substantially smaller hologram data volume.

Phase retrieval encryption in an enhanced optical interference by key phase constraint

In this paper, we demonstrate a security system by using optical interference and phase retrieval algorithm (PRA) techniques. The modified PRA is proposed to encode the target image into random phase distribution. Optical and digital methods can be used for decryption. By using this method, silhouette elimination is realized. In addition, due to this simplified system design, the iterative rate is improved and the optical decryption realization is easier. Validity and performance of the proposed system are demonstrated by means of numerical simulations. The system encryption capacity as to both binary and gray images is numerically investigated. Then, the decryption procedure is demonstrated by optical experiment means and the decryption result is given.

Multiple-image authentication with a cascaded multilevel architecture based on amplitude field random sampling and phase information multiplexing

A multiple-image authentication method with a cascaded multilevel architecture in the Fresnel domain is proposed, in which a synthetic encoded complex amplitude is first fabricated, and its real amplitude component is generated by iterative amplitude encoding, random sampling, and space multiplexing for the low-level certification images, while the phase component of the synthetic encoded complex amplitude is constructed by iterative phase information encoding and multiplexing for the high-level certification images. Then the synthetic encoded complex amplitude is iteratively encoded into two phase-type ciphertexts located in two different transform planes. During high-level authentication, when the two phase-type ciphertexts and the high-level decryption key are presented to the system and then the Fresnel transform is carried out, a meaningful image with good quality and a high correlation coefficient with the original certification image can be recovered in the output plane. Similar to the procedure of high-level authentication, in the case of low-level authentication with the aid of a low-level decryption key, no significant or meaningful information is retrieved, but it can result in a remarkable peak output in the nonlinear correlation coefficient of the output image and the corresponding original certification image. Therefore, the method realizes different levels of accessibility to the original certification image for different authority levels with the same cascaded multilevel architecture.

Analytic known-plaintext attack on a phase-shifting interferometry-based cryptosystem

We demonstrate a new analytic approach to a known-plaintext attack (KPA) on an optical cryptosystem based on the phase-shifting interferometry (PSI) technique. With the proposed analytic attack method, an opponent can access the exact decryption keys and obtain perfect attack results. This demonstration, to the best of our knowledge, shows for the first time that the optical cryptosystem based on the PSI technique is vulnerable to KPA.

Common-path on-axis Fresnel holography based on a pinhole array plate

A common-path and on-axis configuration for improving the resolution power of a lensless Fresnel holographic imaging system is proposed. In this configuration, a pinhole array plate (PAP) is inserted between the object and the recording plane. We demonstrated that the complex amplitude of the object wave can be directly extracted from a single Fresnel hologram of the object wave sampled by the PAP, and the numerical aperture of the effective imaging system can be increased because of the diffraction effect of the pinhole array. It may provide one approach for improving the capabilities of digital holography available for a wide range of wavelengths from far-infrared to x-ray and electron beams.

Three-dimensional information encryption and anticounterfeiting using digital holography

In this work, arbitrary micro phase-step digital holography with optical interferometry and digital image processing is utilized to obtain information about an image of a three-dimensional object and encrypting keys. Then, a computer-generated hologram is used for the purpose of holographic encryption. All information about the keys is required to perform the decryption, comprising the amplitude and phase distribution of the encrypting key, the distance of image reconstruction, zero-order term elimination, and twin-image term suppression. In addition to using identifiable information on different image planes and linear superposition processing hidden within the encrypted information, not only can we convey an important message, but we can also achieve anticounterfeiting. This approach retains the strictness of traditional holographic encryption and the convenience of digital holographic processing without image distortion. Therefore, this method provides better solutions to earlier methods for the security of the transmission of holographic information.

Spatio-temporal scanning modality for synthesizing interferograms and digital holograms

We investigate the spatio-temporal scanning of a single-pixel row for building up synthetic interferograms or digital holograms, shifted each other of a desired phase step. This unusual recording modality exploits the object movement to synthesize interferograms with extended Field of View and improved noise contrast. We report the theoretical formulation of the synthetizing recording process and experimental evidence of various cases demonstrating quantitative phase retrieval by adopting this intrinsic phase-shifting procedure. The proposed method could be particularly suited in all cases where the object shift is an intrinsic feature of the investigated system, as e.g. in microfluidics imaging.

Separating twin images and locating the center of a microparticle in dense suspensions using correlations among reconstructed fields of two parallel holograms

This paper deals with two issues affecting the application of digital holographic microscopy (DHM) for measuring the spatial distribution of particles in a dense suspension, namely discriminating between real and virtual images and accurate detection of the particle center. Previous methods to separate real and virtual fields have involved applications of multiple phase-shifted holograms, combining reconstructed fields of multiple axially displaced holograms, and analysis of intensity distributions of weakly scattering objects. Here, we introduce a simple approach based on simultaneously recording two in-line holograms, whose planes are separated by a short distance from each other. This distance is chosen to be longer than the elongated trace of the particle. During reconstruction, the real images overlap, whereas the virtual images are displaced by twice the distance between hologram planes. Data analysis is based on correlating the spatial intensity distributions of the two reconstructed fields to measure displacement between traces. This method has been implemented for both synthetic particles and a dense suspension of 2 μm particles. The correlation analysis readily discriminates between real and virtual images of a sample containing more than 1300 particles. Consequently, we can now implement DHM for three-dimensional tracking of particles when the hologram plane is located inside the sample volume. Spatial correlations within the same reconstructed field are also used to improve the detection of the axial location of the particle center, extending previously introduced procedures to suspensions of microscopic particles. For each cross section within a particle trace, we sum the correlations among intensity distributions in all planes located symmetrically on both sides of the section. This cumulative correlation has a sharp peak at the particle center. Using both synthetic and recorded particle fields, we show that the uncertainty in localizing the axial location of the center is reduced to about one particle's diameter.

Parallel phase-shifting digital holography using spectral estimation technique

We propose a parallel phase-shifting digital holography using a spectral estimation technique, which enables the instantaneous acquisition of spectral information and three-dimensional (3D) information of a moving object. In this technique, an interference fringe image that contains six holograms with two phase shifts for three laser lines, such as red, green, and blue, is recorded by a space-division multiplexing method with single-shot exposure. The 3D monochrome images of these three laser lines are numerically reconstructed by a computer and used to estimate the spectral reflectance distribution of object using a spectral estimation technique. Preliminary experiments demonstrate the validity of the proposed technique.

Dynamic phase imaging of microscopic measurements using parallel interferograms generated from a cyclic shear interferometer

We present a technique which allows us to generate two parallel interferograms with phase shifts of π/2 using a Cyclic Shear Interferometer (CSI) and a polarizing splitter. Because of the use of a CSI, we obtain the derivative phase data map directly, due to its configuration, it is immune to vibrations because the reference wavefront and the object wavefront have a common path; the shearing interferometer is insensitive to temperature and vibration. To obtain the optical phase data map, two interferograms are generated by collocating a polarizing device at the output of the CSI. The optical phase was processed using a Vargas-Quiroga algorithm. Related experimental results obtained for dynamic microscopic transparent samples are presented.

Optical encryption of unlimited-size images based on ptychographic scanning digital holography

The ptychographic scanning operation is introduced into digital holography to expand the field-of-view (FOV). An optical image encryption method based on this technique is further proposed and analyzed. The plaintext is moved sequentially in the way of ptychographic scanning and corresponding pairs of phase-shifted interferograms are recorded as ciphertexts. Then the holographic processing and the ptychographic iterative reconstruction are both employed to retrieve the plaintext. Numerical experiments demonstrate that the proposed system possesses high security level and wide FOV. The proposed method might also be used for other potential applications, such as three-dimensional information encryption and image hiding.