Complex Amplitude Image Research Articles

Single-pixel complex amplitude imaging (Invited)

Single-pixel complex amplitude imaging (Invited)

Research on optical encryption system based on unequal modulus decomposition and polarized vortex optical holography

In this paper, we present an optical encryption system which uses the principle of unequal modulus decomposition and polarization vortex optical holography to implement encoding and decoding. Firstly, the original image is decomposed into two complex amplitude images by unequal modulus decomposition method, then their polarization states are changed by vortex beams irradiation, and finally they are encrypted in the photorefractive crystals by polarization multiplexing holographic technology. In decryption, the image can be reconstructed successfully when a series of correct keys are provided. The sensitivity of polarization state and the multiplexing performance of topological charge are also analyzed, proving the method has high security.

Measuring the complex spectrum of orbital angular momentum and radial index with a single-pixel detector.

Typical methods to decode a complex orbital-angular-momentum (OAM) spectrum suffer from issues such as a narrow OAM range, unstable interferometer, and long measuring time. In this Letter, we use a single-beam interferometer to measure the complex OAM spectrum with a single-pixel detector. The complex OAM spectrum ranging from -10 to 10 can be measured in 11 ms with the fidelity approach of 97.0%, experimentally. Our approach allows one to characterize an unknown coherent field with any complex basis, e.g., the Laguerre-Gaussian (LG) basis is used for radial index spectrum measurement. Furthermore, single-pixel complex amplitude imaging based on the LG spectrum acquisition is presented, and the advantages in resolution and flexibility are demonstrated.

Low-coherence digital holography with a multireflection reference mirror.

A method for expanding the measurement range of low-coherence digital holography up to several times longer than the coherence length is proposed. The method was implemented with a multireflection reference mirror composed of partially and highly reflective mirrors, in conjunction with the Fourier transform method with spatial filtering for single-shot complex amplitude imaging, making it useful for observing a moving and deforming object. One of the features of the reference arm is that the measurement range is simply controlled by adjusting the position and angle of the highly reflective mirror. The measurement of objects with a general curved shape and a large step height was demonstrated.

Imaging through scattering media using digital holography

The holographic diffraction of a coherently illuminated object forms an in-line hologram behind the random scattering medium. The obstruction of the scattering layer scrambles the in-line hologram into a speckle pattern. We propose and experimentally demonstrate a technique for the single-shot imaging through a scattering medium based on the recovery and reconstruction of the in-line hologram from the far field speckle pattern. Using a new configuration, the proposed method enables the retrieval of the complex amplitude image of an object located at any arbitrary planes behind scattering medium. Experimental demonstration is carried out for both the transmittive and reflective objects. Results are presented for imaging of objects at various planes behind the scattering medium and also the transmitting type polystyrene beads. Furthermore, the quality of reconstruction is assessed by quantitatively evaluating the visibility and reconstruction efficiency of the reconstructed images at various longitudinal distances behind the scattering medium.

Kramers–Kronig holographic imaging for high-space-bandwidth product

Modern optical imaging possesses a huge information capacity whose corresponding space-bandwidth product (SBP) reaches tens of megapixels. However, despite the advances in optical and electronic devices, the SBP of an optical microscope is greatly limited, resulting in a reduced field of view or resolution of an image. In this paper, we exploit the Kramers–Kronig relations in digital holography to achieve high SBP imaging, demonstrating a complex amplitude image that can surpass the SBP of a bright-field image. The capability of the proposed method is demonstrated by imaging static samples and biological tissues. We successfully measure a 4.2-megapixel complex amplitude image whose bright-field counterpart exhibits 16.7 megapixels.

Single-shot and lensless complex-amplitude imaging with incoherent light based on machine learning

We present a single-shot incoherent light imaging method for simultaneously observing both amplitude and phase without any imaging optics, based on machine learning. In the proposed method, an object with a complex-amplitude field is illuminated with incoherent light and is captured by an image sensor with or without a coded aperture. The complex-amplitude field of the object is reconstructed from a single captured image using a state-of-the-art deep convolutional neural network, which is trained with a large number of input and output pairs. In experimental demonstrations, the proposed method was verified with a handwritten character database, and the effect of a coded aperture printed on an overhead projector film in the reconstruction was examined. Our method has advantages over conventional wavefront sensing techniques using incoherent light, namely simplification of the optical hardware and improved measurement speed. This study shows the importance and practical impact of machine learning techniques in various fields of optical sensing.

Complex-amplitude single-pixel imaging.

A single-pixel camera can be represented using complex-amplitude. The complex-amplitude representation of input signals and output signals enables us to perform complex-amplitude imaging of an object, particularly profilometry with reflectance measurements or quantitative phase imaging with transmittance measurements. The complex-amplitude representation of optical coding masks and the coherent addition that is performed by interference can directly represent Hadamard patterns having positive and negative values. Furthermore, the residual area of the mask can be used for a reference beam with phase shifting. Such a complex-amplitude imaging system with a single-beam line structure is highly stabile against external disturbances.

An Early Study on Imaging 3D Objects Hidden Behind Highly Scattering Media: a Round-Trip Optical Transmission Matrix Method

Imaging an object hidden behind a highly scattering medium is difficult since the wave has gone through a round-trip distortion: On the way in for the illumination and on the way out for the detection. Although various approaches have recently been proposed to overcome this seemingly intractable problem, they are limited to two-dimensional (2D) intensity imaging because the phase information of the object is lost. In such a case, the morphological features of the object cannot be recovered. Here, based on the round-trip optical transmission matrix of the scattering medium, we propose an imaging method to recover the complex amplitude (both the amplitude and the phase) information of the object. In this way, it is possible to achieve the three-dimensional (3D) complex amplitude imaging. To preliminarily verify the effectiveness of our method, a simple virtual complex amplitude object has been tested. The experiment results show that not only the amplitude but also the phase information of the object can be recovered directly from the distorted output optical field. Our method is effective to the thick scattering medium and does not involve scanning during the imaging process. We believe it probably has potential applications in some new fields, for example, using the scattering medium itself as an imaging sensor, instead of a barrier.

Lensless complex amplitude image retrieval through a visually opaque scattering medium.

We propose and experimentally demonstrate lensless complex amplitude image retrieval through a visually opaque scattering medium from spatially fluctuating fields using intensity measurement and a phase-retrieval algorithm. The complex amplitude information of the hidden object is encoded in the form of a real and nonnegative amplitude function represented as an interference pattern. A single charge coupled device (CCD) image of the scattered light collected through a visually opaque optical diffuser contains enough information to digitally regenerate the interference pattern. Furthermore, a lensless configuration is implemented which eliminates any possible aberration effects associated with optical components, and this further has promising applications where the use of imaging optics is not feasible. Experimental results for the recovery of complex fields corresponding to optical vortices of two different topological charges are presented.

Parallel ptychographic reconstruction.

Ptychography is an imaging method whereby a coherent beam is scanned across an object, and an image is obtained by iterative phasing of the set of diffraction patterns. It is able to be used to image extended objects at a resolution limited by scattering strength of the object and detector geometry, rather than at an optics-imposed limit. As technical advances allow larger fields to be imaged, computational challenges arise for reconstructing the correspondingly larger data volumes, yet at the same time there is also a need to deliver reconstructed images immediately so that one can evaluate the next steps to take in an experiment. Here we present a parallel method for real-time ptychographic phase retrieval. It uses a hybrid parallel strategy to divide the computation between multiple graphics processing units (GPUs) and then employs novel techniques to merge sub-datasets into a single complex phase and amplitude image. Results are shown on a simulated specimen and a real dataset from an X-ray experiment conducted at a synchrotron light source.

Three random phase encryption technology in the Fresnel diffraction system based on computer-generated hologram

We propose a new method of image encryption using Fourier computer-generated hologram (CGH) in the encryption system of multiple Fresnel diffraction transforms with phase masks. The digital image to be encrypted is modulated by a series of three random-phase masks in Fresnel diffraction system and finally is transformed into a complex-amplitude image which is stationary white noise (in which the information is like stationary-white-noise). Because the complex-amplitude information is not easy to be directly saved, the binary real value Fourier CGH is applied to record it. Compared with the traditional double random-phase image encryption technology, this method adds new keys which enhance the image encryption security and the Fourier CGH greatly improves the antinoise performance.

Super-resolution complex amplitude reconstruction of nanostructured binary data using an interference microscope with pattern matching

We propose a new method of optically reconstructing binary data formed by nanostructures with an elemental size several tens of nanometers smaller than the diffraction limit, implemented with an interference microscope and a complex-amplitude image pattern matching method. We examine the size dependency of the data reconstruction capacity using a light propagation simulation based on the finite-difference time-domain (FDTD) method and the Fourier spatial frequency filtering method. We demonstrated that the readable size of the binary nanostructure depends on the magnitude of noise.

High-speed synthetic aperture microscopy for live cell imaging

We present a high-speed synthetic aperture microscopy for quantitative phase imaging of live biological cells. We measure 361 complex amplitude images of an object with various directions of illumination covering an NA of 0.8 in less than one-thirteenth of a second and then combine the images with a phase-referencing method to create a synthesized phase image. Because of the increased depth selectivity, artifacts from diffraction that are typically present in coherent imaging are significantly suppressed, and lateral resolution of phase imaging is improved. We use the instrument to demonstrate high-quality phase imaging of live cells, both static and dynamic, and thickness measurements of a nanoscale cholesterol helical ribbon.

Quantitative phase microscopy using defocusing by means of a spatial light modulator

A new method for recovery the quantitative phase information of microscopic samples is presented. It is based on a spatial light modulator (SLM) and digital image processing as key elements to extract the sample's phase distribution. By displaying a set of lenses with different focal power, the SLM produces a set of defocused images of the input sample at the CCD plane. Such recorded images are then numerically processed to retrieve phase information. This iterative process is based on the wave propagation equation and leads on a complex amplitude image containing information of both amplitude and phase distributions of the input sample diffracted wave front. The proposed configuration is a non-interferometric architecture (conventional transmission imaging mode) where no moving elements are included. Experimental results perfectly correlate with the results obtained by conventional digital holographic microscopy (DHM).

Multifactor authentication reinforces optical security

A new optical method to obtain multifactor image encoding and authentication is proposed. The encoded complex-amplitude image function fulfills the general requirements of invisible content, extreme difficulty in copying or counterfeiting, and real-time automatic verification. This optical technique is attractive for high-security purposes that require multifactor reliable authentication. A demonstration using a combination of biometric images and key codes is provided. Retina images, which are very effective for authentication, are used as biometric signals. To the best of our knowledge, this is the first report on combined multiple signal encoding and simultaneous AND authentications for optical security reinforcement.

Optical identification using a random phase mask

We propose a novel method for optical identification by using a random phase mask. The identification system is based on a holographic correlator used to verify the access phase mask. The random phase function of the mask works as a code for identification. The database is a holographic memory that records the complex amplitude image of the random phase mask through angle multiplexing. The cross talk between different masks is small and the main restriction of the capacity in this system is the dynamic range of the recording material. Both the theory and the experiment are presented.

Adaptive noise reduction of InSAR images based on a complex-valued MRF model and its application t o phase unwrapping problem

We propose a new adaptive noise reduction method for interferometric synthetic aperture radar (InSAR) complex-amplitude images. In the proposed method, we detect residues (singular points) in the phase image as well as their neighbors at first. Normal areas that contain no residue are used for the estimation of correct pixel values at the marked residues according to 5th order non-causal complex-valued Markov random field (CMRF) model. The process is performed block-wise with the assumption of a locally stationary condition of statistics. Using a CMRF lattice complex-valued neural-network, the error energy defined as the squared norm of distance between signal and estimated values is minimized by LMS steepest descent algorithm. Eventually, the number of residues is decreased. An application is also presented. An InSAR image around Mt. Fuji is processed by the proposed technique and then phase-unwrapped by the branch-cut method. It is found that after the application of the proposed method, a better phase unwrapped image can be obtained successfully.