Multi-derivative method for phase extraction without knowing carrier frequencies in off-axis quantitative phase imaging.

We propose a multi-derivative method to reconstruct the phase of transparent objects in off-axis quantitative phase imaging (QPI). By numerically computing first-, second-, and third-order derivatives of the interferogram, we demonstrate that one can extract the quantitative phase information in a straightforward way, without prior knowledge of the carrier frequencies or Fourier transform. In contrast to existing advanced derivative methods, our approach markedly streamlines the alignment and retrieval processes, all without requiring any special prerequisites. This enhancement seamlessly translates into improved reconstruction quality. Furthermore, when compared to cutting-edge Fourier-division-based methods, our technique distinctly accelerates the phase retrieval speed. We verified our method using white-light diffraction phase microscopy and laser off-axis QPI, and the results indicate that our method can allow a fast, high-quality retrieval with frame rates up to 41.6 fps for one- megapixel interferograms on a regular computer.

Dual-wavelength off-axis digital holography in ImageJ: toward real-time phase retrieval using CUDA streams.

An ImageJ plug-in is developed to realize automatic real-time phase reconstruction for dual-wavelength digital holography (DH). This plug-in assembles the algorithms, including automatic phase reconstruction based on the division algorithm and post-processing. These algorithms are implemented and analyzed using a CPU and GPU, respectively. To hide the CPU-to-GPU data transfer latency, an optimization scheme using Compute Unified Device Architecture (CUDA) streams is proposed in ImageJ. Experimental results show that the proposed plug-in can perform faster reconstruction for dual-wavelength DH, resulting in frame rates up to 48 fps even for one-megapixel digital holograms on a normal PC. In other words, the proposed plug-in can realize real-time phase reconstruction for dual-wavelength digital holographic videos.

Improved multiple-image authentication based on optical interference by wavelength multiplexing.

In this paper, an improved multiple-image authentication based on optical interference by wavelength multiplexing is proposed, which has high security and easy optical implementation. The Fresnel spectra of original images are diffracted from the same axial position but by different wavelengths, which makes the optical implementation easy and stable without any mechanical translation. Then, the Fresnel spectra are sparsely sampled by predesigned binary amplitude masks and diffracted again, and all spectra are multiplexed into one synthetized spectrum. Finally, the synthetized spectrum is analytically decomposed into one phase-only mask and one amplitude-only mask by an improved interference-based encryption (IBE) scheme. Benefiting from the wavelength multiplexing, the encryption capacity is enlarged, and the optical implementation for decryption becomes easy. With the aid of the sparse sampling, every decrypted image could be entirely unrecognizable but authenticated by nonlinear correlation. Moreover, instead of a conventional IBE, an improved IBE is used in this scheme, which can attenuate the information leakage and further enhance the security. Various numerical simulation results are presented to demonstrate the feasibility and effectiveness of this scheme.

Off-axis common-path digital holography using a cube beam splitter.

An off-axis common-path digital holography is built up by inserting a 45° tilted cube beam splitter (CBS) into a 4f system that is described in this paper. Two apertures are set as the input of the 4f system, where one supports the object, and the other is vacant. The CBS divides the incoming beam into two copies, which are symmetrical with each other along the semi-reflecting layer. Due to the separation of two beams in a Fourier plane and the flipping of the field of view induced by the CBS, an off-axis hologram can be captured. Moreover, the carrier frequency can be easily modulated by translating the CBS perpendicular to the optical axis. The new proposed scheme has high light utilization, a compact setup, and high temporal stability. The experiments are carried out to demonstrate the validity and stability of the proposed method.

Asymmetric double-image encryption via wavelength multiplexing.

In this paper, we propose an asymmetric double-image encryption via wavelength multiplexing. First, a novel iterative phase retrieval algorithm, to the best of our knowledge, is developed to encode two images into one complex-valued function via wavelength multiplexing. Then, the function is encoded by equal modulus decomposition (EMD). This cryptosystem not only retains the advantages of EMD but also reduces the number of public keys so as to enhance the resistance to the amplitude-phase retrieval algorithm (APRA). In the decryption, two high-quality decrypted images can be obtained with their corresponding wavelengths. To the best of our knowledge, this is the first time that wavelength multiplexing is used to achieve high-quality two-image encryption and decryption. Numerical simulation results show the effectiveness and robustness of this new method.

Asymmetric multiparameter encryption of hyperspectral images based on hybrid chaotic mapping and an equal modulus decomposition tree.

We present an asymmetric encryption scheme for hyperspectral images using hybrid chaotic maps (HCMs) and an equal modulus decomposition tree (EMDT) structure in a discrete multiple-parameter fractional Fourier transform (dmpFrFT) domain. The original hyperspectral image was scrambled by an HCM and then encrypted into asymmetric ciphertext using the EMDT. In the EMDT, each pair of the band images of the scrambled hyperspectral image were regarded as leaf nodes, while the encryption modules using chaotic random phase mask, dmpFrFT, and improved equal modulus decomposition were regarded as branch nodes, and the encryption process was implemented along the paths from the leaf nodes to the topmost branch node. The EMDT structure could provide multiparameter encryption, real-valued output, and different pairs of band images with different secret keys and encryption/decryption paths. Compared with the previous optical encryption approaches for hyperspectral images, our asymmetric cryptosystem had larger key space, less data amount of storage and transmission, and stronger resistance to statistical attacks. Various numerical simulations verified the performance of our proposed asymmetric cryptosystem.

Simplified dual-channel two-wavelength interferometer using a polarized cube beam splitter.

Two-wavelength interferometers can extend an unambiguous measurement range; however, they suffer from complex optical configurations. To simplify the optical setup for a two-wavelength common-path off-axis interferometer, we propose a dual-channel two-wavelength interferometer using a polarized cube beam splitter. In contrast with the previously presented two-wavelength common-path off-axis interferometer, the proposed method has a simple setup, in which only one polarized cube beam splitter is inserted into the 4f system. With the help of polarization modulation, two single-wavelength interferograms can be captured simultaneously. Several experimental results are presented to demonstrate the advantages and effectiveness of the proposed method.

Deep-learning-enhanced ice thickness measurement using Raman scattering.

In ice thickness measurement (ICM) procedures based on Raman scattering, a key issue is the detection of ice-water interface using the slight difference between the Raman spectra of ice and water. To tackle this issue, we developed a new deep residual network (DRN) to cast this detection as an identification problem. Thus, the interface detection is converted to the prediction of the Raman spectra of ice and water. We enabled this process by designing a powerful DRN that was trained by a set of Raman spectral data, obtained in advance. In contrast to the state-of-the-art Gaussian fitting method (GFM), the proposed DRN enables ICM with a simple operation and low costs, as well as high accuracy and speed. Experimental results were collected to demonstrate the feasibility and effectiveness of the proposed DRN.

Optical excitation and detection of neuronal activity.

Optogenetics has emerged as an exciting tool for manipulating neural activity, which in turn, can modulate behavior in live organisms. However, detecting the response to the optical stimulation requires electrophysiology with physical contact or fluorescent imaging at target locations, which is often limited by photobleaching and phototoxicity. In this paper, we show that phase imaging can report the intracellular transport induced by optogenetic stimulation. We developed a multimodal instrument that can both stimulate cells with subcellular spatial resolution and detect optical pathlength (OPL) changes with nanometer scale sensitivity. We found that OPL fluctuations following stimulation are consistent with active organelle transport. Furthermore, the results indicate a broadening in the transport velocity distribution, which is significantly higher in stimulated cells compared to optogenetically inactive cells. It is likely that this label-free, contactless measurement of optogenetic response will provide an enabling approach to neuroscience.

Simultaneous dual-wavelength off-axis flipping digital holography.

We develop a two-wavelength off-axis digital holography for quantitative phase imaging using flipping in a single interferogram shot. The interference is performed by flipping the relative position of a sample and reference beam, and the two-wavelength information is spatially multiplexed onto a monochromatic charge-coupled device camera simultaneously using polarization modulation. Due to the interferogram containing two-wavelength information with orthogonal interference fringes, the two-wavelength unwrapped information on the phase and thickness for the sample is extracted from a single shot. Our setup requires no pinholes, gratings, or dichroic mirrors with straightforward alignment. We demonstrate the operation of the setup with a step target and circular pillar.

Single-shot dual-wavelength off-axis quasi-common-path digital holography using polarization-multiplexing.

We present a dual-wavelength off-axis quasi-common-path digital holography for quantitative phase imaging using polarization-multiplexing in a single shot. Employing an off-axis nearly common-path configuration, our approach separates the two-wavelength information using a polarizing beam splitter, while modulates the orthogonal fringe directions for each wavelength using two retro-reflector mirrors, and thus generates a single multiplexed off-axis interferogram on a monochrome CCD camera. The information of a specimen, including phase and height, is reconstructed through a division algorithm for dual wavelengths with the help of a specimen-free multiplexed interferogram. The experimental results obtained on a square step target and a circular step target illustrate the validity and stability of our setup.

Silhouette-free image encryption using interference in the multiple-parameter fractional Fourier transform domain.

A novel approach for silhouette-free image encryption based on interference is proposed using discrete multiple-parameter fractional Fourier transform (DMPFrFT), which generalizes from fractional Fourier transform. An original image is firstly applied by chaotic pixel scrambling (CPS) and then encoded into the real part of a complex signal. Using interference principle, the complex signal generates three phase-only masks in DMPFrFT domain. The silhouette of the original image cannot be extracted using one or two of the three phase-only masks. The parameters of both CPS and DMPFrFT can also serve as encryption keys to extend the key space, which further enhance the level of cryptosystem security. Numerical simulations are demonstrated to show the feasibility and validity of this approach.

Refractive index variance of cells and tissues measured by quantitative phase imaging.

The refractive index distribution of cells and tissues governs their interaction with light and can report on morphological modifications associated with disease. Through intensity-based measurements, refractive index information can be extracted only via scattering models that approximate light propagation. As a result, current knowledge of refractive index distributions across various tissues and cell types remains limited. Here we use quantitative phase imaging and the statistical dispersion relation (SDR) to extract information about the refractive index variance in a variety of specimens. Due to the phase-resolved measurement in three-dimensions, our approach yields refractive index results without prior knowledge about the tissue thickness. With the recent progress in quantitative phase imaging systems, we anticipate that using SDR will become routine in assessing tissue optical properties.

White-light diffraction phase microscopy at doubled space-bandwidth product.

White light diffraction microscopy (wDPM) is a quantitative phase imaging method that benefits from both temporal and spatial phase sensitivity, granted, respectively, by the common-path geometry and white light illumination. However, like all off-axis quantitative phase imaging methods, wDPM is characterized by a reduced space-bandwidth product compared to phase shifting approaches. This happens essentially because the ultimate resolution of the image is governed by the period of the interferogram and not just the diffraction limit. As a result, off-axis techniques generates single-shot, i.e., high time-bandwidth, phase measurements, at the expense of either spatial resolution or field of view. Here, we show that combining phase-shifting and off-axis, the original space-bandwidth is preserved. Specifically, we developed phase-shifting diffraction phase microscopy with white light, in which we measure and combine two phase shifted interferograms. Due to the white light illumination, the phase images are characterized by low spatial noise, i.e., <1nm pathlength. We illustrate the operation of the instrument with test samples, blood cells, and unlabeled prostate tissue biopsy.

Statistical dispersion relation for spatially broadband fields.

The dispersion relation is fundamental to a physical phenomenon that develops in both space and time. This equation connects the spatial and temporal frequencies involved in the dynamic process through the material constants. Electromagnetic plane waves propagating in homogeneous media are bound by simple dispersion relation, which sets the magnitude of the spatial frequency, k, as being proportional to the temporal frequency, ω, with the proportionality constant dependent on the refractive index, n, and the speed of light in vacuum, c. Here we show that, for spatially broadband fields, an analog dispersion relation can be derived, except in this case the k-vector variance is connected with the temporal frequency through the statistics of the refractive index fluctuations in the medium. We discuss how this relationship can be used to retrieve information about refractive index distributions in biological tissues. This result is particularly significant in measurements of angular light scattering and quantitative phase imaging of biological structures.

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.

Tri-window common-path interferometer for quantifying phase objects.

A new method is presented using a tri-window common-path interferometer (TriWCPI) for quantitative phase measurement. The prior method obtains the phase shift introduced by the Ronchi grating and the intensity value of the incident light with interferograms acquired offline without any objects. As a consequence, an improved recovery algorithm is established using the phase shift, the intensity value of the incident light, and the interferograms for a phase object acquired by camera in a single shot. The phase of an object then can be reconstructed from the improved algorithm. Because the calculation of phase shift and intensity value can be performed offline only once after the TriWCPI is built, the real-time ability and stability of the TriWCPI remains in this method. But the method avoids the normalization process and thus improves phase-retrieval precision. Experiments are demonstrated to prove the precision, real-time ability, and stability of the proposed method.

Real-time image edge enhancement with a spiral phase filter and graphic processing unit.

Isotropic image edge enhancement with high contrast can be achieved using a spiral phase filter (SPF) in a 4f optical system. However, real-time application of edge enhancement with SPF has generally been limited due to the requirement of coherent light or complex phase-shifting operation. In this paper, we demonstrate a real-time image edge enhancement method using a SPF and a graphic processing unit (GPU). By implementing the process of virtual spiral phase filtering on GPU, we are able to speed up the whole procedure by more than 8.3× with respect to CPU processing, and ultimately achieve video rate for megapixel images. In particular, our implementation can achieve higher speedup for more multiple images. These developments are increasing the potential for image edge enhancement of moving objects.

Two-shot common-path phase-shifting interferometer with a four-step algorithm and an unknown phase shift.

This paper presents a two-shot common-path phase-shifting interferometer that consists of a 4f optical system with two windows in the input plane and a Ronchi grating in the Fourier plane, and generates two adjacent interferograms using only diffraction orders 0 and +1 and 0 and -1. Four phase-shifted interferograms can be obtained in two shots by modulating two linear polarizers with angle difference of π/4 and translating the grating with only an unknown phase shift. An algorithm similar to the standard four-step algorithm is used to retrieve the phase of a specimen, and it requires no knowledge of the phase shift introduced by translation of the grating. The validity and repeatability of the proposed method is proved through simulations and experiments.

Parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating outside the Fourier plane.

A parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating placed outside the Fourier plane is proposed in this paper for quantitative phase imaging. Two phase-shifted interferograms with spatial carrier can be captured simultaneously using the proposed interferometer. The dc term can be eliminated by subtracting the two phase-shifted interferograms, and the phase of a specimen can be reconstructed through Fourier transform. The validity and stability of the interferometer proposed are experimentally demonstrated via the measurement of a phase plate.