Non-interferometric Method Research Articles

Multiple-reflections single-shot dispersion scan for fast ultrashort-pulse measurements.

A single-shot non-interferometric ultrashort-pulse measurement method based on the dispersion scan (d-scan) technique with a substantially extended time span for the pulses to be measured is presented. While single-shot d-scan is typically used for rather short femtosecond pulses, the presented multiple-reflections d-scan (MR d-scan) technique allows measurement of both short and long femtosecond pulses. Single-shot d-scan is currently limited to pulses with a maximum duration of 60 fs using a chromatic dispersion, i.e., a group delay dispersion (GDD) of 4400 fs2 at 840 nm provided by customized random nonlinear crystals. MR d-scan achieves a GDD of 31100 fs2 at 820 nm in this work, but can generally achieve an increase in GDD of up to two orders of magnitude. MR d-scan works with commonly available output couplers, does not rely on a homogeneous, precisely imaged beam profile and has an in-line configuration. As an example, long femtosecond double pulses are measured and reconstructed.

TIE-GANs: single-shot quantitative phase imaging using transport of intensity equation with integration of GANs.

Artificial intelligence (AI) has become a prominent technology in computational imaging over the past decade. The expeditious and label-free characteristics of quantitative phase imaging (QPI) render it a promising contender for AI investigation. Though interferometric methodologies exhibit potential efficacy, their implementation involves complex experimental platforms and computationally intensive reconstruction procedures. Hence, non-interferometric methods, such as transport of intensity equation (TIE), are preferred over interferometric methods. TIE method, despite its effectiveness, is tedious as it requires the acquisition of many images at varying defocus planes. The proposed methodology holds the ability to generate a phase image utilizing a single intensity image using generative adversarial networks (GANs). We present a method called TIE-GANs to overcome the multi-shot scheme of conventional TIE. The present investigation employs the TIE as a QPI methodology, which necessitates reduced experimental and computational efforts. TIE is being used for the dataset preparation as well. The proposed method captures images from different defocus planes for training. Our approach uses an image-to-image translation technique to produce phase maps and is based on GANs. The main contribution of this work is the introduction of GANs with TIE (TIE:GANs) that can give better phase reconstruction results with shorter computation times. This is the first time the GANs is proposed for TIE phase retrieval. The characterization of the system was carried out with microbeads of size and structural similarity index (SSIM) for microbeads was found to be 0.98. We demonstrated the application of the proposed method with oral cells, which yielded a maximum SSIM value of 0.95. The key characteristics include mean squared error and peak-signal-to-noise ratio values of 140 and 26.42dB for oral cells and 100 and 28.10dB for microbeads. The proposed methodology holds the ability to generate a phase image utilizing a single intensity image. Our method is feasible for digital cytology because of its reported high value of SSIM. Our approach can handle defocused images in such a way that it can take intensity image from any defocus plane within the provided range and able to generate phase map.

Semiempirical criterion for eliminating wraparound artifacts in single-grid-based phase-contrast X-ray imaging

Single-grid-based phase-contrast X-ray imaging (SG-PCXI) is a non-interferometric method for the simultaneous retrieval of absorption, phase-contrast (differential), and dark-field images from a single exposure with a common X-ray grid using a spatial harmonic imaging (SHI) technique. However, the retrieved images are often distorted by the wraparound artifacts that are caused by the spectral overlap of adjacent harmonic peaks in the Fourier domain, resulting in the degradation of image quality. In this study, a semiempirical criterion required for eliminating wraparound artifacts in SG-PCXI was established by considering two constraints: one to resolve periodic grid strips by the system resolution to use the SHI technique, and the other to ensure that the spectral contents of adjacent harmonic peaks are separated (not overlapped) to the greatest possible extent during data processing. Further, we assumed that the system resolution can be experimentally determined as the spatial frequency at a 10% modulation transfer function. To verify the efficacy of the semiempirical criterion, we conducted an experiment using a table-top setup, which primarily comprised a microfocus X-ray source with a 20 μm focal spot size, X-ray grids with strip densities of 150, 200, and 254 lines/inch, and a CMOS flat-panel detector with a 49.5 μm pixel size. The experimental measurements of the wraparound artifacts in our system setup were in good agreement with the semiempirical criterion over the entire range of test conditions, thus verifying its efficacy for SG-PCXI. Accordingly, the semiempirical criterion established in this study will be useful for designing a wraparound artifact-free system layout in SG-PCXI.

Comparisons between non-interferometric and interferometric passive surface wave imaging methods—towards linear receiver array

SUMMARYPassive seismic methods in highly populated urban areas have gained much attention from the geophysics and civil engineering communities. Linear arrays are usually deployed for passive surface wave investigations because of their high convenience, and passive surface wave imaging methods commonly used for linear arrays can be grouped as non-interferometric methods (e.g. passive multichannel analysis of surface wave, refraction microtremor) and interferometric methods (e.g. multichannel analysis of passive surface waves and spatial autocorrelation). It is well known that the seismic interferometry method is able to retrieve Green’s function between inter-station pairs based on passive seismic data and that is how interferometric methods work. Although non-interferometric methods are also popular and effective in near-surface seismic imaging, particularly in the geotechnical industry, there is no theoretical proof to clarify the accuracy and/or the bias of these methods. In this study, we use numerical derivations and simulations to demonstrate the underlying physics for both non-interferometric and interferometric methods, under two common noise source environments including a homogeneous source distribution and a dominant in-line source distribution. We also prove the strength of interferometric methods for accurate dispersion imaging over the non-interferometric methods, and provide a way to estimate the biases in non-interferometric measurements. Finally, we present comprehensive comparisons between different passive surface wave methods with three typical field examples considering various observation systems.

Ultrashort Pulse Retrieval from Experimental Spectra Transformed in Chalcogenide and Silica Fibers

The characterization of ultrashort optical pulses is a highly requested task. The most popular commercially available hardware/software systems are based on interferometric measurements and second-harmonic generation, leading to some ambiguities and limitations. Here we experimentally test the non-interferometric method of pulse retrieval from three spectra: the fundamental spectrum and two spectra that transformed in an element with Kerr nonlinearity and accumulated different nonlinear phases (different Β-integrals). This method has no ambiguities related to time direction, and allows simple hardware/software implementation. We test a novel simple algorithm for experimental data processing based on the search for a polynomial-approximated spectral phase. Two experimental cases are considered. In the first one, we retrieved 160 fs pulses using a chalcogenide arsenic sulfide glass fiber as a nonlinear Kerr element. In the second case, we retrieved 670 fs pulses with a complex spectrum using a piece of silica-based fiber. The results are confirmed by independent measurements using a standard SHG-FROG technique (Second-Harmonic Generation Frequency-Resolved Optical Gating).

X-ray Phase Contrast Imaging from Synchrotron to Conventional Sources: A Review of the Existing Techniques for Biological Applications

Since the seminal work of Roentgen, X-ray imaging mainly uses the same physical phenomenon: the absorption of light by matter. Thanks to third-generation synchrotrons that provide a high flux of quasi-coherent X-rays, we have seen in recent years new imaging concepts such as phase contrast or dark-field imaging that were later adapted to conventional X-ray sources. These innovative imaging techniques are particularly suitable for visualizing soft matter, such as biological tissues. After a brief introduction to the physical foundations of these two techniques, we present the different experimental set-ups that are now available to produce such contrasts: propagation, analyzer-based, grating interferometry and non-interferometric methods, such as coded aperture and modulation techniques. We present a comprehensive review of their principles; associated data processing; and finally, their requirements for their transfer outside of synchrotrons. In conclusion, gratings interferometry, coded aperture and modulation techniques seem to be the best candidates for the widespread use of phase contrast and dark-field imaging on low-cost X-ray sources.

Spatial tomography of light resolved in time, spectrum, and polarisation

Measuring polarisation, spectrum, temporal dynamics, and spatial complex amplitude of optical beams is essential to studying phenomena in laser dynamics, telecommunications and nonlinear optics. Current characterisation techniques apply in limited contexts. Non-interferometric methods struggle to distinguish spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or a self-reference, neither of which is universally available. Deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. We harness principles of spatial state tomography to circumvent these limitations and measure a complete description of an unknown beam as a set of spectrally, temporally, and polarisation resolved spatial state density matrices. Each density matrix slice resolves the spatial complex amplitude of multiple mutually incoherent fields, which over several slices reveals the spectral or temporal evolution of these fields even when fields spectrally or temporally overlap. We demonstrate these features by characterising the spatiotemporal and spatiospectral output of a vertical-cavity surface-emitting laser.

The optical refractometry using transport-of-intensity equation

A development of a method for measuring the refractive index of optical media based on the transport-of-intensity equation (TIE) is proposed. The method requires only a complementary metal-oxide semiconductor (CMOS) camera, which registers intensity distributions in several planes. The obtained intensity distributions are used to solve the TIE, known as a non-interferometric and deterministic method of measuring the phase of a light wave. Simple physical relations connecting the phase of the light wave that has passed through an optical medium and its refractive index allows to determine the latter. The results of the experiment confirm the applicability of the proposed method to the problems of optical refractometry.

Real-Time Phase Imaging with an Asymmetric Transfer Function Metasurface

The conversion of phase variations in an optical wavefield into intensity information is of fundamental importance for optical imaging technology including microscopy of biological cells. While conventional approaches to phase-imaging commonly rely on bulky optical components or computational post processing, meta-optical devices have recently demonstrated all-optical, ultracompact image processing methods. Here we describe a metasurface that exploits photonic spin-orbit coupling to create an asymmetric optical transfer function for real time phase-imaging. The effect of the asymmetry on transmission through the device is demonstrated experimentally with the generation of high contrast pseudo-3D intensity images of phase variations in an optical wavefield without the need for post-processing. This non-interferometric method has potential applications in biological live cell imaging and real-time wavefront sensing.

Motion performance measurement and optimization of motorized stages using tightly focused laser marking

Motorized stages are widely used in the fields of processing and measurement, such as lithography, semiconductor packaging, biochips, and micro/nanostructure characterization. We propose a tightly focused laser marking method for measuring the motion performance of motorized stages. In this method, a test sample is coated with heat-mode resist thin films and is fixed onto motorized stages. A tightly focused laser spot with a size of ∼520 nm irradiates the heat-mode resist thin films, which then absorb the laser energy and are heated. A laser-induced marking of the films’ structural change from an amorphous state to a crystalline state occurs when the temperature exceeds the crystallization threshold temperature. The motion locus and performance of motorized stages can be clearly observed via the marking of the structural change of heat-mode resist thin films, which can be further clarified through the lithography developing process in alkaline or acidic solutions. The measurement results showed that the minimum nonuniformity coefficient of the motorized stages was 0.016, the minimum parallelism error was 80 nm, the minimum positional accuracy was 0.76 μm, and the accuracy of the measurement system was within 80 nm. The test results demonstrate that the motorized stage can achieve high-precision uniaxial motion with a period of 300 nm and biaxial coordinated motion with a period of <3 μm through parameter optimization, thereby reaching its ultimate performance. Compared to the non-interferometric methods, this tightly focused laser marking method has the advantages of strong environmental adaptability and high accuracy. This study provides an effective and convenient approach for the measurement and optimization of the motion performance of motorized stages.

Stochastic Gravitational-Wave Backgrounds: Current Detection Efforts and Future Prospects

The collection of individually resolvable gravitational wave (GW) events makes up a tiny fraction of all GW signals that reach our detectors, while most lie below the confusion limit and are undetected. Similarly to voices in a crowded room, the collection of unresolved signals gives rise to a background that is well-described via stochastic variables and, hence, referred to as the stochastic GW background (SGWB). In this review, we provide an overview of stochastic GW signals and characterise them based on features of interest such as generation processes and observational properties. We then review the current detection strategies for stochastic backgrounds, offering a ready-to-use manual for stochastic GW searches in real data. In the process, we distinguish between interferometric measurements of GWs, either by ground-based or space-based laser interferometers, and timing-residuals analyses with pulsar timing arrays (PTAs). These detection methods have been applied to real data both by large GW collaborations and smaller research groups, and the most recent and instructive results are reported here. We close this review with an outlook on future observations with third generation detectors, space-based interferometers, and potential noninterferometric detection methods proposed in the literature.

Non-recursive transport of intensity phase retrieval with the transport of phase.

The transport of intensity equation (TIE) is a non-interferometric phase retrieval method that originates from the imaginary part of the Helmholtz equation and is equivalent to the law of conservation of energy. From the real part of the Helmholtz equation, the transport of phase equation (TPE), which represents the Eikonal equation in the presence of diffraction, can be derived. The amplitude and phase for an arbitrary optical field should satisfy these coupled equations simultaneously during propagation. In this work, the coupling between the TIE and TPE is exploited to improve the phase retrieval solutions from the TIE. Specifically, a non-recursive fast Fourier transform (FFT)-based phase retrieval method using both the TIE and TPE is demonstrated. Based on the FFT-based TIE solution, a correction factor calculated by the TPE is introduced to improve the phase retrieval results.

Quantification of the effects of grid angulation on image quality in single-grid-based phase-contrast x-ray imaging

Single-grid-based phase-contrast x-ray imaging (SG-PCXI) is a single-exposure, non-interferometric method for the simultaneous retrieval of absorption, differential phase-contrast, and dark-field images using a conventional x-ray grid; it requires minimal exposure and minimal system setup for potential medical and industrial imaging applications. However, owing to the Moiré artifact, the retrieved images are often distorted because of the inadequate sampling of the grid strips by the pixel array detector. This attribute can result in the degradation of image quality. Therefore, in this study, we propose a method for effectively removing the Moiré artifact by employing a grid angulation technique to improve image quality in SG-PCXI. We theoretically analyzed the formation of the Moiré artifact in an SG-PCXI setup and quantified the effects of grid angulation on the image quality. We conducted an experiment using a tabletop setup to verify the theoretical quantification of the effects of grid angulation on image quality. The Moiré artifact was completely removed in the retrieved images when the x-ray grid was rotated at θ = 18.2° and 26.3°, which aligned well with the theoretical quantification. Furthermore, the spatial resolution of the retrieved images improved as the grid frequency increased. Thus, the experimental results indicated that the proposed method can effectively eliminate the Moiré artifact; furthermore, it was determined that the size of the window function should be as large as possible to ensure improved image quality. The proposed method significantly improves image quality in SG-PCXI.

Higher-order Stokes-parameter correlation to restore the twisted wave front propagating through a scattering medium

We propose and experimentally demonstrate a noninterferometric method to quantitatively determine the topological charge and complete phase structure of a vortex beam scrambled by a random scattering medium. In the proposed technique, the vortex beam with an arbitrary topological charge coaxially enters into the scattering medium with another nonvortex beam with an orthogonal polarization state. This couples the spatial and polarization modes of the coherent light prior to entering the scattering medium. Correlation of the orthogonal polarization states of a random field encodes the signature of the twisted mode of the vortex beam. Recovery of the complex polarization correlation functions and hence twisted modes of the beam are retrieved from the Stokes parameters of a randomly scattered field. Two-point correlations of the Stokes parameters form a 4 \ifmmode\times\else\texttimes\fi{} 4 matrix with a total of 16 elements. Out of these 16 elements, only four elements of the matrix are used to retrieve real and imaginary parts of the complex polarization correlation function and are subsequently applied in the reconstruction of twisted wavefronts. A complete theoretical basis is developed to retrieve the twisted wavefront of propagating light through random scattering media and is also supported by numerical simulation and experimental demonstration. As an application of the proposed technique, recovery of the complete phase maps of the different vortex beams from the random light is experimentally demonstrated and the twisted modes of the incident light are quantitatively analyzed using orthogonal projections. The experimental results are in good agreement with the theoretical basis and numerical results.

Non-iterative complex wave-field reconstruction based on Kramers–Kronig relations

A non-iterative and non-interferometric computational imaging method to reconstruct a complex wave field called synthetic aperture imaging based on Kramers–Kronig relations (KKSAI) is reported. By collecting images through a modified microscope system with pupil modulation capability, we show that the phase and amplitude profile of the sample at pupil limited resolution can be extracted from as few as two intensity images by using Kramers–Kronig (KK) relations. It is established that as long as each subaperture’s edge crosses the pupil center, the collected raw images are mathematically analogous to off-axis holograms. This in turn allows us to adapt a recently reported KK-relations-based phase recovery framework in off-axis holography for use in KKSAI. KKSAI is non-iterative, free of parameter tuning, and applicable to a wider range of samples. Simulation and experiment results have proved that it has much lower computational burden and achieves the best reconstruction quality when compared with two existing phase imaging methods.

Polarization-Encoded Fully-Phase Encryption Using Transport-of-Intensity Equation

In this study, we propose a novel method to encrypt fully-phase information combining the concepts of the transport of intensity equation and spatially variant polarization encoding. The transport of intensity equation is a non-iterative and non-interferometric phase-retrieval method which recovers the phase information from defocused intensities. Spatially variant polarization encoding employs defocused intensity measurements. The proposed cryptosystem uses a two-step optical experimentation process—primarily, a simple set-up for defocused intensities recording for phase retrieval and then a set-up for encoding. Strong security, convenient intensity-based measurements, and noise-free decryption are the main features of the proposed method. The simulation results have been presented in support of the proposed idea. However, the TIE section of the cryptosystem, as of now, has been experimentally demonstrated for micro-lens.

Non-interferometric phase retrieval for collinear phase-modulated holographic data storage

Because of its simple optical system setup and robust noise tolerance, non-interferometric phase retrieval is an important technique for phase-modulated holographic data storage. Usually, the iterative algorithm of non-interferometry needs hundreds of iteration numbers to retrieve phase accurately, the data transfer rate decreases severely. Strong constraints such as adding embedded data into the phase data page can reduce the iteration numbers, but this method decreases the code rate severely. In this paper, we proposed the advanced non-interferometric phase retrieval method based on the collinear system. By encoding the reference beam of the collinear optical holographic storage system with embedded data, the storage space of the signal beam data page is completely released and the encoding rate is doubled. The embedded data can provide more modulation index including phase and amplitude to shorten iterations, so the data transfer rate is also increased. In the simulation, we recorded a four-level phase pattern and retrieved the phase correctly.

Collinear non-interferometric phase retrieval for holographic data storage.

A collinear non-interferometric phase retrieval method for holographic data storage is proposed. The code rate of the collinear system can be increased by 2 times due to transferring the 50% embedded data from a signal beam to a reference beam. Because the reference beam should be always known both in the recording process and reading process, there is no extra material cost for saving the embedded data. Therefore, the storage density of collinear system is increased by about 2 times compared with previous off-axis non-interferometric phase retrieval systems. Besides, we can enhance the algorithm constraint to shorten iteration numbers by increasing the amplitude weight of the reference beam. In the experiment, we shortened the iteration number and the BER by about 3 times. We also find that the reference number can be reduced by using the collinear way and increasing the amplitude weight of reference. This law allows us to give more code positions to signal so that the data amount in one data page can be increased.

Interferometric sensing of the tilt angle of a Gaussian beam

We investigate interferometric techniques to estimate the deflection angle of an optical beam and compare them to the direct detection of the beam deflection. We show that quantum metrology methods lead to a unifying treatment for both single photons and classical fields. Using the Fisher information to assess the precision limits of the interferometric schemes, we show that the precision can be increased by exploiting the initial transverse displacement of the beam. This gain, which is present for both Sagnac and Mach-Zehnder-like configurations, can be considerable when compared to non-interferometric methods. In addition to the fundamental increase in precision, the interferometric schemes have the technical advantage that (i) the precision limits can be saturated by a sole polarization measurement on the field, and that (ii) the detection system can be placed at any longitudinal position along the beam. We also consider position-dependent polarization measurements, and show that in this case the precision increases with the propagation distance, as well as the initial transverse displacement.

Transport of intensity equation method based on edge detection and duty ratio fusion

The non-interferometric phase recovery method which is based on the transport of intensity equation is an important phase acquisition technique in microscopy imaging. In the actual operational process of this technology, at least three intensity images are needed to solve the equation. In the image acquisition process, the selection of the focused image is very important, but it is usually determined by subjective methods, thus causing inaccurate positioning of the in-focus, which further affects the precision of phase recovery result. A phase recovery algorithm based on edge detection and duty ratio is proposed. Firstly, a series of ‘subjectively determined focused images’ collected by the microscope are edge-extracted to obtain corresponding edge information points. Then the real in-focus position is found by calculating the duty ratio, and the corresponding defocused images are selected according to the position of the focused image. Finally, the high-precision phase recovery result is obtained by using these images of the accurate position to solve the equation. The algorithm does not require complex operations such as hardware modifications and can be applied to both discrete and continuous sample distributions. The experimental results effectively prove that the algorithm can accurately find the in-focus position, which improves the accuracy of phase recovery compared with the traditional method that is subjectively determined in-focus image position.