Multi-wavelength Phase Research Articles

Dual-wavelength terahertz two-dimensional phase gratings based on all dielectric metasurfaces

Efficient and accurate phase gratings hold immense significance in the realization of large format heterodyne array receivers at terahertz frequencies. Metallic phase gratings have made substantial advancements in terms of operating wavelength and the number of diffraction beams. Like most other diffractive optical devices, metallic phase gratings are primarily optimized to operate at one specific wavelength. Metasurfaces compositing arrays of subwavelength nanostructures have been demonstrated with various optical functions, by freely modifying the polarization, phase, and amplitude of light. In this study, we present an approach to create a multi-wavelength phase grating compositing segments that incorporate multiple nanostructures. The resulting transmission phase grating not only exhibits uniform diffraction beams (2 × 2) but also achieves the same diffraction angles at both 1.31 and 2.7 THz. The measured total power efficiency of the diffraction beam pattern is 53.2% for 1.31 THz and 42.4% for 2.7 THz. These devices can be applied in terahertz astronomical observations and fluorescence microscopy applications, where multi-wavelength operation is necessary.

Super-resolution lensless on-chip microscopy based on array illumination and sub-pixel shift search.

The resolution of a lensless on-chip microscopy system is constrained by the pixel size of image sensors. This Letter introduces a super-resolution on-chip microscopy system based on a compact array light source illumination and sub-pixel shift search. The system utilizes a closely spaced array light source composed by four RGB LED modules, sequentially illuminating the sample. A sub-pixel shift search algorithm is proposed, which determines the sub-pixel shift by comparing the frequency of captured low-resolution holograms. Leveraging this sub-pixel shift, a super-resolution reconstruction algorithm is introduced, building upon a multi-wavelength phase retrieval method, enabling the rapid super-resolution reconstruction of holograms with the region-of-interest. The system and algorithms presented herein obviate the need for a displacement control platform and calibration of the illumination angles of the light source, facilitating a super-resolution phase reconstruction under partially coherent illumination.

Multi-wavelength interference phase imaging for automatic breast cancer detection and delineation using diffuse reflection imaging

Millions of women globally are impacted by the major health problem of breast cancer (BC). Early detection of BC is critical for successful treatment and improved survival rates. In this study, we provide a progressive approach for BC detection using multi-wavelength interference (MWI) phase imaging based on diffuse reflection hyperspectral (HS) imaging. The proposed findings are based on the measurement of the interference pattern between the blue (446.6 nm) and red (632 nm) wavelengths. We consider implementing a comprehensive image processing and categorization method based on the use of Fast Fourier (FF) transform analysis pertaining to a change in the refractive index between tumor and normal tissue. We observed that cancer growth affects tissue organization dramatically, as seen by persistently increased refractive index variance in tumors compared normal areas. Both malignant and normal tissue had different depth data collected from it that was analyzed. To enhance the categorization of ex-vivo BC tissue, we developed and validated a training classifier algorithm specifically designed for categorizing HS cube data. Following the application of signal normalization with the FF transform algorithm, our methodology achieved a high level of performance with a specificity (Spec) of 94% and a sensitivity (Sen) of 90.9% for the 632 nm acquired image categorization, based on preliminary findings from breast specimens under investigation. Notably, we successfully leveraged unstained tissue samples to create 3D phase-resolved images that effectively highlight the distinctions in diffuse reflectance features between cancerous and healthy tissue. Preliminary data revealed that our imaging method might be able to assist specialists in safely excising malignant areas and assessing the tumor bed following resection automatically at different depths. This preliminary investigation might result in an effective "in-vivo" disease description utilizing optical technology using a typical RGB camera with wavelength-specific operation with our quantitative phase MWI imaging methodology.

High-speed data transmission based on mode-locked optical frequency comb

<sec>With the rapid development of emerging technologies such as multimedia services, live broadcasting, video conferencing, and high-definition television, traditional radio frequency communication is unable to meet people 's growing demand for communication capacity and transmission rate. In recent years, optical communication has received extensive attention from the industrial and scientific communities due to its advantages of large bandwidth, high speed, low power consumption, light weight, and strong anti-interference ability. As an emerging light source, the optical frequency comb (OFC) has a wide spectral range, multi-wavelength, high stability, and good phase coherence, providing a new idea for studying microwave signals with simple system structure, strong tunability and high frequency stability. At the same time, the multi-optical mode characteristics of OFC are compatible with the current communication system based on wavelength division multiplexing technology. Hundreds of laser arrays in a traditional communication system can be replaced by only one laser, which greatly reduces the power consumption of the system.</sec><sec>Combining the above advantages, in this paper, a large-scale parallel high-speed optical communication system based on mode-locked OFC is proposed. The linewidth of the OFC locked to the rubidium atomic clock can reach 1 Hz, which is sufficient to support the transmission of high-order modulation signals. The electro-optic modulators are used to adjust the amplitude and phase of each optical mode of the mode-locked OFC and self-coherently map to the RF domain. The high-speed high-order modulation signal with coded information is obtained by frequency screening through a narrow-band filter. The communication capability of the microwave photonic modulation signal in the 16 quadrature amplitude modulation (QAM) format is verified by simulation. The 16QAM communication with the rate of 2, 6, and 14 Gbit/s is realized by using the photonic microwave signal on the 100 m space optical link, and the bit error rate (BER) is less than 10<sup>–6</sup>. The proposed large-scale parallel optical communication system based on mode-locked OFC can achieve high-speed information transmission with a compact system structure, which is suitable for inter-satellite communication, emergency communication, military communication and other fields.</sec>

Optimization of the Polarized Imaging Nephelometer (PI-Neph) for continuous monitoring of multiwavelength aerosol phase functions in support of space polarimetry missions

This work deals with the set up and optimization of a commercial multiwavelength polarized imaging nephelometer (PI-Neph, Airphoton PIN100) designed to measure F11 (phase function) and –F12/F11 (polarized phase function) from ambient aerosol samples. Such measurements are critical for the success of upcoming satellite missions based on polarimetry measurements because they will support and validate retrieval techniques. The main novelty of the instrument with respect to previous versions consists of using only one beam instead of a mirror system to fold it, avoiding internal reflections of light and loss of energy within the laser beam. The instrument also includes the automatization of the imaging technique that makes possible continuous measurements in near real time of the aerosol phase functions at different states of linear polarization directly from ambient air. Laser emits at three different wavelengths (405, 515 and 660 nm) and the beam goes through a wire grid polarizer for linearly polarizing the light, followed by two liquid crystal retarders that control the state of linear polarization. The detector is a CMOS camera perpendicular to the beam which allows to obtain final phase functions in the range 5°–175° (losses of some angles by physical limitations and stray light). The calibration of the instrument is discussed and includes geometric calibration (to account for different light paths to the camera) plus absolute calibration (to obtain physical units). Temporal stability of calibrations is observed, and different data quality tests are presented in order to obtain reliable values of F11 and –F12/F11. For an automatic operation of the instrument that permits real time phase matrix measurements, a data quality check algorithm that avoids non-physical measurements and filters outliers has been developed. Validation of the scattering matrix elements based on monodisperse aerosol measurements is also done with polystyrene latex spheres (PSL), showing good agreement with Mie theory. Finally, first results of the instrument operating at the University of Granada (UGR) station from the Andalusian Global ObseRvatory of the Atmosphere (AGORA) since April 2022 are presented. Very good agreements of the integrated scattering coefficients with an integrating nephelometer (TSI, model 3563) were obtained with high correlation coefficients for the three wavelengths (R2 > 0.81). The calculated root-mean-square error (RMSE) reveals that the performance of the PI-Neph in the measurement of the scattering coefficient is better in the 660 nm and 515 nm wavelengths than in the 405 nm one, although differences between datasets are still low. The observed differences in phase functions and especially polarized phase functions (both in shape and spectral differences) under changing atmospheric scenarios (Saharan dust, pollution and background aerosol conditions) indicated that these variables are sensitive and reliable to classify the type of ambient aerosol. Particularly, the combined measurements of F11 and –F12/F11 shows a unique potential of the PI-Neph for aerosol typology.

Analysis of edge jumps in multi-wavelength phasing of segmented-mirror telescopes.

Interferometric methods for phasing the primary mirrors of segmented-mirror telescopes generally need to make measurements at multiple wavelengths in order to achieve suitably large edge height capture ranges. In the presence of measurement errors, such methods have the potential for grossly wrong measurements, so-called edge jumps. In this paper, we investigate the causes of edge jumps using the example of Thirty Meter Telescope (TMT) phasing. We explain the reasons for their occurrence and develop a mathematical understanding of the conditions under which they arise. We describe how stability analyses of the vast parameter space relevant to TMT phasing can be accomplished in an efficient way and present examples of results. These concepts are also applicable to other multi-wavelength interferometric phase measurement techniques.

Projected refractive index framework for multi-wavelength phase retrieval.

Multi-wavelength phase retrieval provides a competitive solution to lensless holographic imaging that features a low-cost, compact design and high data acquisition speed. However, the existence of phase wraps poses a unique challenge for iterative reconstruction, and the resulting algorithms often suffer from limited generalizability and increased computational complexity. Here, we propose a projected refractive index framework for multi-wavelength phase retrieval that directly recovers the amplitude and unwrapped phase of the object. General assumptions are linearized and integrated into the forward model. Based on an inverse problem formulation, physical constraints and sparsity priors are incorporated, which ensures imaging quality under noisy measurements. We experimentally demonstrate high-quality quantitative phase imaging on a lensless on-chip holographic imaging system using three color LEDs.

Large Piston Error Detection Method Based on the Multiwavelength Phase Shift Interference and Dynamic Adjustment Strategy

As the loading space in rockets and mirror fabrication technology is limited, optical systems in space cannot have large optical apertures. However, the successful launch and excellent performance of the James Webb Telescope indicate that segmented mirrors can help realize large-aperture optical systems in space, owing to the fold–unfold mechanism in the telescope. However, all segments in the segmented mirror should be co-phased so that it is equivalent to a monolithic mirror. The co-phasing problem is significant in optical systems in space because of their low error tolerance. Owing to some accident factors, the piston error can be more than 1 mm after the unfolding process. Here, we introduced a multiwavelength interference method and dynamic adjusting strategy, aiming to solve the two problems of co-phasing: large detection range (~2 mm) and high detection precision (<1/20λ). Numerical simulations were performed, and a 400 mm aperture-segmented spherical mirror system was used to verify this method. The original piston error was set to 1 mm, after the coarse co-phasing, and the residual piston error to less than half the wavelength of the monochromatic light; for fine co-phasing, the achieved detection precision was approximately 1.2 nm.

Lensfree on-chip microscopy based on single-plane phase retrieval.

We propose a novel single-plane phase retrieval method to realize high-quality sample reconstruction for lensfree on-chip microscopy. In our method, complex wavefield reconstruction is modeled as a quadratic minimization problem, where total variation and joint denoising regularization are designed to keep a balance of artifact removal and resolution enhancement. In experiment, we built a 3D-printed field-portable platform to validate the imaging performance of our method, where resolution chart, dynamic target, transparent cell, polystyrene beads, and stained tissue sections are employed for the imaging test. Compared to state-of-the-art methods, our method eliminates image degradation and obtains a higher imaging resolution. Different from multi-wavelength or multi-height phase retrieval methods, our method only utilizes a single-frame intensity data record to accomplish high-fidelity reconstruction of different samples, which contributes a simple, robust, and data-efficient solution to design a resource-limited lensfree on-chip microscope. We believe that it will become a useful tool for telemedicine and point-of-care application.

A Multi-Wavelength Phase Retrieval With Multi-Strategy for Lensfree On-Chip Holography

Due to convenient operation and robust imaging, multi-wavelength phase retrieval has been widely applied in lensfree on-chip digital holographic microscope (LFOCDHM). Nevertheless, the insufficient diffraction variation and small number of measurements on the LFOCDHM make it difficult to eliminate the twin image by multi-wavelength phase retrieval. We propose a multi-wavelength phase retrieval for LFOCDHM based on energy constraint, global update strategy, and vector extrapolation acceleration. Simulations and experiments on the LFOCDHM show that our proposed method realizes efficient elimination effect and robust reconstruction with three wavelengths for illumination while maintaining fast convergence. More importantly, the proposed method is simple and non-parametric. It is believed that the proposed method could provide a promising solution for LFOCDHM.

Phase microscopy and surface profilometry by digital holography

Quantitative phase microscopy by digital holography is a good candidate for high-speed, high precision profilometry. Multi-wavelength optical phase unwrapping avoids difficulties of numerical unwrapping methods, and can generate surface topographic images with large axial range and high axial resolution. But the large axial range is accompanied by proportionately large noise. An iterative process utilizing holograms acquired with a series of wavelengths is shown to be effective in reducing the noise to a few micrometers even over the axial range of several millimeters. An alternate approach with shifting of illumination angle, instead of using multiple laser sources, provides multiple effective wavelengths from a single laser, greatly simplifying the system complexity and providing great flexibility in the wavelength selection. Experiments are performed demonstrating the basic processes of multi-wavelength digital holography (MWDH) and multi-angle digital holography (MADH). Example images are presented for surface profiles of various types of surface structures. The methods have potential for versatile, high performance surface profilometry, with compact optical system and straightforward processing algorithms.

Computational multi-wavelength phase synthesis using convolutional neural networks [Invited

Multi-wavelength digital holographic microscopy (MWDHM) provides indirect measurements of the refractive index for non-dispersive samples. Successive-shot MWDHM is not appropriate for dynamic samples and single-shot MWDHM significantly increases the complexity of the optical setup due to the need for multiple lasers or a wavelength tunable source. Here we consider deep learning convolutional neural networks for computational phase synthesis to obtain high-speed simultaneous phase estimates on different wavelengths and thus single-shot estimates of the integral refractive index without increased experimental complexity. This novel, to the best of our knowledge, computational concept is validated using cell phantoms consisting of internal refractive index variations representing cytoplasm and membrane-bound organelles, respectively, and a simulation of a realistic holographic recording process. Specifically, in this work we employed data-driven computational techniques to perform accurate dual-wavelength hologram synthesis (hologram-to-hologram prediction), dual-wavelength phase synthesis (unwrapped phase-to-phase prediction), direct phase-to-index prediction using a single wavelength, hologram-to-phase prediction, and 2D phase unwrapping with sharp discontinuities (wrapped-to-unwrapped phase prediction).

Pluto’s Haze Abundance and Size Distribution from Limb Scatter Observations by MVIC

Abstract The New Horizons spacecraft observed Pluto and Charon at solar-phase angles between 16° and 169°. In this work, we use the Multispectral Visible Imaging Camera (MVIC) observations to construct multiwavelength phase curves of Pluto’s atmosphere, using the limb scatter technique. Observational artifacts and biases were removed using Charon as a representative airless body. The size and distribution of the haze particles were constrained using a Titan fractal aggregate phase function. We find that monodispersed and log-normal populations cannot simultaneously describe the observed steep forward scattering, indicative of wavelength-scale particles, and the non-negligible backscattering indicative of particles much smaller than the wavelength. Instead, we find it necessary to use bimodal or power-law distributions, especially below ∼200 km, to properly describe the MVIC observations. Above 200 km, where the atmosphere is isotropically scattering, a monodisperse, log-normal, or a bimodal/power law approximating a monodispersed population is able to fit the phase curves well. As compared to the results of previously published articles, we find that Pluto’s atmosphere must contain haze particle number densities an order of magnitude greater for small (∼10 nm) and large (∼1 μm) radii, and relatively fewer intermediate sizes (∼100 nm). These conclusions support a lower aggregate aerosol growth rate than that found by Gao et al., indicating a higher charge-to-radius ratio, upwards of 60e − μm−1. In order to generate large particles with a lower growth rate, the atmosphere must also have a lower sedimentation velocity (<∼0.01 m s−1 at 200 km), which is possible with a fractal dimension of less than 2.

Jupiter as an Exoplanet: Insights from Cassini Phase Curves

Abstract Due to its proximity to Earth, Jupiter of the solar system serves as a unique case study for gas-giant exoplanets. In the current Letter, we perform fits of ab initio, reflective, semi-infinite, homogeneous model atmospheres to 61 phase curves from 0.40 to 1.00 μm, obtained from the Cassini spacecraft, within a Bayesian framework. We reproduce the previous finding that atmospheric models using classic reflection laws (Lambertian, Rayleigh, single Henyey–Greenstein) provide poor fits to the data. Using the double Henyey–Greenstein reflection law, we extract posterior distributions of the single-scattering albedo and scattering asymmetry factors and tabulate their median values and uncertainties. We infer that the aerosols in the Jovian atmosphere are large, irregular, polydisperse particles that produce strong forward scattering together with a narrow backscattering lobe. The near-unity values of the single-scattering albedos imply that multiple scattering of radiation is an important effect. We speculate that the observed narrow backscattering lobe is caused by coherent backscattering of radiation, which is usually associated with solar system bodies with solid surfaces and regolith. Our findings demonstrate that precise, multiwavelength phase curves encode valuable information on the fundamental properties of cloud/haze particles. The method described in this Letter enables single-scattering albedos and scattering asymmetry factors to be retrieved from James Webb Space Telescope phase curves of exoplanets.

Multi-wavelength phase retrieval for coherent diffractive imaging.

Phase retrieval is a numerical procedure concerned with the recovery of a complex-valued signal from measurements of its amplitude. We describe a generalization of this method for multi-wavelength data acquired in a coherent diffractive imaging experiment. It exploits the wavelength-dependent scaling of the support domain to recover separate reconstructions for each wavelength, providing new possibilities for coherent diffractive imaging experiments. Limitations on the number of wavelengths are discussed through adaptation of the constraint ratio, and the method's performance is investigated as a function of the source spectrum, sample geometry, and degree of complexity through numerical simulations.

Wavelength-Demultiplexed Laser Interferometry for Metrology

Non-contact, cost-efficient, and long-range precision metrology is essential for applications in diverse areas, from 3D sensing and robotics to automated manufacturing, and multiwavelength interferometry is a compelling candidate. Here, we present a new arithmetic approach for multiwavelength phase unwrapping, with the maximum theoretical range and tolerance to measurement noise in phase. We supplement our formulation with a simultaneous phase shifting interferometry setup with a low measured standard deviation of phase, σφ = 2π/1325. We unwrap the interferometric phases of experiments performed through wavelengths with a greatest common divisor of 25 nm, demonstrate a range equal to their lowest-common-multiple with the precision of a single wavelength interferometer, and reconstruct three-dimensional scenes based on a single-pixel 3D imaging system.

Highly temporal stable, wavelength-independent, and scalable field-of-view common-path quantitative phase microscope.

.Significance: High temporal stability, wavelength independency, and scalable field of view (FOV) are the primary requirements of a quantitative phase microscopy (QPM) system. The high temporal stability of the system provides accurate measurement of minute membrane fluctuations of the biological cells that can be an indicator of disease diagnosis.Aim: The main aim of this work is to develop a high temporal stable technique that can accurately quantify the cell’s dynamics such as membrane fluctuations of human erythrocytes. Further, the technique should be capable of acquiring scalable FOV and resolution at multiple wavelengths to make it viable for various biological applications.Approach: We developed a single-element nearly common path, wavelength-independent, and scalable resolution/FOV QPM system to obtain temporally stable holograms/interferograms of the biological specimens.Results: With the proposed system, the temporal stability is obtained without using any vibration isolation table. The capability of the proposed system is first demonstrated on USAF resolution chart and polystyrene spheres ( diameter). Further, the system is implemented for single shot, wavelength-independent quantitative phase imaging of human red blood cells (RBCs) with scalable resolution using color CCD camera. The membrane fluctuation of healthy human RBCs is also measured and was found to be around 47 nm.Conclusions: Contrary to its optical counterparts, the present system offers an energy efficient, cost effective, and simple way of generating object and reference beam for the development of common-path QPM. The present system provides the flexibility to the user to acquire multi-wavelength quantitative phase images at scalable FOV and resolution.

High-quality multi-wavelength lensfree microscopy based on nonlinear optimization

In multi-wavelength lensfree microscopy (MWLM), a laser source is usually replaced with a light-emitting diode for a low-cost and portable configuration. However, the trade-off between noise suppression and resolution enhancement puts a challenging issue for high-quality imaging. Here we propose a noise-robust multi-wavelength phase retrieval to increase the stability of MWLM. To solve the inverse problem of phase retrieval, we derive an optimization procedure to iteratively minimize the data fidelity and impose a total variation term for noise suppression. The experimental results of resolution target, stained human goblet cell, and label-free microglia cell demonstrate that our method could hold a better noise tolerance without the loss of imaging resolution. We believe that our method will become a powerful tool for a resources-limited scene.

Off-axis digital holographic multiplexing for rapid wavefront acquisition and processing

Off-axis holographic multiplexing involves capturing several complex wavefronts, each encoded into off-axis holograms with different interference fringe orientations, simultaneously, with a single camera acquisition. Thus, the multiplexed off-axis hologram can capture several wavefronts at once, where each one encodes different information from the sample, using the same number of pixels typically required for acquiring a single conventional off-axis hologram encoding only one sample wavefront. This gives rise to many possible applications, with focus on acquisition of dynamic samples, with hundreds of scientific papers already published in the last decade. These include field-of-view multiplexing, depth-of-field multiplexing, angular perspective multiplexing for tomographic phase microscopy for 3-D refractive index imaging, multiple wavelength multiplexing for multiwavelength phase unwrapping or for spectroscopy, performing super-resolution holographic imaging with synthetic aperture with simultaneous acquisition, holographic imaging of ultrafast events by encoding different temporal events into the parallel channels using laser pulses, measuring the Jones matrix and the birefringence of the sample from a single multiplexed hologram, and measuring several fluorescent microscopy channels and quantitative phase profiles together, among others. Each of the multiplexing techniques opens new perspectives for applying holography to efficiently measure challenging biological and metrological samples. Furthermore, even if the multiplexing is done digitally, off-axis holographic multiplexing is useful for rapid processing of the wavefront, for holographic compression, and for visualization purposes. Although each of these applications typically requires a different optical system or processing, they all share the same theoretical background. We therefore review the theory, various optical systems, applications, and perspectives of the field of off-axis holographic multiplexing, with the goal of stimulating its further development.

Multi-wavelength phase-shifting interferometry based on a two-step phase-shifting phase retrieval algorithm with a color CMOS

By combining the advantages of multi-wavelength phase-shifting interferometry and two-step phase-shifting phase retrieval algorithm, a measured phase with high precision and a large measuring range can be retrieved rapidly from three multi-wavelength interferograms with unknown phase shifts, recorded by a single-chip color CMOS. Firstly, two normalized differential interferograms without backgrounds are obtained by means of subtraction followed by normalization between the three color interferograms. Next, the wrapped phases of a single wavelength are retrieved via the Gram–Schmidt orthonormalization approach. Finally, the unambiguous phase of the three synthetic wavelengths can be achieved by subtraction between the wrapped phases of corresponding wavelengths. To reduce the phase noise amplification introduced by the magnification of wavelengths, the phase unwrapping algorithm of reducing the noise of the three- synthetic wavelength to the level of a two-synthetic long wavelength, a single-wavelength, and a two-synthetic short wavelength are implemented in turn. Compared with conventional multi-wavelength phase shifting interferometry, only three interferograms with unknown phase shifts are needed to reconstruct the actual phase of the measured object to a high degree of measurement resolution, and with a large measurement range; this approach would be useful in dynamic phase measurement. Both simulation and experimental results validate the performance of the proposed method.