Amount Of Phase Shift Research Articles

High-precision frequency-controlled optical phase shifter with acousto-optic devices.

A fundamental parameter to determine how electromagnetic waves interfere is their relative phase, and achieving a fine control over it enables a wide range of interferometric applications. Existing phase control methods rely on modifying the optical path length either by changing the path followed by the light or by altering the thickness or index of refraction of an optical element in the setup. In this Letter, we present a novel, to the best of our knowledge, method, based on acousto-optic modulators (AOMs), which allows adjusting the phase by shifting the frequency of the light in a segment of its path. Since the amount of phase shift depends on the length of the segment, an optical fiber is used to realize a 2π shift. Two experimental implementations are described which deal with different sources of phase fluctuations. The first addresses fluctuations resulting from the optical fiber, while the second tackles unwanted variations originating from the AOMs.

Phase-shifted fiber Bragg grating filters based on counter-propagating cladding modes coupling.

In this paper, we comprehensively analyze counter-propagating cladding mode assisted phase-shifted fiber Bragg gratings (FBGs) and propose an ultra-narrow bandwidth laser line filter based on such gratings. Full vector modal analysis has been used to obtain the mode guiding and its coupling characteristics. We show that the transmission spectrum of the counter-propagating cladding mode assisted FBGs can be tailored by incorporating single or multiple phase shifts along the grating length. Phase shifts open up narrowband transmission windows inside the stop band of the Bragg grating, and the transmitted wavelength can be altered by controlling the amount of phase shift. Unlike conventional FBGs, the grating discussed here has access to the evanescent field of the excited counter-propagating cladding mode, which opens up the possibility of refractive index based tuning of resonance wavelength. Further, the bandwidth of the proposed grating is two orders of magnitude smaller than that of the conventional LPGs. As an alternative application, we also show that with the right length ratio, the multiple phase shifts can also be used to create a very flattened single transmission peak inside the stop band. The effects of grating regulating factors such as the grating length, grating strength, location of the phase shift, and index apodization on the linewidth of the narrow central peak of π PS-FBG are also investigated. We present a clear physical explanation of various factors involved in the counter-propagating cladding mode coupling in such phase-shifted Bragg grating. Due to its extremely narrow transmission window, our study can find application in developing sensors for measuring parameters with greater accuracy. Such phase-shifted Bragg gratings can also be used to create an all-fiber demultiplexer for multichannel systems and fiber optic sensors as a particular application.

High-resolution reconstruction of spectrum-overlapped off-axis holography by deflecting reference beam of Gaussian symmetry

In digital holography, extracting the +1-order spectrum accurately and making full utilization of the spatial bandwidth of the CCD sensor are essential for high-resolution and artifacts-free quantitative phase imaging. In this paper, using the light intensity symmetry of the Gaussian laser beam, we delicately eliminate the zero-order spectrum by means of subtraction of two off-axis hologram spectra acquired by symmetrically deflecting the reference beam. Therefore, the +1-order spectrum can be extracted accurately even if it is completely overlapped with the zero-order spectrum. Compared with phase-shifting methods, such as pi-phase and random phase, which require accurate control or calculation of the phase-shifting amount, this proposed method does not need to precisely control the deflection angle of reference beam. Being achievable the maximum utilization of half-space bandwidth of the CCD sensor, the proposed method has realized high-resolution imaging demonstrated by the experimental results of three specimens. This method has general applications in digital holography, such as eliminating the zero-order spectrum and extracting the +1-order spectrum.

Temporal phase unwrapping based on unequal phase-shifting code.

In fringe projection profilometry (FPP) based on temporal phase unwrapping (TPU), reducing the number of projecting patterns has become one of the most important works in recent years. To remove the 2π ambiguity independently, this paper proposes a TPU method based on unequal phase-shifting code. Wrapped phase is still calculated from N-step conventional phase-shifting patterns with equal phase-shifting amount to guarantee the measuring accuracy. Particularly, a series of different phase-shifting amounts relative to the first phase-shifting pattern are set as codewords, and encoded to different periods to generate one coded pattern. When decoding, Fringe order with a large number can be determined from the conventional and coded wrapped phases. In addition, we develop a self-correction method to eliminate the deviation between the edge of fringe order and the 2π discontinuity. Thus, the proposed method can achieve TPU but need to only project one additional coded pattern (e. g. 3+1), which can significantly benefit dynamic 3D shape reconstruction. The theoretical and experimental analysis verify that the proposed method performs high robustness on the reflectivity of the isolated object while ensuring the measuring speed.

Efficient phase-shift error compensation algorithm based on probability density function

In non-digital projection systems, the inaccuracy of phase shifts is one of the most important nonlinear errors. In this paper, an efficient and universal compensation algorithm is proposed, which does not need to find the exact phase shift amounts, but to compensate the periodical errors by a universal two-coefficient error model. With this model, only two error coefficients should to be searched for any multi-step phase shift algorithm. To find the error coefficients, a correlation process and a tool known as the probability density function (PDF) are used. First, a set of pre-simulated PDF curves are generated with the different error coefficients. Second, a practical PDF curve from captured fringes is calculated. Finally, the correlation process is carried out to locate the most similar simulated PDF curve, whose error coefficients are the practical ones. In this paper, we demonstrate the compensation for three, four and five-step phase-shifting algorithms separately. Experimental results show that this method has high universality, and can meet the requirements of rapid and high accuracy measurement.

Spectral phase sensitivity of frequency resolved optical switching for broadband IR pulse characterization.

In this work, we demonstrate the sensitivity of the frequency-resolved optical switching (FROSt) technique to detect a small amount of spectral phase shift for the precise characterization of ultrashort laser pulses. We characterized fs pulses centered at 1.75 µm that are spectrally broadened up to 700 nm of bandwidth in a hollow-core fiber and subsequently compressed down to 2.3 optical cycle duration by propagation in the air at atmospheric pressure. By inserting thin fused silica windows of different thicknesses in the beam path, we accurately retrieve group delay dispersion (GDD) variations as small as 10 fs2. Such GDD variations correspond to a change of the pulse duration of only 0.2 fs for a Fourier transform limited 2-cycle pulse at 1.75 µm (i.e., 11.8 fs). The capability to measure such tiny temporal variations thus demonstrates that the FROSt technique has sufficient sensitivity to precisely characterize single-cycle pulses.

The Absolute Phase Retrieval Based on the Rotation of Phase-Shifting Sequence

The absolute phase retrieval has been the focus of developments in three-dimensional (3D) shape measurement. The traditional absolute phase retrievals based on phase-shifting algorithm mainly utilize extra patterns to generate fringe order map, which decreases the measuring speed and income more phase shift error. In this paper, the cue of fringe order is directly embedded into phase-shifting patterns to minimize the number of projecting patterns. Fringe order is encoded by rotating the sequence of phase shift amounts, causing the 2&#x03C0; discontinuity to be extended into &#x00B1;2&#x03C0;/<i>N</i>, &#x00B1;4&#x03C0;/<i>N</i>,..., &#x00B1;2(<i>N</i>-1)&#x03C0;/<i>N</i>, &#x00B1;2&#x03C0;. Due to the coding periodicity, the regional wrapped phase without 2&#x03C0; ambiguity can be extracted from different wrapped phase maps. When decoding, the coding phase jump points can be located and identified from one or multiple wrapped phase maps, and then used to determine fringe order by the bidirectional data processing. Experimental results have proved that the proposed method without extra coding patterns not only provides high robustness to shadow and considerable accuracy closed to that of traditional phase-coded method, but also inherits the performance to measure the complex and colorful object using traditional sinusoidal phase-shifting patterns.

Dynamic deformation measurement of dual-wavelength arbitrary phase-shifting digital holography with automatic phase-shift detection

Dual-wavelength arbitrary phase-shifting digital holography with automatic phase-shift detection is first proposed in this study. Holograms with two wavelengths and the interference fringes used to detect the phase-shifting amount for each wavelength were simultaneously recorded in one image using the space-division multiplexing technique. Compared with conventional methods, the proposed approach can achieve simultaneous phase shifting of the reference beams of two wavelengths, which substantially reduces recording time and does not require excessive phase-shifting device precision. The proposed and conventional methods were quantitatively evaluated with numerical simulations, and a dynamic deformation measurement was obtained using the system. In the quantitative evaluation of the simulation, the root-mean-square errors of amplitude and phase images reconstructed by the proposed method were reduced by 12% and 19% compared to the conventional method, respectively. Both numerical simulations and experiments verified the effectiveness of the proposed method.

Generalized 2-step phase-shifting algorithm for fringe projection

Fringe projection profilometry using the phase-shifting technique enables high-precision, high-speed and flexible measurements. Among them, the two-step phase-shifting method has become an important approach to coordinate the accuracy and measurement speed; methods especially based on the amount of phase-shift of π/2, π or 3π/2 can improve time efficiency by reducing steps in unique way. In this paper, a phase iterative technique is proposed and established for two-step phase-shifting with arbitrary phase shift. The general mathematical scheme and parameters linear and nonlinear optimization of the proposed method are described in detail. The simulational and experimental results show that the proposed technique is an effective and precise phase detection method for two-step phase-shifting profilometry.

Absolute phase retrieval for colored objects based on three phase-shifting amount codes.

We propose an absolute phase retrieval method based on three phase-shifting amount codes (3-PSA-codes) to measure the colored object with one additional pattern. 3-PSA-codes adopt the coding concept of 3-digit-codes, in which the code elements of three consecutive periods are treated as a unique code word for one period. However, to measure the colored object more effectively in the proposed method, each code element is embedded into the PSA domain and retrieved from the phase difference. Fringe patterns for the wrapped phase are artfully employed in the code element retrieval. Hence, for the first time, to the best of our knowledge, the code element related to the phase can be determined by one additional pattern. It breaks the constraint that temporal methods require multiple additional patterns to overcome the adverse effect of the surface color of objects on absolute phase retrieval. Experimental results demonstrate that the proposed 3-PSA-codes have strong robustness in the measurement of the colored object.

An improved approach to eliminate the error induced by vibrations for laser speckle interferometry under tokamak vibrational environments

To build an online and non-contact diagnosis system of surface morphology of Plasma-Facing Components (PFCs) in fusion devices, a measurement system based on Laser Speckle Interferometry (LSI) is in development in our laboratory. To preserve high resolution, the temporal phase-shifting technique which is sensitive to vibration was introduced. Considering that periodic vibration of the tokamak device will cause the phase shift which is not equal to the special constant value in each step, which will lead to the distortion of the reconstructed surface. In this paper, we introduced an improved phase distribution extraction approach based on Least-square iteration to deal with the vibrational effect. In the process of phase extraction, we combined the amount of phase shift and the phase introduced by vibration together and treated them as an unknown parameter. Then the amount of phase-shifts and the phase distribution could be determined by means of the iteration process. Benchmark tests were conducted on Tungsten (W) material which related to PFCs. A laser ablation method was used to simulate the erosion process during the Plasma-Wall Interaction (PWI) of the tokamak environment. Results show that the morphology results measured by the Least-square iteration approach is very close to the measurement results from the confocal microscopy with the relative error rates within 20%. This indicates that the LSI measurement system based on the Least-square iteration approach is promising for real-time online monitoring in Experimental Advanced Superconducting Tokamak (EAST) vibration environments.

Recent Progress on Ultrathin Metalenses for Flat Optics.

SummaryAs technology advances, electrical devices such as smartphones have become more and more compact, leading to a demand for the continuous miniaturization of optical components. Metalenses, ultrathin flat optical elements composed of metasurfaces consisting of arrays of subwavelength optical antennas, provide a method of meeting those requirements. Moreover, metalenses have many other distinctive advantages including aberration correction, active tunability, and semi-transparency, compared to their conventional refractive and diffractive counterparts. Therefore, over the last decade, great effort has been focused on developing metalenses to investigate and broaden the capabilities of metalenses for integration into future applications. Here, we discuss recent progress on metalenses including their basic design principles and notable characteristics such as aberration correction, tunability, and multifunctionality.

Time and phase synchronization in communication system with a digital pseudo-random modulation

The paper is concerned a model of a digital communication system where the samples of white Gaussian noise with zero mean and dispersion σ2are used as a modulated (carrier) low-frequency signal. Methods of the digital-phase modulation are used in a system for transmission of information message. The communication technology reminds CDMA (Code Division Multiple Access). However, a key of feature of this system is that digital samples of white Gaussian noise are used to increase the spectrum of the information message instead of traditional Walsh-Hadamard binary sequences. In this system the repeat period of the pseudo-random sequence values is specified by the parameter and can be equal to the time (duration) of several information symbols contrast to CDMA, in which the duration of repetition period equals to the duration of modulating symbol. On the one hand, the solution allows you to increase the confidentiality of the transmitted message and more evenly expand its frequency spectrum as compared with the existing of CDMA methods. On the other hand, scientists face two significant scientific tasks that make the work meaningful. First, it is necessary to ensure the synchronous operation of pseudo-random sequence generators in the receiving and transmitting devices. Secondly, it is necessary to define a phase shift amount of the frequency-change oscillator in receiving device. Both problems are the result of the asynchronous starting of the receiver. A control signal is used to solve these problems in the radio communication system which is transmitted simultaneously with an information message. So the result of modulator work is the sum of both information and control modulated signals. The proposed methods and algorithms provide the coherent signal processing with the digital pseudorandom modulation in the receive path of communication channel. The paper is a course of early research studies and it contains a detailed mathematical description of modulation and demodulation signals in the communication system with the digital pseudorandom modulation. The numerical model of the system is described in MatLab language. All numerical experiments were carryout in a mathematical computing system of MatLab.

Multibeam Phased-Arrays Using Dual-Vector Distributed Beamforming: Architecture Overview and 28 GHz Transceiver Prototypes

This article presents a dual-vector distributed beamformer architecture that employs a series-feed network and is capable of supporting up to four simultaneous beams. The multibeam array uses scalar functions within each front end to create Cartesian-weighted signals needed for phase shifting. A dual-vector series-feed network combines/distributes these signals for the receiver/transmitter whereas a global quadrature interpolator is used to create two conjugate beams. By using an interpolator on either end of the series feed, a total of four beams can be obtained. Among these four beams, a first beam can be controlled independently, a second beam is formed as an image of the first, a third beam is offset from the first based on the amount of phase shift within the series-feed structure, and a fourth beam is an image of the offset beam. In this work, the theory of operation of the series-feed DVDB is presented and then two different four-element 28 GHz DVDB transceiver array prototypes in 120 nm SiGe BiCMOS technology are described. One uses a hybrid coupler for global interpolation at radio frequency (RF) and the other uses quadrature mixers for global interpolation at baseband. Measurement results for the array employing passive interpolation at RF show excellent phase-shifting performance, including < 1 dB root-mean-squared (RMS) gain error, < 2 degree RMS phase error, 24% 3 dB bandwidth, with 16–18.6 dBm saturated output power in transmit mode and 4.9–7.3 dB noise figure in receive mode. Measurement results for the array employing mixer-based interpolation likewise show excellent phase-shifting performance with similar RMS gain and phase errors and slightly degraded overall RF performance. Comparing the two, we conclude that the DVDB with passive interpolation at RF is better suited for partitioned systems where beamformers and transceivers are realized on separate chips to support larger, scalable arrays. In contrast, the DVDB with mixer-based interpolation is better suited for integrated systems where beamformers and frequency translation functions must be integrated together.

Vibration-resistant interference microscope with assistant focusing for on-machine measurement of surface topography

The interference microscope is a powerful tool for surface topography measurement, but its high sensitivity to vibration hinders its application to on-machine use. To measure surface roughness on a machine for the ultra-precision machining, a vibration-resistant interference microscope (VRIM) with an assistant focusing function is developed. The basic principle of VRIM is an error-compensated phase-shifting interferometry. An iterative algorithm is presented to calculate the surface phase with the phase shift amounts as unknown variables, where the phase shift amounts are calculated and compensated with least-squares method. A narrow bandwidth illumination is employed to alleviate coherence envelop influence, and a simplified intensity model is established to decouple the variables. Assisting the microscope to find fringe quickly, the focusing is realized by introducing an off-axis thin beam to generate two spots, of which their relative position relates to the defocus. The focusing method is directional and determinant, and has a large range up to 0.3 mm. In the vibration disturbances of 0.2 μm and 0.4 μm amplitudes over 0 Hz to 20 Hz frequency region, the roughness accuracy and repeatability of measuring an ultra-precision machined surface are both up to the sub-nanometer level. The developed instrument is applied to a single-point diamond turning machine and achieves a sub-nanometer accuracy and repeatability.

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

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

Fast and accurate two-frame phase demodulation algorithm with statistical averaging

This paper introduces a fast, compact phase demodulation method for two-frame random phase-shifting interferometry. A set of sine and cosine components is obtained with the addition and subtraction of two pre-filtered fringe patterns. Then, using the properties of the trigonometric function, the amount of phase shift is obtained by statistically averaging all the pixels. Finally, the phase distribution of the interferogram is obtained by the arctangent operation. The proposed algorithm has a very low computation burden and does not require iteration, optimization, and orthogonalization while ensuring measurement accuracy; as a result, the consumed time is very short. Simulation and experimental results are presented to verify the accuracy and efficiency of the proposed method.

Removal of Instantaneous Reactive Power From High-Conversion-Ratio Bidirectional Resonant Converter With Balanced Capacitor Voltage

This article presents bidirectional operation of a resonant converter that features high step-up/down capability, high efficiency, and balanced capacitor voltage. When transferring power in the backward direction, the original converter may suffer from significant reverse current due to large fluctuation of the resonant capacitor voltage. By applying the right amount of phase in the pulsewidth-modulation signal, we can remove the instantaneous reactive power generated during the backward operation. We first derive the nominal duty ratio of the secondary side in terms of the backward voltage gain, then derive the threshold load level, above which the instantaneous reactive power appears, and compute the required amount of phase shift to remove it. We also analyze the sensitivity of the required amount of phase with regard to resonant tank parameters. A 400-W prototype converter has been built to demonstrate the performance of the proposed converter.

Michelson-interferometric-configuration-based incoherent digital holography with a geometric phase shifter

The phase-shifting method is a simple and efficient approach to extract complex hologram information free of bias and twin-image noise. In this study, the geometric phase-shifting method is utilized for a self-interference incoherent digital holographic recording system based on the Michelson-type interferometer. The phase-shifting module consists of a horizontal polarizer, and two achromatic quarter-wave plates are employed inside the interferometer, replacing conventional phase-shifting devices, such as the piezo-actuated mirror. Since the phase-shifting amount of the introduced method herein is theoretical, regardless of the input wavelength, the simultaneous recording of step-wise phase-shifted interferograms for different color channels is available. Therefore, the multi-color hologram recording is achieved with fewer numbers of exposures. The demonstration of multi-color hologram recording and reconstruction are presented to validate the proposed idea.

Phase-extraction algorithm for a single-shot spatial-carrier orthogonal fringe pattern with least squares method

In traditional phase measurement deflectometry (PMD), a number of sinusoidal fringe patterns are displayed on the screen in two orthogonal directions, which is time-consuming and not suitable for dynamic measurements. A phase-extraction algorithm based on the spatial-carrier phase-shifting technology for a single-shot spatial-carrier orthogonal fringe pattern is proposed. The phase increment of each pixel in two orthogonal directions is obtained by the least squares method and then the amount of spatial phase shift of all pixels relative to the probe pixel in the rectangular neighborhood centered on the probe pixel can be obtained. The number of fringe patterns required for the PMD is reduced to one by displaying a spatial-carrier orthogonal fringe pattern. Finally, the feasibility of the algorithm is verified by simulation and experiment.