Path Interferometer Research Articles

Simultaneous path weak-measurements in neutron interferometry

The statistical properties of the detection events constituting the interference fringes at the output of an interferometer are well-known. Nevertheless, there is still no unified view of what is happening to a quantum system inside an interferometer. Strong measurements of path operators destroy the interference effect. In weak measurements, an observable is weakly coupled to a pointer system and the resulting weak values quantify the observable by minimally disturbing the system. Previous which-way experiments with weak measurements could extract either the real or imaginary part of a single weak value with each ensemble. Here, we present the simultaneous full complex quantification of two path weak values with a single ensemble in a Mach–Zehnder neutron interferometer. Magnetic fields, oscillating with different frequencies, change the energy state in each interferometer path. The time-dependent phase between the energy states distinctly marks each path. The resulting beating intensity modulation at the interferometer output gives both path weak values. For the present experiment, the weak values’ absolute value and phase directly describe the observed amplitude and phase of the intensity modulation.

One-shot self-calibrating phase-shifting interferometry by direct normalization of interferograms

Dynamic phase measurement is a valuable technique applied across various scientific and technological domains due to its high accuracy, non-contacting method, and numerous practical applications. In this manuscript, we present a phase retrieval method capable of measuring the object’s phase in real-time. Our proposal is based on a double aperture common-path interferometer adapted for polarization modulation in the input windows, enabling the superposition of two fields with orthogonal circular polarizations. Two interferograms and two intensities are captured in a single shot, showcasing the possibility of obtaining two normalized interferograms directly and straightforwardly. This allows for the derivation of expressions for phase recovery and, additionally, the determination of the arbitrary phase step. We demonstrate that this method is easy to implement, highly accurate, and sufficiently fast for real-time applications. To validate the effectiveness of the method, we conduct numerical error analysis and laboratory experiments.

Measurement of space charge density distributions and dielectric resonance enhancement of beam deflection properties of KTN crystal

In recent years, potassium tantalum niobate (KTN) electro-optical deflection devices have gained considerable attention because of their notable advantages, such as large deflection angles, low operational voltage requirements, and compact dimensions. This study uses the phase-shifted interferometric optical path to characterize the influence of direct current (DC) voltage on charge density. An interferogram is acquired using the four-step phase-shifting technique, enabling the calculation of phase delays and deducing the variation in charge density. Experimental results demonstrate that the charge density near the cathode increases with an increase in DC voltage. Subsequently, we utilize the frequency dependence of the dielectric constant of the KTN crystal on the electric field. The dielectric constant can be enhanced when the characteristic frequency of the motion of the polar nanoscale region matches the frequency of the electric field. This field-induced enhancement effect improves the beam deflection performance of the KTN crystal. Application requirements in the field of high-speed random scanning can be realized through the mechanism of the KTN crystal co-acting with DC and alternating current electric fields.

Wide-Angle Repeat Pass Bistatic SAR Interferometry: A Geometrical Introduction

Positioning a Synthetic Aperture Radar (SAR) receiver at a significant distance from an illuminator in a Low Earth Orbit (LEO) enables wide-angle repeat-pass bistatic interferometry. It’s crucial to define the positioning limits of the receiver with respect to the illuminator to ensure reasonable coherences, altitudes of ambiguity, and a suitable common wavenumber support. I extended the standard monostatic formula, which yields the change in the interferometric travel path due to the vertical baseline. In the wide-angle bistatic case, the range-azimuth coordinate system is no longer orthogonal and we must consider the full 2D vector nature of the LOS orthogonal components. The two vertical baselines and the horizontal baseline of the receiver are needed to parameterize the system. Their impact on the interferometric coherence is quantified and bistatic limits are seen to be more flexible than those in the monostatic case due to the combination of independent baselines. I estimated the coherence, and then extended the analysis to the wavenumber domain, to quantify the common spectral support due to the wavenumber shifts due to the three baselines. The analysis carried out geometrically allows for combining together the effects of the transmitter’s and receiver’s vertical baselines and thus representing the residual spectral fraction with two instead of three parameters. Finally, I examined the achievable spatial resolution of the position of the interferer obtainable from the delay of the arrival of the interference between the illuminator (supposed to be silent) and the receiver.

Generation of interferometrically stable pulse pairs from a free-electron laser using a birefringent interferometer

We present a compact, intrinsically stable common path interferometer for the seeding of free-electron lasers (FELs). The interferometer can handle the required ultraviolet seed wavelengths and features an excellent phase stability of 10 mrad at 265 nm. By seeding the FEL FERMI, we demonstrate the generation of extreme ultraviolet (XUV) pulse pairs with tunable delay and a delay stability of 6 as at 52.5 nm. Prospective applications are Fourier transform spectroscopy, nonlinear spectroscopy and coherent control experiments in the XUV and x-ray domain.

ANALYSIS OF NULL RESULTS OF HAMMAR EXPERIMENT BY CLASSICAL MECHANICS WITHOUT SPECIAL THEORY OF RELATIVITY

In optics interferometers are used for precision measurements. In interferometry two waves of light are superimposed to generate interference fringes. The interference pattern is observed and analyzed to measure physical process. Gustaf Wilhelm Hammar conducted an experiment in the year 1935 to test aether drag hypothesis. The null results of this experiment were interpreted in consistent with special theory of relativity. Hammar used common path interferometer and observed the changes in interference fringes due to motion of earth. The present work describes that when there is no aether and no medium drags the light in its direction of motion than what will be the behaviour of light.The analysis has been made according to classical mechanics keeping in view Huygen’s principle by tracking the pathways of both the rays of light.It is established that speed of light is independent of velocity of any object,apparatus or any observer and there is no effect of motion of earth.The null results of Hoek’s experiment and Hammar experiment are in consistent with classical mechanics.

Polarizing white light interferometry for phase measurements using two simultaneous interferograms.

Our research introduces a design for a polarization phase-shifting white light interferometric system (PPS-WLIS) that operates in a transmissive mode for measuring the slope phase of transparent objects. It comprises a cyclic path interferometer (lateral shear interferometer) coupled with a multiplexing Michelson interferometer. The system uses polarization to produce two parallel interferograms with polarization modulated with relative shifts simultaneously. To determine the optical phase, we used a two-step algorithm for phase demodulation that does not necessitate precise phase shifts, making the system more straightforward to operate. As a result, we could observe variations in the object associated with optical phase changes. Furthermore, our method simplifies the phase-shift interferometry process by requiring only one capture, making it an effective way to examine objects at dynamic events. As an illustration, we demonstrated the temperature measurement generated by a section of a candle flame.

Measuring the transmitted wavefront of large-aperture flat optics

This paper proposes a scanning distance measuring interferometer (SDMI) method to measure the transmitted wavefront of large-aperture flat optics accurately. The biaxial positioning mechanism moves the test component through the interferometric path of a differential distance-measuring interferometer; both the optical path difference and distribution are obtained; thus, the wavefront can be reconstructed. A Ø360 mm flat optical substrate is measured, and the result is compared with a phase measuring interferometer (PMI). The SDMI result is 68 nm in PV and 13 nm in RMS. The PMI result is 90.8 nm in PV and 16.4 nm in RMS. The forms of the two results show a good correlation, which gives confidence in the viability of the SDMI method for large-aperture optical transmitted wavefront measurements out of range of the commercial PMI.

Robust Ramsey interferometer based on a single Rydberg polariton

We demonstrate a robust single-photon Ramsey interferometer based on a single Rydberg excitation, where the photon is stored as a Rydberg polariton in an ensemble of atoms. This coherent conversion of the photon to Rydberg polariton enables to split an incoming photon into a superposition state of two Rydberg states by applying microwave fields, which constructs two paths of interferometer. Ramsey interference fringes are demonstrated when we scan either the detuning of the microwave or the free evolution time, from which we can obtain the resonant transition frequency of two Rydberg states. We use the Ramsey-like sequence to demonstrate coherent manipulation of the stored single-photon to construct different interference patterns. In addition, the robustness of the Ramsey interferometer to the fluctuation of incoming photon numbers and optical depth (OD) of the atomic ensemble is tested, showing that the coherent of Ramsey interferometer is preserved for input photon number in a range of R in < 15 and for OD varying from 1.0 to 4.0. The robust interferometer will find its applications in quantum precision measurement.

Retrace error calibration for interferometric measurements using an unknown optical system.

In classical interferometric null test measurements, the measurement and reference beam path should be the same. A difference in the beam paths results in the so called retrace error. One very common approach to avoid retrace errors is to adapt the measurement wavefront to the reference wavefront with a computer generated hologram (CGH), which is costly and time consuming. A much more flexible approach is to do non nulltest measurement in combination with mathematical treatment of retrace errors. Most of such methods are based on iterative optimization or calibration of the nominal optical design of the interferometer. While this may be a convenient solution in the context of research, the more common use may be limited due to the need of the optical design of all interferometer components. In many cases, the optical designs of standard off the shelf optical assemblies are not available or disclosed by the manufacturer. This is especially true for transmission spheres of interferometers. We introduce the so called Black Box Model (BBM), used in the well known Tilted Wave Interferometry (TWI), as a mathematical model to account for retrace errors in interferometry. The Black Box Model is based on point characteristic functions which are adapted to the result and behavior of a real interferometer by calibration. With an extended calibration method, the need of a specific optical design of the interferometer is no longer necessary. Thus the method is attractive for a wide field of use in interferometry with standard off the shelf components.

Ultra-high sensitivity microwave-photonic sapphire fiber Fabry-Perot interferometry based on the Vernier effect.

The wavelength of microwave is longer than that of lightwave, causing the interferometric optical path difference induced by the measurand changes to be relatively smaller than that of microwave, which results in the lower sensitivity of sapphire fiber Fabry-Perot interferometer (FPI) sensor in microwave band. To improve sensitivity, a parallel FPI sensing system is constructed, in which a section of sapphire fiber connected to a single-mode transmission fiber is used as a sensing FPI, and a single-mode fiber (SMF) with a slightly different optical path from a sensing FPI is utilized as a reference FPI. By connecting two FPIs in parallel, Vernier effect is formed to improve sensitivity. The influence of relationship between the optical path difference of the reference FPI and the sensing FPI on the sensitivity amplification factor is analyzed based on the microwave interference spectrum of the parallel FPI. A section of sapphire fiber with the length of 8 cm is used as temperature sensor to construct high-temperature sensing system. The results demonstrate that the temperature sensitivity reaches about 2338.68kHz/°C, which is approximately 130 times higher than that of the sensing FPI alone. Furthermore, when the difference of optical path between the sensing FPI and the reference FPI is kept constant while the sensing FPI is unchanged, the amplification factor of the temperature sensitivity is approximately 2.64 times higher with longer length of the reference FPI compared to the situation with shorter length of the reference FPI.

Linear broadband interference suppression circuit based on GaN monolithic microwave integrated circuits

AbstractThis paper presents simulation and measurement results of a 2–4 GHz octave bandwidth interference suppression circuit. The circuit accomplishes the function of a tunable frequency notch through an interferometer architecture. The relative delay in the interferometer paths is varied with GaN monolithic microwave integrated circuit tunable delay lines. The delay is adjusted by varying the drain voltage of cold‐FET connected high electron mobility transistors acting as varactors. Two types of periodically‐loaded delay lines are compared: a uniform and a tapered design. A simple theoretical study, relating the delays and amplitudes in the interferometer circuit branches, is developed to inform the design. Two interference suppression hybrid circuits are implemented, and measurements demonstrate a 25–40 dB notch across the 2.24–4 GHz range for the uniform delay line, and 2.32–4.13 GHz for the tapered design. The return loss for both designs remains below 10 dB. Measurements with two tones spaced 0.5 and 1 GHz for varying tone power are performed to quantify suppression. The circuit can handle an input power of 37 dBm and maintains performance with two simultaneous 25 dBm tones spaced 0.5 GHz apart. Linearity is characterised with 10 MHz two‐tone measurements, and the circuit demonstrates a 3rd‐order intercept input power larger than 30 dBm for control biases above −12 V.

Detection of Atmospheric Wind Speed by Lidar Based on Quadrichannel Mach–Zehnder Interferometer

For a long time, wind speed profile measurement has been the primary task of weather forecasting. Therefore, the detection of atmospheric wind speed is extremely important for studying the changes in atmospheric motion. In order to solve the problems of insufficient data collection, low resolution, and low accuracy in atmospheric wind field detection, this paper introduces the relevant theories of wind speed detection, completes the optical design of the system according to the research objectives, and determines the selection of optical devices. At the same time, a Doppler wind lidar system based on a quadrichannel Mach–Zehnder interferometer is designed and built to carry out ground-based observation experiments, collect echo signal data, and inverse the atmospheric radial wind speed. Furthermore, the wind measurement error is analyzed. Firstly, the paper introduces the basic principle of the wind measurement system, i.e., using the Doppler effect of light, and then analyzes the frequency discrimination device of the system in detail, and obtains the theoretical calculation method of atmospheric wind speed inversion. At the same time, the relevant datasets of wind measurement system are analyzed, including backscattering ratio, aerosol, and molecular extinction coefficient, and the emission mechanism of the large pulse laser is also studied in detail, which provides a theoretical basis for the model construction of Doppler lidar and the research on the enhancement of pulsed laser emission energy. Secondly, according to the research index of wind measurement, a Doppler wind measurement lidar system based on a quadrichannel Mach–Zehnder interferometer is designed, including the design of ab external light path transceiver system, internal light path interferometer, software and hardware, and algorithm. The calibration of the quadrichannel Mach–Zehnder interferometer is completed, with its maximum interference contrast reaching 0.869. Through the self-developed optical transceiver system and data acquisition system, the echo signal of lidar is received and detected. Lastly, the data of echo signals collected by the interferometer are analyzed, the radial atmospheric wind speed profile is inversed, and the signal-to-noise ratio and wind speed measurement error of the system are evaluated. The experimental results show that the maximum signal-to-noise ratio (SNR) of the system can reach 1433 when the emission pulse energy of the large pulse laser is adjusted to 255 mJ, and the farthest wind speed detection distance is about 8 km. The high-precision wind speed detection range can reach 2 km, the actual wind measurement errors in this range are all within 1.593 m/s, and the minimum error is only 0.418 m/s. In addition, the backscattering coefficient and extinction coefficient of atmospheric molecules and aerosols in the range of 8 km and the atmospheric temperature in the range of 10 km are also measured. The measurement accuracy of the aerosol extinction coefficient is ±0.001 m−1, and the measurement error of atmospheric temperature within 10 km is within 2 K, achieving the expected goals.

Design and implementation of an electromechanical gear system for optimization of automatic phase-shifting of a Dual Aperture Common-Path Interferometer

In this work, we report experimental results of a proposed gear system for optimization of phase shifts used for extraction of phase between a reference and a test object in a Double Aperture Common Path Interferometer. The electromechanical approach is designed to increase the precision and control of automated transverse translation of a diffraction grating to obtain equidistant displacements, typically carried out manually. Calculations and analytics for the design and operation of the mechanical gear system are presented. The experimental results demonstrate significant error minimizing for equally spaced phase shifts compared to a previously reported implementation of our research group. The proposed system represents a reliable and low-cost implementation to improve the obtaining of suitable interferogram captures for equally spaced phase-shifting interferometry techniques.

Diferential method for the formation of relative phase shifts between light beams in two-arm interferometer

The possibility of improving technical means that make it possible to introduce phase shifts into light beams in the interferometer paths is considered. An optical-mechanical phase modulator in the form of a plane-parallel glass plate rotated around an axis lying in its plane was adopted as the initial version of these technical means. A differential method is proposed for the formation of relative phase shifts between beams in a two-arm interferometer. A variant of the modulator has been developed in the form of a pair of rigidly interconnected plates, the planes of which are initially rotated at a given angle. In this case, each of the parallel light beams in the interferometer passes through its own plate. It is shown that in this case a practically linear relationship is provided between the generated relative phase shift and the total angle of rotation of the plates. A variant of using a single plate as a modulator under the established conditions for the incidence of two beams propagating in different arms of the interferometer is considered. The operability of the proposed differential method for controlling the phase shift between light beams is confi rmed by the data of a test experiment. The results obtained will be useful in the development of special tools based on the method of digital speckle pattern interferometry for measurements of the displacement fields of deformable bodies

Mach–Zehnder Modulator Output in Time and Frequency Domain—Calculation and Experimental Confirmation

The Mach–Zehnder intensity Modulator (MZM), named after Ludwig Mach and Ludwig Zehnder, is based on the corresponding interferometer. It splits light into two counter-rotating partial beams, which are later recombined with a controlled phase difference. The output of the MZM depends on the phase difference of the interferometer paths. This phase difference is usually adjusted by an electrical voltage applied to a Phase Shifter (PS) placed in one of the interferometer arms. For MZM applications in which the wavelength is changing, the applied voltage must be adjusted accordingly. We derived the equations describing the MZM output in the frequency domain for the case of a triangular PS voltage (necessary for a sinusoidal output) and compared the analytical results with measurements. Our setup uses an Optical Parametric Oscillator (OPO) with a tunable wavelength from 3.2–3.5 μm as the light source and a Lithium Tantalate (LT)-PS for the MZM’s phase modulation. The novel insights enable new control methods for MZMs particularly suited for spectroscopic applications where the wavelength is scanned or otherwise altered.

Classical Doppler shift explains the Michelson‐Morley null result

Here we review Michelson‐Morley's original analysis of their interferometer experiment and discuss its use of optical distance. We derive a formula for transverse Doppler shift from geometric considerations, apply this to the Michelson‐Morley interferometer, and present a phase analysis for the experiment. Furthermore, we present an equation for Doppler shift at a general angle and use this to derive the null phase shift result for round-trip interferometer paths at any arbitrary angle. We do not dispute the validity of the null result, nor the prediction of an arrival-time difference for the transverse and longitudinal arms of the interferometer; rather, we challenge the implicit assumption that an arrival time difference will necessarily result in an observable fringe shift.

Phase-stabilized UV light at 267 nm through twofold second harmonic generation.

Providing phase stable laser light is important to extend the interrogation time of optical clocks towards many seconds and thus achieve small statistical uncertainties. We report a laser system providing more than 50 µW phase-stabilized UV light at 267.4 nm for an aluminium ion optical clock. The light is generated by frequency-quadrupling a fibre laser at 1069.6 nm in two cascaded non-linear crystals, both in single-pass configuration. In the first stage, a 10 mm long PPLN waveguide crystal converts 1 W fundamental light to more than 0.2 W at 534.8 nm. In the following 50 mm long DKDP crystal, more than 50 µW of light at 267.4 nm are generated. An upper limit for the passive short-term phase stability has been measured by a beat-node measurement with an existing phase-stabilized quadrupling system employing the same source laser. The resulting fractional frequency instability of less than 5×10-17 after 1 s supports lifetime-limited probing of the 27Al+ clock transition, given a sufficiently stable laser source. A further improved stability of the fourth harmonic light is expected through interferometric path length stabilisation of the pump light by back-reflecting it through the entire setup and correcting for frequency deviations. The in-loop error signal indicates an electronically limited instability of 1 × 10-18 at 1 s.

Pixel level control of amplitude, phase, and polarization of an arbitrary vector beam

The generation of vector beams with complex spatial distributions is significant in the field of optical manipulation, optical metrology, optical microscopy, and so on. In this work, we propose a method to generate arbitrary vector beams, which is based on the complex amplitude beam shaping technology and the interferometric optical path configuration. With the method, we can achieve pixel-level control of amplitude, phase, and polarization of an arbitrary vector beam. Furthermore, different polarization states and orientations can be designed to coexist in one beam. The method has been verified with theoretical analysis and experimental results. The proposed method expands the application range of vector beams and provides a conducive way to explore the optical properties of the vector beams.

Label free optical transmission tomography for biosystems: intracellular structures and dynamics.

There is an increasing need for label free methods that could reveal intracellular structures and dynamics. In this context, we develop a new optical tomography method working in transmission - full-field optical transmission tomography (FF-OTT). The method can measure the forward scattering signals and reveals the time-dependent metabolic signals in living cells. FF-OTT is a common path interferometer taking advantage of the Gouy phase shift - a π phase shift that the light wave experiences around the focus. By modulating the position of the focus one can alter the phase of the scattered light. Demodulation of images with different phases rejects the background and enhances the light from the depth-of-field, thus producing an optical section. We test FF-OTT by imaging single-cell diatoms and ex vivo biological samples. In fresh samples, we show that the intracellular motions create visible intensity fluctuations in FF-OTT so that the method is able to reveal a metabolic dynamic contrast. FF-OTT was found to be an efficient label free technique that can be readily implemented thanks to a robust common-path speckle-free interferometer design using an incoherent light source.