Fringe Shift Research Articles

SPECIAL THEORY OF RELATIVITY IS ALSO FAILED TO EXPLAIN NULL RESULT OF MICHELSON AND MORLEY EXPERIMENT

Michelson and Morley conducted an experiment in the year 1887 to measure the speed of earth in luminiferous aether. In this experiment Michelson’s interferometer was used in which two waves are superimposed to generate interference fringes. Keeping in view known velocity of earth around the sun a fringe shift of 0.44 fringe was expected on the rotation of interferometer at an angle of 900, but surprisingly no fringe shift was observed. The experiment was conducted so many times and at so many places but always null results were obtained. The null result of MMX could not be explained by classical mechanics. A number of explanations for null results were submitted but no one was found to be correct. George Fitzerald and Hendrick Lorentz proposed length contraction hypothesis in the direction of motion of earth, but it was also rejected being an adhoc hypothesis. Albert Einstein submitted his famous theory “The special theory of relativity” in the year 1905. The second postulate of the STR states that speed of light is constant in all directions of inertial frames of reference irrespective of motion of source of light or the observer and states that no luminiferous aether exist as a medium, light waves do not require any medium to propagate. As light travels with constant velocity in both the arms of interferometer irrespective of motion of interferometer and there involves no time difference between the two rays hence null results of MMX were explained by special theory of relativity. Michelson and Morley experiment is based on the wave nature of light. In such experiments wavefront of light plays very important role but behaviour of wavefront of light was not taken into consideration while deriving the time taken by the light rays in the arms of interferometer due to motion of earth resulting into wrong derivation of time. The present article describes the principle and realization of role of wavefront of light in MMX. The time taken by light rays in the arms of the interferometer due to motion of earth depends upon the behaviour of wavefront of light. It has been established by results of Fizeau experiment and steller aberration of light that speed of light is not effected by velocity of moving medium. The derivation of time has been worked out keeping in view constancy of speed of light, wavefront of light and laws of reflection of light according to Huygen’s principle. Contrary to earlier beliefs the Lorentz length contraction hypothesis is not able to explain the null results of MMX. In the light of new facts it is established that there is no difference between theorectical results derived by classical mechanics and special theory of relativity. Special theory of relativity is also failed to explain the null result of MMX. The null result of Michelson and Morley experiment has again become a perplexing question for physicists.

Relativistic analysis of the Michelson-Gale experimental result.

The result of the Michelson-Gale experiment, which shows fringe shifts by the interference between two light beams traversing a rectangular loop in opposite directions, has been nonrelativistically analyzed based on the Galilean transformation. We relativistically analyze it via the transformation under the constant light speed (TCL) and via the framework of Mansouri and Sexl (MS). The TCL provides a coordinate transformation between the isotropic frame and a rotating frame, in which the two-way speed of light is a constant c irrespective of direction on the surface that has the same radius of rotation. When using TCL, we assume that the Solar System is isotropic so that the one-way speed of light is c in it. On the contrary, considering its movement, the analysis is carried out without the assumption of isotropy based on the MS framework. The analysis results via the TCL and via the MS framework correspond to each other and are in agreement with the result of the experiment. It is shown that the difference between the travel times of the counter-propagating light beams, which results in the fringe shift, takes place due to the two factors, the anisotropy of the one-way speed of light in inertial frames and the different rotation radii at different latitudes on the Earth surface.

Artery Pulse Waveform Acquired with a Fabry-Perot Interferometer.

For most patients admitted to a hospital, it is a requirement to continuously monitor their vital signs. Among these are the waveforms from ECG and the pulmonary arterial pulse. At present, there are several electronic devices that can measure the arterial pulse waveform. However, they can be affected by electromagnetic wave radiation, and the fabrication of electronic sensors is complicated and contributes to the e-waste, among other problems. In this paper, we propose an optical method to measure arterial pulse based on a Fabry-Perot interferometer composed of two mirrors. A pulse sensor formed by an acrylic cell with a thin membrane is used to gather the vasodilatation of the wrist, forming an air pulse that is enacted by means of a tube to a metallic cell containing a mirror that is glued to a thin silicone membrane. When the air pulse arrives, a displacement of the mirror takes place and produces a shift of the interference pattern fringes given by the Fabry-Perot. A detector samples the fringe intensity. With this method, an arterial pulse waveform is obtained. We characterize this optical device as a test of concept, and its application to measuring artery pulse is presented. The optical device is compared to other electronic devices.

A novel hybrid model based on integrating RGB and YCrCb color spaces for demodulating the phase map of fibres using a color phase-shifting profilometry technique

In this paper, a refined color phase- shifting profilometry technique is suggested for accurate examining of the phase and optical features of polymeric fibres. It is based on combining the RGB and the YCrCb color spaces. The primary components of the suggested model (RGCb) are red (R), green (G), and blue chrominance (Cb). This model is considered an early study in combining color spaces to demodulate the phase map of the tested fibre. The suggested model enhances affects that arise from color crosstalk and chromatic aberration, especially in the blue color channel. The Pluta polarizing interference microscope is utilised for capturing RGB interference fringe pattern for polypropylene (PP) fibre. The wrapped and unwrapped phase maps of this fibre are demodulated via the traditional, the corrected RGB color phase shifting algorithms and the suggested RGCb model. For evaluating the accuracy of the suggested model, the contour line method is used. The obtained results confirm that the demodulated phase using the suggested RGCb model has the least standard deviation from the reference phase value compared to the other two algorithms. The validation of the suggested model for investigating the optical properties of drawn fibres with a high order of fringe shift is checked. Based on the demodulated phase maps from the suggested model, the 2.5D birefringence profile of a PP fibre is examined.

Pockels Effect of Interfacial Water on a Mono-Electrode Induced by Current Parallel to the Electrode Surface

When an electric field is applied between two electrodes facing each other immersed in a liquid, the interfacial Pockels effect, a refractive index change proportional to the electric field, occurs in the electric double layer at the liquid–electrode interface. Here, we report that the Pockels effect of interfacial water can be observed even when an electric field is applied parallel to the surface of a “single” electrode in an electrolyte solution. This is a non-trivial result since the electric field parallel to the interface should not cause a broken spatial inversion symmetry, which is required for the Pockels effect. The Pockels signal was detected as a change in the transmitted light intensity due to the field-induced spectral shift of the interference fringes of the transparent conductive oxide electrode layer on a glass substrate. The magnitude of the signal increased as it approached the ends of the electrode, and the sign reversed across the center of the electrode. The electric field distribution calculated from the interfacial potential difference due to the in-plane parallel current showed that an electric field perpendicular to the interface was induced, whose distribution was consistent with the position dependence of the Pockels signal. A similar phenomenon was also observed for a single copper electrode, confirming that this is a universal effect.

A pointwise separation algorithm to separate plasma density and thickness in two-beam interferometry

The conventional two-beam interferometry adopts only one expression about plasma density and thickness because only fringe shift is recognized from the recorded fringes. Therefore, the prior hypotheses that the plasma is thickness-uniform or circular symmetry have to be introduced to separate them, which limits the applied range and accuracy of the conventional method. This paper found that the laser beam will be deflected if the thickness changes, leading the recorded fringes to be defocused. As a result, a new expression relying on recognizing the defocus parameter of the recorded fringes is derived, and a pointwise separation algorithm to separate density and thickness is proposed based on the two expressions. Compared to the conventional algorithms, the new algorithm requires no hypotheses and thus has a wider applied range.

Probing the electron motion in molecules using forward-scattering photoelectron holography.

Charge migration initiated by the coherent superposition of several electronic states is a basic process in intense laser-matter interactions. Observing this process on its intrinsic timescale is one of the central goals of attosecond science. Here, using forward-scattering photoelectron holography we theoretically demonstrate a scheme to probe the charge migration in molecules. In our scheme, by solving the time-dependent Schrödinger equation, the photoelectron momentum distributions (PEMDs) for strong-field tunneling ionization of the molecule are obtained. For a superposition state, it is shown that an intriguing shift of the holographic interference appears in the PEMDs, when the molecule is aligned perpendicularly to the linearly polarized laser field. With the quantum-orbit analysis, we demonstrate that this shift of the interference fringes is caused by the time evolution of the non-stationary superposition state. By analyzing the dependence of the shift on the final parallel momentum of the electrons, the relative phase and the expansion coefficient ratio of the two electronic states involved in the superposition state are determined accurately. Our study provides an efficient method for probing the charge migration in molecules. It will facilitate the application of the forward-scattering photoelectron holography to survey the electronic dynamics in more complex molecules.

Emission, propagation, and reflection of light as mechanical phenomena applied to the Majorana experiment

Emission, propagation, and reflection of light as mechanical phenomena applied to the Michelson‐Morley experiment offer a zero-fringe shift in Earth's inertial frame. Differently, in the Majorana experiment, the light from a fixed source reflected by moving and fixed mirrors enters the Michelson interferometer with unequal arms and offers a noticeable fringe shift. According to Majorana's interpretation, the fringe shift is proof of the constancy of light velocity. In contrast to Majorana's conclusion, the light reflected by a moving mirror has a different speed, wavelength, and frequency from the incident light, and the fringe shift observed in Majorana's experiment indicates that the velocity of light depends on its source velocity. Majorana's derivation predicts a <mml:math display="inline"> <mml:mrow> <mml:mn>0.71</mml:mn> </mml:mrow> </mml:math> fringe shift, and this study predicts a <mml:math display="inline"> <mml:mrow> <mml:mn>0.27</mml:mn> </mml:mrow> </mml:math> fringe shift.

Method for a deflection-type refractometer measuring the fringe shift by using linear Fresnelzone plates.

This study describes the design and performance of a deflection-type refractometer based on measuring the fringe shift from the Fresnel diffraction pattern to solve some major limitations of conventional differential refractometers, such as measurement range, resolution, zero balancing, and monitoring analysis. The refractometer apparatus comprises a coherent light source, linear Fresnel zone plate, measuring cell, and image capture device mounted on a movable platform. The distance measurement unit is configured to detect fringe deflection due to the difference in refractive index between the sample and the reference. To achieve this, distance measurements with an accuracy of a few nanometers by using the local frequency method and fringe shift measurement method are quite feasible. The uncertainty in this technique is determined by the smallest change in the longitudinal displacement of the image for which the CCD camera can detect a change in pixel position. The refractive index is obtained with a highly extended measurement range of at least ±0.4R I U and precision of the order of 2×10-4 R I U. A numerical comparison between computer simulation of the diffraction patterns that occur when the linear Fresnel zone plate is illuminated by a plane light traveling parallel to the z axis.

Cascaded anti-resonant reflecting waveguides for simultaneous measurement of temperature and curvature

An optical fiber sensor based on combined anti-resonant reflecting (ARR) mechanism is experimentally demonstrated for simultaneous measurement of temperature and curvature. The sensor head consists of a section of liquid infiltrated simplified hollow core photonic crystal fiber (PCF) spliced to a section of silica capillary. Two types of ARR mechanisms are involved in the sensor structure: the double-layer ARR guidance in the infiltrated PCF, and the single-layer ARR guidance in the silica capillary, which result in two sets of ARR fringes in the transmission spectrum. Due to the difference in the guiding mechanism and waveguide components, the two ARR fringes exhibit different responses to temperature and curvature. By measuring the wavelength shift of the double-layer ARR fringe and the intensity variation of the single-layer ARR fringe, temperature and curvature can be determined simultaneously.

Detection of vortex charge and beam displacement by wavefront division interferometry

In this work, a wavefront division interferometry method for determining the topological charge (l) of vortex beams (VB) is proposed and utilized for the detection of beam displacement. The method uses Fresnel biprism as a single element to determine vortex charge for up to l = ±10. Additionally, the interference pattern configuration is utilized to detect beam displacement in orthogonal directions. To accurately determine the shift in pattern due to beam displacement, a fringe scanning algorithm based on image correlation is proposed. The algorithm quantifies the fringe shift in terms of pixel units that is used to estimate the beam displacement. Sensitivity of 80 px/0.5 mm beam displacement along the x-direction is achieved with the system. The proposed method is single ended that can be integrated with optical assemblies for fast VB recognition. Furthermore, the displacement sensing utility could be used for precision alignment, propagation analysis, and monitoring physical fields.

Near-field diffraction of protons by a nanostructured metallic grating under external electric field: asymmetry and sidebands in Talbot self-imaging

Self-imaging in near-field diffraction is a practical application of coherent manipulation of matter waves in Talbot interferometry. In this work, near-field diffraction of protons by a nanostructured metallic grating under the influence of (a) uniform, (b) spatially modulated, and (c) temporally modulated electric fields are investigated. Time-domain simulations of two-dimensional Gaussian wave packets for protons are performed by solving the time-dependent Schrödinger’s equation using the generalized finite difference time domain method for quantum systems. Effects of strength (E 0) and orientation (θ) of the uniform electric field on the diffraction properties, such as fringe pattern, intensity of the peaks, fringe shift, and visibility, are investigated. The results show that the Talbot fringes shift significantly in the transverse direction even for a small change in the applied electric field ( V m−1) and its orientation (). Moreover, electric field-dependent fringe visibility is observed, which can be tuned by E 0 and θ. The potential barriers arising from a spatially modulated electric field are observed to cause significant distortions in the Talbot patterns when the modulation length () is equal to the de Broglie wavelength (). Sidebands are observed in the Talbot pattern due to the efficient transfer of energy from the oscillating field to the wave packet when the frequency of oscillation (ω) is of the order of ω 0 (), where T 0 is the interaction time. This study will be helpful in uniform electric field-controlled precision metrology, developing a highly sensitive electric field sensor based on Talbot interference, and precisely aligning the matter wave optical setup. Furthermore, the sidebands in the Talbot fringe can be used as a precise tool for momentum splitter in matter wave interferometry.

Ultrasensitive temperature sensor based on optic fiber Fabry–Pérot interferometer with Vernier effect

An ultrahigh sensitivity optic fiber temperature sensor with cascaded two Fabry–Pérot​ interferometers (FPIs) based on the Vernier effect has been fabricated and experimentally demonstrated. One polymer-cavity FPI is used as a sensing FPI and another fiber-cavity is used as a reference FPI to generate the Vernier effect. The experimental results show that the fabricated FPIs sensor has the high temperature sensitivity of −83.130 nm/°C and a high linear response (R-square: 0.9976), which is almost ∼39 times higher than that of an individual polymer-cavity FPI sensor (∼2.080 nm/°C). The stability experiment is also carried out, and the maximal variation of the wavelength shift of the interference fringes is 2.005 nm for a long-term testing. With its advantages of easy fabrication, low cost and small volume, the proposed sensor has significant benefits in terms of various practical applications that need high precision temperature measurement.

Two-beam interferometry with a definitive phase-shift sign

Subject of study. The shift direction of interference fringes depending on the sign of the local phase shift introduced to one of the interfering waves was investigated in terms of two-beam interferometry. Aim of study. This study aimed to validate the fact that two-beam interferometry based on a single interferogram enables definitive determination of the phase-shift sign using the shift direction of the interference fringe. Method. Positions of the interference fringes and their shifts were calculated considering the phase distribution of interfering waves in the observation plane. The Mach–Zehnder interferometer was used to experimentally confirm the obtained theoretical results. Two closely adjacent substrates were used as objects. A subwavelength layer of a standard material was deposited on a part of the surface of one substrate, and a layer of metamaterial was deposited on the part of the second substrate. Main results. Expressions determining the direction and amplitude of the shift of interference fringes depending on the sign and amplitude of the local phase shift in one of the two interfering waves with a plane or spherical front were obtained. Strict rules of interference fringe shift depending on the sign of the phase shift were formulated based on the calculations. Results of the experiment using the Mach–Zehnder interferometer with different combinations of beams with spherical and plane wavefronts confirmed the theoretical calculations. Practical significance. Classic interferometric methods require significant time and the application of complex experimental procedures to determine the sign of the phase shift. The application of the results obtained in this study enables the determination of the sign of the introduced local phase shift based on a single interferogram without additional time expenditures. Thus, the method investigating the metamaterial layers of a subwavelength thickness is significantly simplified.

Fiber Optic Temperature Sensor System Using Air-Filled Fabry-Pérot Cavity with Variable Pressure.

We report a high-resolution fiber optic temperature sensor system based on an air-filled Fabry-Pérot (FP) cavity, whose spectral fringes shift due to a precise pressure variation in the cavity. The absolute temperature can be deduced from the spectral shift and the pressure variation. For fabrication, a fused-silica tube is spliced with a single-mode fiber at one end and a side-hole fiber at the other to form the FP cavity. The pressure in the cavity can be changed by passing air through the side-hole fiber, causing the spectral shift. We analyzed the effect of sensor wavelength resolution and pressure fluctuation on the temperature measurement resolution. A computer-controlled pressure system and sensor interrogation system were developed with miniaturized instruments for the system operation. Experimental results show that the sensor had a high wavelength resolution (<0.2 pm) with minimal pressure fluctuation (~0.015 kPa), resulting in high-resolution (±0.32 ℃) temperature measurement. It shows good stability from the thermal cycle testing with the maximum testing temperature reaching 800 ℃.

Velocity of light through a moving medium applied to the Fizeau experiment

Light travels in a moving medium through densities that differ from the density of that medium at rest. This study derives a formula for the velocity of light through a moving medium for any direction of light propagation that, applied to the Fizeau experiment, gives a fringe shift of 0.23541. The Fresnel drag coefficient applied to the Fizeau experiment offers a fringe shift of 0.20466. The mean of 0.23016 for the fringe shift observations in the Fizeau experiment confirms both expectations.

Design and fabrication of Mach-Zehnder interferometers in soda-lime glass for temperature sensing applications.

High sensitivity represents one of the main goals that sensing devices need to satisfy for their applications. This work presents to the best of our knowledge the first integrated Mach-Zehnder interferometer (MZI) embedded in soda-lime glass with comparable sensitivity to silicon-on-insulator (SOI) devices. We manufactured the MZIs by the femtosecond direct laser writing (FDLW) technique and characterized them with temperature. Four buried MZIs were manufactured by slightly increasing the optical path due to separation between the arms of the interferometer (Δ s). We achieved a fringe shift of ∼8n m for an increase of 0.18µm. We have characterized one of these devices with temperature from 30°C to 70°C obtaining a sensitivity of ∼28p m/ ∘ C. We improved the sensitivity of the device to ∼54p m/ ∘ C due to the advantage of the unique three-dimensional (3D) capabilities that FDLW provides, overcoming the characteristically low thermo-optic coefficient of soda-lime glass just by rotating the MZI structure 11°.

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.

Long Period Grating Mach–Zehnder Interferometer Based Immunosensor with Temperature and Bulk Refractive Index Compensation

A long period grating Mach-Zehnder interferometer (LPGMZI) that consists of two identical long period gratings (LPGs) in a single fibre was developed to measure immunoglobulin M (IgM). The measured spectrum has fringes due to the interference between the core mode and cladding mode. This immunosensor inherits the advantages of an LPG and has the potential to compensate for unwanted signal changes due to bulk refractive index (RI) and temperature fluctuations by analysing interference fringes and their envelope. The external RI was measured from 1.3384 to 1.3670 in two different cases: (i) only the connecting section between the two LPGs is immersed or (ii) the whole LPGMZI is immersed. The fringes shift with an external RI in both scenarios, whereas the envelope stays still in case (i) or shifts at the same rate as the fringes in case (ii). The LPGMZI was also characterised at different temperatures between 25 °C and 30 °C by placing the whole LPGMZI in a water bath. The fringes and envelope shift at the same rate with temperature. The LPGMZI platform was then used to create an IgM immunosensor. The connecting section between the two LPGs was functionalised with anti-IgM and immersed into solutions with IgM concentrations from 20 μg/mL to 320 μg/mL. The fringes shift with IgM concentration and the envelope remains static. The results from this work show that LPGMZI has the potential to compensate for the temperature and bulk RI fluctuations and perform as a portable biosensor platform.

Refractive index sensitivity enhancement of SF-MZI through metal film deposition

A simple and unique methodology predicting the influence of metal film coating, on non-adiabatic tapered fibers constituting single-fiber Mach-Zehnder interferometer (SF-MZI) configuration, on output fringe pattern of the interferometer, without inducing surface plasma resonance, has been proposed. The suggested approach reveals increase in losses and degree of fringe shift in the output wavelength spectrum of the SF-MZI depending on the properties and thickness of the metal deposited on fiber tapers. In order to substantiate the theoretical findings, layers of aluminium (Al) metal of different thicknesses are deposited on tapered regions of the SF-MZI and refractive index sensing experiments for identifying the presence and concentration of Fluoride ions and Sucrose in water are conducted. The impression of metal coating envisaged by the proposed methodology in terms of sensitivity enhancement (from 291.43 nm/RIU to 368.57 nm/RIU for Fluoride ion and 33.85 nm/RIU to 77.89 nm/RIU, for Sucrose solution), exponential decay of extinction ratio (with attenuation parameter of 0.05 nm−1 and 0.037 nm−1 for Fluoride ion and Sucrose sensing, respectively), fluctuations in free spectral range (FSR) (from 0.6 to 1.3 nm) at the output port of the interferometer have been quantified and validated by the experimental findings.