Speed Of Light In Air Research Articles

Speed of light measurement with a picosecond diode laser and a voltage-controlled oscillator

This work describes an experimental method for measuring the speed of light in air. It uses optical feedback from a visible picosecond diode laser operated below the threshold and a voltage-controlled oscillator to determine the time required for a pulse to travel a known distance. The experimental setup is compact, fitting into a space of 1 × 0.5 m2, and at the same time, can determine the speed of light with an uncertainty of 0.03%. The method does not require fast detectors or oscilloscopes.

Measurement of airborne ultrasound using laser Doppler vibrometry

The speed of light in air is dependent on the air's instantaneous density. Since air density is modulated by sound, sound in the air can be observed and measured using optical methods. One such optical method is Laser Doppler Vibrometry (LDV). Most commonly, LDVs measure the mechanical velocity of a surface. However, by placing a rigid reflector beneath a sound beam in air, it is possible to measure the time rate-of-change of optical refractive index and thus to measure dynamic changes in air density, or sound. In prior demonstrations, this method has been used to visualize sound fields in the audible frequency range and ultrasonic range underwater. Here, we present the first measurements of high-intensity airborne ultrasound beams in the frequency range spanning 100 kHz–300 kHz. We observe accumulated distortion, wave steepening, and weak shock formation as high intensity sound beams propagate. LDV measurements are compared against numerical simulations of the sound field. Advantages of the LDV technique are discussed, and we also attempt to quantify limitations of the technique which include spatial averaging of the measurand along and normal to the optical beam path.

Development of a permanent vacuum hollow prism air refractometer for use in dimensional metrology

Refractive index measurements are required when light is used as the basis of a measurement system. In dimensional metrology, refractive index measurements are used to compensate for the change in the speed of light. This is crucial because the SI unit for the metre is defined as the speed of light in a vacuum. Air refractometers are the most accurate way to measure the speed of light in air. Many research works to date have been performed to measure the refractive index of air using refractometers. This research uses a commercial prism as the vacuum etalon instead of the tube that is used most often. This novelty and newness of our research were to focus on the design, fabrication and testing of a refractometer which uses a permanent vacuum for ease of use but that will still have the same accuracy of other refractometers currently in use. Modifications to existing designs improved the long-term stability compared to other prism refractometers and are also potentially more accurate than tube refractometers. The results achieved with this permanent vacuum refractometer are accurate to 8.4 × 10–8, which compares favourably with other refractometers on accuracy. It also has the added advantage that it does not require a vacuum pump, and with added laser path improved long term stability but still portable and robust enough to use in everyday applications.

Eliminating above-surface diffractions from ground-penetrating radar data using iterative Stolt migration

Above-surface diffractions (ASDs) received by unshielded ground-penetrating radar (GPR) antennas are known to contaminate subsurface reflections and diffractions. Existing ASD-removal methods either leave relatively strong residual ASDs within subsurface reflections or attenuate them excessively. We have developed an iterative migration-based ASD-removal method to address this issue that separates ASDs from subsurface reflections via surgical mute. First, we isolate ASDs within the GPR profile using an optimal window function, generated using the focal center of ASDs within the migrated domain. The remainder signifies the zeroth-order separation of subsurface reflections. Second, we perform Stolt migration on the isolated ASDs using the speed of light in air. Then, we mute out the regions dominated by ASDs from the migration results, characterized by highly focused ASDs that are well separated from the majority of subsurface reflections. Following that, we demigrate the separated ASDs and subsurface reflections back to the unmigrated domain using the speed of light in air. Next, we combine the demigrated subsurface reflections with the zeroth-order subsurface reflections, thereby completing the first iteration of the separation process. The entire aforementioned process is then repeated twice on the residual data to obtain further residual subsurface reflections from ASDs, using a lower velocity and a higher velocity in sequence. Our method is verified to suppress ASDs more effectively than existing approaches by retaining a greater proportion of subsurface reflections, and its residual error is negligible. It is robust with respect to energy levels, window widths of ASDs, and clustered ASDs.

First Observation of an X-Ray Beam Following a New Geodesic When Gravitational Waves Deform Space-Time

By using X-rays of a linear accelerator (LINAC Siemens X rays, 6 MeV) for medical use, we were able to measure gravitational waves, GW, (amplitude = 56:385mm, frequency =1 = 3Hz, velocity = c and polarization) and its threedimensional effect on X-ray trajectories. The collimated X-ray beam, which is in the plane (X; Y); travels on the Z axis at the speed of light in air and passing through the machine isocenter, until it reaches the target and, ultimate, is recorded in a radiographic film. Apparently, there is an exceptional coincidence in the operation of LINAC and the presence of GW. This coincidence occurred in VIRGINIA, GPS (38.634 351 1, -77.282 523 9), UTC (12/06/2011: 12: 56: 01). This important event, but not sui generis, was recorded in the LINAC computer system, on a film for radiography, in the log file of the cancer treatment center and it was reported to SIEMENS in order to try to find an explanation of a possible hardware failure, some abnormality or any software issue. The physicist and Siemens service engineer on site concluded that such event should never happened because LINAC was not malfunctioning. Consequently, for the X-rays, there was a deviation of the isocenter of the LINAC (△X = (11:5 ± 0:5)mm, △Y = (48 ± 0:5)mm), by the action of the amplitude of GW. The tolerance of a LINAC is lower than these measurements, and the equipment will stop working if they are greater than ±1:0mm for isocenter (zero position) and ±2:0mm for other collimator leaf positions. Therefore, this constitutes a register of space-time alteration with a consequent variation of the path of the X-ray beam. Finally, the registered gravitational waves leave invariant the angle between the axes (X; Y), of the X-ray beam, indicating a constant polarization.

Single-shot ultrafast imaging via spatiotemporal division of femtosecond laser pulses

We have developed a single-shot imaging technique that can capture ultrafast events occurring on femtosecond to picosecond time scales. The technique is based on an optical pump-probe method, in which multiple time-delayed femtosecond pulses simultaneously probe a pump-excited sample. Here we use two sets of 2-by-2 mirror arrays for spatial/temporal division and routing of multiple probe pulses. This single-shot scheme is successfully applied to capture femtosecond ionization fronts propagating at the speed of light in air, as well as laser-induced ablation of solid targets.

Longitudinal-differential interferometry: direct imaging of axial superluminal phase propagation

We introduce and demonstrate a new interferometric method called longitudinal-differential (LD) interferometry, which measures the spatially resolved phase difference of the scattered field by an object relative to the illumination. This method is combined with a high-resolution interference microscope that allows recording three-dimensional field distributions in amplitude and phase. The method is applied to study the axial phase behavior of Arago spots, an effect observable in low-Fresnel-number systems behind objects with a size comparable to the wavelength. We directly observe the initial phase delay in the Arago spot and prove that the local phase velocity exceeds the speed of light in air. Such LD phase studies are applicable not only to the Arago spot but also to other kinds of light interactions with wavelength-scale objects, e.g., photonic nanojets.

Measurements of the speed of light in water using Foucault’s technique

We describe how to modify an existing speed-of-light apparatus to measure the speed of light in water. We derive the necessary formulas to account for refraction and light’s passage through both water and air. We obtain (3.00±0.09)×108 m/s for the speed of light in air and (2.1±0.1)×108 m/s for the speed of the light in water. Both results are within 7% of established values.

Measuring the speed of light using beating longitudinal modes in an open-cavity HeNe laser

We describe an undergraduate laboratory that combines an accurate measurement of the speed of light, a fundamental investigation of a basic laser system, and a nontrivial use of statistical analysis. Students grapple with the existence of longitudinal modes in a laser cavity as they change the cavity length of an adjustable-cavity HeNe laser and tune the cavity to produce lasing in the TEM00 mode. For appropriate laser cavity lengths, the laser gain curve of a HeNe laser allows the simultaneous operation of multiple longitudinal modes. The difference frequency between the modes is measured using a self-heterodyne detection with a diode photodetector and a radio frequency spectrum analyzer. Asymmetric effects due to frequency pushing and frequency pulling, as well as transverse modes, are minimized by simultaneously monitoring and adjusting the mode structure as viewed with a Fabry–Pérot interferometer. The frequency spacing of longitudinal modes is proportional to the inverse of the cavity length with a proportionality constant equal to half the speed of light. By changing the length of the cavity, without changing the path length within the HeNe gas, the speed of light in air can be measured to be (2.9972±0.0002)×108 m/s, which is to high enough precision to distinguish between the speed of light in air and in vacuum.

Absence of Cherenkov properties of coherent radio emission from atmospheric showers at frequencies below 100 MHz

In many modern papers devoted to the calculation of radio emissions from extensive atmospheric showers (EASs) in the 10–100 MHz range, the radiation from EASs of charged particles moving with a velocity higher than the speed of light in air is identified as Vavilov—Cherenkov radiation (VCR). In this paper it is shown that radio emissions from EASs at frequencies less than 100 MHz do not possess the properties of VCR recorded from EASs in the optical range.

Electromagnetic models of the lightning return stroke

Lightning return‐stroke models are needed for specifying the source in studying the production of transient optical emission (elves) in the lower ionosphere, the energetic radiation from lightning, and characterization of the Earth's electromagnetic environment, as well as studying lightning interaction with various objects and systems. Reviewed here are models based on Maxwell's equations and referred to as electromagnetic models. These models are relatively new and most rigorous of all models suitable for computing lightning electromagnetic fields. Maxwell's equations are numerically solved to yield the distribution of current along the lightning channel. Different numerical techniques, including the method of moments (MoM) and the finite difference time domain (FDTD) method, are employed. In order to achieve a desirable current‐wave propagation speed (lower than the speed of light in air), the channel‐representing wire is embedded in a dielectric (other than air) or loaded by additional distributed series inductance. Capacitive loading has been also suggested. The artificial dielectric medium is used only for finding the distribution of current along the lightning channel, after which the channel is allowed to radiate in air. Resistive loading is used to control current attenuation with height. In contrast with distributed circuit and so‐called engineering models, electromagnetic return‐stroke models allow a self‐consistent full‐wave solution for both lightning‐current distribution and resultant electromagnetic fields. In this review, we discuss advantages and disadvantages of four return‐stroke channel representations: a perfectly conducting/resistive wire in air, a wire embedded in a dielectric (other than air), a wire in air loaded by additional distributed series inductance, and a wire in air having additional distributed shunt capacitance. Further, we describe and compare different methods of excitation used in electromagnetic return‐stroke models: closing a charged vertical wire at its bottom with a specified grounded circuit, a delta‐gap electric field source, and a lumped current source. Finally, we review and compare representative numerical techniques used in electromagnetic modeling of the lightning return stroke: MoMs in the time and frequency domains and the FDTD method. We additionally consider the so‐called hybrid model of the lightning return stroke that employs a combination of electromagnetic and circuit theories and compare this model to electromagnetic models.

The Speed of Light: Making an Easy Time of It

Time-of-flight measurements of the speed of light in air are conceptually easy. The outgoing modulated light from a HeNe laser and the returned light from a distant reflector may be sampled using two photodetectors. The two signals can be displayed on a reasonably fast dual-trace oscilloscope to determine the transit time. In practice, however, obtaining a satisfactory return beam from the distant mirror can be difficult. I have found that, with a few hours of setup time, a common garden reflector may be used as the distant “mirror,” along with a large plastic Fresnel lens to collect the somewhat dispersed returned light, to determine the speed of light in air to within 10%.

Meteorological influences on Loran- C ground wave propagation

Phase variations of approximately 36° (one microsecond) have been observed and recorded on a 1000 km Loran- C overland propagation path. This path extends from Carolina Beach, N.C., to Dana, Indiana, the Master and Z-slave, respectively, of the U.S. East Coast Loran- C chain. These phase variations are large compared with the receiver resolution of 0.1 μs or better. A special test to study this propagation path was conducted by the U.S. Coast Guard in the winter and spring of 1970. Analysis of data taken between 11 and 22 February from five monitoring stations is presented. Four stations measured Loran phase variations, and three stations recorded weather parameters. A significant correlation was obtained between the secondary phase delay and the dry term of the refractive index. Since the phase variations are at least an order of magnitude greater than can be explained by the wave propagation time at the speed of light in air, the correlation obtained is explained in terms of the α factor. The α factor is related to the lapse rate of the refractive index (with altitude), and these low frequency measurements appear to be a sensitive means for detecting changes in the lapse rate. As a consequence of this analysis, we can predict that a phase change will occur before the passage of a warm front and after the passage of a cold front at the surface of the ground.

A Determination of the Speed of Light by the Phase-Shift Method

A low-frequency, phase-shift method for the measurement of the speed of light has been developed. This technique gives results commensurate with other advanced laboratory methods. One advantage of this technique is that the apparatus is of reasonable size and most of the circuitry involves widely known amateur radio techniques. Furthermore, our use of a low modulating frequency permits use of the solid-state, electro-optical light shutter. This eliminates the rather dangerous liquid Kerr cell, thus making our apparatus more acceptable to application in the undergraduate advanced laboratory. From a pedagogical point of view, the student is allowed to use and become acquainted with the lock-in amplifier which is so commonly found in the modern research laboratory. Two rather novel techniques were employed in this apparatus. These were phase multiplication and mixing of the rf signal in the last stages of the photomultiplier. Our value for the speed of light in air was 2.937 × 108 m /sec. The accepted value of the speed of light in air to the same number of significant figures is 2.997 × 108 m /sec.

Precision of the Geodimeter as Affected by the Speed of Light in Air

The Geodimeter has been analyzed as to limitations on its precision in range measurement imposed by uncertainties in the velocity of propagation of light in the atmosphere. The instrument has been found elsewhere to be somewhat more consistent than the best current value of the velocity of light in vacuo, that is, to about one part in 3 million. On the basis of the analysis reported here, routine measurements to one part in 106 are concluded to be warranted, as far as propagational errors are concerned, up to ranges of about 100 km. Higher precisions, up to 1 in 107, are concluded to be attainable.

The Effect of Wave-length on the Differences in the Lags of the Faraday Effect behind the Magnetic Field for Various Liquids

The lag of the Faraday effect behind the magnetic field was measured by the method of Beams and Allison in carbon bisulphide, toluene, carbon tetrachloride, benzene, xylene, chloroform, and bromoform for various wave-lengths of light from 4481 to 5896A. It is found in every case that the difference in the lags of the Faraday effect behind the magnetic field increases as the wave-length of the light decreases. The extreme magnitudes observed in these time-lag differences range from 0.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ sec. for the longest wave-lengths to 12.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ sec. for the shortest, depending upon the two liquids compared. The precision is about 0.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ sec.Effect of temperature on the lag of the Faraday effect.---Observations made on carbon bisulphide, toluene and chloroform failed to detect any effect of temperature on the lag of the Faraday effect for temperature differences of 40\ifmmode^\circ\else\textdegree\fi{}C.Ratio of the speed of electric impulses along wires to the speed of light in air.---The method of the experiment affords a means of measuring the ratio of the speed of electric impulses along copper wires to the speed of light. The value obtained for the ratio was about 96 percent.