Entanglement-enabled interferometry using telescopic arrays

ABSTRACT

A protocol of measuring interferometric visibility function using imperfectly entangled states shared between remote telescopes is proposed. We demonstrate how quantum entanglement can be utilized to increase the baseline size of telescopic arrays thereby providing substantial enhancement to the resolution of direct-detection interferometric measurements. We demonstrate, through a comprehensive analysis, how errors in visibility measurements and in the intensity distribution of a distant object show dependence on the entanglement degree of the shared quantum resource. We analyse the feasibility of the protocol using currently available technology and identify the nature of sources that can benefit most from it.     

Intersatellite range monitoring using optical interferometry

We report on an interferometer designed to provide 1-10 nm/square root(Hz) displacement measurement resolution, in the range 0.01 Hz to 1 Hz, while in low Earth orbit. The interferometer comprises two units, each with its own laser and in separate satellites, which would be in the same orbit separated by approximately 50 km. We discuss the requirements on the interferometer subsystem and describe the optical transponder distance measurement, including a phase locking method to generate a heterodyne beat signal between the two lasers. Design, fabrication, and testing of a "flightlike" engineering model interferometer is outlined, and results from environmental and performance tests are reported.     

Optical-fiber vibration sensor using step interferometry

An all-fiber vibration sensor based on step interferometry is described. The sensor consists of a modified Michelson interferometer in which the ends of the reference and signal arms are assembled and fixed together to produce regular distributed interference fringes. Five photodetectors with relative phase shifts of π/2 placed on the fringes acquire five intensity patterns simultaneously. One reconstructs the vibration amplitude by using the well-known five-step algorithm. A vibration sensor with these characteristics was constructed, and its performance was investigated.     

Sub-Nyquist interferometry using a computer-stored reference

Abstract

In the testing of deep aspheric wavefronts using the phase-shifting technique a CCD video camera and a digital computer is limited by the so-called Nyquist frequency. The Nyquist frequency limits the maximum wavefront slope that can be measured over the CCD array to π radians per pixel. A wavefront containing spatial frequencies beyond this limit gives a sub-sampled or aliased interferogram. If the wavefront under test is assumed to be smooth up to its first or second derivative, then it is possible to recover the deep aspheric wavefront. Here we present a new and simple technique to recover a deep aspheric wavefront under test whenever a close estimation of the wavefront being tested is available.     

Multiplicative phase-shifting interferometry using optical flow

Fringe patterns with a multiplicative phase shift among them appear in experimental techniques as photoelasticity and RGB shadow moiré, among others. These patterns cannot be processed using standard phase-shifting demodulation techniques. In this work, we propose to use a multiframe regularized optical flow algorithm to obtain the interesting modulating phase. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results.     

Measurement of temperature using speckle shearing interferometry

A laser speckle shearing interferometric technique is used for measuring the temperature profile inside a gaseous flame. The experimental results are compared with the values obtained by a thermocouple and also by speckle photography. Good agreement is seen among the temperatures measured by speckle shearing interferometry, speckle photography, and the thermocouple. Speckle shearing interferometry is easier to implement than speckle photography. This is because in speckle shearing interferometry the accurate positions of the fringes can be known without point-by-point analysis and correction for the halo effect.     

Modelling spatial density using continuous wavelet transforms

Due to increase in the satelite launch activities from many countries around the world the orbital debris issue has become a major concern for the space agencies to plan a collision-free orbit design. The risk of collisions is calculated using the in situ measurements and available models. Spatial density models are useful in understanding the long-term likelihood of a collision in a particular region of space and also helpful in pre-launch orbit planning. In this paper, we present a method of estimating model parameters such as number of peaks and peak locations of spatial density model using continuous wavelets. The proposed methodology was experimented with two line element data and the results are presented.     

Image magnification using families of fast orthogonal transforms

We outline a method if image magnification based on parametric families of fast orthogonal transforms which arise from the multiresolution/wavelet paradigm of Mallat and Meyer. The essential idea is to consider the original image as a low-frequency component of a family of potential enlargements, all of which are computable in real time. We sketch the underlying theory and pertinent algorithms. Several specific examples are detailed. © 1996 John Wiley & Sons, Inc.     

Automated small tilt-angle measurement using Lau interferometry

A technique for a tilt-angle measurement of reflecting objects based on the Lau interferometry coupled with the moire readout has been proposed. A white-light incoherent source illuminates a set of two gratings, resulting in the generation of the Fresnel image due to the Lau effect. The Fresnel image is projected onto a reflecting object. The image reflected from the object is superimposed onto an identical grating, which results in the formation of a moiré fringe pattern. The inclination angle of moiré fringes is a function of tilt angle of the object. Theory and experimental arrangement of the proposed technique is presented and results of the investigation are reported.     

Experimental study of laser-generated shear waves using interferometry

The shear displacements generated by short laser pulses have been measured in aluminum semicylindrical samples, both in the thermoelastic and ablation regimes. We measured the waveforms at different angles and obtained the angular distribution pattern of the amplitudes. For the thermoelastic regime good agreement has been found between the measured and the theoretically predicted shear waveforms. In the ablation regime, the absolute values of the amplitudes are comparable to the ones of compressional waves. The shear waveforms are difficult to interpret, particularly in the case where both thermoelastic and ablative effects play a role, because the phases of the shear pulses are opposite to one another in these two regimes. To measure the in-plane displacements, and hence the shear displacement field generated by the pulsed laser, a speckle heterodyne interferometer was used.This article is dedicated to Professor Dr. Paul Höller on the occasion of his 65th birthday.     

Primary calibration of ultrasonic hydrophone using optical interferometry

A primary calibration method for ultrasonic hydrophones which uses a Michelson interferometer to determine the particle displacement in an ultrasonic field is discussed. The acoustic pressure is derived from this measurement and used to determine the free-field sensitivity of a hydrophone in the frequency range 0.5-15 MHz. The random uncertainty of the method is typically 1%, whereas the systematic uncertainty varies from 2.3 to 6.6% over the frequency range. To obtain this accuracy, the performance of the system has been carefully examined and appropriate correction factors derived. The greatest difficulty in the method lies in determining the frequency response of the optical detection system, and two different approaches have been used to measure this response. Several acoustical effects have also been studied and the calibration procedure modified to take account of them. The calibration results are in agreement with those of other methods and with the theoretically predicted frequency response of a hydrophone. The method has been used to determine the temporal stability of a hydrophone over a period of two years.     

Reducing the peak-to-average power ratio using unitary matrix transformation

A theoretical analysis is presented to show that in orthogonal frequency division multiplexing systems, the peak-to-average power ratio (PAPR) can be reduced by performing a unitary matrix transformation on the input vector of N symbols. The authors also prove that this transformation does not degrade the bit error rate (BER) or power spectral density (PSD) performance. Based on this, the inverse discrete Fourier transform matrix is proposed as the unitary matrix to reduce the PAPR. The simulation results show that the proposed scheme can obtain significant PAPR reduction while maintaining good performance in the BER and the PSD. To further evaluate the performance of the proposed scheme, the authors compare it with some well known PAPR reduction techniques by simulations. It is demonstrated that the proposed scheme can offer better system performance and achieve a better compromise with regard to the PAPR reduction, BER, spectral efficiency and computational complexity.     

Phase-shifting interferometry using a two-dimensional regularized phase-tracking technique

Abstract

Phase-shifting interferometry is the most used method whenever the optical stability of the interferometer remain high when several phase-shifted interferograms are taken. In this work we present a two-dimensional regularized phase-tracking (RPT) technique applied to demodulate multiple phase-shifted interferograms. The main advantage of this technique with reference to classical phase-shifting interferometry is its higher signal-to-noise rejection as well as a higher signal′s harmonics rejection. In the RPT technique the unwrapping process is implicit; so it is achieved simultaneously with the phase estimation process; then, no additional unwrapping process is required.     

Multiple-wavelength digital holographic interferometry using tunable laser diodes

Here we present multiple-wavelength digital holographic interferometry with a wide measurement range using laser diodes. Small wavelength differences can be easily realized by the wavelength tuning of laser diodes with injection current controls. A contour map of an object with a wide measurement range and a high sensitivity is demonstrated by combining a few contour maps with several measurement sensitivities. Synthetic wavelengths are calibrated using a known height difference. This alleviates the need to have high precise knowledge of the recording wavelengths. The synthetic wavelengths ranged from ~3 mm for high measurement sensitivity to ~4 cm for wide measurement range. An rms error of ~35 mum for a ~1 cm height measurement is shown. The measured profile of holographic interferometry agrees with a standard stylus instrument.     

Three dimensional displacement measurement using Moiré interferometry

Moiré interferometry is used to simultaneously measure the in plane and out of plane displacement components. The high sensitivity of displacement measurement is maintained and high contrast fringes are obtained without recourse to additional filtering.