Dual beam interferometry and double chopping for scintillation free measurements

A dual beam interferometer with two inputs and two outputs is described. The instrument allows measurements of difference reflectivities in the far infrared region (10...500 cm^–1). In the high vacuum compartment cryogenic equioment, like a superconducting magnet or a cryoflow cryostat can be installed. However the step scan version of the interferometer is sensitive to any fluctuation of source intensity, base-line shift in the interferogram and thermal distortions, effects causing scintillation noise in the spectra. A method is described which suppresses scintillation noise by additional chopping at the output of the interferometer and rationing digitally difference and sum interferograms. These are acquired by phase sensitive detection with two lock ins.Work supported by the Jubiläumsfonds der Österreichischen Nationalbank under Grant 1569.     

Suppression of Multiple-Beam Interference Noise in Testing an Optical-Parallel Plate by Wavelength-Scanning Interferometry

Measurements of optical parallel plates in a Fizeau interferometer lead to problems from multiple-beam interference noise unless the back surface of the plate has an additional treatment to prevent its reflection from reaching the detector. Such internal-reflection noise can be separated from the fundamental interference signal by its modulation frequency in a wavelength-scanning interferometer. However, to completely eliminate the noise, the air-gap distance between the testing and reference surfaces of the interferometer must be adjusted to a specific value, depending on the thickness and refractive index of the plate. This adjustment requires an undesirable change in the air gap, which is related to the phase modulation rate of the interferometer, and also requires additional information regarding the testing plate, which makes the measurement laborious. We show that if we add new symmetries to the sampling functions of the phase measuring algorithm, we can obtain significantly greater tolerance for the air-gap error. A new 19-sample algorithm allows a tolerance of ±23% while keeping the systematic errors at less than λ/200. The periodicity of the new algorithm and an integrating bucket technique also provide more options for the thickness of the testing plate, which guarantees an air-gap distance more independent of this thickness.     

The effects of external optical feedback on the power penalty of DFB-LD modules for 2.5Gbs−1 optical transmission systems

We report the effects of external optical feedback on the power penalty of commercial distributed feedback laser diode (DFB-LD) modules for 2.5Gbs–1 optical transmission systems. External optical feedback presented to the DFB-LD modules causes the excitation of external cavity modes, resulting in increased relative intensity noise (RIN) and intensity noise ripples at low frequency region below 500MHz. For a 10–10 bit error rate (BER), the minimum power penalty is as much as 1.25dB for a feedback ratio of –8.8dB. An excess power penalty of 0.5dB per 3dB increase in the feedback ratio was also empirically obtained. We suggest that optical isolators in 2.5Gbs–1 DFB-LD modules used in conventional optical transmission systems or WDM systems must have a peak isolation ratio of better than 54.5dB, instead of the previously recommended 30dB, for negligible power penalty induced by external optical feedback.     

Quantitative phase imaging using actively stabilized phase-shifting low-coherence interferometry

We describe a quantitative phase-imaging interferometer in which phase shifting and noise cancellation are performed by an active feedback loop using a reference laser. Depth gating via low-coherence light allows phase measurement from weakly reflecting biological samples. We demonstrate phase images from a test structure and living cells.     

Zygo interferometer for measuring refractive index of photorefractive bismuth silicon oxide (Bi12SiO20) crystal

An application of the Zygo system for measuring the refractive index of optical materials such as bismuth silicon oxide (BSO) having a higher value of the refractive index than that of glass is presented. The setting accuracy is found to be of the order of 1 μm in the Zygo phase measuring interferometer. The mean value of refractive index of BSO crystal measured by the interferometer for several samples of thickness in the range of 3–9 mm is 2.542 at a wavelength of 632.8 nm. The accuracy of measurement is ±0.002. It is possible to achieve an accuracy of ±0.0003 for a sample of thickness of 30 mm in the measurement of refractive index due to high setting accuracy of the Zygo system.     

Small Deformation Measurements of Diffuse Objects: Phase Stepping by Frequency Drift of a He-Ne Laser

We describe a simple phase-stepping speckle interferometer with large path difference, in which phase modulation is achieved by thermal frequency drift of the He-Ne light source. This system is easy to set up, requires no specialised components, is immune from the effects of piezo actuator hysteresis, and is capable of producing phase maps in which the noise is less than 1/20λ.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27-29, Saitama, Japan.     

Laser excess noise and interferometric effects in frequency-modulated diode-laser spectrometers

Tunable Diode-Laser Absorption Spectroscopy (TDLAS) is increasingly being used to measure trace-gas concentrations down to low part-per-billion levels (1 ppbv = 10^–9 volume mixing ratio). Semiconductor lead-salt diode lasers give access to the mid-infrared spectral region and the application of high-Frequency Modulation (FM) schemes can further improve the sensitivity and detection speed of modern instrumentation. Several factors influence or even limit spectrometer performance. The central elements in such spectrometers are lead-salt diode lasers. Experimental data will be presented, which demonstrate that high-frequency excess-noise contributions above several MHz can be attributed to mode hopping and mode partition noise during multimode laser operation. Additionally it will be discussed how a FM-TDLAS spectrometer can be interpreted as an optimized Michelson interferometer for absolute distance measurements and, therefore, is extremely sensitive towards drift effects. The higher the modulation frequency, the higher is the drift sensitivity of the spectrometer due to interferometric effects. These drift effects are a second factor affecting ultrasensitive measurements. While wideband-laser noise characteristics call for high modulation frequencies, the aforementioned interferometric effects in the spectrometer require low modulation frequencies.     

Phase measurement accuracy of feedback interferometers

Feedback interferometers are described with specific reference to potential applications in micro-machines. A theoretical analysis is developed to determine the linearity, stability, and noise performance of this type of interferometer. The theoretical analysis was tested using a prototype high-precision feedback interferometer which showed that, at a feedback loop gain which enabled the system to track 6 fringes, the linearity of the interferometer was better than λ/100 and single phase measurements could be made with an accuracy of λ/80.     

A phase quadrature interferometer for measuring the small optical rotation angle of a chiral medium

The passage of a linearly polarized beam through a chiral material and a phase retarder will induce a phase difference between the s and p polarizations of the beam. In this study, a phase quadrature interferometer is designed to measure the phase difference variation proportional to the optical rotation. The proportionality constant (or measurement sensitivity) can be greatly enhanced by setting the retardation of the phase retarder close to 0° or 180°. The experimental results demonstrate that with our system we can obtain a measurement resolution for the rotational angle of better than 3.5° × 10⁻⁴. This method has several advantages such as a simple optical setup, easier operation in real time, and low cost. In addition, due to the common-path arrangement, surrounding noise can be eliminated.     

Influence of laser diode wavelength tunability on the range, resolution and repeatability of interferometric distance measurement

The coherence length of a single mode laser diode (LD) can reach more than 10 m. It allows the application of this source of light to interferometric distance measurement, with a measurement range of several meters. However, the LD's wavelength tunability, which is a result of the dependence of the lasing wavelength on the injection current, prevents the realization of the theoretically possible metrological parameters of the interferometer. In this study, we analyze the influence of a low-frequency signal disturbance, e.g., noise or disturbing modulation inherent to the injection current of the LD, on the repeatability and measurement range of an LD interferometer used for displacement measurements. Both the measurement range and the resolution of the interferometer are found to be highly limited by this factor.     

Sinusoidal Phase-Modulating Superluminescent Diode Interferometer with Fabry-Perot Etalone for Step-Profile Measurement

In this paper we use a superluminescent diode (SLD) as the light source of an interferometer and extract a narrow spectrum from a wide spectrum of the SLD with a Fabry-Perot Etalone (FPE). By varying sinusoidally the distance between the two mirrors of FPE, the central wavelength of the narrow spectrum is scanned sinusoidally. The distance between the mirrors is exactly set by a feedback control system, and sinusoidal phase-modulated SLD light that has a large scanning width of about 10 nm can be obtained with high stability and spatial uniformity. The phase of the interference signal has two different components. One is amplitude Z_b of sinusoidal phase modulation, which is proportional to the optical path difference (OPD) and the scanning width. The other is conventional phase α, which provides a fractional value of the OPD in the range of the wavelength. By combining the two values of the OPD obtained from Z_b and α, an exact OPD larger than the wavelength can be measure with ment accuracy in α. Characteristics of the interferometer are made clearly through step-profile measurements.     

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0×10⁻⁴ corresponding to 1 °C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10⁻⁸ rad.     

Phase determination in holographic Moiré in presence of nonsinusoidal waveforms and random noise

This paper proposes a subspace parameter estimation method which besides allowing for accommodating multiple PZTs in an optical interferometer permits for extracting in real time values of phase shifts between data frames at each pixel point. The technique enables to freely choose values of phase shifts between 0 and π. A generalized phase measurement algorithm allows for computing multiple phase information present in the interferometer. The method facilitates the use of spherical beams, addresses errors arising from the miscalibration of the phase shifting devices, and is capable of handling nonsinusoidal waveforms in an effective manner. Numerical simulations demonstrate that phase distributions can be measured with high accuracy even in the presence of noise.     

Fringe Locking in a Laser Diode Interferometer by Optical Feedback During Modulation of Injection Current

A fringe locking phenomenon in a two beam interferometer using a semiconductor laser subject to optical feedback was, whose injection current is modulated. When a path difference of the interferometer is sufficient, fringes taken by a charge coupled device camera are seen to be stationary and the rms fluctuations of fringe phase is reduced to as low as 0.2ϖ radians from more than 8ϖ radians without the optical feedback. The rms phase fluctuation is independent of frequency and amplitude of the current modulation. The fringe locking has also been observed in the presence of both injection current modulation and piezoelectric transducer mirror vibration.     

Quadrature phase-shifting interferometer using spatial carrier

We propose a high-speed phase measurement using a phase calculation algorithm in a quadrature phase-shifting interferometer (QPI), which is applied to tilted fringes. Although the spatial carrier method is useful for a high-speed measurement with a single imaging sensor, the spatial resolution in conventional phase calculation algorithms is reduced owing to the use of three or more phase-shifted data at different sample points. Phases in the QPI method can be calculated with only two quadarture phase-shifted data extracted from the tilted fringes before and after a phase change of the interferometer. Thus, the proposed method can suppress the reduction of the spatial resolution compared with that in conventional methods, and makes it possible to measure a phase at high-speed. The principle and experimental results of this technique are presented.     

Surface-profile measurement by means of a polarization Sagnac interferometer with parallel optical feedback

We describe a novel feedback interferometer for real-time, unambiguous measurement of surface profiles that consists of a polarization Sagnac interferometer and an optically addressed phase-only spatial light modulator. In this system the output intensity from the Sagnac interferometer is optically fed back to the phase modulator placed in one arm of the interferometer, which produces a sawtooth fringe intensity profile (instead of the conventional cosinusoidal one) that is directly and unambiguously related to the surface profile. Preliminary experimental results demonstrate the feasibility of applying this system to surface-profile measurement.     

Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system

A highly stabilised vibration-displacement measurement system, which employs fiber Bragg gratings (FBGs) to interleave two fiber Michelson interferometers that share the common-interferometric-optical path, is presented. The phase change in the interferometric signals of the two fiber Michelson interferometers have been tracked, respectively, with two electronic feedback loops. One of the fiber interferometers is used to stabilise the system by the use of an electronic feedback loop to compensate the environmental disturbances. The second fiber interferometer is used to perform the measurement task and employs another electronic feedback loop to track the phase change in the interferometric signal. The measurement system is able to measure vibration-displacement and provide the sense of direction of the displacement. The frequency range of the measured vibration-displacement is from 0.1 to 200 Hz and the measurement resolution is 10 nm.     

高灵敏度的量子迈克耳孙干涉仪

迈克耳孙干涉仪不仅可以用来研究物理学的基本问题,而且能够用于精密测量,比如引力波信号的测量.因此,构建高灵敏度的迈克耳孙干涉仪是实现微弱信号测量的关键.目前,人们利用压缩态可以降低迈克耳孙干涉仪的噪声;通过光学四波混频过程能够放大马赫·曾德尔干涉仪中的相位信号,从而提高干涉仪的信噪比和灵敏度.本文研究了一种用于高灵敏度相位测量的量子迈克耳孙干涉仪.在迈克耳孙干涉仪中,利用非简并光学参量放大器取代干涉仪中的线性光学分束器;并且将压缩态注入干涉仪的真空通道,可以得到高信噪比和高灵敏度的干涉仪.由于存在不可避免的光学损耗,分析了迈克耳孙干涉仪内部和外部的损耗对相位测量灵敏度的影响.通过理论计算研究了干涉仪的相位测量灵敏度随系统参数的变化关系,得到了高灵敏度的相位测量量子迈克耳孙干涉仪的实现条件,为用于精密测量的干涉仪的设计提供了直接参考.     

基于光纤3×3耦合器干涉仪及相位跟踪的振动测量系统

研究了基于光纤3×3耦合器迈克尔逊干涉仪及反馈跟踪相位变化的振动测量系统。该测量系统包含两个反馈控制环节:一个反馈控制环节用于补偿由于环境干扰引起的相位随机漂移;另一个反馈控制环节用于跟踪由于振动引起的相位变化,从而实现对振动幅值及振动方向的测量。该系统可对频率为1.5~200Hz的振动进行测量,测量分辨率可达到10nm。     

Injection locking semiconductor lasers with phase conjugate feedback

Phase conjugate injection locking is shown to couple coherently two semiconductor lasers through a double phase conjugate mirror geometry. The mutual coherence and stability of the lock band are characterized from the visibility and relative intensity noise measurements for various levels of phase conjugate coupling and frequency detunings. Side mode phase conjugate injection locking is demonstrated by high mutual coherence with visibility 0.93 and detunings up to nine longitudinal mode spacings at injection levels of −22 dB. Central mode phase conjugate injection locking with high mutual coherence is also possible for feedback levels of −36 dB and exhibiting an asymmetric stable locking region of 350 MHz bandwidth within the locking band. The phase locking is unstable though, the reasons for which are discussed. Increased phase conjugate feedback extends the lock band to greater detunings and asymmetry as in direct injection locking with only a small region showing high mutual coherence. Intensity noise measurements are also discussed.