Sinusoidal Phase-modulating Interferometry Research Articles

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system.

Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We demonstrate a full-range parallel Fourier-domain optical coherence tomography (FD-OCT) in which a tomogram free of mirror images as well as DC and autocorrelation terms is obtained in parallel. The phase and amplitude of two-dimensional spectral interferograms are accurately detected by using sinusoidal phase-modulating interferometry and a two-dimensional CCD camera, which allows for the reconstruction of two-dimensional complex spectral interferograms. By line-by-line inverse Fourier transformation of the two-dimensional complex spectral interferogram, a full-range parallel FD-OCT is realized. Tomographic images of two separated glass coverslips obtained with our method are presented as a proof-of-principle experiment.

Movement measurement with a grating interferometer using sinusoidal phase-modulation

Movements of a surface profile are measured with a two-grating interferometer using sinusoidal phase-modulation. Since sinusoidal phase-modulating (SPM) interferometry can record a phase change due to the movement of an object in the interference signal, the SPM interferometer is suitable for measuring the movement of the object. Some experiments show that the two-grating interferometer can measure a sinusoidal vibration with amplitude of several tens of microns and a step movement with a magnitude of several microns.

Measurement of sectional profile of V-shaped metal cylinders using a sinusoidally vibrating interference pattern

A method is proposed for accurately measuring a sectional profile of a metal cylinder. In this method a sinusoidally vibrating sinusoidal interference pattern is used to generate an exact spatial scale along one direction. Light from top points of a metal cylinder surface is extracted by spatial filtering in an afocal imaging system to form an image of the top points. A time-varying signal is detected in the image, and a sectional profile of the metal cylinder is measured from the phase of the detected signal on a position where the amplitude of the signal has a maximum value. Detection of the amplitude and the phase is carried out easily and exactly with sinusoidal phase-modulating interferometry.

Two-grating interferometer with sinusoidal phase modulation for surface profile measurement

A two-grating interferometer for measurement of profiles of polished surfaces is proposed. The ±first-order beams diffracted by the first grating produce parallel fringes of about 50-µm spacing on an object surface. By using the second grating, we eliminate the parallel fringes and extract a phase distribution produced by the surface profile of the object. Moreover, the vibration of the second grating of a small size enables us to use the sinusoidal phase-modulating interferometry. Measurement resolution is higher than 0.3 µm at the equivalent wavelength of 35 µm.

Sinusoidal phase-modulating laser diode interferometer for measuring angular displacement

We propose a sinusoidal phase-modulating laser diode interferometer for measuring small angular displacement. The interferometer is based on a Fabry-Perot plate. It has a simple structure and is insensitive to external disturbance. Sinusoidal phase-modulating interferometry is used for improving the measurement accuracy. A charge-coupled device (CCD) image sensor is used for measuring the distance between the reflected beams from two faces of the Fabry-Perot plate. From the distance, the initial angle of incidence is calculated. Compared with Michelson interferometers and autocollimators, this interferometer has the advantage of compact size and simple structure. The numerical calculation and experimental results verify the usefulness of this novel interferometer.

Two-dimensional rotation angle measurement using a sinusoidal phase-modulating laser diode interferometer

We propose a simple setup for measurement of a small 2-D rotation angle using a Twyman-Green laser diode interferometer. Sinusoidal phase-modulating interferometry is adopted to detect the phase of the interference signal with a high accuracy and to perform the phase lock to eliminate the phase fluctuation at the standard detection point. By detecting the phases at three points along an axis, the 1-D rotation angle is measured with an accuracy of 0.5 arcsec in the range of 282 arcsec and with a spatial resolution of 3 mm. The 2-D rotation angle measurement is easily made by adding two more detection points.

Nanometer measurement with a dual Fabry–Perot interferometer

On the basis of analyzing sinusoidal phase-modulating Fabry-Perot interferometry, a method, believed to be novel, is proposed for achieving nanometer measurement accuracy by measuring the time interval between equal amplitudes of the two elementary frequency signals of the transmitted intensities of a dual Fabry-Perot interferometer. A nanometer measurement system based on the method was designed and tested. The experimental results show that the displacement resolution of the system is 0.32 nm at a 1-kHz modulating signal.

Sinusoidal wavelength-scanning interferometer with a superluminescent diode for step-profile measurement

In sinusoidal phase-modulating interferometry an optical path length (OPD) larger than a wavelength is measured by detection of sinusoidal phase-modulation amplitude Z(b) of the interference signal that is produced by sinusoidal scanning of the wavelength of a light source. A light source with a large scanning width of wavelength is created by use of a superluminescent laser diode for the error in the measured value obtained by Z(b) to be smaller than half of the central wavelength. In this situation the measured value can be combined with a fractional value of the OPD obtained from the conventional phase of the interference signal. A sinusoidal wavelength-scanning interferometer with the light source measures an OPD over a few tens of micrometers with a high accuracy of a few nanometers.

Exact measurements of surface profiles of a glass plate by a superluminescent diode interferometer

A superluminescent diode interferometer that uses sinusoidal phase-modulating interferometry and the shifting method is applied to measure the front and rear surface profiles of a glass plate with an accuracy of a few nanometers. Since the roughness of the reference surface is large, a glass plate is put behind the object as another reference surface, which is estimated by the shifting method with an accuracy of a few nanometers.

Superluminescent diode interferometer using sinusoidal phase modulation for step-profile measurement

We propose an interferometer in which the relationship between the degree of coherence (DCH) and the optical path difference (OPD) is utilized for determining an OPD longer than a wavelength. A superluminescent diode is employed as the source of the interferometer, and sinusoidal phase-modulating interferometry is used to detect the DCH and the phase of the interference signal. The combination of the OPD determined from the DCH and the phase of an interference signal enables us to measure an OPD longer than a wavelength with a high accuracy of a few nanometers. Experimental results show clearly the usefulness of the interferometer for a step-profile measurement.

Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances

We describe a two-wavelength laser-diode interferometer that is insensitive to external disturbances such as fluctuations in the wavelength of the laser diode and mechanical vibrations of the optical components. In sinusoidal phase-modulating interferometry this insensitivity is easily obtained by controlling the injection current of the laser diode with a feedback control system. Using an equivalent wavelength of 152 microm provided by two single-frequency laser diodes, we can measure the distance, rotation angle, and surface profile measurements with great accuracy.

Double sinusoidal phase-modulating laser diode interferometer for distance measurement

Sinusoidal phase-modulating interferometry is used to detect exactly the sinusoidal phase variation of an interference signal even when the amplitude of the interference signal is varied by modulation of the injection current. We can easily provide a sinusoidal phase-modulating interferometer with a feedback control system that eliminates the phase fluctuations caused by mechanical vibrations. The methods using sinusoidal phase-modulating interferometry improve the resolution of distance measurements. Experimental results show that the thickness of gauge blocks is measured with a resolution of approximately 0.5 microm.

Analysis of measurement accuracy in sinusoidal phase modulating interferometry

A theoretical analysis of the measurement accuracy in sinusoidal phase modulating (SPM) interferometry is presented. The measurement accuracy is dependent on multiplicative and additive noise. The characteristics of SPM interferometry in the presence of this noise are made clear. Theoretical results show clearly that SPM interferometry has a high measurement accuracy of the order of 1 nm.