Low-coherence Interferometer Research Articles

High-speed 3D imaging using photorefractive holography with novel low-coherence interferometers

The paper reports recent progress in developing high speed 3D imaging systems based on low coherence photorefractive holography with high-speed depth-sectioned imaging at 476 frames per second. It is demonstrated that photorefractive holography can utilize a wide variety of sources of differing spatial and temporal coherence, including a novel all-solid-state broadband laser. Also presented is a novel real-time optical sectioning technique based on structured illumination combined with photorefractive holography that provides real-time optical sectioning when imaging with reflected light or with fluorescence.

Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness.

We have developed a low-coherence interferometer system used for the simultaneous measurement of refractive index n and thickness t of transparent plates. Both the phase index n(p) and group index n(g) can be determined automatically in a wide thickness range of from 10 microm to a few millimeters. Two unique techniques are presented to measure n(p), n(g), and t simultaneously. One allows us to determine n(p), n(g), and t accurately by using a special sample holder, in which the measurement accuracy is 0.3% for the thickness t above 0.1 mm. In the other technique the chromatic dispersion delta n of index is approximately expressed as a function of (n(p) - 1) on the basis of measured values of n(p) and n(g) for a variety of materials, and then the simultaneous measurement is performed with a normal sample holder. In addition, a measurement accuracy of less than 1% is achieved even when the sample is as thin as 20 microm. The measurement time is also 3 min or more.

2π ambiguity-free optical distance measurement with subnanometer precision with a novel phase-crossing low-coherence interferometer

We report a highly accurate phase-based technique for measuring arbitrarily long optical distance with subnanometer precision. The method employs a Michelson interferometer with a pair of harmonically related light sources, one cw and the other low coherence. By slightly detuning (~2 nm) the center wavelength of the low-coherence source between scans of the target sample, we can use the phase relationship between the heterodyne signals of the cw and the low-coherence light to measure the separation between reflecting interfaces with subnanometer precision. As this technique is completely free of 2pi ambiguity, an issue that plagues most phase-based techniques, it can be used to measure arbitrarily long optical distances without loss of precision. We demonstrate one application of this technique, the high-precision determination of the differential refractive index.

Influence of Phase Errors on the Spectral Response of AWG Multiplexers

PHASARs or Arrayed Waveguide Grating (AWG) multiplexers are key elements for Dense Wavelength Division Multiplexing (DWDM) in optical networks. The knowledge of phase errors and their impact on the characteristics of the transmission spectrum of a PHASAR is of great importance for improvements of the fabrication process. Using Fourier transform spectroscopy employing a low coherence interferometer, the power-distribution coefficients and the phase distribution in such components are evaluated. A calculation of the transmission spectrum with the phase and power coefficients shows excellent agreement with direct transmission measurements of a 16 channel 100 GHz PHASAR. The behaviour of phase deviations on the transmission peak shape is evaluated by simulations with linear, parabolic, periodic and single phase fluctuations. In consequence wavelength shift, peak broadening, increase of crosstalk and the existence of sidelobes at characteristic wavelength positions can be assigned to certain types of phase distributions. Even only one particular phase error significantly enhances the crosstalk of a device. In detail, the observed sidelobes in the transmission spectrum of a 16 channel PHASAR with 100 GHz channel spacing can be assigned to sinusoidal phase deviations with periodicities of 20 and 11 waveguides. This corresponds to a length scale of 800-900 μm for changes in refractive index and/or layer thickness. Thus, improvements in fabrication processes of PHASARs can be monitored by this technique.

Transmission of optical length information through single-mode fiber by a low-coherence tandem interferometer

A novel technique for the transmission of optical length information using a low-coherence tandem interferometer and a single-mode optical fiber is developed. The optical path length with a step gauge in the first low- coherence interferometer is transmitted through the optical fiber to the second interferometer. The interference fringes containing the length information of the gauge are generated with high accuracy by compensating the optical path difference in the second interferometer.

Simultaneous low coherence interferometry imaging at two depths using an integrated optic modulator

A Mach–Zehnder unbalanced LiNbO3 integrated modulator with independent control of the phase of each arm is incorporated into the reference arm of a low coherence interferometer set-up. Using different RF modulation frequency and processing electronics tuned to these frequencies, the system can be used for simultaneous interrogation of the signal reflected from two different depths in tissue or from two different axial positions in profilometry. When a pair of XY scanning mirrors are incorporated into the sensing arm, then two en-face images from different axial positions can be simultaneously produced. The depth separation between the axial positions of the points or layers interrogated is equal to half of the modulator path difference. The operation of the system is illustrated by displaying simultaneously two images from a coin.

Phase-resolved correlation and its application to analysis of low-coherence interferograms

A new signal-processing technique is proposed that involves a phase-resolved correlation method that one can use to determine the phase distribution of low-coherence interferograms. This method improves the sensitivity and resolution of low-coherence interferometers. The depth structure of an aluminum oxide-coated aluminum mirror was determined by use of a low-coherence interferometer with this method. Three signal peaks were successfully extracted from a noisy interferogram.

Resolution improvement in optical coherence tomography based on destructive interference

A novel low coherence interferometer (LCI) is proposed for obtaining higher resolution in optical coherence tomography. Three reference mirrors are used in this LCI to generate reference lights. The output signal of this LCI is a superposition of interference of signal light with three reference lights. Through adjusting relative intensities of reference lights, the width of the axial point spread function for the LCI can be reduced, then the resolution will be improved. The influences of fluctuations of wavelength and mirror separation on the resolution are investigated. It is expected that this new approach may provide an effective and useful technique for optical measurement.

Interferometric testing of optical surfaces at its current limit

Summary Today the production of microlithographic projection lenses drives interferometry to its very limits. Resolutions to a fraction of an Angstrom when measuring surface figure are necessary. Especially EUV lithography needs mirror surface qualities of approximately 0.1 nm RMS, with the consequence that metrology needs accuracies significantly below 1 Angstrom. Repeatability of a measurement is limited by the quality of the interferometric setup itself. Reproducibility is mainly influenced by handling, adjustment and thermal adoption to the testpiece, whereas accuracy is limited by the calibration process and procedure. Carl Zeiss uses a low coherent Fizeau interferometer with multi-fringe evaluation technique (DMI = Direct Measuring Interferometry) to accumulate many phase maps at video rate. Cavities are kept short, air ventilation of the cavity during the measurements is applied. A weak aspheric surface for EUV application (so called ELT2-EUV asphere) was tested with a special interferometric setup using a single lens compensating system. The reproducibility of the measurement came out as 0.07 nm RMS (surface figure). The setup has been calibrated using a spherical calibration surface, whose accuracy was cross checked by two different absolute measurement procedures. We found that both measurements differ by an amount of only 0.15 nm RMS (surface figure). Taking into account the systematic errors of the interferometric setup, the accuracy of the asphere measurement can be estimated to 0.2 nm RMS (surface figure). Further improvements are necessary to drive accuracy to even lower limits and to make test procedures ready for production process.

Sensing applications of a low-coherence fibre-optic interferometer measuring the refractive index of air

A remote fiberised low-coherence interferometric sensor has been used to measure the refractive index of air. The relative humidity, temperature, pressure or carbon dioxide content may be determined from the measurement of the refractive index of air if the values of the other parameters are known. The sensor works linearly, for example, over the full range of humidity and does not suffer from aging or hysteresis. This maintenance-free sensor has a relative accuracy of 1.6% with a fast response time. The relative sensitivity of the sensor to changes in the values of the other parameters influencing the refractive index of air has also been deduced. The sensor is designed primarily for industrial applications where conventional electronic sensors cannot be used in environments where materials degradation prevents the use of conventional gas and humidity sensors.

An Approach to Optical Reflection Tomography along the Geometrical Thickness

We propose and demonstrate a novel optical reflection tomography along the geometrical thickness. This technique is based on simultaneous measurement of refractive index n and thickness t of a sample using the combination of a low coherence interferometer and confocal optics. The interferometer provides optical coherence tomography (OCT) of the dimension of the optical thickness (=n × t) along the optical axis, while the confocal optics gives us another type of reflection tomography, having the thickness dimension of nearly t/n along the optical axis. This sort of tomography can be called confocal reflection tomography (CRT) and has not yet been demonstrated, to our knowledge. Simple image processing of OCT and CRT results in the desired reflection tomographic image, showing two-dimensional refractive index distribution along the geometrical thickness.

Observation of the Sagnac effect in a ring resonant interferometer with a low-coherence light source

A fibre-optic resonant ring interferometer with a low-coherent light source was investigated experimentally. The feasibility of measuring the parameters of ring cavities characterised by very narrow lines (of the order of tens of kilohertz) was demonstrated by using a broad-band light source and a retroreflecting Doppler mirror. The Sagnac effect was first observed in a ring resonant interferometer with a low-coherence light source. Modulation and compensation of the phase nonrecriprocity in a low-coherence resonant interferometer with the aid of an optical frequency shifter located outside a sensing fibre loop were observed experimentally.

Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope

An improved system for the separate measurement of the refractive index and the geometrical thickness that constitutes a hybrid configuration of a confocal microscope and a wavelength-scanning heterodyne interferometer with a laser diode is presented. The optical path difference can be measured in less than 1 s, which is 10 times quicker than with the low-coherence interferometry previously used, and with a resolution of 10 microm with a fixed reference mirror. Separate measurement of the refractive index and the geometrical thickness of glass plates was demonstrated by use of the arrangement in place of the low-coherence interferometer used previously.

Differential phase contrast in optical coherence tomography

We report on a modification of optical coherence tomography (OCT) that allows one to measure small phase differences between beams traversing adjacent areas of a specimen. The sample beam of a polarization-sensitive low-coherence interferometer is split by a Wollaston prism into two components that traverse the object along closely spaced paths. After reflection at the various sample surfaces, the beams are recombined at the Wollaston prism. Any phase difference encountered between the two beams is converted into a change of polarization state of the recombined beam. This change is measured, and the resulting signals are converted to differential phase-contrast OCT images. The first images obtained from simple test objects allowed us to determine path-difference gradients with a resolution of the order of 5 x 10(-5) .

低コヒーレンス複合干渉計による水晶振動子の厚さ測定

A low coherence interferometry is a method for non-invasive optical ranging measurement of microstructures. A simultaneous measurement method of geometrical thickness and refractive index of quartz crystal with the low coherence interferometry has been proposed. However, it is hard to align a sample arm in the Michelson interferometer, because a beam of measurement arm must be incident on both sample and measurement mirror. Moreover, only the geometrical thickness and refractive index at the edge of sample can be measured. In this study, a novel configuration of low coherence interferometer is proposed in order to solve these problems. This system utilizes double Michelson interferometers. The interferometer consists of two reference mirrors which are used for scanning an optical path length and for determining a reference point. Both distributions of geometrical thickness and refractive index with this method can be measured. An experimental verification of our method is demonstrated by the use of microscope glass cover-slip and quartz crystal as samples. It was found that the measurement values of samples were in good agreement with the thickness measured by a dial gauge and the refractive index cited from the literature.

Resonance ring interferometry with incoherent light

A new method of measuring the phase nonreciprocity in a passive ring resonator using a light source of low coherence is described. The method provides effective suppression of noise from the backscattering of light in the ring resonator and insensitivity of the interferometer to excursions of the resonance frequencies of the resonator due to reciprocal effects (e.g., thermal expansion) and also permits modulation and compensation of the phase nonreciprocity by using a device outside the resonator to shift the frequency of the light. One version of a low-coherent resonance ring interferometer is examined, viz., a two-transit asymmetric interferometer with a rotating mirror.

Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry

We propose and demonstrate a novel technique for simultaneous measurement of the phase index, n(p) , the group index, n(g) , and the thickness, t , of transparent plates by use of a low-coherence interferometer. The output light from a superluminescent diode is focused upon the front plane of a transparent plate that is used as the sample. The sample stage is subsequently moved until the light is focused upon the rear plane of the plate. Measurement of the stage movement distance and the corresponding optical path difference allows us to determine both n(p) and n(g) . By placing the sample between two glass plates, we measured n(p) , n(g) , and t simultaneously, with an error of 0.3% or less, for nearly 1-mm-thick transparent plates, including glass and electro-optic crystals.

Low-coherence fibre heterodyne interferometer for both dc and high-frequency vibration measurements in the inner ear

Low-coherence fibre heterodyne interferometer for both dc and high-frequency vibration measurements in the inner ear

Low-coherence fibre heterodyne interferometer for both dc and high-frequency vibration measurements in the inner ear

A coherence encoded heterodyne interferometer with a fibre-optic sensor head of 1.8mm diameter designed to detect both high-frequency vibrations as well as low-frequency non-harmonic phase shifts in the inner ear is presented. The light source was a laser diode with a multimode spectrum of width 4.6nm. In order to achieve low sensitivity to spurious phase drifts, a coherence selective configuration was used, comprising an entrance Mach–Zehnder interferometer, so that object and reference light travel the same path in the fibre. Phase measurements yielded a square root of the Allan variance of [sgrave] z = 0.26 Å for an integration time of 0.1 s and [sgrave] z = 3.6 Å for an integration time of 3.2s. A phase measurement, at an object of 1.18 × 10−4 reflectivity, showed a rms resolution of 0.46° over a measurement duration of 10s, corresponding to a distance resolution of 5.2 Å.

Analysis of Multiple Layers of Transparent Objects Using a Confocal Microscope with Low-Coherence Interferometer.

In industrial applications, thickness and refractive index measurements of transparent plates and films are very important for quality control. For these purposes, several methods using lightwaves are available for noncontact and nondestructive measurement. However, because the refractive index and geometrical thickness are always correlated to each other, the separation of these two quantities is required for accurate inspection. In this review, we explain the principle and the apparatus for separate measurement of the refractive index and the geometrical thickness applicable to multiple layers. Several applications of this method are also described.