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It is known that the periodic error of heterodyne interferometers limits the accuracy of measurement to nanometre order. It is mainly derived from frequency mixing in the interferometer optics and this can be resolved using the configuration with two spatially separated beams. However, there remains a periodic error associated with parasitic reflections. Recently, we have developed a differential single-path heterodyne interferometer with two spatially separated beams, which was constructed within a single small quasi-cubic optical unit to minimize the parasitic reflections. In this work, the residual periodic error of this interferometer was evaluated with two evaluation methods, ‘the amplitude method’ and ‘the subtraction method’, and their results were compared. By applying uncertainty estimation procedures to the results, these two methods were shown to be highly consistent, confirming the reliability of our evaluation results. The error in λ/2 period of this interferometer was 7.6 pm.

A signal-processing method is proposed in the fully interferometric three-dimensional (3D) imaging spectrometry. This processing computes a 3D interferogram, in which recorded fringe patterns do not directly reflect wavefront forms propagated from a polychromatic light source under measurement. This paper presents a procedure for signal processing including a synthesis of the 3D interferogram and retrieval of a set of spectral components of 3D images. We demonstrate retrieving 3D images for spectral components of two planar light sources by means of the proposed method. The procedure to synthesize the 3D interferogram in this method suggests the possibility of direct measurement of the 3D interferogram.

The refractive index of air is accurately measured using a vacuum cell and a tandem low-coherence interferometer with a communication optical fiber of 30 km length with standard uncertainties of 0.20 ppm for the phase refractive index and 0.29 ppm for the group refractive index. Experimental results are compared with the value calculated from the equation for the refractive index of air using data obtained from measurements of the surrounding air, with a standard uncertainty of 0.22 ppm, and the difference between the average values is within 0.1 ppm. This method is applicable to the in situ high-precision measurement of optical length.

The group refractive index of BK-7 glass material is accurately measured using a tandem low-coherence interferometer, which is composed of a Mychelson interferometer and a Fizeau interferometer, within a combined standard uncertainty of 8.4 ppm. The experimental results are compared with the value calculated from the conventional data base on the phase refractive index, within a difference of about 4.7 ppm. This new method is applicable to in situ measurement due to the principle of its common optical path.

A new remote-measurement technique of length is developed, in which a low-coherence tandem interferometer and a single-mode optical fiber are used. The optical path difference provided in the first low-coherence interferometer, which corresponds to the length being measured, is transmitted through the optical fiber to the second low-coherence interferometer. Interference fringes are generated when the optical path difference in the second interferometer compensates that of the first interferometer. End standards up to 10 mm have been calibrated remotely through the single-mode optical fiber of 10 m length with a standard deviation of 0.14 μm.

A prism-pair interferometer for a spectrum lamp was developed for precise measurement of the refractive index of a prism of optical glass. Previously we reported the prism-pair interferometer with a He-Ne laser light source, resulting in a measurement uncertainty of 1.1×10⁻⁶. However, most of the refractive-index values managed by optical glass manufacturers are conventionally measured with spectrum lamps. We have optimized the prism-pair interferometer for spectrum lamps and implemented a signal-processing technique from Fourier-transform spectroscopy. When the refractive index is measured, the wavelength of the spectrum lamp is simultaneously calibrated by part of the interferometer, so that the resulting refractive index is traceable to a national standard of length. The combined standard uncertainty for a refractive index measured with the e-line (546 nm) of a Hg lamp is 6.9×10⁻⁶.

We developed a white-light interferometer that uses pseudo random-modulation for high-sensitivity, high-selectivity measurements of the surface profile of three-dimensional objects. The pseudo random-modulation is achieved by using a multi-segment mirror, where each segment has a different height in a maximum shift-register sequence (M-sequence). Preliminary experiments, where the white-light source was a halogen lamp and the test object was a plane mirror, show that our M-sequence modulated white-light interferometer (MMWI) had a four-time improvement in the signal-to-noise (SNR) ratio compared with that of a conventional interferometer.

Editors:Prathan Buranasiri,Sarun Sumriddetchkajorn, We have studied a method to obtain both three-dimensional (3-D) spatial information and spectral information of a usual polychromatic object by a fully passive interferometric technique that is strongly coupled with digital signal processing. Our method can be used for a vast range of wavelengths, because no special imaging devices, such as lenses, are required. In addition, coherent light sources are not necessary. A hyperbolic-type volume interferogram is one type of the volume interferogram, which is used for retrieve the object information, and an interferometer to measure directly this volume interferogram has been introduced. This paper introduces a method to measure the hyperbolic-type volume interferogram with high sensitivity in fully interferometric 3-D imaging spectrometry. This is accomplished by coupling of interferometer to measure directly the hyperbolic-type volume interferogram and heterodyne detection system for broadband light. We also report a preliminary experimental result based on the interferometer to measure directly the hyperbolic-type volume interferogram.

We propose a variable-path interferometric technique for the measurement of the absolute refractive index of optical glasses. We use two interferometers to decide the ratio between changes in the optical path in a prism-shaped sample glass and in air resulting from displacement of the sample. The method allows precise measurements to be made without prior knowledge of the properties of the sample. The combined standard uncertainty of the proposed method is 1.6x10(-6).

For remote and in-situ calibration of translation stage, system comparing optical-path-differences of two distantly-located low-coherence-interferometers through a single-mode-optical-fiber has been developed. Results of 52 nm-deviation and 30 nm-standard deviation for 39 mm-displacement is achieved.

Practical lengths are remotely measured by excess fraction method using a tandem low-coherence interferometer through optical fiber networks. Interference fringes of high S/N are generated when the path difference between two interferometers is equal.

Deep, stable starlight suppression is needed for the direct interferometric detection of Earth-like planets and requires careful control of the intensity and phase of the beams that are being combined. We have developed a novel compensator for the Terrestrial Planet Finder Interferometer based on a deformable mirror to correct the intensity and phase at each wavelength across the bandwidth of 8 to 12 microns wavelength. This paper will discuss the results of using the adaptive nuller to achieve deep broadband nulling in the mid-IR.

Technique of transferring length-information between two distantly-located low-coherence-interferometers through a single-mode-optical-fiber for remote and in-situ calibration of linear scale is developed. Results of 200 nm-deviation and 100 nm-standard deviation for 50 mm-length is preliminary achieved.

Deep, stable starlight nulls are needed for the direct detection of Earth-like planets and require careful control of the intensity and phase of the beams that are being combined. We have tested a novel compensator based on a deformable mirror to correct the intensity and phase at each wavelength across the bandwidth of 8 to 12 microns wavelength. This paper will cover the results of the adaptive nuller tests performed in the mid-IR.

Deep, stable starlight nulls are needed for the direct detection of Earth-like planets and require careful control of the intensity and phases of the beams that are being combined. We are testing a novel compensator based on a deformable mirror to correct the intensity and phase at each wavelength and polarization across the nulling bandwidth. We have successfully demonstrated intensity and phase control using a deformable mirror across a 100nm wide band in the near-IR, and are in the process of conducting experiments in the mid-IR wavelengths. This paper covers the current results and in the mid-IR.

A technique for the group refractive index dispersion measurement of transparent materials using a low-coherence tandem interferometer without knowledge of the sample thickness is proposed. The experimental result of BK7 show an accuracy of 10-5.

Deep, stable nulling of starlight requires careful control of the amplitudes and phases of the beams that are being combined. The detection of earth-like planets using the interferometer architectures currently being considered require that the electric field amplitudes are balanced at the level of ~ 0.1% and the phases are controlled at the level of 1 mrad (corresponding to ~ 1.5 nm for a wavelength of 10 microns). These conditions must be met simultaneously at all wavelengths across the science band and for both polarization states, imposing unrealistic tolerances on the symmetry between the optical beamtrains. Lay et. al. proposed the concept of a compensator that is inserted into the beamtrain, which can adaptively correct for the mismatches across the spectrum enabling deep nulls with realistic, imperfect optics. This proposed design uses a deformable mirror to adjust the amplitude and phase of the electric field that couples into the single-mode spatial filter. We have demonstrated amplitude and phase control at a single wavelength in the near-IR. We are preparing to demonstrate control with our deformable mirror actuator in the near-IR and in parallel are preparing a demonstration in the mid-IR where the compensator will be required to operate.

A low-coherence tandem interferometer with a single-mode optical fiber is developed for remote-measurement of length. The optical path difference provided in the first low-coherence interferometer is transmitted through the optical fiber to the second low-coherence interferometer. Low-coherence interference fringes are generated when the optical path difference in the second interferometer, which correspond to the length being measured, compensates that of the first interferometer. A gauge block of 50 mm long has been calibrated remotely through the single-mode optical fiber of 3 km length with a stnadard deviation of 0.12 μm.

A new remote-measurement technique of length is developed, by using a low-coherence tandem interferometer and a single-mode optical fiber. The optical path length with a gauge block in the first low-coherence interferometer is transmitted through the optical fiber to the second interferometer. And then the interference fringes containing the length information are generated and detected with high accuracy.

A Novel setup for two-dimensional (2-D) parallel measurements of low-coherence heterodyne signal by using a tandem interferometer and a 2-D sensor has been developed. Generally speaking, it is difficult to obtain heterodyne signals whose frequencies are much higher than the frame rate of the coventional 2-D sensor. A mode-locked femtosecond laser (MLFL) is used as a light source.

A new low-coherence interferometric technique is proposed for measuring the group refractive indices of dispersive samples with high accuracy. A tandem configuration of interferometers is used to compensate for the asymmetrical distortion of interferograms that results from the broad spectrum of the light source. The group refractive index can be measured without knowledge of the geometrical thickness of the sample under test. The proposed technique can successfully measure even a thick sample. Computer calculations have shown the effectiveness of the proposed technique, which was verified by preliminary experiments; the difference between the experimental result and the catalog data was 7 x 10(-4).

Two types of heterodyne broad-spectrum interferometers for highly-sensitive measurements are described. One uses two acoustooptic modulators and the other a diffraction grating to provide the optical frequency shift of a broad spectrum of light. The principle and some experimental results arc shown.

We have developed a gauge block measurement system that uses three frequency-stabilized lasers. The stabilized lasersare as follows: an 12-stabilized offset locked He-Ne laser (633 nm), an 12-stabilized Nd:YAG laser (532 nm), and a Rb-stabilized diode laser (780 nm). The 12-stabilized offset locked He-Ne laser is commercially available (NihonkagakuEngineering Co., Ltd.) and its relative wavelength uncertainty is 2.5 X 10' ' . An 12-stabilized Nd:YAG laser and a Rb-stabilized diode laser was developed in our institute and their relative wavelength uncertainties are 5 X 1 O12 and 1 X 1 O, respectively. In the measurement system, laser beams were introduced to the interferometer using an optical multimodefiber. An interferometric fringe pattern was taken using a CCD camera and the excess fraction parts were calculated from the fringe pattern using the Fourier transform method. The excess fraction part obtained from the Rb-stabilized semiconductor laser was used only to determine the integer part of the fringe order, because the accuracy and stability ofthe wavelength were not sufficient for the long gauge block measurements. This interferometer can measure gauge blocksofup to 1000 mm long and the standard uncertainty ofthe interferometer is about 75

The low-coherence interferometric technique is proposed for the in-situ measurement of the refractive index of dispersive samples with high accuracy. A tandem configuration of a Michelson interferometer and a triangular interferometer is used to compensate for the chirping effect which results from the broad spectrum of the light source. Thick samples can be successfully measured with the low- coherence interferometer, therefore the relative accuracy of the refractive index can be improved.

Heterodyne white-light interferometer that uses an optical grating to shift the optical frequency of the white light is proposed. By moving the optical grating, the diffracted lights undergo the frequency shift. The dependency of diffraction angle on wavelength can be resolved by using a spherical mirror, and then heterodyne detection of white-light can be realized with the combination of the optical grating and the spherical mirrors. In practical uses, a tandem-configuration interferometer is useful. The principle was demonstrated and the effect was confirmed experimentally for the first time The surface profile of a step-like object was measured. The signal-to-noise ratio of heterodyne signal is increased by thousand times from that of homodyne signal.

A novel low-coherence interferometer has been developed, based on the heterodyne technique for highly accurate and sensitive positioning of a three-dimensional (3-D) object, which uses two acousto-optic modulators (AOM's) and two spherical reflecting mirrors in a Michelson interferometer. By using this technique in a tandem interferometer, the profiles of diffusing and mirror-likes surfaces of the 3-D objects are measured with a high accuracy of 50 nm from the heterodyne signals of 200 kHz.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The results of the APMP key comparison on calibration of gauge blocks by interferometry (APMP.L-K1.1) are reported. The comparison was planned to follow up the previous comparison APMP.L-K1. The comparison involved the measurement, by seven participating institutes, of ten steel gauge blocks ranging from 0.5 mm to 100 mm in length using techniques based on interferometry. The results are analyzed using En values with weighted mean values as the reference values. For calculating the reference values some measurement results had to be excluded by application of the En-criterion. Investigations of the reasons for the deviations have already been started by the respective institutes. Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCL, according to the provisions of the CIPM Mutual Recognition Arrangement (MRA).

A bilateral comparison of refractive index measurements between the National Metrology Institute of Japan (NMIJ) and the Istituto Nazionale di Ricerca Metrologica (INRiM) was carried out in 2008. Each laboratory developed a measurement system based on different principles. NMIJ's system was based on the interferometric technique and INRiM's system was based on a modified method of the traditional refractive technique. A comparison using a prism-shaped glass made of OHARA BSL7Y was carried out in order to evaluate the newly developed methods and confirm the consistency of the results. The details of the comparison artefacts, measurement conditions and uncertainty factors and their degrees of freedom of each laboratory are described here. The measurement results for the glass at 633 nm at 20 °C and 23 °C are within each laboratory's claimed expanded uncertainty (coverage factor k = 2) which was of the order of 10−6. The agreement between the two different measurement approaches shows that both systems can be used to obtain accurate measurements.

A prism-pair interferometer comprising two homodyne interferometers with a common light source was developed for high-precision measurements of the refractive index of optical glasses with an uncertainty of the order of 10(-6). The two interferometers measure changes in the optical path length in the glass sample and in air, respectively. Uncertainties in the absolute wavelength of the common light source are cancelled out by calculating a ratio between the results from the interferometers. Uncertainties in phase measurement are suppressed by a quadrature detection system. The combined standard uncertainty of the developed system is evaluated as 1.1×10(-6).

A technique for the measurement of the group refractive index wavelength dependence of optical materials using a low-coherence tandem interferometer and a spectrometer is proposed. Four channeled spectra resulting from interferences of light beams from different pairs of optical paths are used for the calculation of optical path differences. The group refractive index wavelength dependence is calculated from these optical path differences generated from the sample under measurement. No a priori information of the geometric thickness of a sample is required. The wavelength dependence of the group refractive index of the samples BK7 parallel plate of 5.200 and 10.025 mm from 675 to 850 nm is experimentally measured with an accuracy of the order of 10(-5) and a repeatability of the order of 10(-9).

The results of the APMP key comparison on calibration of gauge blocks by interferometry (APMP.L-K1) are reported. The comparison involved the measurement, by ten participating institutes, of eight steel gauge blocks and ten ceramic gauge blocks ranging from 0.5 mm to 100 mm in length using techniques based on interferometry. The results are analysed using En values with weighted mean values as the reference values. Some measurement results had to be excluded by application of the En-criterion for the steel and ceramic gauges. Investigations of the reasons for the deviations have already been started by the respective institutes, including follow-up gauge block comparison, APMP.L-K1.1 with the same pilot laboratory as APMP.L-K1. Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCL, according to the provisions of the CIPM Mutual Recognition Arrangement (MRA).

The length information of end standards is transmitted through a 103-km-long optical fiber in the experimental room. The system uses a low-coherence tandem interferometer and a single-mode optical fiber in the wavelength range of 1500 nm. Interference fringes are generated when the optical path difference of the first interferometer compensates that of the second interferometer. The end standards of up to 50 mm in length have been calibrated remotely with a standard deviation of about 34 nm.

The information of practical length standards is transmitted through 47-km-long optical fiber network between Tsuchiura city and Kashiwa city in Japan. Interference fringes are generated when the optical path difference of a low-coherence interferometer in the Tsuchiura relay station compensates that in the Kashiwa station. End standards of 100 mm length in the Kashiwa station are calibrated remotely within a standard deviation of 118 nm with the reference standards in the Tsuchiura station.

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.

A tandem white-light interferometer has been developed, based on the heterodyne technique, for highly accurate and sensitive surface profiling of a three-dimensional (3-D) object. Two acousto-optic modulators (AOMs) and two spherical reflecting mirrors are used in a Michelson interferometer to provide the optical frequency shift for white light. By using this technique in the tandem interferometer, the profiles of mirrorlike and diffusing surfaces of 3-D objects are measured with heterodyne signals of 200 kHz. The optical path difference of the interferometer can be stabilized by simultaneously using coherent and incoherent light. The experimental results show a 27-fold improvement in the stability of the interferometer and the possibility of achieving high accuracy of several tens of nanometers.

We developed a prism-pair interferometer which measures precise refractive index of glasses while ensuring the SI-traceability of a lamp wavelength. The measurement result agrees with manufacture's value within 1×10−5.

Uncertainty of refractive-index measurements of optical-glasses are further reduced in a prism-pair interferometer by a quadrature-detection and a shared light-source. Uncertainty of 1.50 × 10−6 is confirmed by an interlaboratory comparison based on other methods.