Spectrally resolved white-light interferometry for measurement of ocular dispersion.

Spectrally resolved white-light interferometry was used to measure the wavelength dependence of refractive index (i.e., dispersion) for various ocular components. Verification of the technique's efficacy was substantiated by accurate measurement of the dispersive properties of water and fused silica, which have both been well-characterized in the past by single-wavelength measurement of the refractive index. The dispersion of bovine and rabbit aqueous and vitreous humors was measured from 400 to 1100 nm. In addition, the dispersion was measured from 400 to 700 nm for aqueous and vitreous humors extracted from goat and rhesus monkey eyes. An unsuccessful attempt was also made to use the technique for dispersion measurement of bovine cornea and lens. The principles of white-light interferometry, including image analysis, measurement accuracy, and limitations of the technique, are discussed. In addition, alternate techniques and previous measurements of ocular dispersion are reviewed.     

Direct measurement of refractive-index dispersion of transparent media by white-light interferometry

We report on a technique for measuring the refractive indices of nonabsorbing media over a broad spectral range from 0.5 to 5 microm. White-light interferometry based on a double-interferometer system consisting of a fixed Mach-Zehnder interferometer and a Fourier-transform spectrometer is used for direct measurement of the absolute rotation-dependent phase shift induced by an optical element. Refractive index n(lambda) over the whole investigated spectral range is thus obtained directly to an accuracy of 10(-4) without the need for any specific assumption about dispersion. Results for synthetic fused silica are presented and discussed.     

Group velocity dispersion of dyes in solution measured with white-light interferometry

The group velocity dispersion (GVD) coefficient of four different dyes in solution is measured as a function of wavelength and concentration using a white-light Michelson interferometer. We find that the wavelength dependence of the GVD can be considerably different at wavelengths above and below the absorption resonance in a dye. Above the absorption resonance, the dye molecules can make a strong, wavelength-dependent contribution to the GVD of the solution. Below the absorption resonance, the dye molecules tend to contribute negligibly to the GVD of the solution. We find that the contribution of the dye molecules to the GVD can be modeled quite accurately using a simple Lorentz model with parameters set using the measured linear absorption properties of the dye.     

Measurement of the influence of dispersion on white-light interferometry

White-light interferometry is a well-established method for measuring the height profiles of samples with rough as well as with smooth surfaces. Because white-light interferometry uses broadband light sources, the problem of dispersion arises. Because the optical paths in the two interferometer arms cannot be balanced for all wavelengths, the white-light correlogram is distorted, which interferes with its evaluation. We investigate the influence of setup parameters on the shape of the correlogram. Calculated values are compared with experimental results.     

High-precision shape measurement by white-light interferometry with real-time scanner error correction

White-light interferometric techniques allow high-precision shape measurement of objects with discontinuous structures by detecting the peak of the coherence envelope. These techniques assume a specific change in the optical path difference (OPD) between the interfering beams; however, the scanning device effecting that change often introduces OPD errors that are carried over to the measurements. We present a technique for measuring OPD changes from the collected interference fringes during each measurement. Information about the scan is directly fed into the algorithm, which compensates for the errors, resulting in improved measurement accuracy. The method corrects not only the scanner errors but also slowly varying vibrations. In addition, this technique can be easily adapted to any existing low-coherence interferometer because no large data storage or postprocessing is required.     

Theoretical measurement uncertainty of white-light interferometry on rough surfaces

A great advantage of the white-light interferometry is that it can be used for profile objects with a rough surface. A speckle pattern that arises in the image plane allows one to observethe interference; however, this pattern is also the source of the measurement uncertainty. We derive the theoretical limits of the longitudinal uncertainty by virtue of the first-order statistics of thespeckle pattern. It is shown that this uncertainty depends on the surface roughness of the measured object only; it does not depend on the setup parameters.     

Rotation angle measurement based on white-light interferometry with a standard optical flat

We propose a simple white-light interferometric method of measuring a one-dimensional rotation angle with use of an optical plane parallel plate of standard refractive index. The phase change of the interference pattern of the interferometer during the rotation of the flat plate of known refractive index and thickness placed in one of the interferometer's arms is used for determination of the rotation angle. This method has been demonstrated for an accurate angle measurement over the angle range from 0° to 40° within a maximum uncertainty of 0.057°.     

Single-shot two-dimensional surface measurement based on spectrally resolved white-light interferometry

By analyzing the spectral domain's phase information, one can use spectrally resolved white-light interferometry (SRWLI) to obtain the profile with a single frame of an interferogram. We present here a two-dimensional (2D) SRWLI method that can be applied to measure narrow rectangle areas. A frequency comb is produced by using a Fabry-Perot (F-P) etalon to filter the broadband source. With the filtered frequency comb illumination, the interference patterns under adjacent wavelengths would be separated by a little distance, which enables us to obtain a 2D profile with a small width. The experimental details of measurement on a step sample are discussed in this paper.     

Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry

White-light scanning interferometry is increasingly used for precision profile metrology of engineering surfaces, but its current applications are limited primarily to opaque surfaces with relatively simple optical reflection behavior. A new attempt is made to extend the interferometric method to the thickness-profile measurement of transparent thin-film layers. An extensive frequency-domain analysis of multiple reflection is performed to allow both the top and the bottom interfaces of a thin-film layer to be measured independently at the same time by the nonlinear least-squares technique. This rigorous approach provides not only point-by-point thickness probing but also complete volumetric film profiles digitized in three dimensions.     

Dispersion measurement of tapered air-silica microstructure fiber by white-light interferometry

Dispersion properties of novel, tapered, air-silica microstructure fibers are measured between 1.3 and 1.65 microm by white-light interferometry. Dispersion values (beta2) of -181 and -152 ps2/km were obtained for 2.2- and 3-microm core sizes, respectively, at lambda = 1.55 microm.     

Characterization of birefringence dispersion in polarization-maintaining fibers by use of white-light interferometry

A new method for measuring the birefringence dispersion in polarization-maintaining fibers (PMFs) with high sensitivity and accuracy is presented. The method employs white-light interferences between two orthogonally polarized modes of PMFs. The group birefringence of the fiber is calibrated first. Then the birefringence dispersion and its variation along different fiber sections are acquired by analyzing the broadening of interferograms at different fiber lengths. The main sources of error are investigated. Birefringence dispersions of two PANDA fibers at their operation wavelength are measured to be 0.011 ps/(km nm) and 0.018 ps/(km nm). A measurement repeatability of 0.001 ps/(km nm) is achieved.     

Chromium-doped forsterite: the influence of crystal characteristics on laser performance

A study of the dependence of the gain-switched laser operation of chromium forsterite on crystal parameters is presented. Results are reported for a wide range of chromium (IV) ion concentration: 0.02-0.12 at. % and 12-41 figure of merit, with emphasis on performance of the recently developed material with a dopant level of >0.10 at. %. Threshold and slope efficiency calculations are compared with measured performance for all crystals, with variation of pump polarization and output coupling. With 3% output coupling, the lowest threshold of 1.8 mJ, and highest slope efficiency of 13% were measured for a short, high-dopant-level crystal. With 33% output coupling a slope efficiency of 44% was measured for this crystal. Results demonstrate the considerable potential of short, high-dopant-level crystals for applications such as amplification, diode pumping, and narrow-bandwidth operation.     

Measuring intermodal dispersion in optical fibres using white-light spectral interferometry with the compensated michelson interferometer

Abstract

Employing a low-resolution miniature fibre-optic spectrometer, it is demonstrated that the spectral interference fringes are resolved at the output of a tandem configuration of the compensated (non-dispersive) Michelson interferometer and a two-mode optical fibre only in the vicinity of two different equalization wavelengths. Namely, the overall equalization wavelength at which the optical path difference (OPD) in the interferometer is the same as the group OPD between modes, and the fibre equalization wavelength at which the group OPD between modes is zero. Moreover it is shown that the OPD adjusted in the interferometer and measured as a function of the overall equalization wavelength gives directly the spectral dependence of the intermodal group OPD in an optical fibre. Thus the new technique of white-light spectral interferometry is used to measure intermodal dispersion in two different two-mode optical fibres in the spectral range approximately from 620 to 850 nm.     

Sensitivity analysis of thin-film thickness measurement by vertical scanning white-light interferometry

The spectral nonlinear phase method and the Fourier amplitude method have been applied to measure the thin-film thickness profile in vertical scanning white-light interferometry (VSWLI). However, both the methods have their disadvantages, and accordingly their applications are limited. In the paper we have investigated the dependence of the sensitivities of both the methods on the thin-film thickness and refractive index, the objective numerical aperture, and the incident light spectral range of VSWLI. The relation of the Fresnel reflection coefficients on the wavelength effect is also discussed. Some important research results reveal that the combination of both Fourier amplitude and nonlinear phase methods may provide a new approach to improve the VSWLI measurement sensitivity for thin-film thickness profile.     

Dispersion measurements of water with white-light interferometry

We measure the second- and third-order dispersion coefficients, d(2)k/domega(2) and d(3)k/domega(3), of water for wavelengths from 0.45 to 1.3 mum using a Michelson white-light interferometer. In this interval, the second-order dispersion ranges from 0.068 to -0.1 fs(2)/mum, and the third-order dispersion ranges from 0.048 to 1.18 fs(3)/mum. We observe an oscillation in d(2)k/domega(2) near 1.1 mum that is due to water absorption features near that wavelength. From the dispersion coefficients, derivatives of the index of refraction of water are calculated and compared with available equations. These measured values of d(2)n/dlambda(2) and d(3)n/dlambda(3) should be useful in the evaluation and improvement of existing equations for n(lambda) in water.     

Achromatic phase-shifting for white-light interferometry

The geometric (Pancharatnam) phase provides a method of introducing a variable phase shift that is almost independent of the wavelength and opens up new possibilities in broadband interferometry.     

Surface profile measurement in white-light scanning interferometry using a three-chip color CCD

White-light scanning interferometry (WLSI) is a useful technique to measure surface profile when a test object contains discontinuous structures or microstructures. A black and white CCD camera is usually utilized to capture interferograms, and a series of corresponding algorithms is used to achieve the profile measurement. However, the color information in the interferograms is lost. A novel profile measurement method that uses phase information in different color channels (red-green-blue) of an interferogram obtained using a three-chip color CCD in WLSI is proposed. The phase values are extracted by a windowed Fourier transform algorithm. Simulation and experimental results are presented to demonstrate the validity of the proposed method.     

Chromium-doped forsterite laser with 1.1 W of continuous-wave output power at room temperature

We demonstrate stable continuous-wave operation of a Cr:forsterite laser pumped by a cw Nd:YAG laser at 288 K. We use no choppers to limit the duty cycle of the cw system. The proper adjustment of the pump- and cavity-mode overlap based on the ABCD concept simulation eliminates the output power decrease at the high-level pump power. An output power of 1.1 W and slope efficiency of 26% are derived.     

Wavenumber scanning-based Fourier transform white-light interferometry

Fourier transform white-light interferometry recovers the optical path difference of an interferometer by measuring the phase change caused by scanning wavelength. However, the optical spectrum, obtained by wavelength scanning method (λ-method), contains a chirp in period. The chirp would induce deviation and decrease the measurement accuracy. An improved method, the wavenumber scanning method (k-method), is proposed and experimentally demonstrated, in which there is no chirp in the optical spectrum. The measurement results using the k-method and the λ-method are compared experimentally. The experimental results show that the standard deviation of the measurement results decreases from 0.015 to 0.004?μm, when an extrinsic Fabry-Perot interferometer with a cavity length of 387?μm is interrogated.     

白光频闪散斑干涉术的研究

在利用白光对振动物体进行测量时,由于白光的相干性较差,难以得到质量较好的图像,为了克服这一缺点,本文提出了一种用白光光源照明进行振动测量的新方法-白光频闪散斑干涉术.阐述了白光频闪散斑干涉术的基本原理,分析了提高图象质量的主要原因,采用了相干性较好的白光光源和合理的光路,使系统的时间相干性和空间相干性得到提高,从而提高了图像的质量.实验结果表明,该方法用于振动的测量,能给出物体在任一瞬时的振动信息,得到清晰的、高对比度的全场干涉条纹图,图像的质量得到大大提高.