White-light interferometry with an extended zoom range

Abstract

Optical sensors are designed usually for microscopic or for macroscopic applications. White-light interferometry on the other hand enables high-resolution measurements to be made for small and for large fields. In this paper we present a flexible set-up that can be used for both microscopic and macroscopic applications. The magnification can easily be changed in seconds and the zoom range is greater than 160. This set-up is especially designed for the investigation of optically rough surfaces. A novel filtering technique enables fast and accurate data acquisition and evaluation with standard hardware components. Further we demonstrate results of roughness measurements in different scales.     

White-light interferometry with polarization phase-shifter at the input of the interferometer

Abstract

In white-light interferometry the surface profile is determined by measuring the fringe contrast function of the white-light interferogram. One of the techniques proposed for the measurement of the fringe contrast function is the use of the phase shifting technique with the help of an achromatic phaseshifter. The available phase-shifters employ a rotating polarization component at the output end of the interferometer. Using a rotating polarization component at the input end, rather than at the output end, has certain advantages. In this paper we investigate a rotating half-wave plate phase-shifter at the input end for its applications to a white-light interferometer.     

White-light interferometry on rough surfaces--measurement uncertainty caused by noise

White-light interferometry on rough surfaces is an optical method for the measurement of the geometrical form of objects. The longitudinal coordinate of the measured surface is obtained from the measured interferogram by means of an evaluation method. However, the longitudinal coordinate cannot be determined completely accurately because the interferogram is affected by noise. We calculate the lower limit of the longitudinal measurement uncertainty caused by noise by use of the Cramer-Rao inequality. Additionally, we calculate the lower limit of the longitudinal measurement uncertainty caused by shot noise only.     

White-light interferometry on rough surfaces--measurement uncertainty caused by surface roughness

White-light interferometry measuring an optically rough surface commonly does not resolve the lateral structure of the surface. This means that there are height differences within one resolution cell that exceed one-fourth of the wavelength of the light used. Thus the following questions arise: Which height is measured by white-light interferometry? How does the surface roughness affect the measurement uncertainty? The goal of the presented paper is to answer these questions by means of numerical simulations. Before the aforementioned questions can be answered, the distribution of the intensity of individual speckles, the influence of surface roughness, and the spectral width of the light source used are discussed.     

White-light interferometry using a channeled spectrum. I. General models and fringe estimation algorithms

Astrometric measurements using stellar interferometry rely on the precise measurement of the central white-light fringe to accurately obtain the optical path-length difference of incoming starlight to the two arms of the interferometer. Because of dispersion in the optical system the optical path-length difference is a function of the wavelength of the light and extracting the proper astrometric signatures requires accommodating these effects. One standard approach to stellar interferometry uses a channeled spectrum to determine phases at a number of different wavelengths that are then converted to the path-length delay. Because of throughput considerations these channels are made sufficiently broad so that monochromatic models are inadequate for retrieving the phase/delay information. The presence of dispersion makes the polychromatic modeling problem for phase estimation even more difficult because of its effect on the complex visibility function. We introduce a class of models that rely on just a few spectral and dispersion parameters. A phase-shifting interferometry algorithm is derived that exploits the model structure. Numerical examples are given to illustrate the robustness and precision of the approach.     

White-light interferometry using a channeled spectrum. 2. Calibration methods, numerical and experimental results

In the companion paper, [Appl. Opt. 46, 5853 (2007)] a highly accurate white light interference model was developed from just a few key parameters characterized in terms of various moments of the source and instrument transmission function. We develop and implement the end-to-end process of calibrating these moment parameters together with the differential dispersion of the instrument and applying them to the algorithms developed in the companion paper. The calibration procedure developed herein is based on first obtaining the standard monochromatic parameters at the pixel level: wavenumber, phase, intensity, and visibility parameters via a nonlinear least-squares procedure that exploits the structure of the model. The pixel level parameters are then combined to obtain the required "global" moment and dispersion parameters. The process is applied to both simulated scenarios of astrometric observations and to data from the microarcsecond metrology testbed (MAM), an interferometer testbed that has played a prominent role in the development of this technology.     

White-light ellipsometer with geometric phase shifter

We describe a simple spectroscopic ellipsometer that uses a geometric phase shifter and a white-light source to generate a small number of phase-stepped intensities I(λ), which are recorded by a spectrometer. The ellipsometric angles ψ and Δ are easily calculated from these intensities at each wavelength simultaneously. We show that errors in Δ due to the nonideal behavior of the achromatic quarter-wave plate in the phase shifter can be made small by suitably adjusting the azimuth of the linearly polarized light incident on the sample. Two silicon dioxide films were measured with this instrument between 450 and 850?nm and yielded best fit film thicknesses of 1000.6±0.1 ? and 20.6±0.1 ?, in excellent agreement with those obtained using a commercial ellipsometer.     

Topological depolarization of laser radiation in multimodal step-index fibers with square cross section

Translated from Izmeritel'naya Tekhnika, No. 10, pp. 22–23, October, 1992.     

White-light implementation of the Wigner-distribution function with an achromatic processor

A temporally incoherent optical processor that combines diffractive and refractive components is proposed for performing two different operations simultaneously: an achromatic image along an axis and an achromatic one-dimensional Fourier transformation along the orthogonal axis. These properties are properly employed to achieve the achromatic white-light display of the Wigner-distribution function associated with a one-dimensional real signal, with high redundancy and variable scale.     

Autodyne interferometry for range-finding under laser radiation wavelength modulation

The results of solution of the inverse problem of determining the distance to the reflector in the case of current modulation of the laser radiation wavelength are presented. It is shown that current modulation of the autodyne signal amplitude can reduce the inverse problem of finding the distance to the reflector to a state of affairs characteristic only of phase modulation. The technique that we propose provides a higher range-finding accuracy than does direct analysis of the autodyne signal.     

白光干涉测量系统的测量不确定度评定

白光干涉测量系统(white-light interference system,WLIS)广泛用于微纳米表面形貌的精密测量,其测量不确定度评定是研究白光干涉测量系统计量特性的一项重要工作.基于微纳米线间隔和台阶,建立了 WLIS测量表面形貌时的测量模型,明确了测量不确定度来源;以5000 nm的线间隔和180 nm的...     

White-light optical implementation of the fractional fourier transform with adjustable order control

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.     

白光LED用光转换材料的研究

白光LED是新型的固体照明光源,具有耗电量小、寿命长、环保、响应速度快等优点.主要介绍了与白光LED相匹配的光转换材料的种类及每种光转换材料的研究进展,并比较了其优缺点.单一基质白光荧光粉因颜色稳定、色彩还原性好,成为白光LED用光转换材料的研究热点,此外由于近紫外LED芯片的研究也比较活跃,所以目前对于单一基质白光荧光粉的研究多是基于近紫外芯片激发.随着研究的深入,近紫外LED与单一基质白光荧光粉相匹配实现白光发射有望成为白光LED产业化的主体.     

Optical interferometry with pulsed fields

The problem of predicting and interpreting the results of interferometric optical experiments involving pulse trains is addressed. Specifically, a cyclostationary field arising from the modulation of a stationary, stochastic source is considered in the classical Young's experiment. It is shown that the effects of modulation may be identical to unrelated statistical interference effects.     

White-light interferometer with dispersion: an accurate fiber-optic sensor for the measurement of distance

We present a fiber-optical sensor for distance measurement of smooth and rough surfaces that is based on white-light interferometry; the sensor measures the distance from the sample surface to the sensor head. Because white light is used, the measurement is absolute. The measurement uncertainty depends not on the aperture of the optical system but only on the properties of the rough surface and is commonly approximately 1 microm. The measurement range is approximately 1 mm. The sensor includes no mechanical moving parts; mechanical movement is replaced by the spectral decomposition of light at the interferometer output. The absence of mechanical moving parts enables a high measuring rate to be reached.     

Holographic interferometry with multiple wavelengths

One of the unsolved problems in the well-established field of holographic interferometry is identification of zeroth-order fringes in cases in which the locations of zero displacement are unknown. We offer a simple solution: By making the double-exposure hologram of a white object in full color by using three or more wavelengths, the zeroth-order fringes will be indentified by their white color.     

White-light Phase-stepping Interferometry: Measurement of the Fractional Interference Order

Abstract

Intensity data obtained with white light and an achromatic phase shifter in an interferometric surface profiler can be used to locate the peak of the visibility curve as the test surface is moved in steps along the height axis. We show that the same intensity data can also be used to find the fractional interference order at each point on the test surface, at the position of the test surface nearest to the visibility peak and, hence, its height at that point, with a high degree of accuracy.     

Error analysis of null ellipsometry with depolarization

Null ellipsometry is analyzed for components with depolarizations for unpolarized incident light. Serious imperfections include sample depolarization D < 0.2, misalignment (deltaC < 2 degrees ) and off-quarter-wave retardance (deltatau < 5 degrees ) of the compensator. The four-zone null positions are derived analytically to the second order of serious imperfections and are also simulated based on Mueller matrices with depolarization. Errors of all four-zone nulls increase with increasing D. Depolarizations of all components except the analyzer cause errors to the nulls. The errors associated with D always couple with the second order of deltaC and deltatau and are enhanced by csc(2) 2psi. These divergent errors limit the applicable region of null ellipsometry where the errors in psi and D are within 0.1 degrees , and the simulation agrees well with the analytic solutions.     

White-light performance of a polarization-independent liquid-crystal phase modulator

The broadband performance of a polarization-insensitive liquid-crystal phase modulator is analyzed, and its effect on an adaptive optics system is quantified.