White Light Interference Fringes Research Articles

Dimensional metrology of smooth micro structures utilizing the spatial modulation of white-light interference fringes

Dimensional metrology for micro structure plays an important role in addressing quality issues and observing the performance of micro-fabricated products. In white light interferometry, the proposed method is expected to measure three-dimensional topography through modulation depth in spatial frequency domain. A normalized modulation depth is first obtained in the xy plane (image plane) for each CCD image individually. After that, the modulation depth of each pixel is analyzed along the scanning direction (z-axis) to reshape the topography of micro samples. Owing to the characteristics of modulation depth in broadband light interferometry, the method could effectively suppress the negative influences caused by light fluctuations and external irradiance disturbance. Both theory and experiments are elaborated in detail to verify that the modulation depth-based method can greatly level up the stability and sensitivity with satisfied precision in the measurement system. This technique can achieve an improved robustness in a complex measurement environment with the potential to be applied in online topography measurement such as chemistry and medical domains.

A Novel White Light Interference Based AFM Head

A novel atomic force microscope (AFM) head based on white light interference (WLI) is developed for nanoscale surface measurement. In this head, instead of an optical beam deflection (OBD) technique for AFM probe position, WLI fringes on the surface of the probe cantilever are analyzed for probe position. The probe adjustment mechanism is designed, an algorithm based on wavelet transform and Hilbert transform is presented for accurate zero-order fringe positioning, and a calibration method is developed for the relationship between the position of the interference fringes on the surface of the probe cantilever and the vertical displacement of the probe. By these approaches, advantage of high vertical resolution of WLI is combined with that of high horizontal resolution of atomic force probe for nanometer resolution surface measurement. Experiments have been carried out to verify the feasibility and accuracy of the head for AFM measurement. And compared with a commercial AFM, 3-D measurement results of a standard grating prove that the measurement speed of proposed AFM head is 22% faster.

Effect of ocular transverse chromatic aberration on detection acuity for peripheral vision.

We examined the effect of transverse chromatic aberration (TCA) on detection acuity for white-light interference fringes seen in Maxwellian view at various orientations and locations in the visual field. A circular patch (3.5° diameter, 3.2 log Trolands) of nominally high-contrast fringes was produced on the retina by a commercial instrument (the Lotmar Visometer, Haag Streit) mounted on a gimbal for controlled positioning of the stimulus in the visual field from 0° to 35° eccentricity. Detection acuity for white light fringes for all meridians and eccentricities ≥15° was maximum when fringes were oriented parallel to the visual meridian line. This meridional effect disappeared when a narrow-band filter was used to eliminate TCA. The meridional effect also disappeared when the interferometric stimulator was displaced laterally to align the instrument with the eye's local achromatic axis. Modelling confirmed that TCA is the major factor responsible for white-light meridional bias, with minor contribution arising from higher-order monochromatic aberrations and neural factors.

White-light fringe detection based on a novel light source and colour CCD camera

We describe in this paper a pilot experiment of optimization of a white-light source for a low-coherence interferometry. The white-light source combines the light beams generated with colour LEDs. By modelling the white-light spectra, the contrast of a white-light interference fringe could be changed and set to the maximal value. The second part of this paper is a description of a white-light fringe analysis ensured with a low-cost colour CCD camera. The used detection technique employs a phase-crossing algorithm which identifies a zero optical path difference as the point where the phase difference between the red, green and blue parts of the white-light interference fringe becomes equal to zero. The optimized white-light source is designed to be a crucial part of an experimental setup for the surface diagnostics and automatic calibration of gauge blocks.

White-light channeled imaging polarimeter using broadband polarization gratings

A white-light snapshot channeled linear imaging (CLI) polarimeter is demonstrated by utilizing polarization gratings (PGs). The CLI polarimeter is capable of measuring the two-dimensional distribution of the linear Stokes polarization parameters by incorporating two identical PGs, in series, along the optical axis. In this configuration, the general optical shearing functionality of a uniaxial crystal-based Savart plate is realized. However, unlike a Savart plate, the diffractive nature of the PGs creates a linear dependence of the shear versus wavelength, thus providing broadband functionality. Consequently, by incorporating the PG-based Savart plate into a Savart plate channeled imaging polarimeter, white-light interference fringes can be generated. This enables polarimetric image data to be acquired at shorter exposure times in daylight conditions, making it more appealing over the quasi-monochromatic channeled imaging polarimeters previously described in the literature. Furthermore, the PG-based device offers significantly more compactness, field of view, optical simplicity, and vibration insensitivity than previously described white-light CLI polarimeters based on Sagnac interferometers. Included in this paper are theoretical descriptions of the linear (S(0), S(1), and S(2)) and complete (S(0), S(1), S(2), and S(3)) channeled Stokes imaging polarimeters. Additionally, descriptions of our calibration procedures and our experimental proof of concept CLI system are provided. These are followed by laboratory and outdoor polarimetric measurements of S(0), S(1), and S(2).

Double-Glazing Interferometry

This note describes how white light interference fringes can be seen by observing the Moon through a double-glazed window. White light interferometric fringes are normally observed only in a well-aligned interferometer whose optical path difference is less than the coherence length of the light source, which is approximately one micrometer for white light. Obtaining such fringes in a Michelson interferometer is not a trivial task.1 The interferometer is typically illuminated with a monochromatic source and the path length difference adjusted with a wedge angle between the interferometer mirrors so that five or six vertical fringes are visible, indicating nearly equal paths. Then the mirrors are adjusted until the fringes are almost perfectly straight. Finally we use a white light source and carefully scan through the approximately equal path range until five or six white light fringes are seen to sweep rapidly by.

Simple technique for the measurement of two-dimensional linear retardation distributions of wave plates with a phase-shifting Nomarski prism

What we believe to be a new technique for the measurement of two-dimensional retardation distributions of a wave plate (WP) is presented. Phase-shifting interferometry has been applied for determining the relative retardation distribution using a Nomarski prism (NP) as a phase shifter. Absolute retardation distribution is obtained by accurately determining the position of zero retardation in the interference field using white light interference fringes and adjusting the phase distribution with respect to the zero retardation position. The measured absolute retardation distribution of the NP is subtracted from that obtained for the combination of the WP and NP, to get the desired retardation distributions for the WP. The technique is suitable for the measurement of phase retardation of both single and multiple order WPs, as the actual phase retardation distributions are obtained. Results obtained for WPs are presented.

백색광주사간섭계에서 편광을 고려한 반사시 위상 변화에 대한 연구

백색광주사간섭계는 금속 물질의 반사시 발생하는 위상 변화에 의해 금속의 두께 측정에서 수십 나노 미터(nm)의 오차를 갖는다. 실제로 반도체 공정이나 초 정밀가공 부품에 많이 쓰이는 금, 은, 알루미늄, 크롬 등의 금속은 약 10∼30 nm의 측정 오차를 야기 시킨다. 본 논문에서는 수치 해석을 통해 백색광의 편광을 고려한 반사시 위상 변화에 의해서 간섭무늬의 두 정점, 위상 정점과 가시도 정점이 이동함을 보인다. 또한 백색광의 두 편광성분, 수직 편광성분과 수평 편광성분에 의해 재구성된 간섭 무늬식을 제안한다. The phase change due to the reflection from target surfaces in a white-light interferometer induces measurement errors when target surfaces are composed of dissimilar materials. We prove that this phase change on reflection as the polarization of the white-light changes causes a shift of both envelope peak position and fringe peak position of several tens of nanometers as the polarization of the white-light changes. In addition, we propose a new equation for white-light interference fringes depending on the polarization of the source.

A white-light trap for Bose–Einstein condensates

We propose a novel method for trapping Bose-condensed atoms using a white-light interference fringe. Confinement frequencies of tens of kHz can be achieved in conjunction with trap depths of only a few micro-K. We estimate that lifetimes on the order of 10 s can be achieved for small numbers of atoms. The tight confinement and shallow depth permit tunneling processes to be used for studying interaction effects and for applications in quantum information.

A white-light interferometer using a lamp source and heterodyne detection with acousto-optic modulators

A heterodyne technique for white-light interferometer with a lamp source, which uses two acousto-optic modulators, is developed for high-sensitivity detection of weak light. By using converging input beams input into a Michelson interferometer with spherical mirrors, the spectral dependence of the modulators is canceled, and the white-light heterodyne interference fringes are generated at 200 kHz. Using a tandem interferometer, the object surface which has a low surface reflectivity of less than 10 −4 was detected with a good signal-to-noise ratio.

On the formation of white-light interference fringes

We describe an experiment in which the white-light interference fringes appearing at the output of a Michelson interferometer are observed through a spectrograph. In this manner the relative positions of monochromatic interference fringes come into sight and it allows a better understanding of the formation of the white-light fringes. A simple model is described for determining the shape of the spectrally resolved white-light interference fringes. An expression for the relationship between the slope of the fringes and the arm length difference of the interferometer is derived and is demonstrated experimentally. In addition, an intuitive explanation based on this experiment is given for the washing out of the white-light fringes.

Application of multiple-beam white-light fringes for measuring the refraction and dispersion of mica

Multiple-beam white-light interference fringes are applied to measure the two refractive indices of a mica sample and their dispersion across the visible spectrum. In addition, the mica birefringence and its dispersion are measured. A mica sample of dimensions 2 x 5 mm 2 and an immersion liquid of nearly the same refractive index are used. Only a single shot interferogram is needed to measure all the aforementioned parameters. Cauchy's and a modified single-term Sellmeier dispersion formula are used for fitting the experimental data and extracting the parameters required.

The Geometric Phase: Interferometric Observations with White Light

Abstract Observations on white-light interference fringes show that the effects due to the introduction of a variable geometric phase, which is independent of the wavelength, differ significantly from those due to a change in the optical path difference.

Thermal window interferometer

Some double-glazed windows produce white-light interference fringes. How can they do that? Such fringes occur only when the superposed waves have an optical path difference of no more than a few wavelengths. This paper points out two different situations which allow multiple reflections, between and within the glass plates, to give the necessary small path difference. In one case the plates must be almost exactly the same thickness and in the other it is sufficient that one of the plates be of nearly uniform thickness.

Prism coupler jig: interference fringes enable observation of the coupling gap

A prism coupler jig is described which enables a coupling region to be quickly and easily found when the waveguide is a thin film on a microscope slide. Interference fringes formed on reflection allow observation of the air gap. Consideration is given to the formation of white light and quasi-monochromatic interference fringes. A suitable choice of the refractive index of the right-angle prism enables the m lines to be observed in a convenient observation space.

XXXI New contributions to interferometry. Part V.—New multiple beam white light interference fringes and their applications

XXXI New contributions to interferometry. Part V.—New multiple beam white light interference fringes and their applications

White-Light Interference Fringes with a Thick Glass Plate in One Path

In Part I of this paper [1] the writer developed a theory of the white-light fringes observed in the Michelson interferometer when a thick plate of glass, or other refractive substance, is placed in one of the paths. Part I treated of the axial beam, whose composition determines the color of the central spot in the fringe pattern. An explanation was given of the very great number of colored fringes, running up to several thousand, which is observed under these conditions. In this part we discuss certain phenomena which depend for their explanation upon the analysis of a beam oblique to the optical axis. To observe these phenomena we obtain, as described in Part I, circular fringes in sodium light, insert the thick plate in one of the paths, shorten that path until in the neighborhood of the most brilliant sodium maximum, in which position colored fringes will be seen with white light. If we observe these fringes through a spectroscope with the slit placed across the center of the system, the slit being long enough to cut across the whole field, the spectrum is seen to be crossed by a system of concentric dark rings, looking very much like a shadow of the fringe system itself. If now one of the paths is slowly shortened or lengthened, these dark rings expand or contract, as the case may be, just as in the fringe system. In addition, the center of the system on the spectrum travels very slowly from one end of the spectrum to the other. These phenomena may be observed easily and distinctly if a rather wide slit, cut in a card, is placed in the path of the light before it enters the interferometer, and the fringes are then viewed through a direct-vision spectroscope, without slit.