Spectrally Resolved White Light Interferometry Research Articles

Minimization of spectral phase errors in spectrally resolved white light interferometry by the iterative least-squared phase-shifting method

We introduce an iterative least-squared phase-shifting method, reported as inherently insensitive to any types of phase-shifting errors, to calculate the spectral phase in phase-shifting spectrally resolved white light interferometry (PS-SRI). The actual phase shifts corresponding to all wavelengths can be reversely determined from the phase-shifted spectral interference fringes through least-squares fitting and the spectral phase is calculated by using the actual phase shifts in an iterative numerical manner. Because this method reduces the phase-shifting errors for calculating the spectral phase effectively, it can contribute to improving the accuracy of measuring topographic surface profiles. Moreover, it leads to accomplishing thin film thickness measurements less than 100 nm, in which most white light scanning interferometry and spectrally resolved white light interferometry (SRI) have difficulty because of mismatching measured spectral phase with the theoretical model by the spectral phase error. In this paper, a short description of the iterative least-squared phase-shifting method is presented and verified with simulations for calculating the topographic surface and thin film thickness profiles in PS-SRI.

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.

Evaluation of spectral phase in spectrally resolved white-light interferometry: Comparative study of single-frame techniques

Spectral phase in a white-light interferogram contains information about the absolute optical path difference (OPD) in the interferometer. Evaluation of spectral phase is therefore important in applications such as profilometry with white light. In spectrally resolved white-light interferometry (SRWLI) the white-light interferogram is spectrally decomposed by a spectrometer in order to determine this phase. Several single-frame techniques in SRWLI have been proposed for the evaluation of the phase including Fourier transform, Hilbert transform, spatial phase shifting, windowed Fourier transform and wavelet transform. In this paper we present a comparative study of these techniques in this application in relation to the temporal phase-shifting technique which is a multi- frame method. Further, we also propose a modified method to remove the influence of source spectrum modulation in Hilbert transform procedure.

Improved optical profiling using the spectral phase in spectrally resolved white-light interferometry

In spectrally resolved white-light interferometry (SRWLI), the white-light interferogram is decomposed into its monochromatic constituent. The phase of the monochromatic constituents can be determined using a phase-shifting technique over a range of wavelengths. These phase values have fringe order ambiguity. However, the variation of the phase with respect to the wavenumber is linear and its slope gives the absolute value of the optical-path difference. Since the path difference is related to the height of the test object at a point, a line profile can be determined without ambiguity. The slope value, though less precise helps us determine the fringe order. The fringe order combined with the monochromatic phase value gives the absolute profile, which has the precision of phase-shifting interferometry. The presence of noise in the phase may lead to the misidentification of fringe order, which in turn gives unnecessary jumps in the precise profile. The experimental details of measurement on standard samples with SRWLI are discussed in this paper.

Analysis of spectrally resolved white light interferograms: use of a phase shifting technique

The phase at different pixels along the direction of dispersion, also known as the chromaticity axis, is determined in spectrally resolved white light interferometry (SRWLI). Phase shifting interferometry has been used for this purpose. Previously, the phase shifted intensity values required for phase calculation were obtained from phase shifts due to wavelength variation (spatial phase shifting). This required the intensity values from different pixels be used in the calculations, resulting in errors due to variation in pixel sensitivity. We propose to use multiple intensity values, required for phase calculation obtained from the same pixel, and investigate the use of a polarization phase shifter and the conventional PZT phase shifter for this purpose. The polarization phase shifter aims at introducing nearly the same phase shift (achromatic phase shift) at all the pixels receiving light of different wavelengths. In the PZT phase shifter, the phase shift varies considerably at different pixels, but analysis shows that good measurements can still be made with it. © 2001 Society of

Spectrally-resolved white-light interferometry as a profilometry tool

Phase-shifting interferometry and white-light interferometry are reliable techniques for surface analysis in which the optical path difference has to be changed by some transducer to evaluate the phase. We present here a different procedure in which optical path modulation is completely avoided. This technique is based on the spectral analysis of white-light interferograms. By means of a spectroscopic device, a non-visible interferogram is split into its monochromatic components and absolute, unambiguous values of the phase are obtained along the spectral axis. Only one interferogram is required to obtain the profile of one-dimensional surfaces with nanometric resolution.

Refractive index distribution measurements by means of spectrally-resolved white-light interferometry

A new procedure to measure the spatial distribution of the refractive index in transparent media is presented. It is based on the spectral analysis of optical interferograms obtained from a wide, continuous-spectrum light source. The method yields fairly high precision (up to 10 -8) in the measurements of local values of differential refractive index, Δn ( Δn= n− n ref ), along a line in the sample. By means of a CCD TV-camera linked to a microcomputer, fast recording and automatic data processing are achieved. As an application, we present an experimental study of a thermal gradient in a liquid sample.