Jose E. Calatroni

Optical implementation of frequency domain analysis for white-light interferometry

The purpose of recent developments of profilometry by using white light interferometry is to provide new tools for the analysis of rough samples which when studied by monochromatic phase-shifting interferometry, may cause phase calculation ambiguities. The usual way to perform depth measurements by white light interferometry is to analyze the coherence-limited interference fringes while the optical path difference is scanned. The method proposed here does not use optical path difference scanning. A spectroscopic device is used instead to separate the interference intensities associated to each spectral component of the light source. Phase variations due to wavelength change are proportional to the optical path difference and allows depth measurement to be performed without axial scanning. The profile of one line of the inspected sample is obtained from only one 2D interferogram. In this 2D interferogram one direction corresponds to the inspected direction of the surface while the other one is the chromatic axis which allows phase to change with wavelength. Experimental results show the ability of the proposed method to obtain the profile of 1D surface with nanometric resolution.

Surface profiling by means of double spectral modulation

Double modulation-in frequency and intensity-of the power spectral distribution of a light beam is proposed for interferometric profilometry. The procedure is based on two facts: (1) the continuous spectrum of a light source is frequency modulated by the path difference in an interferometric device, (2) the continuous spectrum of a light source is intensity modulated by the transparency of an object placed in the exit plane of a spectroscopic device. Both procedures can be used to measure the profile of a surface with high precision. Moreover, phase shifting is automatically performed by the continuous wavelength variation along the spectrum, so that no piezoelectric transducers are necessary. The method is adaptable for the analysis of remote surfaces through optical fibers.

White light interferometry: innovative algorithms and performances

White light interferometry can be seen as a multichannel process since each wavelength constitutes an independent information carrier. The simultaneous observation of different wavelengths allows the absolute evaluation of optical path differences (OPD). Two basic detection schemes are available which are chosen as a function of the application requirements. In the first one, all wavelengths are superimposed on the photodetector and we get a single composite output signal. Therefore, the OPD has to be scanned in order to detect the interference fringe pattern which appears only for OPD shorter than the light source correlation length. The second scheme consists to separate optically the different wavelengths for a parallel detection and to measure the absolute value of the OPD without any mechanical displacement of the interferometer. This paper explores the case of surface profilometry for the presentation of the latest proposed signal processing algorithms and to compare the capabilities and perspectives of those two approaches.

Multichannel chromatic interferometry: metrology applications

The modulation of the spectrum of a light beam is consider as a metrological tool. In particular, double spectral modulation of a Super Luminiscent Laser Diode (SLD) is used to analyze surfaces profiles. Intensity and frequency modulation allows absolute measurements of the surface without any auxiliary phase shifting. Depth and lateral resolution is determined by the spectral resolution of the involved spectroscopic devices.

Stationary phase in Spectrally Resolved White Light Interferometry (SRWLI) as a refractometry tool

A new method for real-time obtention of the dispersion behavior n=n(λ) of a transparent media is presented. The procedure stands on the analysis of the hybrid bidimensional fringe pattern obtained at the exit plane of a spectrometer which performs the spectral analysis of a white light interferogram. The phase of the signal depends both on a spatial coordinate and the chromatic variable wavenumber σ=λ-1. Taking profit of the dispersion behavior of the sample the phase of the signal can be forced to become stationary at certain points of this hybrid plane. The line which connects the stationary phase points can be experimentally obtained through an appropriate numerical fitting. It stores the parameters of a Cauchy approximation for the refractive index.

Measurement of both sample width and differential refractive index through spectrally resolved white light interferometry

Spectrally Resolved White Light Interferometry (SRWLI) is used for precise measurements of both the sample width and the differential refractive index, attaining precision of about 10-6 in the refractive index. This is achieved through the experimental simulation of a thin virtual cell about 40μm wide.

Real-time dispersion curve measurement from spectrally resolved white-light interferometry

Spectrally-resolved white-light interferometry (SRWLI) is used for real-time measurement of dispersion functions. SRWLI consists in the spectroscopic analysis of the interferograms which are produced when a wide, continuous- spectrum light-source is used to illuminate a 2-wave interferometric device. This produces incoherent superposition of many monochromatic interferograms, one for each resolved wavelength in the source spectrum. Each monochromatic interferogram at wavelength (lambda) stores the optical delay in the interferometer at that particular wavelength. When a transparent, dispersive specimen is introduced in the interferometer, the optical delay becomes a function of (lambda) , and this function is stored in the incoherent superposition of the whole set of monochromatic interferograms. We propose in this paper the use of a prismatic specimen with a linear variable thickness. In this way the interferometry gives rise, for each wavelength, to a classical Young fringe pattern whose spatial frequency stores the dispersion function. The spectroscope, in series with the interferometer, splits the incoherent superposition of the different monochromatic patterns. The recorded image is processed by measuring the frequency of the fringes at each resolved wavelength. Precision in refraction index is about 10-6. The method is well adapted for measuring dispersion curves of evolving specimens because only one image is sufficient to determine the dispersion curve in the useful spectral range. Experimental results are presented for an optical glass in the visible spectrum.

Surface profilometry in the spectral domain

Spectrally resolved white light interferometry (SRWLI) is applied to 1-D profilometry. The technique allows us to deal with discontinuous profiles without any ambiguity. Experimental results show good agreement with phase shifting profilometry; nanometric resolution is attained. In order to extend the method to 2-D samples, double spectral modulation (DSM) is applied using a new experimental set-up which enhances luminosity.