Fourier transform approach in modulation technique of experimental measurements

Khazimullin, M. V.; Lebedev, Yu. A.

doi:10.1063/1.3327844

Cited by 7 publications

(5 citation statements)

References 33 publications

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“…For this the polarization of the probe light beam needs to be changed in a defined manner during the measurement. How this is done divides ellipsometers into three categories, namely with slow (based on rotating wave-plates [1,10,11]), medium (with liquid crystals retarders [3]), and fast polarization modulation (based on a PEM -Photo-Elastic Modulator [2,4,5,8,12]). The first method produces extremely accurate results +/-0.001° at very low sampling rates (several seconds for one sample).…”

Section: Introductionmentioning

confidence: 99%

“…Due to the limitations of electronics and due to the use of a lamp (as necessary for spectroscopic ellipsometry) the accuracy and measurement velocity is much lower than in the system presented here. Further we refer to recent work [5], where a detailed error analysis for a digital (Fourier) evaluation is presented and applied to a birefringence measurement, based again on a classical PEM, and similar to an ellipsometric measurement.…”

Section: Introductionmentioning

confidence: 99%

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Fast ellipsometric measurements based on a single crystal photo-elastic modulator

Petkovšek¹,

Petelin²,

Možina³

et al. 2010

Opt. Express

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For quality control in high volume manufacturing of thin layers and for tracking of physical and chemical processes, ellipsometry is a common measurement technology. For such kinds of applications we present a novel approach of fast ellipsometric measurements. Instead of a conventional setup that uses a standard photo-elastic modulator, we use a 92 kHz Single Crystal Photo-Elastic Modulator (SCPEM), which is a LiTaO3 crystal with a size of 28 × 9 × 4 mm. This small, simple, and cost-effective solution also offers the advantage of direct control of the retardation via the current amplitude, which is important for repeatability of the measurements. Instead of a Lock-In Amplifier, an automated digital processing based on a fast analog to digital converter controlled by a highly flexible Field Programmable Gate Array is used. This and the extremely compact and efficient polarization modulation allow fast ellipsometric testing where the upper limit of measurement rates is mainly limited by the desired accuracy and repeatability of the measurements. The standard deviation that is related to the repeatability +/-0.002° for dielectric layers can be easily reached.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast ellipsometric measurements based on a single crystal photo-elastic modulator

Petkovšek¹,

Petelin²,

Možina³

et al. 2010

Opt. Express

View full text Add to dashboard Cite

show abstract

“…(3) where F denotes the numerical low-pass filter. Such a digital Fourier analysis for the modulated data has been widely utilized in other spectroscopy measurements [35,36]. After the numerical lock-in process, the time-dependent noise signal b(t) in A RF (t) is excluded.…”

Section: Instrumentationmentioning

confidence: 99%

Radio frequency self-resonant coil for contactless AC-conductivity in 100 T class ultra-strong pulse magnetic fields

Nakamura

Altarawneh

Takeyama

2018

Meas. Sci. Technol.

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A contactless measurement system of electrical conductivity was developed for application under pulsed high magnetic fields over 100 T by using a self-resonant-type, high-frequency circuit. Electromagnetic fields in the circuit were numerically analysed by the finite element method, to show how the resonant power spectra of the circuit depends on the electrical conductivity of a sample set on the probe-coil. The performance was examined using a high-temperature cuprate superconductor, La2−xSrxCuO4, in magnetic fields up to 102 T with a high frequency of close to 800 MHz. As a result, the upper critical field could be determined with a good signal-to-noise ratio.

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“…Phase modulated apparatus is also involved in the ellipsometric measurement. The ellipsometer based on the use of a photoelastic modulator (PEM) is the most prevalent configuration; it has a typical modulation frequency of 50 kHz with no moving parts [11][12][13]. For single spot measurement, one can employ either lock-in amplifiers or the Fourier analysis technique to obtain the ellipsometric parameters in near real-time, but this approach is not applicable for a two-dimensional measurement, because the modulation frequency of the PEM is too high to compare it with the exposure times of the CCD camera.…”

Section: Introductionmentioning

confidence: 99%

Photoelastic Modulated Imaging Ellipsometry

Han¹,

Chao²,

Tsai³

2017

Ellipsometry - Principles and Techniques for Materials Characterization

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Photoelastic modulator (PEM)-based ellipsometry employed either lock-in amplifiers or the Fourier analysis technique to obtain the ellipsometric parameters almost in real-time that makes the system with a feature of fast measurement speed, higher stability, and sensitivity at small retardations. Since the PEM modulation frequency is too high to compare it with the exposure time of the camera, photoelastic modulator-based approach is not applicable for a two-dimensional ellipsometric measurement. Here, we represent a novel technique that coordinates with the light pulses and PEM modulation that can freeze the time-varied signals. Thus, two-dimensional ellipsometric parameters can be obtained within few seconds. In addition to ellipsometric measurement, this approach also can be extended to other imaging polarimetry measurements, such as Stokes parameters and Mueller matrix. Moreover, since the chromatic dispersion of birefringence was also a significant issue in the polarization modulation systems, we proposed an equivalent phase retardation technique to deal with this issue. This technique was confirmed by a dual wavelength measurement result without changing the optical configuration of the system. The concept and the theory of this system were indicated in the preceding section, and the passage below described some calibration issues for the photoelastic modulator. Some measurement results were revealed in the final part of this chapter.

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Fourier transform approach in modulation technique of experimental measurements

Cited by 7 publications

References 33 publications

Fast ellipsometric measurements based on a single crystal photo-elastic modulator

Fast ellipsometric measurements based on a single crystal photo-elastic modulator

Radio frequency self-resonant coil for contactless AC-conductivity in 100 T class ultra-strong pulse magnetic fields

Photoelastic Modulated Imaging Ellipsometry

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