Phase-stepping interferometry: methods for reducing errors caused by camera nonlinearities

Schödel, René; Nicolaus, Arnold; Bönsch, G.

doi:10.1364/ao.41.000055

Cited by 31 publications

(22 citation statements)

References 6 publications

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“…For this, sample 2 with the same dimensions and specifications but a slightly better parallelism was used. The length of the sample was measured at different temperatures by high-resolution phase stepping interferometry [26][27][28]. Two J 2 -stabilized lasers at 532 and 633 nm were used subsequently for this purpose, and the results were averaged.…”

Section: Methodsmentioning

confidence: 99%

Thermo-optic properties of Yb:Lu2O3 single crystals

et al. 2015

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Lu 2 O 3 ). Initial growth attempts of sesquioxides utilized the Verneuil method [2,3] or the floating zone technique [4]. The resulting mm-size crystals of low quality were utilized for the initial determination of the optical and thermomechanical properties of these materials and even allowed for first flash-lamp-pumped laser experiments [5]. Afterward, different growth methods such as the laser-heated pedestal growth (LHPG) [6], the micro-pulling down technique [7] and the Czochralski technique [8] were applied, but still the crystals were limited in size and quality. It was not before 2008 that by the optimization of the heat exchanger method [9] the growth of cm-scale single-crystalline sesquioxides with excellent optical quality became possible [10]. In the following years, in particular cubic sesquioxide host material lutetia (Lu 2 O 3 ) has been shown to be an excellent host material for various rare earth ions [11]. Efficient and high-power laser operation has been demonstrated utilizing various laser ions such as Yb 3+ [12,13] at 1 µm, Tm 3+ [14] and Ho 3+ [15] at 2 µm as well as Er 3+ at 3 µm [16].These outstanding laser results obtained in the past motivate a reexamination of the thermo-optic properties of Lu 2 O 3 that affect the parameters of the thermal lens. The lens-like behavior is related with three main effects, namely temperature dependence of the refractive index (expressed by the thermo-optic coefficient, dn/dT), end-bulging related to the thermal expansion coefficient α, as well as photoelastic effect that is responsible for the lens astigmatism and birefringence losses. Under the plane stress approximation (that refers to the diode pumping case), first two terms are dominant [17]. Thus, the knowledge of dn/dT and α values as well as their combination, called thermal coefficient of the optical path (TCOP) [18], is crucial for the determination of the thermal lens parameters and, hence, the cavity design. Indeed, non-compensated thermal lens can lead to Abstract A detailed study of thermo-optic properties of 1.5 at.% Yb:Lu 2 O 3 single crystal is performed. Thermooptic dispersion formulas are derived for dn/dT coefficient and thermal coefficient of the optical path. At the wavelength of 1.03 μm, dn/dT = 5.8 × 10 −6 K −1 . High-precision temperature-dependent measurements of the thermal expansion coefficient α are performed. At the room temperature (RT), α = 5.880 ± 0.014 × 10 −6 K −1 . Temperature dependence of the bandgap is analyzed, yielding RT value of E g = 5.15 eV and dE g /dT = -3.7 × 10 −4 eV/K. Sensitivity factor of the thermal lens is calculated for a diodepumped Yb:Lu 2 O 3 crystal versus the pump spot radius and crystal temperature.

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Section: Methodsmentioning

confidence: 99%

Thermo-optic properties of Yb:Lu2O3 single crystals

et al. 2015

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“…A 512 x 512 pixel camera system (Photometrics CH 350) provides data frames at 16-bit per pixel. Phase stepping interferometry based on intensity frames at 8 different phase steps is used to obtain the phase map of the sample including the end plate [12]. The centre position of the samples' front faces with respect to the camera pixel coordinates is assigned [13].…”

Section: Precise Length Measurements Of Prismatic Bodiesmentioning

confidence: 99%

Multi-Wavelength Interferometry for Length Measurements Using Diode Lasers

Meiners-Hagen¹,

Schödel²,

Pollinger³

et al. 2009

Measurement Science Review

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This paper describes the principle of precise length measurements using multi-wavelength interferometry. Three different examples are given in order to demonstrate PTB's ability in this field: 1) Measurements of absolute distances up to 10 m performed by combination of the variable wavelength interferometry with fixed wavelength interferometry using two wavelengths simultaneously, 2) a three-wavelength diode laser interferometer for precision measurements of surface profiles (< 100 µm) and 3) PTB's Precision Interferometer for length measurements of prismatic bodies, e.g. gauge blocks, using three wavelengths. The setup and principle of measurements and some results are presented and discussed in each case.

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“…To overcome this, the fiber is manipulated during measurement by a specially designed fiber shaker. 12 Here, the fiber is looped many times and fixed to the central cone of an audio loudspeaker ͑8 ⍀, diameterϭ165 mm). A laboratory signal generator feeds a low frequency ͑64.5 Hz͒ sinusoidal signal into a hi-fi audio amplifier and either the input amplitude or amplifier volume is adjusted so that the loudspeaker is driven at low amplitude.…”

Section: B Illumination Sourcementioning

confidence: 99%

Development of a combined interference microscope objective and scanning probe microscope

Tyrrell

Savio

Krüger-Sehm

et al. 2004

Review of Scientific Instruments

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A compact sensor head combining optical interference and scanning probe microscopy in a single instrument has been developed. This instrument is able to perform complementary quantitative measurements, combining fast nondestructive three-dimensional surface analysis with high lateral resolution imaging. A custom interference microscope sensor head has been designed as the optical microscope objective and integrated within the architecture of a commercial interference microscope. The combined instrument makes available both the acquisition software and the hardware interface of the commercial microscope. The latter is able to function as a phase-shift interferometer or white light interferometer. Furthermore, the use of an optical fiber to transmit light from an external laser: (i) removes a major heat source from the measurement environment and (ii) makes aperture correction unnecessary. The lateral resolution of the instrument has been extended by the addition of a previously developed compact scanning probe microscope (SPM) module to the custom interference microscope objective. This SPM unit is based upon piezoresistive cantilever technology. The “piezolevers” are self-sensing and therefore require no additional systems, such as optical beam deflection or fiber interferometry, to monitor their displacement. The mechanical simplicity of the piezolever SPM unit allows for a small physical size and can thus be added to the custom optical sensor head without violating constraints on the working distance defined by the optics. A major benefit of the system, in terms of a quantitative nanometrology, is the possibility to perform a traceable and direct calibration of the SPM module. This calibration is achieved practically by measuring an appropriate sample at a common location using both techniques. Results are presented here for the measurement of two calibration standards and a test sample to demonstrate the increased lateral resolution of the instrument.

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Phase-stepping interferometry: methods for reducing errors caused by camera nonlinearities

Cited by 31 publications

References 6 publications

Thermo-optic properties of Yb:Lu2O3 single crystals

Thermo-optic properties of Yb:Lu2O3 single crystals

Multi-Wavelength Interferometry for Length Measurements Using Diode Lasers

Development of a combined interference microscope objective and scanning probe microscope

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