Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry

We present a measurement technique to determine the thickness of a transparent glass plate (GP) by using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI). In the technique, the GP introduces a longitudinal shift in the focus of the beam and, as a result, a spherical wavefront emerges from the lens, which is otherwise set for producing a collimated beam. Using CPOC, two laterally sheared orthogonally polarized beams are generated from the incident spherical wavefront. By applying PPSI, the slope of the optical path difference variation between the laterally sheared interfering beams is evaluated, and the radius of the spherical wavefront and the longitudinal shift of the beam focus are calculated. The thickness of the GP is determined from the standard relation between the longitudinal shift of the focus introduced by the GP and the thickness of the GP. Results obtained for a GP of 9.810mm thickness are presented.     

Measurement of longitudinal displacement using lateral shearing cyclic path optical configuration setup and phase shifting interferometry

We present a technique for the measurement of longitudinal displacement using a lateral shearing cyclic path optical configuration (CPOC) setup and phase shifting interferometry. In the technique, a plane mirror mounted on a linear translation stage, placed slightly away from the focal plane of a lens, introduces a longitudinal focal shift to the incident focusing beam. The resulting spherical wavefront emerging from the lens is sheared into two orthogonally polarized beams using the CPOC setup. By applying polarization phase shifting interferometry (PPSI), the longitudinal focal shift of the beam focus is calculated by determining the slope of the optical path difference variation between the sheared beams. Similarly, the additional focal shift introduced due to longitudinal translation of the mirror, by an unknown amount, is determined using PPSI. Half of the difference between the two longitudinal focal shifts measured gives the longitudinal displacement of the mirror. The technique can be used for an extended range of distance measurement. The novelty of the technique is the introduction of CPOC for the distance measurement. The advantages of the technique compared to other related methods are discussed.     

Self-referenced rectangular path cyclic interferometer with polarization phase shifting

A polarization phase shifting interferometer using a cyclic path configuration for measurement of phase nonuniformities in transparent samples is presented. A cube beam splitter masked by two linear polarizers is used to split the source wavefront into two counter propagating linearly polarized beams that pass through the sample. At the output of the interferometer, the two orthogonally polarized beams are rendered circularly polarized in the opposite sense through the use of a quarter wave plate. Finally, phase shifting is achieved by rotating a linear polarizer before the recording plane. In a rectangular path interferometer, although the two counter propagating wavefronts are laterally folded with respect to each other in the interferometer arms, the beams finally emerge mutually unfolded at the output of the interferometer. This phenomenon is utilized to create a reference if the sample is introduced in one lateral half of the beam in any one of the interferometer arms. The polarization phase shifting technique is used to generate four phase-shifted interferograms, which are utilized to evaluate the phase profile of the phase sample. Experimental results presented validate the proposed technique.     

The measurement of thin film stress using phase shifting interferometry

Abstract

A new technique for determining the stress of thin films is described. This technique combines digital phase shifting interferometry with image-processing software. A circular disc polished on one side is used as the coated substrate during film deposition. The average stress in thin films can be derived by comparing the deflection of the substrate before and after film deposition. The deflection of the substrate by the deposited film is obtained by the phase map. Using the Zernike polynomial fitting algorithm, a three-dimensional contour map is generated from the polynomial coefficients to visualize the deformation of the thin film and to examine the tensile or compressive stress after film deposition. Four oxide films prepared by ionbeam sputter deposition are investigated for their film stresses. The experimental results show that the stress values are concordant with measurements using other methods.     

Single-shot parallel four-step phase shifting using on-axis Fizeau interferometry

The purposes of the paper are threefold: (1) to show the possibility to perform parallel phase-shifting Fizeau interferometry by using a quarter waveplate with high flatness as a reference, (2) to present a comparative study between the phase-shifting algorithm and the off-axis geometry in surface microtopography measurement, and (3) to show the advantages of using the proposed common path Fizeau interferometry over the quasi-common path Michelson interferometry in terms of accuracy in measurement. The compelling advantage of the proposed parallel phase-shifting Fizeau interferometric technique is the long-term stability that leads to measuring objects with a high degree of accuracy.     

Robust, common path, phase shifting interferometer and optical profilometer

We describe an improved implementation of our previously reported common-path, phase shifting, and shearing interferometer. Using a time-multiplexed phase shifting scheme, we demonstrate higher sampling resolution, better light sensitivity, and use of arbitrary phase shifting algorithms. We describe microscopic imaging of the surface profile of a copper-plated silicon wafer and demonstrate that the system is vibration insensitive with approximately lambda/100 repeatability. In a more general discussion of our method, we describe the different functional elements and suggest alternative designs and improvements. Possible uses include full-field coherent imaging and high dynamic range wavefront sensing, which we briefly discuss.     

Spatial mismatch calibration using circular carrier technique in the simultaneous phase shifting interferometry

In most simultaneous phase shifting interferometry (SPSI) systems, a group of phase shifting interferograms are captured simultaneously at the different physical locations to retrieve the phase. The data of different interferograms should be spatially matched correctly, which is hard to realize by existing methods or this spatial mismatch will lead to phase retrieving error. In this paper, a spatial mismatch calibration method is proposed, where the circular carrier is introduced in the interferograms of the SPSI system, and the modulating phases of any two interferograms can be retrieved by the demodulation technique of circular carrier interferogram. The slope of the difference between these two phases is proportional to the mismatch value, so this error can be extracted and the experiment setup calibrated. The main error sources of the proposed method are analyzed with the conclusion that its match precision can be achieved up to 0.5 pixel. In addition, the simulated interferograms and actual interferograms captured in a SPSI system are processed to validate our proposed method.     

Measurement of the surface profile of a curved optical surface with rotation phase-shifting lateral shear cyclic path optical configuration

We present a new (to our knowledge) technique for introducing phase shifts between the laterally sheared emergent beam components of a cyclic path optical configuration (CPOC). The phase shifts are introduced by applying a small change in the angle of incidence of the incident beam due to the small angular rotation of the CPOC setup. Phase-shifting interferometry has been applied along with this phase-shifting technique for a CPOC with lateral shear to find the surface slope/profile of curved optical surfaces. Results for a spherical optical surface have been discussed. An optical setup for measurement of the surface profile of toroidal beam line mirrors of synchrotron radiation sources is proposed.     

Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.     

Effects of step slope on thickness measurement by optical interferometry for opaque thin films

Optical interferometry is a simple, quick and cheap method to measure the thickness of opaque thin films. The film edge, being formed as a step on the sample surface, is lighted with monochromatic light in an interference microscope, producing the interferogram that is recorded with a CCD camera. The film thickness (step height) is calculated by measuring offsets of the fringes across the step. However, the morphology of the film edge (step) significantly affects the thickness measurement, in some cases even yields false results. In this work, three kinds of methods were adopted to mask a part of the substrate surface during the deposition for fabrication of the step. The mask used was a thin silicon slice, a straight line of ink imprinted by a pen, or an Aluminum film. The step morphology recorded by a profilometer revealed large variation from one method to another. Accordingly, the accuracy of film thickness (step height) measurement by interferometry varies significantly. Results showed that large error occurs when the slope of the step is small and the step out spans the view field of the microscope. Therefore, the step should be fully visible in the view field of the microscope for reasonable measurement of thickness. A simple equation, in terms of geometrical configuration, is developed for this requirement.     

Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors

In both temporal and spatial carrier phase shifting interferometry, the primary source of phase calculation error results from an error in the relative phase shift between sample points. In spatial carrier phase shifting interferometry, this phase shifting error is caused directly by the wavefront under test and is unavoidable. In order to minimize the phase shifting error, a pixelated spatial carrier phase shifting technique has been developed by 4D technologies. This new technique allows for the grouping of phase shifted pixels together around a single point in two dimensions, minimizing the phase shift change due to the spatial variation in the test wavefront. A formula for the phase calculation error in spatial carrier phase shifting interferometry is derived. The error associated with the use of linear N-point averaging algorithms is presented and compared with those of the pixelated spatial carrier technique.     

Phase shifting Fizeau interferometry of front and back surfaces of optical flats

The interpretation of Fizeau interferograms of optical flats is not straightforward because they are composed of more than two reflections. This results in a confusing fringe pattern. There are three main contributions to the interferogram given by the reflections from the reference surface, the front and the rear surface of the sample. We present a new to the best of our knowledge solution to the problem. We use phase shifting measurements of the wave fields, which are reflected by and transmitted through the sample. This eliminates the need for the suppression of reflections by immersion or other methods. As an illustration of this method, several examples will also be presented.     

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.     

A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry

This paper reviews recent work in the field of displacement measurement using optical and X-ray interferometry at the sub-nanometre level of accuracy. The major sources of uncertainty in optical interferometry are discussed and a selection of recent designs of ultra-precise, optical-interferometer-based, displacement measuring transducers presented. The use of X-ray interferometry and its combination with optical interferometry is discussed.     

Dual in-plane electronic speckle pattern interferometry system with electro-optical switching and phase shifting

A dual in-plane electronic speckle pattern interferometry (ESPI) system has been developed for in situ measurements. The optical setup is described here. The system uses an electro-optical switch to change between the illumination directions for x and y sensitivity. The ability of the electro-optic device to change the polarization of the laser light forms the basis of this switch. The electro-optic device is a liquid-crystal layer cemented between two optically flat glass plates. An electric field can be set up across the layer by application of a voltage to electrodes. The speckle interferometry system incorporates two additional liquid-crystal devices to facilitate phase shifting, and the overall system is controlled by advanced software, which allows switching between the two perpendicular planes in quasi real time. The fact that there are no moving parts is an advantage in any ESPI system for which mechanical stability is vital.     

Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry

We describe a low-coherence interferometric technique for simultaneous measurement of geometric thickness and group refractive index of highly dispersive samples. The technique is immune to the dispersion-induced asymmetry of the interferograms, thus overcoming limitations associated with some other low-coherence approaches to this simultaneous measurement. We use the experimental configuration of a tandem interferometer, with the samples to be characterized placed in an air gap in one arm of the measurement interferometer. Unambiguous, dispersion-insensitive measurements of critical group-delay imbalances in the measurement interferometer are determined from the optical frequency dependence of interferogram phases, by means of dispersive Fourier transform spectrometry. Sample thickness and group refractive index are calculated from these group delays. A thickness measurement precision of 0.2 mum and group index measurement accuracy of 5 parts in 10(5) across a wavelength range of 150 nm have been achieved for BK7 and fused-silica glass samples in the thickness range 2000 to 6000 mum.