Self-referenced rectangular path cyclic interferometer with polarization phase shifting
TL;DR: 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.
Abstract: 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.
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TL;DR: In this article, a rectangular path cyclic interferometer has the unique property that the counter-propagating wavefronts travelling in the inter-ferometer arms are folded with respect to each other in the plane of the interferometers, although the two wave fronts finally emerge from the interferer unfolded.
Abstract: A rectangular path cyclic interferometer has the unique property that the counter-propagating wavefronts travelling in the interferometer arms are folded with respect to each other in the plane of the interferometer although the two wavefronts finally emerge from the interferometer unfolded. A phase disturbance introduced in one lateral half of the interferometer arm is therefore manifested in complementary lateral halves of the observed interference pattern. This phenomenon is utilized to evaluate the surface profile of a reflecting sample placed on one of the interferometer mirrors. The sample phase is retrieved using polarization phase shifting. Experimental results showing three-dimensional surface morphology of a small scale integrated circuitry directly etched on silicon are presented.
9 citations
TL;DR: In this article, a method for generating carrier fringes and a nonconventional rotational shear in a triangular cyclic-path interferometer, while simultaneously suppressing the presence of typical lateral and radial shearing, is presented.
Abstract: This work presents a method for generating carrier fringes and a nonconventional rotational shear in a triangular cyclic-path interferometer, while simultaneously suppressing the presence of typical lateral and radial shearing. To carry out this method, a 4f optical system is implemented into the cyclic interferometer. The most important contributions of this paper are its demonstration of the linear dependence of the movable mirror displacement with the carrier frequency introduced, and the realization of a nonconventional rotational shearing interferometer. Additionally, we think that one of its possible potential applications is the observation of the angular derivative of parallel projections of a phase object placed at the output plane, generating a great advantage in edge-enhancement optical tomography. In this paper, we develop a theoretical model and show experimental results.
6 citations
Cites methods from "Self-referenced rectangular path cy..."
...Introduction A cyclic path optical configuration (CPOC) has been used extensively to measure many physical quantities in many fields in science and technology [1-21]....
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TL;DR: In this paper, a single-shot phase-visibility modulating interferometry (SVMIM) method was proposed to achieve phase visibility modulation in a 4f optical system with three apertures at the input and a grid with a fill factor of 1/2 at the Fourier plane.
6 citations
TL;DR: In this paper, an interferometer capable of retrieving phase information in a single shot was implemented, the system was made by taking into account the double interferogram output obtained in a Mach Zehnder interferometers and then retrieving the phase information using a two-step algorithm already encountered in the literature, the configuration presented does not require micro-polarizer arrays or diffraction gratings presenting the advantage of avoiding the use of conventional polarizing filters to control the phase shift.
Abstract: Abstract An interferometer capable of retrieving the phase information in a single shot was implemented, the system was made by taking into account the double interferogram output obtained in a Mach Zehnder interferometer and then retrieving the phase information using a two-step algorithm already encountered in the literature. By controlling the polarization properties of the system, a new polarization phase shifting technique was implemented based upon the rotation of two quarter wave retarders placed in each of the arms of the interferometer. We present the analytical model taking into account the necessary conditions presented by the demodulation method. The configuration presented does not require micro-polarizer arrays or diffraction gratings presenting the advantage of avoiding the use of conventional polarizing filters to control the phase shift. Experimental results are presented.
3 citations
11 Nov 2014
TL;DR: In this article, the application of the polarizing triangular cyclic interferometer to distinguish different types of polarizing components is investigated, and distinct output signals from polarizer and wave plates under examination can clearly be observed.
Abstract: The application of the polarizing triangular cyclic interferometer to distinguish different types of polarizing components is investigated. The distinct output signals from polarizer and wave plates under examination can clearly be observed.
2 citations
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TL;DR: The phase modulation in an interferometer can be induced by moving a mirror, tilting a glass plate, moving a grating, rotating a half-wave plate or analyzer, using an acoustooptic or electro-optic modulator, or using a Zeeman laser as mentioned in this paper.
Abstract: Publisher Summary This chapter describes the phase-measurement interferometry techniques. For all techniques, a temporal phase modulation is introduced to perform the measurement. By measuring the interferogram intensity as the phase is shifted, the phase of the wavefront can be determined with the aid of electronics or a computer. Phase modulation in an interferometer can be induced by moving a mirror, tilting a glass plate, moving a grating, rotating a half-wave plate or analyzer, using an acousto-optic or electro-optic modulator, or using a Zeeman laser. Phase-measurement techniques using analytical means to determine phase all have some common denominators. There are different equations for calculating the phase of a wavefront from interference fringe intensity measurements. The precision of a phase-measuring interferometer system can be determined by taking two measurements, subtracting them, and looking at the root-meansquare of the difference wavefront. The chapter discusses the simulation results. The elimination of the errors that reduce the measurement accuracy depends on the type of measurement being performed. Phase-measurement interferometry (PMI) can be applied to any two-beam interferometer, including holographic interferometers. Applications can be divided into: surface figure, surface roughness, and metrology.
1,340 citations
"Self-referenced rectangular path cy..." refers methods in this paper
...The sample phase distribution is then extracted by applying phase shifting interferometric techniques [18,19]....
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TL;DR: A cyclic interferometers can be used for both lateral and radial shearing, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.
Abstract: A cyclic interferometer can be used for both lateral and radial shearing. Being common-path this interferometer is quite stable. The use of a cyclic shear interferometer for phase shifting interferometry is discussed. The phase shifting is provided here by polarization techniques. Some useful cyclic phase shifting interferometer arrangements are discussed, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.
112 citations
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01 Jul 2007
83 citations
"Self-referenced rectangular path cy..." refers methods in this paper
...The phase profiles in the two lateral halves are evaluated by employing the standard four phase-step algorithm [21],...
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TL;DR: In this article, a fiber-optic acoustic sensor array that is based on the Sagnac interferometer was proposed and compared to acoustic sensor arrays based on Mach-Zehnder (MZ) interferometers, including a stable bias point, a reduced conversion of source phase noise into intensity noise, and a frequency response that matches the ambient ocean noise.
Abstract: We propose a novel design for a fiber-optic acoustic sensor array that is based on the Sagnac interferometer. The performance of this Sagnac sensor array (SSA) design is analyzed and compared to acoustic sensor arrays based on the Mach-Zehnder (MZ) interferometer. It is found that the SSA exhibits several decisive advantages, including a stable bias point, a reduced conversion of source phase noise into intensity noise, and a frequency response that matches the ambient ocean noise. It is also shown that the SSA can be easily designed to have a much larger dynamic range than an MZ-based sensor array. Potential noise sources are analyzed and shown to be manageable. A means for eliminating polarization-induced signal fading is presented. The applicability of time-division, frequency-division, and code-division multiplexing schemes for the proposed design is presented.
51 citations
"Self-referenced rectangular path cy..." refers methods in this paper
...Sagnac interferometers have been used to build optical gyroscopes [3] and for detection of electo-optic effects in Fresnel flow probes [4] and fiber-optic sensor arrays [5,6]....
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TL;DR: In this paper, a wavefront shearing interferometer is described, which can be used for routine tests of optical systems with relative apertures of f/6 or less.
Abstract: A wavefront shearing interferometer is described which can be conveniently used for routine tests of optical systems with relative apertures of f/6 or less. The necessity of equalizing the two optical paths has been eliminated in this instrument, making it extremely easy to adjust and handle. At the same time, the shear can be continuously varied, so that zonal errors can be easily identified.
38 citations
"Self-referenced rectangular path cy..." refers methods in this paper
...A variety of cyclic shearing interferometers [12] has been constructed along with polarization phase shifting techniques [13–15] by using polarizing beam splitters and half wave plates, as well as other polarizing components to incorporate the phase shifting 1559-128X/12/010126-07$15....
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