Measurement of the surface profile of a curved optical surface with rotation phase-shifting lateral shear cyclic path optical configuration.
TL;DR: In this article, phase shifts between the laterally sheared emergent beam components of a cyclic path optical configuration are introduced by applying a small change in the angle of incidence of the incident beam due to the small angular rotation of the setup.
Abstract: 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.
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TL;DR: A technique for the measurement of roll angular displacement of a rotary stage using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI).
Abstract: We present a technique for the measurement of roll angular displacement of a rotary stage using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI). The CPOC setup, aligned on the rotary stage, laterally shears the input plane polarized spherical beam into a pair of orthogonally polarized beams, which when brought to the same state of polarization by a polarizer produce interference fringes similar to Young's fringes. Rotation of the CPOC setup in its plane introduces a phase change between the orthogonally polarized lateral sheared beams due to the change in angle of incidence of the input beam. The change in the phase results in spatial displacement of the interference fringes. Using PPSI, the phase, or the optical path difference change between the laterally sheared beams that is related to the rotation angle of the CPOC setup, is measured.
17 citations
Cites methods from "Measurement of the surface profile ..."
...In [11] and [12], we have utilized the CPOC setup as a phase shifting device by rotating the CPOC setup in its plane, and the present paper is the application of the principle to measure the roll angle of the rotary stage accurately by applying PPSI....
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TL;DR: In this paper, a 3D measurement method based on blue sinusoidal structured light is proposed, and a method for filtering deformed pattern images is presented for correction of the unwrapping phase.
Abstract: The visible light radiated by some high temperature objects (less than 1200 °C) almost lies in the red and infrared waves. It will interfere with structured light projected on a forging surface if phase measurement profilometry (PMP) is used to measure the shapes of objects. In order to obtain a clear deformed pattern image, a 3D measurement method based on blue sinusoidal structured light is proposed in this present work. Moreover, a method for filtering deformed pattern images is presented for correction of the unwrapping phase. Blue sinusoidal phase-shifting fringe pattern images are projected on the surface by a digital light processing (DLP) projector, and then the deformed patterns are captured by a 3-CCD camera. The deformed pattern images are separated into R, G and B color components by the software. The B color images filtered by a low-pass filter are used to calculate the fringe order. Consequently, the 3D shape of a high temperature object is obtained by the unwrapping phase and the calibration parameter matrixes of the DLP projector and 3-CCD camera. The experimental results show that the unwrapping phase is completely corrected with the filtering method by removing the high frequency noise from the first harmonic of the B color images. The measurement system can complete the measurement in a few seconds with a relative error of less than 1 : 1000.
14 citations
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 background or methods from "Measurement of the surface profile ..."
...Typical schemas of a CPOC have been carried out principally in lateral shearing interferometry (LSI) [3-8] (Fig....
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...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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...The retrieved phase in these kinds of interferograms is done by applying phaseshifting interferometry (PSI) [4,6,12] or carrier fringe interferometry (CFI) [13]....
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TL;DR: In this article, a modified Saunders method and phase shifting techniques are combined to generate a method for wavefront reconstruction, which is a wavefront with an error below 0.7 λ and without any global high frequency filtering.
3 citations
References
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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
TL;DR: La difference de phase entre les 2 faisceaux interferant varie de maniere connue et on fait des mesures de the distribution d'intensite a travers la pupille correspondant a au moins 3 dephasages differents.
Abstract: La difference de phase entre les 2 faisceaux interferant varie de maniere connue et on fait des mesures de la distribution d'intensite a travers la pupille correspondant a au moins 3 dephasages differents
979 citations
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
TL;DR: In this article, a simple averaging technique is used to minimize systematic errors in phase shift interferometry, which can be used to map the deviations of optical surfaces from a reference plane or reference sphere, but the accuracy of such measurements is limited by sys- tematic errors due to several causes.
Abstract: Phase-shifting interferometry is now used widely to map the deviations of optical surfaces from a reference plane or reference sphere. However, the accuracy of such measurements is limited by sys- tematic errors due to several causes. These systematic errors can be minimized by a simple averaging technique. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)02103-6)
52 citations
TL;DR: In this article, an interferometer operating purely on the geometric phase is described, and the optical paths traversed by the two beams in this interferometers are always equal.
Abstract: An interferometer operating purely on the geometric phase is described. The optical paths traversed by the two beams in this interferometer are always equal, and the phase difference between the beams is varied by operating on the geometric phase
48 citations