(2011) Random-Phase-shift Fizeau Interferometer

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    Random-phase-shift Fizeau interferometer

    Hagen Broistedt,1,* Nicolae Radu Doloca,2 Sebastian Strube,2 and Rainer Tutsch1

    1Institut fr Produktionsmesstechnik, Technische Universitt Braunschweig,

    Schleinitzstrae 20, 38106 Braunschweig, Germany

    2Physikalisch-Technische Bundesanstalt, Bundesallee 100D-38116 Braunschweig, Germany

    *Corresponding author: h.broistedt@tubs.de

    Received 6 June 2011; revised 28 September 2011; accepted 28 September 2011;

    posted 4 October 2011 (Doc. ID 148803); published 13 December 2011

    A new and potentially cost efficient kind of vibration-tolerant surface measurement interferometer basedon the Fizeau-principle is demonstrated. The crucial novelty of this approach is the combination of twooptoelectronic sensors: an image sensor with high spatial resolution and an arrangement of photodiodeswith high temporal resolution. The photodiodes continuously measure the random-phase-shifts causedby environmental vibrations in three noncollinear points of the test surface. The high spatial resolutionsensor takes several frozen images of thetest surface by using short exposure times. Under theassump-tion of rigid body movement the continuously measured phase shifts of the three surface points enablethe calculation of a virtual plane that is representative for the position and orientation of the whole testsurface. For this purpose a new random-phase-shift algorithm had to be developed. The whole systemwas tested on an optical table without vibration isolation under the influence of random vibrations. Theanalysis of the root-mean-square (RMS) over ten different measurements shows a measurement repeat-ability of about 0.004 wave (approximately 2:5nm for 632:8nm laser wavelength). 2011 OpticalSociety of America

    OCIS codes: 120.3180, 120.3940, 120.6650, 110.3175.

    1. Introduction

    The interferometric measurement techniques pro-vide the most accurate noncontact 3D measurementtests for reflective surfaces and most particularlyfor high-quality optical components such as lenses,microscope objectives, camera lenses, prisms, opticalflats, or even large telescope mirrors. The high accu-racy of the measurements is related to the wave-length of the light, which is used as the measuringreference in all interferometric measurements. In

    many applications frequency stabilized lasers areused.

    The basic principle of the interferometric 3D formtests of reflective surfaces is that the 3D shape of thesurface is encoded in the reflected wavefront (knownas the test wavefront). The test wavefront is com-pared to a reference wavefront, which is generated byreflection from a reference surface. The interference

    between the two coherent wavefronts generates theso called interference fringe pattern, which can bedigitized using an image sensor array. In case ofa flatness test, the deviations from planarity of thesurface under test deform the ideal straight-lineequidistant interference fringes.

    A single fringe pattern can be numerically anal-yzed using either data interpolation methods orFourier analysis methods. These techniques arecapable of a resolution of about =50, where is the

    laser wavelength [1]. In most cases, however, phaseshifting interferometry (PSI) techniques are applied.These methods require a sequence of interferenceimages. By sequentially shifting the reference platewith well-defined steps by means of a piezo-actuator,several interference images at well-known and pre-defined phase-shifts are sequentially acquired. Thesequentially recorded gray values are used to calcu-late the 3D information of the test wavefront at eachpixel. In this way a pixilated analysis of the testwavefront results.

    0003-6935/11/366564-12$15.00/0 2011 Optical Society of America

    6564 APPLIED OPTICS / Vol. 50, No. 36 / 20 December 2011

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    Because the phase-shifted interferograms are se-quentially recorded and very precise phase-shiftsare required, the PSI methods prove to be very sen-sitive to vibration. This is why every PSI interferom-eter must be mounted and utilized on an optical tablewith vibration isolation and, even so, the measure-ments have to take place under special laboratoryconditions far from the manufacturing process.The measurement accuracy of the PSI methods is

    anyway better, compared to the fringe pattern anal-ysis methods. Commercial PSI interferometers typi-cally show a resolution of about =1000.

    Nowadays there is a general tendency for integra-tion of the quality testing in the manufacturingprocess. As a consequence, there is an increasing de-mand for new interferometric concepts that allow theutilization of the interferometers concomitant withand close to the manufacturing process. In this con-text, the purpose of this work is to develop and to ver-ify an innovative interferometric system that copeswith the presence of vibrations in order to omit vibra-tion isolation equipment. As it will be described, thisnew measurement principle actually makes use of

    the vibrations.

    2. Vibration-Tolerant Interferometers

    The data acquisition time in sequential PSI takesseveral frame times of the electronic camera, addingup to about 100ms. The frequency spectrum ofmechanical vibrations in buildings typically is domi-nated by the region between 20Hz and 200Hz [2].Conventional PSI therefore is very sensitive tofloor vibration, making expensive vibration isola-tion equipment necessary. In the last few yearsnew PSI techniques have been developed that canbe applied in the presence of vibrations. The basic

    idea of all these new techniques is to record thesequence of interferograms in a very short time in-terval or even simultaneously, resulting in the effectof shifting the sensitivity of the system to higherfrequencies.

    In Wizinowich [3], a 2 1 algorithm is describedthat uses two interferograms with =2 phase-shifttaken very rapidly by using a Pockels cell to switchbetween two phase-shifted, orthogonally polarizedwaves synchronously to the switch between the twohalf-frames of an interline-transfer CCD image sen-sor. A third image gives the average intensity acrossthe aperture, which is obtained by superposition

    and averaging of two interferograms phase-shiftedby . Several other approaches use the simultaneousphase-shifting interferometry.

    In Koliopoulos [4] and Millerd, et al. [5], a methodis described where polarizing beam splitters and re-tardation plates are used to create four phase-shiftedinterferograms on four image sensors. In a similarway in Kihm [6] and Smythe and Moore [7] fourphase-shifted interferograms are generated andimaged on one image sensor. In Millerd, et al. [8] animproved point diffraction interferometer that ap-plies a polarizing point diffraction plate is presented.

    With a further implementation of a holographicelement in combination with a birefringent maskof four elements in front of the image sensor, also fourphase-shifted interferograms are created on oneCCD-chip.

    An alternative approach to the others is the use ofa pixilated phase mask, which uses an array of mi-cropolarizers very precisely matched to a CCD sensorarray [9]. The array contains different types of

    elements with the transmission axis at0

    ,45

    ,90, 135, which are arranged in groups of four andform the superpixel. Different types of phase-shift-interferometers that make use of this method canbe seen in Millerd [10] and Kimbrough [11].

    Several vibration-tolerant phase-shifting solutionshave been developed and demonstrated. Recordingthe interferograms at higher frame rates has theeffect of moving the sensitivity to higher vibrationfrequencies. Instantaneous phase-shifting techni-ques use polarization components or holographic ele-ments, splitting the beams in multiple paths, andphase-shifted interferograms are simultaneously re-corded. In conclusion, the already available phase-shifting interferometric configurations that handlethe presence of vibrations are quite complex andexpensive systems. There is still a demand for low-budget interferometers that work in the presenceof vibration.

    3. Random-Phase-Shift Interferometer

    The interferometer presented in this paper wasdesigned to work without vibration isolation and touse the random floor vibration as phase-shifter.In the case when the mechanical vibrations are notsufficient, the interferometer (more precisely the testplate) has to be deliberately perturbed to achieve ran-dom vibrations. This could be easily done by e.g.slightly striking the mechanical holder of the testplate with a finger or by mounting a small electro-motor to the mechanical holder that has an imbal-ance. The challenging goal of this new approach isto determine the random-phase-shifts that are gener-ated in this manner.

    We will begin by describing the experimental setup(Section 3.A) and randomly oscillating test plate(Section 3.B). We will then discuss the low spatial re-solution detector system (Section 3.C), how it is usedto determine the phase-shift (Section 3.D and 3.E)between interferograms, and how it is registered tothe interferograms (Section 3.F). We complete thissection by discussing a four-step algorithm appropri-ate to these random-phase-shifts.

    A. Experimental Setup

    The experimental arrangement of the Fizeau config-uration is shown in Fig. 1. A He-Ne laser beam of632:8nm wavelength is directed to the spatial filterSF, using the mirrors M1 and M2 and is collimatedwith the collimating lens L1 to the test and referenceround plates T and R.

    20 December 2011 / Vol. 50, No. 36 / APPLIED OPTICS 6565

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