Spatial coherence radar applied for tilted surfaceprofilometryMark GokhlerBen Gurion University of the NegevDepartment of Electrical and ComputerEngineeringP.O. Box 653Beer-Sheva 84105, IsraelZhihui DuanThe University of Electro-Communications1-5-1 Chofugaoka, ChofuTokyo 182-8585, JapanJoseph Rosen, MEMBER SPIEBen Gurion University of the NegevDepartment of Electrical and ComputerEngineeringP.O. Box 653Beer-Sheva 84105, IsraelE-mail: rosen@ee.bgu.ac.ilMitsuo Takeda, FELLOW SPIEThe University of Electro-Communications1-5-1 Chofugaoka, ChofuTokyo 182-8585, JapanAbstract. A new method of spatial coherence profilometry is demon-strated. The surface profile is measured by shifting the spatial degree ofcoherence gradually in its own space of existence, and modulating itsphase angle. In each point of the sample we analyze the change of lightintensity versus the phase of a Fresnel zone pattern used as the intensitydistribution of an incoherent quasimonochromatic source. The tilt of thesurface is measured by gradually shifting the Fresnel zone plate on itstransverse plane. This shift of the light source rotates the spatial degreeof coherence around the coordinate origin until the condition of maximuminterference visibility is fulfilled. The method works without any mechani-cal movement and a quasimonochromatic light illuminates the interfero-metric system. Experimental demonstration of the new method is pre-sented. © 2003 Society of Photo-Optical Instrumentation Engineers.[DOI: 10.1117/1.1542893]Subject terms: coherence; tomography; interferometry; surfaces.Paper 020144 received Apr. 15, 2002; revised manuscript received Sep. 5, 2002;accepted for publication Sep. 5, 2002.1 IntroductionOptical coherence profilometry 1,2 is a noninvasive sensingmethod that provides profile information with high resolu-tion and high sensitivity. Most of the systems of this kindoperate by the principle of temporal coherence. 3 Recently,several attempts to explore the principle of longitudinalspatial coherence for coherence profilometry have beenmade. 4–6 The coherence between two points along thepropagation axis can be determined purely by the extent ofa quasimonochromatic incoherent planar source accordingto a particular interpretation of the Van Cittert-Zerniektheorem. Rosen and Takeda 5 have shown that the effectcould be useful for measuring three-dimensional profiles ofrough surfaces. Two features are characteristic of this newtechnique. First, a quasimonochromatic light illuminatesthe system, and that gives an inherent immunity from ef-fects of dispersion. Second, the surface profile is measuredwithout shifting the sample or the reference mirror. Thislast feature can save mechanical movements and may en-able the measurement of surfaces that cannot move relativeto the reference mirror.In this study we explore more deeply the recently in-vented method of spatial coherence profilometry withoutmechanical movements. 5,6 The heart of the method is thecontrol on the shape of the spatial degree of coherence. Thesurface profile is measured by means of nonmechanicallyshifting the spatial degree of coherence gradually in itsspace of existence while keeping the optical path differencebetween the interferometer’s measured surface and a refer-ence plane constant. Appearance of high interference vis-ibility on the detector is an indication that the optical pathdifference is equal to the amount of the shift of the spatialdegree of coherence. A key element in this scheme is anelectrically addressed spatial light modulator ~SLM! thatcan spatially modulate the intensity distribution of the light.Using SLM, one can get complete control on the shape andthe phase of the degree of coherence in the system withoutmoving any component in the interferometer. There are twonew elements in this study compared to Refs. 5 and 6; firstthe transverse, additionally to the axial, movement of thedegree of coherence is demonstrated. This additional fea-ture enables us to measure not just the elevation of a sur-face but also its angle of tilt relative to the reference plane.Second, the phase of the degree of coherence is modulated.This additional feature enables us to measure altitudes ofsmall surfaces, smaller than the size of a single interferencefringe.2 Description of Spatial Coherence ProfilimeterSince the theory of operation of the spatial coherence pro-filometer has already been reported in detail, 5,6 it is onlybriefly reviewed here. A schematic illustration of the pro-filometer is shown in Fig. 1. A Fresnel zone pattern ~FZP!is imaged by lens L 0 on a rotated diffuser, thus creating adynamic incoherent light source. The FZP is displayed onan electrical-addressed SLM and illuminated by a laser.Light from this quasimonochromatic incoherent sourcepropagates through lens L 1 and is split into two beams by abeamsplitter. One beam is reflected from the tested surfaceS and the other is reflected from the reference mirror R. Thetwo reflected beams are combined and recorded by a CCDcamera after passing through lens L 2 . Lens L 2 images the830 Opt. Eng. 42(3) 830–836 (March 2003) 0091-3286/2003/$15.00 © 2003 Society of Photo-Optical Instrumentation Engineers
