Correction for lateral distortion in coherence scanning interferometry Andrew Henning a , Claudiu Giusca a , Alistair Forbes a , Ian Smith a , Richard Leach (3) a, *, Jeremy Coupland b , Rahul Mandal b a National Physical Laboratory, Teddington, Middlesex TW11 0LW, UK b Loughborough University, Loughborough, Leicestershire LE11 3TU, UK Submitted by Chris Evans (1), Charlotte, USA. 1. Introduction Coherence scanning interferometry (CSI) is a versatile three- dimensional (3D) imaging technique which is widely used for the measurement of surface topography [1–3]. CSI is a non-contacting optical method that combines the lateral resolution of a high power optical microscope with the axial resolution of an interferometer and is becoming an increasingly popular alter- native to traditional stylus profilers for the measurement of areal surface texture parameters [3]. In essence, CSI exploits broadband, incandescent or LED illumination and a Mirau or Michelson interference objective to record the interference between light reflected from a reference surface and that scattered by the object [2]. Since the source illumination is limited in both temporal and spatial coherence, the interference fringes are observed over a finite scan range and it is relatively straightforward to locate the bright zero order fringe that identifies when path length is balanced in the interferogram. Despite significant advantages, CSI can exhibit certain problems that restrict its use as a traceable measurement tool in some domains. At present, the causes of measurement error are poorly understood but it is generally accepted that errors are exacerbated by surface tilt [4]. Despite this, CSI instrumentation is usually calibrated axially using step height artefacts and laterally using calibration cross gratings [5], and with this approach, step height measurements have been demonstrated with nanometre-level uncertainty [5]. Recently, a method to calibrate and adjust a CSI instrument has been demonstrated that is based on a determination of the instrument’s optical transfer function [6]. This method relies on the assumption that the transfer function is the same throughout the field of view (shift invariance), which implies that there is no lateral distortion of the image. In this paper, it will be shown that commercial CSI instruments can exhibit a significant amount of lateral distortion. This distortion not only affects the lateral capability of the instrument, but if a surface with significant slope is measured, there will also be errors introduced into measurement of heights (and hence surface texture parameters). A method will be described which allows the distortion to be measured and corrected. A commercial CSI instrument was used to obtain the measurement results presented in this paper. The CSI was fitted with a 5 magnification objective lens (in a Michelson configuration, 0.4 numerical aperture, working field of view 0.9 mm by 0.9 mm and sampling distance of approximately 0.88 mm). Note that third order distortion in a Fizeau interferometer produces a tilt dependent height error which typically appears as comatic aberration [7]. The height error can be calibrated and compensated and has been applied to CSI [8]; however, although height errors are corrected in this way, lateral distortion remains. 2. Measurement strategies In order to assess the distortion in the image gained using the CSI instrument, an artefact with calibrated lateral features is required. The calibration of the artefact, a 17  17 array of square pits on a flat surface, is obtained using two separate methods. In the first method, the positions of an array of pits are measured using a traceable areal surface topography measuring instrument, such as the NPL Areal Instrument [9] – a primary contact stylus instrument that measures the motion of the stylus tip using laser interferometers. While the NPL Areal Instrument provides the information that is needed, such a calibration is not widely available and so a second method was also used. In the second method, three images of the object are recorded, with the object being rotated between the first and second images, and with a translation of the object between the second and third images (similar to techniques developed for ball-plate measurement and in lithography [7]). The information contained in these three CIRP Annals - Manufacturing Technology 62 (2013) 547–550 A R T I C L E I N F O Keywords: Surface analysis Measurement Distortion correction A B S T R A C T For a complete calibration of optical surface topography measuring instruments, which encompass their ability to measure slope and curvature, a determination of their optical transfer function is required. Errors induced by non-linearity of the scales of the instrument can affect their shift invariant properties, which in turn affect their transfer function. The non-linearity can be caused by distortion produced by the quality of the optical setup. A method to develop a correction model that combines a simple model of optical distortion with error separation techniques is discussed. Experimental tests of the method are presented and measurement uncertainties are investigated. ß 2013 CIRP. * Corresponding author. Contents lists available at SciVerse ScienceDirect CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp 0007-8506/$ – see front matter . ß 2013 CIRP. http://dx.doi.org/10.1016/j.cirp.2013.03.026