Beam Profile Reflectometry (BPR) and Beam Profile Ellipsometry (BPE), described in U.S. Pat. Nos. 4,999,014 and 5,042,951 respectively, are established methods for measuring the thicknesses of thin films and coatings deposited upon flat substrates. Each of these techniques makes use of data contained in the cross-sectional profile of a laser beam which has been reflected from the sample under test. As described in each of these patents, each technique relies on the sample under test being (a) perfectly flat and (b) aligned so that an incident probe beam is focused substantially normal to the surface of the sample.
In practice, known implementations of BPR rely on a very high degree of accuracy in achieving this alignment, since only when the alignment is perfect are the beam profiles obtained symmetrical, and this in turn is an assumption made in the subsequent analysis. To this end, the present inventor has devised a sophisticated five-axis stage arrangement (described in WO2008/119982) which, when used in combination with optical feedback from a BPR system, can be used to align a sample (including samples with complex shapes) to an arbitrarily high degree of accuracy.
However, the requirement for this alignment (whether achieved statically for flat samples by very accurate construction of supporting hardware, or dynamically for curved surfaces using a stage such as that referred to above) introduces significant cost and complexity into a BPR or BPE system.
More specifically, BPR and BPE tend to rely on the ability to fit a calculated optical interference fringe pattern to an experimentally-measured interference fringe pattern obtained from appropriate optical hardware. Where the sample being measured is misaligned, an essential part of this process is to be able to ascertain the nature of the misalignment (i.e. the actual orientation of the sample), which in practice means locating the centre of the beam profile, which, in the case of BPR and BPE comprises an interference fringe pattern. As disclosed in the Applicant's earlier application WO2008/119982, misalignment of the sample causes the image of the reflected laser beam's profile, after it has been refracted through the main objective lens, to become asymmetrical with more light being reflected in the direction towards which the sample is tilted. In that application, however, no quantitative estimate of the amount of misalignment was made, it being sufficient to know in which direction a motorised axis needed to be moved while an optical feedback loop was provided to monitor the changing alignment state.
In addition to the effect of misalignment in the sample's orientation, where the measured data is collected using a coherent laser beam as the light source, the interference fringe pattern is typically contaminated by a large amount of so-called ‘speckle’ noise caused by interference between specularly-reflected light from the sample and scattered light from surface defects and/or dust particles on the system's optical components.
The Applicants have found that, despite the existence of many algorithms for filtering noisy data and locating the centre of an interference pattern, none of them have proved suitable for the peculiar characteristics of BPR and BPE fringe patterns where (a) the fringe spacing is not regular but becomes much ‘denser’ as one goes from the centre to edge of the pattern, with the rate-of-change depending on the sample refractive index which is not known beforehand, and (b) misaligned fringe patterns do not consist of perfect concentric circles but of ‘distorted’ circles which are also unevenly illuminated.
It is therefore an aim of the present invention to address these issues in order both to smooth out a noisy interference pattern and to accurately locate its centre.
By way of further background, FIG. 1 illustrates a typical BPR beam profile in the form of an interference fringe pattern 10 for a misaligned sample. As can be seen, this pattern 10 comprises a set of nominally concentric fringes 12 (however, such fringes are not always present in the interference pattern, for example, where very thin coatings are provided on the sample). It will also be clear from FIG. 1 that the interference pattern 10 comprises numerous ‘asymmetries’. In particular, an essentially random laser speckle pattern is overlaid on the fringe pattern itself, and can cause intensity variations of ˜10% of the fringe intensity, sometimes more. Even for a well-aligned sample, if the light source is plane-polarised then the fringes 12 are not perfectly circular: they have reflection symmetry (in the case of a horizontal or vertical polarisation, the symmetry is top/bottom and left/right) but not rotation symmetry. Also, when there are multiple fringes 12, the fringe 12 spacing decreases rapidly as one goes from the centre of the pattern 10 to the edge, but the rate at which this happens depends upon the very properties of the sample that one is usually trying to measure with the BPR apparatus (for example, the thickness of one or more thin film coatings on the sample). This last feature, in particular, rules out the standard method of filtering an image for speckle noise, namely to produce a two-dimensional Fourier transform and then remove the high-frequency components, because the level of filtering necessary to smooth the widest, innermost fringes 12 is likely to obliterate the outermost fringes 12 altogether. Furthermore, when the sample is misaligned, the fringes 12 become ‘compressed’ in the direction of the misalignment and ‘stretched’ elsewhere, so that even the top/bottom and left/right reflection symmetry is lost and the illumination is such that neither the brightest part of the image, nor its centroid (which can be thought of as the ‘centre of gravity’ of the image where brightness corresponds to mass) correspond to the centre of the fringe pattern 10.
It is therefore an aim of the present invention to provide an apparatus and method that addresses at least some of the afore-mentioned problems.