3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry. Page: 3 of 9
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limited surface sampling distance (1 mm). Standard commercial PMIs, on the other hand, can provide 3-dimensional
(3-D) surface measurements with nanometer accuracy and a few hundred micron lateral resolution, but their field of
view is generally much smaller (typically 100 to 150 mm) than the size of a typical x-ray mirror (1 m). Therefore,
the mirror has to be measured at a glancing incidence angle, which results in the following: a) the glancing angle
spreads the sampling of surface measurement points by a factor 1/sin 0(0 being the glancing angle relative the
surface) and decreases height sensitivity by the same factor; b) a return flat mirror is required to reflect the test beam
back onto the interferometer detector, thus adding further complication to the measurements; and c) the overall
measurement setup results in a longer beam path, which makes the system prone to thermal drift- and vibration-
induced errors.
An alternative to the above methods consists of using a large PMI system with an aperture the size of the optic to be
measured. Large PMI systems with a test beam diameter up to 800 mm have been built and can be commercially
procured. However, they are expensive and cumbersome. Furthermore, because a large-aperture PMI is usually
made by simply expanding the beam from a smaller-aperture PMI, the result is measurements with poor lateral
resolution, and the system becomes less attractive as a tool for measuring long grazing-incidence x-ray mirrors,
because only a few pixels are utilized in the lateral dimension of the mirror surface. Finally, such a large system
would need a long stabilization time and a very good optical system to obtain the desired resolution.
A promising approach to achieving high-resolution measurements with nanometer accuracy required for next-
generation x-ray mirrors is the technique that combines high-resolution interferometric measurements and stitching.2z-
The technique holds the potential for providing high-resolution surface topography with accuracy and resolution
better than that of other existing noncontact profiling techniques. The obtained data can be valuable for mirror
quality checks both during and after fabrication. For example, the data can be used to compute the deviation from a
specified surface profile, and the result can be used as feedback for a computer-controlled polishing system. The
surface data can also be used as input for simulating and predicting the performance of an optic under realistic
conditions.
In this paper, we report experimental results obtained using a semiautomated stitching system built at the Advanced
Photon Source (APS) x-ray optics metrology laboratory.
2. BASIC PRINCIPLE
The stitching concept is not new and has been the subject of many papers.2z- However, it has not been widely
considered until recently, and the stitching option is now becoming available in many commercial metrology tools,
such as roughness measuring instruments and scanning probe microscopes. Here we focus on its application to the
specific case of long-grazing-incidence x-ray mirrors, such as those used in synchrotron radiation beamlines.
The basic principle of the stitching technique is quite simple: It consists of using a standard small-field-of-view,
high-resolution interferometer to measure the surface of an oversized optic at a number of locations, resulting in
overlapped subaperture measurements that cover the entire optical surface (Fig. 1). Then these subaperture
measurements are stitched together with a computer program to construct a full 3-D surface profile.
Discussion on stitching algorithms can be found in references 9 and 10. The computer code used to stitch the data
obtained in this work was developed by one of the authors.l1 The details of the algorithm will not be discussed in
this paper. However, a brief description of the basic concept is as follows: The mathematical treatment consists of
computing and subtracting individual tip-tilt piston functions (f(x,v)ax+bx+c, with a, b, and c being the stitching
coefficients) from each subaperture measurement, and as a criterion for stitching quality, the software, in its present
first version, uses the global rms of all height errors (along the vertical "z axis") over all pairs of overlapping
subapertures.
One should be aware that the main (and almost the only) advantage of this criterion is its simplicity. Deriving
second-order functions generates first-order functions, which are readily solved using matrix formulation. However,
this linear processing implies that measurement errors are of Gaussian statistics. But if this were so, doors would
never slam during measurement and air disturbance would be negligible. This is because such phenomena generate
errors of amplitude many times the desired standard deviation (which is, say, 1 nm rms). According to Gaussian
statistics, these "events" should hardly ever happen.
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Assoufid, L.; Bray, M.; Qian, J. & Shu, D. 3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry., article, September 12, 2002; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc741012/m1/3/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.