In Figure 2, measurement point coordinate P and normal vector N are shown in Equations 1 and 2, in regard to coordinate system F. (1) (2) Figure 2 Overall coordinate system in this measurement. F, the coordinate system of the optical system. W, a coordinate system of the sample system. S, the coordinate system of the main body of sample. Because

there is the distance of coordinate system www.selleckchem.com/products/cb-839.html F and coordinate system W ‘L−Δy + R y ’ apart on Y 1-axis, in regard to coordinate system W, measurement point coordinate P is expressed by the coordinate transformation that Equation 1 is translated. In regard to coordinate system W, normal vector N becomes the same as coordinate system F. Therefore, Equation 3 translated Equation 1, in regard to coordinate system W. (3) In regard to coordinate system S, when measurement point coordinate P and normal vector N are also translated, they become Equations 1 and 2, respectively. (4) (5) Here, the shape derived by using y and n y has low precision. Therefore, the shape is derived by

assigning P(x, z) and N(n x , n y ) to derivation algorithm. This profiler determines the surface shape from the normal vectors and their coordinates by rotational motion, which is more accurate than linear motion and requires no reference optics. Therefore, there are no limitations on the measured shape, and free-forms can be directly measured [11]. Algorithm for obtaining the surface profile We developed an algorithm for selleck compound calculating the three-dimensional surface profile from the acquired normal vectors and their coordinates. A normal vector is equivalent to the surface slope or derivative of the surface profile. In this algorithm, to derive a figure from a normal vector and the coordinate, we express the figure by a model function and then fit the differential calculus function (slope function) to data on the normal vector by using the least-squares method. By calculating each coefficient of the series, the surface profile is determined. very Equations 6 and 7 represent the surface shape and slope for the two-dimensional case, respectively;

the same approach applies to the three-dimensional case. (6) (7) (8) (f j , normal vector or slope; x j , its coordinates). High-speed nanoprofiler Figures 3 and 4 show a photograph and a schematic view, respectively, of the newly developed nanoprofiler for normal vector tracing. The maximum mass of the main body of this machine is approximately 1,200 kg. The measurement sample can set up a greatest dimension to Φ = 50 mm × 40 mm, with a maximum mass of 1 kg and an optical pass length of 400 mm between the sample and the detector. Additionally, each optical element is set by the alignment that a laser beam changes 10 nm on QPD, when a normal vector changes 0.1 μrad. This machine has two pairs of two-axis rotational stages with resolutions of 0.17 μrad and one linear motion stage with a resolution of 1 nm.