In AFM measurements it is obvious that the shape of the tip scanning the surface function determines the measurement result: a certain tip radius will result in a remarkable distortion of edges. These effects are usually treated in a more or less heuristic way. Morphological operations to determine the tip shape were derived from image processing almost 15 years ago. They are also used to recalculate the original surface from the distorted measurement. They have also been explained as a convolution, which brings up the idea that a deconvolution could be applicable. The current paper deals with a mathematical model leading to a spectral description of the resulting signal. This is of interest in several aspects: (i) identification of the actual nonlinear nature of the distortion process, (ii) estimation of the influence of the tip geometry on reconstruction, (iii) consequences for the time/time-frequency-domain characteristics of the AFM and its closed-loop control. The presented approach is neither based on morphological image processing nor on convolution. It can be utilized to determine the obtainable quality of AFM measurements and the limits of surface reconstruction.
For the fast acquisition of large amounts of BRDF data over wavelength to be compiled into libraries, a small, fast and rugged spectro-radiometer without moving parts for angular resolution is being developed. The system consists of an elliptical mirror which maps a semi-hemisphere onto a CMOS-detector with a dynamic range of 140dB. The detector has 32887 pixels which are calibrated radiometrically in the range from 10 -5 W/m² to 100 W/m² (7 decades). The system can take 30 semi-hemispherical BRDFs per second, i.e. nearly 1 million solid angles per wavelength per second. The smallest illumination spot has an area of 0.03mm², for spatial averaging the sample is mounted on x-y-stages, so the largest avaraged spot can be about 50.000 mm². Incoherent illumination is provided by a set of assorted LED´s. The paper deals with the instrument design, and gives some measurement results.
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