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Related Concept Videos

Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
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Atomic Force Microscopy

Atomic force microscopy (AFM) is a type of scanning probe microscopy that can analyze topographic details of various specimens like ceramics, glass, polymers, and biological samples. AFM offers over 1000 times more resolution than the optical imaging system. Images generated from AFM are three-dimensional surface profiles, offering an advantage over the flat, two-dimensional images from other imaging techniques.
The AFM Probe
The probe is regarded as the heart of any AFM setup and comprises the...

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High-speed Particle Image Velocimetry Near Surfaces
11:59

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Published on: June 24, 2013

Interpolated local model fitting method for accurate and fast single-shot surface profiling.

Tatsuya Yokota1, Masashi Sugiyama, Hidemitsu Ogawa

  • 1Department of International Development Engineering, Tokyo Institute of Technology, 2-12-1-W8-74 O-okayama, Meguro-ku, Tokyo 152-8552, Japan.

Applied Optics
|June 23, 2009
PubMed
Summary
This summary is machine-generated.

The interpolated local model fitting (iLMF) algorithm improves surface profiling accuracy. This new method overcomes limitations of the original local model fitting (LMF) by analyzing errors when surfaces are not locally flat.

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Area of Science:

  • Optical Metrology
  • Surface Metrology
  • Computational Imaging

Background:

  • Local model fitting (LMF) is a single-shot algorithm for surface profiling using spatial carrier frequency fringe patterns.
  • The LMF method's accuracy depends on the assumption of a locally flat target surface.

Purpose of the Study:

  • To analyze the measurement error of the LMF method when the locally flat assumption is violated.
  • To develop a more accurate and computationally efficient surface profiling algorithm.

Main Methods:

  • Theoretical analysis of measurement error in LMF.
  • Development of the interpolated local model fitting (iLMF) algorithm.
  • Experimental validation of the iLMF method.

Main Results:

  • Measurement error is theoretically proven to be zero at fringe intensity extrema, even with a non-flat surface.
  • The proposed iLMF algorithm demonstrates higher accuracy compared to the original LMF method.
  • Experimental results confirm the practical utility and improved performance of iLMF.

Conclusions:

  • The iLMF algorithm offers a significant advancement in surface profiling by addressing the limitations of the LMF method.
  • This new method provides a more robust and efficient solution for accurate surface measurements.
  • The findings have implications for various applications requiring precise surface characterization.