In a next step, the height information is added separately to both parts of the contour line. This is the result of the sum of clockwise and counterclockwise revolutions, which in a closed 2D curve must differ by 1. If the contour line were left unprocessed as a single closed loop, the start and end point of the numerical processing, which are adjacent, would show a height difference of Δ nλ. This cutting process is necessary because the contouring method automatically generates two contour lines for each intensity fringe-which are displaced to the left and to the right with respect to the fringe center. The two parts are indicated by a green and a blue line.
It is cut into two parts in regions where the surface is flat (extrema or background).
#Contour interval software
This line is extracted by standard image-processing software and connects points of equal intensity. The upper right image displays the processed and smoothed contour line. The upper left image shows the corresponding spiral interferogram. Figure 28 shows an example for this demodulation for an immersion oil drop placed on a coverslip.
Contour line demodulation.Ī seemingly straightforward method to reproduce the surface profile makes use of contour lines. Two methods of single-image demodulation are now explained. For a visual improvement, an interpolation algorithm between adjacent lines can be applied. Now the sample structure is represented by a 3D spiral curve. To retrieve the absolute phase level, the number of complete revolutions must be kept in mind. This tangential direction reproduces after each complete 2 π-revolution this would not be enough to reconstruct the sample topography uniquely. The local tangential direction is determined, which is proportional to the height h of the phase profile at each position within the sample this height is given in units of the optical wavelength λ. (22), the topographic information of a pure phase sample can be reconstructed by using a standard contouring algorithm that proceeds through the entire spiral. Here Δ n is the difference between the refractive indices of the object and the surrounding medium, and λ the illumination wavelength. (22) h = − δ Ph Δ n λ 2 π up to multiples of Δ n λ. lt is, however, interesting to compare estimates of the same quantile using alternative methods. Note that because µ and σ have different meanings in the two different distributions, they are not comparable. Individual profile likelihood plots for µ and σ (not shown here) were used to obtain the likelihood-based confidence intervals.
The numerical values of the likelihood-based confidence intervals and intervals based on the normal-theory approximation are given in Table V. 100 provides an approximate 90%joint confidence region for µ and σ. For example, the region R > exp ( − χ ( 90.2 ) 2 / 2 ) =. Escobar, in Methods in Experimental Physics, 1994 8.4.3 Confidence Regions and intervals for µ and σ and for Functions of µ and σĪs described in Section 8.3.3, a contour line on Figure 4 defines an approximate joint confidence region for µ and σ that can be accurately calibrated, even in moderately small samples, by using the large sample χ 2 approximation for the distribution of the likelihood-ratio statistic.
0 kommentar(er)
