Magnification factor

The detection of the profile edges gives the projected wall thickness in pixels of the image data. The next step of data processing is the compensation of the magnification factor in the used tangential projection method. 

Calculate the magnification factor in Fig. XVIII-3. Assuming the scanning tip to be 2 A wide and the tip force to be 3 nN, calculate the pressure exerted on the DNA strand. 

The accuracy of any expression for first order errors can be improved as much as desired (so long as the expression is differentiable) by including additional terms of its Taylor expansion. For example, the error magnification factor in the age equation for the 230Th/238u term, (p, can be improved to include the second derivative, so the estimate of the effect of a given error in cp on the age becomes ... 

These designs avoid the possible stress developed in stepped horns. The amplification factor for either a linear or an exponential horn is the ratio of the end diameters (not areas as with stepped). The linear taper is the easier design to manufacture but its potential magnification is normally restricted to a factor of approx. 4-fold. The exponential taper offers higher magnification factors than the linear taper. Its shape makes it more difficult to manufacture but the small diameter of the working end and its length make it particularly suited to micro applications. 

In addition to penumbral blur, there is also a small magnification factor (A) at the edge of the mask. This is termed run-off distortion and results from the separation of source and mask as shown in the following equation ... 

Bioaccumulation is generally referred to as a process in which the chemical concentration in an organism achieves a level that exceeds that in the respiratory medium (e.g., water for a fish or air for a mammal), the diet, or both. The extent to which chemicals bioaccumulate is expressed by several quantities, including the bioconcentration factor (BCF), bioaccumulation factor (BAF), biomagnification factor (BMF), and trophic or food web magnification factor (TMF) [6]. The ecological, biological and chemical parameters involved in the transfer and accumulation of contaminants in food webs are complex. 

Small precipitates must be carefully inspected using polarized light because it may contain a microcrystalline shower. A microscope with a magnification factor greater than 100-fold can be useful in this case. 

Q is always positive and is essentially the error magnification factor from (7r /Rm to CTc/C. 

Example. Calculate the magnification factor for the above four examples related to Rb, Sr, U and Th. 

Note that for U and Th measurements, the use of man-made isotopes that are no longer existing in natural samples ( h and U) can minimize the magnification factor. In the above cases, only 0.08% and 0.03% increase in the relative uncertainties for U and Th concentrations. 

Example. Suppose we have =10 for the natural sample and =1000, find the optimal R and the magnification factor at optimal... 

Fig. 11.2. Plot of magnification factor as a function of when =0.1 and /Jj=150. The optimal value is = -v/o.lxlSO = 3.873. For a wide range 0.5 < < 30, the magnification factor is <1.26.

Note that the first derivative is always positive (cannot be zero), suggesting that error magnification increases with increasing when = 0. In this case, we can add a small amount of artificial spike to the mixture (to reduce magnification factor and to save often expensive artificial spikes). As long as is significantly less than/ , the error magnification factor remains small, as can been seen from the above examples for U and Th isotope dilution). 

Fig. 6 2PA spectrum of octatetraene in n-octane at 1.8 K. The total excitation energy is given by the sum of the number in the upper right corner of each strip and the values in the abscissa (both are in cm ). There is an overlap of about 300 cm between two consecutive strips. The numbers after x in each panel are magnification factors for the ordinate. Reproduced with permission from [71]. 1996, American Institute of Physics... 

Table 14 Comparison of trophic magnification factors (TMFs) for toxaphene congeners and recalcitrant organochlorines in food webs of large oligotrophic lakes1... 

Figure 4.31 Data for the characterization of an electrostatic lens, (a) Positions of the focal and principal planes (left-hand and right-hand sides are indicated by the subscripts Y and r respectively) and their distances (optical sign conventions are disregarded, i.e., the distances are described only by their lengths). (b) Geometrical construction applied to image the arrow ye by means of characteristic asymptotic trajectories, (c) Geometrical construction for an asymptotic ray with a pencil angle a,e. The shaded areas are needed for the derivation of the linear and angular magnification factors of the lens. For details see main text.

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