Characteristic Curve

Figure 6-14. Typical Characteristic Curve

TM-1-1500-335-23 Nondestructive Inspection Methods Manual
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T.O. 33B-1-1 6-30 6.4.1.5.1 Logarithms provide a convenient method of multiplying and dividing. To multiply two numbers, you take the logarithms of both numbers and add them to get the logarithm of the product. To obtain the product, you then take the antilogarithm of this sum. The antilog is the inverse function of the log. In other words, the antilog of x is equal to 10^x. Table 6-11 lists the antilogs for mantissas of 0.000 to 0.999. The value of x is then obtained by properly placing the decimal point according to the characteristic of the sum of the logarithms. Example: Multiply 20 times 8 using logarithms. (1) Take the log of 20: log 20 = 1.3010 (2) Take the log of 8: log 8 = 0.9031 (3) Take the sum of these logarithms: 1.301 + 0.9031 = 2.2041 (4): Take the antilog of the sum: The antilog of 0.2041 = 1600 The characteristic of 2 indicates a number between 100 and 999. Therefore the answer is 160. This of course is the answer that we expected. In this example, the regular mathematical calculation is simpler. However, with very large numbers, the use of logarithms significantly simplifies calculation. 6.4.1.5.2 Division is accomplished by taking the difference between the logs of the two numbers. Example: 6/73 = antilog (log 6 - log 73). 6.4.1.5.3 In radiography, logarithms find particular use in the preparation of exposure charts and in film characteristic curves which plot film density against relative exposure as explained in paragraphs 6.4.1.6. Logarithms to the base 10 may be converted to natural logarithms by the equation ln x = 2.3 log x. 6.4.1.6 Characteristic Curve. The characteristic curve is the response of a type of film to radiation of a particular energy. It is obtained by plotting the film-image density against the logarithm of relative exposure. Since density is a logarithm, log-log scales are used for the plot. Log-log scales not only make interpretation of the graph easier, but also the all important values of relative exposure can be derived easily by subtracting one logarithm value from another. Study of Figure 6-14, shows that at low exposures, a large change in exposure is needed to produce a significant change in density. As the relative exposure increases, the film emulsion becomes more sensitive and the same exposure change produces a greater density difference. The gradient (slope) of the curve in Figure 6-14 increases with increasing exposure. At very high values the gradient may start to decrease; that is, the film again becomes less sensitive. However, this effect, although common with medical film, is not often encountered in industrial radiography. The term used to refer to the gradient of the characteristic curve is "film contrast."

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