Substitution method

In optical fiber technology, the substitution method is a method of measuring the transmission loss by (a) using a stable optical source, at the wavelength of interest, to drive a mode scrambler, the output of which overfills (drives) a 1-meter to 2-meter reference fiber having physical and optical characteristics matching those of the fiber under test, (b) measuring the power level at the output of the reference fiber, (c) repeating the procedure, substituting the fiber under test for the reference fiber, and (d) subtracting the power level obtained at the output of the fiber under test from the power level obtained at the output of the reference fiber, to get the transmission loss of the fiber under test.

Note 1: The substitution method has certain shortcomings with regard to its accuracy, but its simplicity makes it a popular field test method. It is conservative, in that if it were used to measure the individual losses of several long fibers, and the long fibers were concatenated, the total loss obtained (excluding splice losses) would be expected to be lower than the sum of the individual fiber losses.

Note 2: Some modern optical power meters have the capability to set to zero the reference level measured at the output of the reference fiber, so that the transmission loss of the fiber under test may be read out directly.

Source: from Federal Standard 1037C

The substitution method can also refer to an algebraic method for solving a system of equations (finding the point where two graphed lines intersect). The substitution method, unlike the elimination method, will solve for any type of system, whereas the elimination method will only solve for linear systems. In the substitution method, you do not have to have the equations in the same form. The substitution method infers that since the same variables are used, they equal the same thing. For example, for functions, two y's in an equation, although they may differ in the terms that they are said to be dependent upon, must equal the same thing. Take the equations y = x and y = 2x - 10. Since the same variables are used, they can be easily substituted. In this set of circumstances, you should take one equation (y = x for here), and substitute it in for the y in the other equation. You receive: x = 2x - 10. Then, simply solve it for x. Since there is a difference of 10 between the two, you should receive x = 10. Then, take the other equation (y = 2x - 10), and substitute 10 in for the x's. You should receive: y = 2(10) - 10. This simplifies to 20 -10 = y. Therefore, y = 10. The solution for the system is the ordered pair (10, 10). Always remember to substitute into DIFFERENT equations when you have solved for the first variable. You will not receive a correct answer if you substitute into the same equation.

Source: from <http://cstl.syr.edu/fipse/Algebra/Unit5/subst.htm>