Biophotonics_Concepts_to_Applications

level reaches its destination at either the light delivery site or at the photodetector
where the signal is evaluated and interpreted.
A standard and convenient method for measuring attenuation through an optical
link or an optical device is to reference the output signal level to the input level. For
convenience in calculation, signal attenuation or amplification can be designated in
terms of a logarithmic power ratio measured indecibels(dB). The dB unit is
defined by

Power ratio in dB¼10 log

Pout

Pin

ð 1 : 4 Þ

where Pinand Poutare the input and output optical powers, respectively, to an optical
fiber or an optical component andlogis the base-10 logarithm. The logarithmic
nature of the decibel allows a large ratio to be expressed in a fairly simple manner.
Power levels differing by many orders of magnitude can be compared easily through
an addition and subtraction process when they are in decibel form. For example, a
power reduction by a factor of 1000 is a−30 dB loss, an attenuation of 50 % is a
−3 dB loss, and a 10-fold amplification of the power is a +10 dB gain. Thus an
attractive feature of the decibel is that to measure the changes in the strength of a
signal, the decibel loss or gain numbers in a series of connected optical link elements
between two different points are merely added. Table1.6shows some sample values
of power loss given in decibels and the percent of power remaining after this loss.

Example 1.3Assume that after traveling a certain distance in some trans-

mission link, the power of an optical signal is reduced to half, that is,

Pout= 0.5 Pin. What is the loss in dB of the link?

Solution: From Eq. (1.4) it follows that the attenuation or loss of power is

10 log

Pout

Pin

¼10 log

0 :5Pin

Pin

¼10 log 0: 5 ¼ 10 ð 0 : 3 Þ¼3dB

Thus, the value−3 dB (or a 3 dB loss or attenuation) means that the signal

has lost half its power.

Table 1.6 Representative
values of decibel power loss
and the remaining percentages

Power loss (in dB) Percent of power left

0.1 98

0.5 89

179

263

350

625

10 10

20 1

1.5 Signal Attenuation 13