1.3. Application of the measuring system's dimension lowering principle.
As it could be shown from formula (2) active systems of remote sensing are typical representatives of informational systems class with fading of signal. In order to synthesize an according subclass, now we consider major parameters of such systems, which could be interconnected:
Tk
max
- maximum duration of signal, reflected from mutual borders of layers;
Tk
max
- duration of holding of signal, during which signal, is faded.
Obvioully, that
Tkmax = 2 Tkmax;
Tkmin = 0;
Tkmin=0
As a result, averaged value of T
h could be assessed as
Thus, dimension of such a system could be lowered, if we accept that
T
hav=T
k.
Now we analuse two cases of influence of energetic lossess to the informational characteristics of such systems:
1) Fading of signal is not taken into account, when number of separable grandes of signal is determined;
2) Fading of signal is taken into account during aforesaid process.
Now we prove two following theorems, according to above cases.
Theorem 1: When correction of energetic losses is lacking in a system of active remote sensing, maximum amount of information could be reached at the output of system, if two - grade regime of output signal is chosen.
Prove: We use linear equivalent system of above one. Weight function
h(t), determined as reaction of a system to the input signal with one - grade amplitude is used as common charateristic.
Output signal of considered systems is determined as
Uout=Uin·h(t)
Number of grade in output signal
Where
D t - time period of passing of sensing light beam through layer of an object by thickness
D l. We consider the amount of information containing in received signal as a criterion of quality.
In order to investigate function (3) for extremum, we obtain its first derivative and equate it to zero. As a result we obtain following equation:
Where
Solution of transcendental equation (4) gives us
x
»0,8, which conforms to m=2 .
Thus, theorem 1 is proved.
Theorem 2. Maximum amount of output information could be reached in the systems of active remote sensing where correction of systemayic energetic losses (fading) is corrected, if multigrade regime of output signal is closen.
Prove: Correction of fading of received signal leads us to the fact, that number of separable grades in it could be assessed as
Where
s - noise of the system, including noise of receiver.
Consequently, amount of information in the output signal could be determined as
Investigating function (5) for maximum, we obtain its first derivative on n and equate it to sero. As a result we receive following equation
Where:
For example, if
y0=30, so
b and m=10.
Thus, theorem 2 is proved.
