Keywords: Optimization, Dimension Remote sensing, Theorem, Optical channel
Abstract Questions related with optimization of systems of active remote sensing (lidars, radars, sonars etc.) taking into account of energetic losses of sensing signal in the investigated medium are considered in first part of this submission. Physical model of such systems, envisaging energetic losses is considered.
It is shown, that mathematical model of remote sensing process, according which signal, reflected from the
n - th border doesn't contain influence of previous reflections from n-1 borders, could be obtained from considered physical model. In this case, signal reflected from
n - th border will contain of influence of systematic energetic losses in homogenous layers of the investigated object.
Theorems, optimizing grade regimes of system's output signals when correction of fading is carried out and is not carried out are proved.
In second part of this submission grounding of synthesis of optimal passive remote sensing systems is given. As a result of held research it was shown, that optimum value of band width of radiometers is existed within transparent wavelength band 3 - 5 mcm.
1. Optimization Of Active Remote, Sensing Systems
1.1. Principle of the measuring systems dimension lowering
Criterion of effectiveness of any class of measuring systems, could be expressed by functional
U = F (X, Y)
where X=(x
1, x
2, . . ., x
n) - vector, characterizing system's parameters, which could be managed;
Y=(y
1, y
2, . . ., y
n) - vector, composed of non - managed parameters of a
system.
If according to the principle of measuring system's dimension lowering [1], we assume, that vector
X=(x
1, x
2, . . ., x
n) characterizes determined class of n - dimensioned systems, so any specific lowering of
X's dimension will characterize some subclass of such systems. For lowering of
X's dimension we suppose, that some components of vector X are not independent and managed by other independent components of vector
X . Thus, vector X is substituted by two vectors:
X
1 - independent or managing one, and
X
2 - dependent, or managed one. The criterion of effectiveness for such systems is functional of following type
U1=F(X1, X2, Y)
In common case, designating above dependence as
X
2 =
ø(X
1) we obtain
U
1F[X
1,
ø(X
1), Y] (1)
Therefore, the task of synthesis is lead to the searching of maximum of functional (1) for subclass of systems.
It should be noted, that two variants synthesis of subclasses are possible: 1. Function
ø(X
1) is unknown and should be determined [1]; 2. function
ø(X
1) is known [2].
In this submission we consider the second variant of synthesis applied for active and passive systems of remote sensing.
1.2. Model of researched object
A multilayered model, consisting of n - number of various homogenous layers is accepted as a basic model of studied object of active remote sensing. We assume, that sensing signal loses its own energy as a result of two processes:
1. Reflections from mutual border of any two various contiguous homogenous layers.
2. Fading in homogenous layers of studied object.
Working principle of the considered systems is explained by figure 1, where numbers mean: 1 - light emitter; 2 - studied objects; 3 - receiver.
Figure explaining work principle of active remote sensing.
Now we assess the value of the signal in the output of such systems. If could be shown, that signal reflected from
n - th border could be assessed using formula:
where d
o - coefficient indicating fading of signal during its propagation till object;
d
i - fading in i - th homogenous layer; k
i - coefficient of reflection from i - th border.
We could assume, that signals are corrected by multilication to the coefficients
In this case signal from n - th border is calculated as
Thus, corrected model fully keeps informativeness, because, information of signal reflected from n - th border is characterized by coefficient
k
n.
