Апрель 2003

(письмо, отправленное профессору Л.П. Литхарту с проектом ответа на замечания рецензентов)

 

Dear Prof. Ligthart,	Уважаемый профессор Литхарт!
below I give my analysis of the last comments.	Ниже я предлагаю свой анализ последних замечаний.
As a basis for correction, I used the paper's version ("Algorithms of estimating corrected-4.doc") you sent me. I did not remove yellow marks. All my suggested corrections and renumbering were marked by green. The part to be deleted is colored by red. Finally, I made some remarks for you, to clear my position.	В качестве основы для исправлений я использовал вариант статьи ("Algorithms of estimating corrected-4.doc"), который Вы мне прислали. Выделение текста желтым цветом я не удалял. Все мои исправления и повторная нумерация выделены зеленым цветом. Фрагменты, которые нужно удалить, выделены красным цветом. В заключении, я предлагаю ряд своих соображений, чтобы прояснить свою позицию.
I attach the new version of the paper as "Algorithms_of_estimating_corrected-5.doc".	К письму прикладываю файл с новым вариантом статьи "Algorithms_of_estimating_corrected-5.doc".
Sincerely yours, Dr. V. Karnychev	С уважением, д-р В. Карнышев

 

 

Replay on Comments of Reviewer 1

 

Comment 1

1) reference 4 still has not been modified. The reference given in the paper is inadequate and will be difficult to obtain by readers. The full ref I gave in the first review should be used.

 

I agree with this comment and suggest the following:

1. REPLACE the reference

 

1. Lueneburg E. "Radar Polarimetry: A Revision of Basic Concepts". Int. Workshop on Direct and Inverse Electromagnetic Scattering, Marmara Research Center, Gebze-Turkey, 1995

 

by

 

4. Serbest, A.H., Cloude S.R. (eds). "Pitman Research Notes in Mathematics", Vol. 361, Longman 1996, pp. 257-275

 

Comment 2

2) The authors have not related their main results (equations 16 and 25) to the pauli matrices. These matrices are widely used by the community to analyse polarimetric problems and so to make a connection between your work and the algebra of these matrices would help clarify your contribution.

 

In order to answer this remark, I suggest to do the following:

DELETE the paper text selection (starting from the first paragraph before Eqn. (10) up to Eqn. (13) inclusive

 

From elementary matrix theory it is known that any asymmetric matrix can be decomposed into a symmetric (S^(s)) and a skew-symmetric (S^(a)) component. The initial scattering matrix (9) is written as:

,

(10)

 

where

 

,	(10a)
.	(10b)

 

It is easily seen that these matrices take the form

 

,

(11)

 

and

 

,

(12)

 

where Δ is the complex weighting coefficient

 

.

(13)

 

INSERT the following text instead of the deleted selection

 

Let us decompose S with using the orthogonal system of Pauli matrices added by unitary matrix

 

, , , ,

(10)

 

so that the matrix (9) takes the form

 

,

(11)

 

where

 

.

(12)

 

Thus, the scattering matrix S is represented as follows

 

.

(13)

 

It is clear that the first three terms of the decomposition (13) form a symmetric component S^(s)

 

,

(14)

 

аnd the fourth term is a skew-symmetric component

 

 

or

 

,

(15)

 

where

 

.

(16)

 

As a result, the origin matrix is written as

 

.

(17)

 

Since "j" factor in (15) is not important for the further analysis, it will be omitted below.

 

RENUMBER all subsequent equations and the corresponding cross-references in the paper (the renumbering is marked out by green color in the corrected version)

 

INSERT the text in the paragraph that was after Eqn. (18) in the previous version (Eqn. (22) in the corrected version with the renumbered equations), so that this paragraph takes the form:

 

Since the ellipticity and orientation angles are chosen arbitrarily, it is possible to conclude that the second item in (22) with the proportional factor will not depend on e¢, q¢ parameters in the transformation matrix U¢ . Returning to Pauli matrices (10), one can say that this result is the consequence of the fact that is invariant to congruent unitary transformations. This also secures the fact that in backscatter if the S matrix is symmetric in one base it is symmetric in all bases (reciprocity theorem). In other words, the difference of the off-diagonal elements of the scattering matrix will be invariant to the radar polarization basis. Therefore, the parameter will only be determined by the non-reciprocal properties of radar object and can be considered as an objective characteristic of this object.

 

INSERT the text in the paragraph that was after Eqn. (26) in the previous version (Eqn. (30) in the corrected version with the renumbered equations), so that this paragraph takes the form:

 

It implies that the term in the decomposition (11) can be compared to a target which orthogonalises all incident polarisations (see, for example [17]). Thus, such target (by definition) will not take part in copolar RCS. That means that the signal scattered by a non-reciprocal object and received in a single-channel system will depend only on the «symmetric» part of the object's scattering matrix

 

Comment 3

3) The most important issue is the relation of this work to SVD. The basic problem is that for bistatic systems the maximum RCS will not be obtained for copolarised antennas..as I showed in my first review.. the authors make no mention of the importance of this 'mixed' antenna optimisation. The main contribution of this paper is in bistatic systems and so to miss out such a basic observation is I think poor.

I think your paper in this form is misleading. Readers may get the impression that they can calculate maximum RCS from the Huynen pa-rameters...this is not true for bistatic systems.

 

In order to answer this remark, I suggest to do the following:

 

INSERT the following paragraph before the point "Orientation angle" with Eqn. (45) in the previous version (Eqn. (49) in the corrected version with the renumbered equations)

 

It should be noted that "m" parameter ("maximal polarization") will unambiguously characterize a non-reciprocal object for monostatic case. However, this value can not be considered as the maximum response in the general case of bistatic configuration. Therefore, this parameter ("m") should be used with care in the latter case.

 

Below I would like to make some my remarks in reply to the 3^rd comment of the Reviewer 1.

 

I think there is a logic contradiction in the first reviewer's position. It is known a good rule: one should criticize a work for what it includes, but not for what it does not have.	В позиции первого рецензента есть логическое противоречие. Существует хорошее правило – критиковать работу за то, что в ней есть, а не за то, чего в ней нет.
The initial idea of the paper was to demonstrate an example of approach to estimating the polarization properties of an object with asymmetrical scattering matrix (by the example of non-reciprocal object) by measurement results of the scattering matrix quadratures. That is why we mentioned monostatic case and linear basis. If to agree with the reviewer, that the basic purpose of the paper should be bistatic systems, the significance of the paper in such form is really lost, because it would require the full and fundamental rewriting for bistatic configuration.	Все-таки первоначальный замысел статьи заключался в том, чтобы показать пример похода к оценке поляризационных свойств объекта с несимметричной матрицей рассеяния (на примере невзаимного объекта) по результатам измерения квадратур матрицы рассеяния. Именно отсюда следуют упоминания об однопозиционном случае и линейном базисе. Если согласиться с автором, что основное назначение статьи – это двухпозиционные системы, то, действительно, смысл публикации статьи в представленном виде теряется, потому, что в этом случае потребуется ее кардинальная переделка для двухпозиционной конфигурации.
I not quite agree with the reviewer's statement that "paper in this form is misleading. Readers may get the impression that they can calculate maximum RCS from the Huynen parameters". In the given paper the "maximum polarization" parameter is the similar value as well as, for example, SKK parameter in work [19], which considers bistatic problem from the very beginning.	Я не согласен, с высказыванием рецензента о том, что в представленном виде статья вводит читателя в заблуждение относительно полной ЭПР объекта. Параметр «максимальной поляризации» в данной статье служит такой же оценкой величины цели, как и параметр SKK в статье [19], но рассматривающей двухпозиционную постановку задачи изначально.