Linear and Angolar Moment of a General Spherical TEM and DEM Beam Radio Wave Detection with a Quadratic Order System Processor in State of Art Technology Implementation: A Three Axis Sensors Array Quadratic Order Correlator for the 21cm Radiation Radio Detection Coming from Early Universe

摘要

The paper focuses on an innovative spherical wave beam quadratic order processor, HSCS~(-1). It is an IP, Coulob Gauge based, to directly mesure, At and in any single P AP (along the propagation axis too) the quadratic order Poynting Vector, with both the complex Linear Momentum (LiM) and Angolar Momentum (AnM) contributions, as well as the the mutual quadratic order coherence function of any total or pseudo monochromatic observed beam wave. The focoused spherical quadratic order method, directly mesure the spherical complex OAM (time and propagation axsis invariant) which is composed by the observed beam wave modes. Such solenoidal energy modes, becomes relevant to mesure far distance (as exemple: distance greater than billions of light years away) sources radiations. Furthermore, HSCS~(-1) contemporary and directly mesure the mutual (spatial as well as temporal) complex coherence of any general complex divergent or not strictly TEM (as example: TEM+DEM) observed radiations. Tipically TEM+DEM radiations are characterized by N=LPM+1 complex wave beam modes. N is the number of considered EM fields modes, as great as requested; N and L are integer, which values are internal to a closed interval [0; ∞]; p and M are integer, which values are internal to a closed interval [1;∞]; n=0,l,...,N is the mode or beam channel index; with 1=0, 1,...,L; p= 1,..., P; and m = 1,.. .,M; n=/=0 is the fundamental mode index). Here are considered only the wave beam modes which satisfy the related Helmoltz monochromatic wave equation soluctions. As well known in Physics, only adopting a quadratic order energy processor it is possible Vt to contemporary and directely mesure in P, (A)P(θ; Φ; z) and (A)(P-P_0), both the proper P_0 position and quantity of motion (proper space time variations), or by a Fourier Transformation to contemporary and directely mesure proper phase and frequency spectrum variations, of the observed general radiation source. Effectively a quadratic order energy processor, like HSCS~(-1), directly mesure power spectrum related to both the first and the second observed wave beam time derivatives. Then it exstracts the proper Linear phase (Φ =ω t, with waves beam medium frequency ω in Δt=t) and Quadratic phase (θ depending on the waves beam frequency ω time derivatives in Δt=t)variations values which satisfy the observed source motion equation. Furthermore, HSCS~(-1) quadratic Poynting Vector and complex spherical Visibility processor is immune by planar interpherometric Phase error and mesurement ambiguity. Contrary, because any 1st order planar interferometry TEM system mesures only the TEM linear power density spectrum (LiM) contributions, it is impossible directly and without ambiguity mesure or assigne both spherical spazial position and quantity of motion of a general TEM+DEM wave beam source, At and (A)P(θ;Φ; z) and (A)(P-Po). Because 1st order TEM Systems are insensitive to longitudinal quadratic orders Fields modes, then a lot of energy related to the transverse AnM of observed wave beam is definitively lost. Morever 1storder measurement systems are affected by planar interpherometric distructive phase error and measurement ambiguity, because the measurement is sensitive to trasversal wave field modes (TEM, TE, TM) only. Effectively, HSCS~(-1) is sensitive to the quadratic spatial fast beam spherical phase variation [△ψ_(HSCS)-_LPM = ± (Δθ_(LPM) - ΔΦ_(LPM))] as well as to the linear temporal beam phase variation [coot] of the observed field. It extracts both transverse and longitudinal components of the observed solenoidal and/or irrotational fields (elecromagnetic, termodinamic, etc). The complex TEM+DEM wave mutual quadratic order coherence function γ, and the "Quadratic order fringes Visibility" as well as the related mutual quadratic order coherence degree may be directly computed by the innovative depositated IP, the synthetic spherical quadratic order system HSCS~(-1). The HSCS~(-1) direct measure of the mu