Passive synthetic aperture imaging with limited noise sources

Abstract

We consider a passive synthetic aperture imaging problem. A single moving receiver antenna records random signals generated by one or several distant noise sources and backscattered by one or several reflectors. The sources emit noise signals modeled by stationary random processes. The reflectors can be imaged by summing the autocorrelation functions of the received signals computed over successive time windows, corrected for Doppler factors and migrated by appropriate travel times. In particular the Doppler effect plays an important role and it can be used for resolution enhancement. When the noise source positions are not known, the reflector can be localized with an accuracy proportional to the reciprocal of the noise bandwidth, even when only a very small number of sources are available. When the noise source positions are known, the reflector can be localized with a cross range resolution proportional to the carrier wavelength and inversely proportional to the length of the receiver trajectory (i.e., the synthetic aperture), and with a range resolution proportional to the reciprocal of the bandwidth, even with only one noise source.

Detection of delayed target response in SAR

“…The simplified expression (25) allows us to attribute the range-delay ambiguity to W 0 R , which becomes the range factor of the imaging kernel in the case of a standard SAR, see (27). As the linearized approximation of T ϕ given by (22) is found insufficient to resolve the range-delay ambiguity, we bring along the quadratic terms in the expansion of cos ϕ and sin ϕ, which yields:…”

“…The condition κζ max b Φ means that the two-way travel distance difference 2 |x −z d |−|x − (z d + se 2 )| varies by at least (b Φ /2π)λ ≈ 3λ as x scans the synthetic aperture of angular width ϕ T . An analogy can be found in the expression (29) for ∆ A : it corresponds to the angle ϕ T such that for a pair of points z and (z + ∆ A e 1 ), the similar variation of the two-way travel path difference 2cT ϕ lin (see (22)) equals to λ.…”

“…Unlike previously, the imaging kernel W lin of (21) does depend on the crossrange coordinates. Moreover, the range coordinates y 2 and z 2 appear only in combination with (t y − t z ) as in T 0 , see (22). This, in particular, means:…”

“…where W 0 R = τ sinc(BT 0 ) as in (25), with T 0 defined by (22). This form of the imaging kernel will be used throughout the rest of this paper.…”

Mathematical modeling of the photoacoustic effect generated by the heating of metallic nanoparticles

“…But this is not the case in our problem, since our objective is to determine ε s pxq, while ε m pωq is known (which is the complete opposite of the setting where small inhomogeneities are imaged). Here to overcome these difficulties we may propose the use of multifrequency measurements H 2 pxq, ω P pω, ωq to localize z ‹ [15,28], where ω, ω are two strictly positive constants satisfying ω ăă ω. We will study this specific inverse problem in future works.…”