Re-Imaging Phased Array (RIPA)

• RIPA is a high-resolution imaging architecture that integrates phased arrays, confocal reflector geometries, and reconfigurable intelligent surfaces for adaptive beam steering and minimal electromagnetic blockage.
• It employs electronic beam steering and interpolation-free reconstruction algorithms to achieve precise focal mapping and noise-robust imaging in the Fresnel region.
• RIPA supports dynamic refocusing and programmable synthetic aperture imaging, enabling advanced applications in biomedical diagnostics, industrial inspection, and wireless communications.

The Re-Imaging Phased Array (RIPA) is a class of architectures and computational methodologies for high-resolution imaging and wave control that synthesizes the benefits of electronically scanned phased arrays, confocal reflector geometries, and, in recent implementations, reconfigurable intelligent surfaces (RIS). RIPA enables re-imaging of a phased-array aperture onto a focal-plane zone in the Fresnel region, achieving minimal electromagnetic blockage, adaptive beam steering, electronic refocusing, and interpretable mapping between physical and computational domains. This technology underpins advanced near-field imaging systems, facilitates programmable synthetic aperture approaches with single-antenna hardware, and supports robust, noise-tolerant reconstruction algorithms without spatial-frequency interpolation (Ghamsari et al., 27 Jan 2025, Patole et al., 2013, Goïcoechea et al., 13 Dec 2025).

1. Geometric and Electromagnetic Principles of RIPA

The canonical RIPA implementation employs a dual-reflector confocal ellipsoidal geometry, in which the phased-array feed (often a Vivaldi array) is located at one focus (O) of the ellipsoidal system. Both primary and sub-reflectors are generated as surfaces of revolution from ellipses with shared or distinct pairs of foci. The main reflector maps rays from the shared focus (P₁) to the image-plane focus (P₂), satisfying:

$|M - P₁| + |M - P₂| = 2a$

for any point M on the reflector surface, where 2a is the total focal separation (Ghamsari et al., 27 Jan 2025). Precise design relations govern focal mapping, eccentricity, and conic constants, establishing the path for each wavefront from feed to focal plane.

The system operates predominantly in the Fresnel region, mapping the phased-array feed aperture to a target region in the focal plane via deterministic geometric optics. This re-imaging inherently reduces central aperture blockage, since the confocal arrangement enables rays at small angles to traverse an engineered central opening in the primary reflector—an improvement over conventional Gregorian optics, where central blockage is substantial.

2. Beam-Forming, Phased-Array Integration, and Electronic Steering

A typical RIPA system integrates a 4×4 Vivaldi phased-array, tuned for a central frequency (e.g., 28 GHz) with unit-cell spacing selected to avoid grating lobes (d ≈ 0.42λ). The feed array employs electronic beam steering by applying spatially-varying phase shifts to each element, forming a directionally controlled main lobe:

$$W_{\theta,\phi}(a,b) = \exp\left[-j\,k\,(a\sin\theta\cos\phi + b\sin\theta\sin\phi)\right]$$

where $(a, b)$ are the element coordinates and $k = 2\pi/\lambda$ (Patole et al., 2013). The output beam from the array is redirected by the dual-reflector arrangement onto the focal zone, with the scan angle in the focal plane $θ_s$ approximately coinciding with the feed steering angle $θ_f$, provided the focal distances are suitably matched ($d_s ≫ d_1$), and with negligible scan error within the operational range.

Electronic beam-steering in two dimensions enables continuous scan of the field of view (FoV) without mechanical movement, yielding a lateral scan range consistent with the system's geometric field of regard. This approach offers a substantial signal-to-noise improvement relative to switched arrays, with theoretical SNR gain scaling as $N_a^4$ for an $N_a \times N_a$ array.

3. Imaging Algorithms: Interpolation-Free Reconstruction and Noise Robustness

In RIPA-enabled imaging, both the transmit and receive arrays coherently steer beams over a selected set of angles, systematically sampling reflected signals $s(\theta,\phi)$ that encode the spatial Fourier components of the scene's reflectivity $f(x,y)$:

$$s(\theta, \phi) = \frac{e^{-2jkz_0\cos\theta}}{k \cos\theta} F_{2D}\{f(x, y)\}(2k\sin\theta\cos\phi,\, 2k\sin\theta\sin\phi)$$

The inversion process applies phase and amplitude corrections before a two-dimensional inverse FFT on a uniform $(k_x, k_y)$ grid:

$$S_{\mathrm{corr}}(k_x, k_y) = [k\cos\theta]\, e^{2jk\,z_0\cos\theta} s(\theta, \phi)$$

$$f(x,y) = F_{2D}^{-1}\{S_{\mathrm{corr}}(k_x, k_y)\}$$

The steering angles are explicitly chosen to place measurements on a rectilinear spatial-frequency lattice, completely eliminating the need for interpolation between polar and Cartesian coordinates (Patole et al., 2013). The computational burden is minimized to a single inverse FFT and sample-level corrections, with noise performance enhanced by full-array gain.

Phase quantization and timing jitter in the steering network impose practical limits, but with phase shifter resolution $b \ge 4$–6 bits and precise timing ($σ_φ$, the phase noise, below sidelobe-raising breakpoints), array performance remains robust.

4. Dynamic Refocusing and Field-of-View Tuning

RIPA confocal systems support focal-plane position tuning—stand-off adjustment—by lateral displacement of the phased-array feed. In geometric terms, a lateral feed shift $\Delta x$ yields a focal-plane shift $\Delta z$:

$\Delta z = M_s \Delta x,\quad M_s=\frac{d_2}{d'_1}$

where $d_2$ is the second focus distance and $d'_1$ is the sub-reflector's first focal length. For example, with $M_s ≈ 6.5$, a 2.5 cm feed translation yields over 60 cm standoff variation. This enables dynamic refocusing without moving the reflectors themselves, validated via full-wave and ray-tracing simulations (Ghamsari et al., 27 Jan 2025).

The effective field of view is defined by the achievable steering angle, sub-reflector aperture, and main reflector geometry. For a 2 m stand-off and ±30° scan, the total lateral FoV is approximately 40 cm, with diffraction-limited spatial resolution:

$\delta_\perp \simeq 0.886 \frac{\lambda d_s}{D_M}$

yielding, for λ = 10.7 mm, $D_M$ = 0.8 m, and $d_s$ = 2 m, a spot size $\delta_\perp \approx 1.2$ cm.

5. Programmable Synthetic Arrays via Reconfigurable Intelligent Surfaces

The RIPA paradigm generalizes to architectures where physical phased arrays are replaced by a single antenna working in conjunction with a reconfigurable intelligent surface (RIS). In such a system, the RIS is programmed across a sequence of binary phase masks $\Phi_n$, each producing an electromagnetic field pattern that emulates a unique virtual transmit-receive configuration:

$y_n = a(\Phi_n)^\top R a(\Phi_n)$

$a(\Phi_n) = \Gamma(\Phi_n) G$

where $R$ is the scene's reflection matrix in the RIS element basis, $\Gamma(\Phi_n)$ encompasses RIS polarizability and coupling, and $G$ is the free-space coupling vector (Goïcoechea et al., 13 Dec 2025). Calibration of the RIS is obtained by measurements in the absence of the scene, permitting accurate recovery of physical array parameters and enabling the RIS to function as a full $N^d$-element synthetic array.

Linear inversion techniques, typically via pseudo-inverse SVD, facilitate direct reconstruction of $R$, from which high-fidelity confocal images, singular-vector wavefronts for selective focusing, and real-time tracking of moving objects can be derived. This enables full-aperture phased-array imaging and wavefront shaping with a single RF chain and a reprogrammable metasurface, vastly reducing hardware requirements.

6. Comparative Blockage, Performance Validation, and Hardware Considerations

Blockage, a central limitation in conventional array imaging with reflectors, is quantified as the ratio of the projected area of the sub-reflector to the primary reflector aperture. Confocal ellipsoidal RIPA designs achieve near-zero blockage ($B ≈ 0$), corroborated by COMSOL ray-tracing, while Gregorian counterparts exhibit blockage ratios up to 10–20% (Ghamsari et al., 27 Jan 2025).

Full-wave simulations and ray-tracing demonstrate diffraction-limited focusing (caustic formation), lateral scan ranges of ±20 cm, and sidelobe levels below –15 dB across the FoV. Phase errors are maintained within ±15°, preserving imaging fidelity.

The RIS-based synthetic array implementation further diminishes hardware requirements: a single vector network analyzer or software-defined radio, an RIS with rapid (≤1 kHz) switching, and simple calibration suffice for imaging with lateral resolution matching traditional multi-channel phased arrays. The computational inversion of the scene matrix ($N^d \times N^d$) is feasible within milliseconds for small to moderate array sizes, and frame rates approaching real-time can be achieved by mask optimization and parallelization (Goïcoechea et al., 13 Dec 2025).

7. Applications and Broader Implications

RIPA systems are applicable to near-field imaging, biomedical diagnostics, industrial inspection, and wireless communication environments where low-blockage, electronic scanning, and hardware efficiency are essential. The ability to refocus electronically, dynamically adjust FoV, and implement programmable wavefronts positions RIPA as a core architecture in adaptive wave control and sensing.

The generalization to matrix imaging with RIS platforms extends RIPA methodology to single-antenna systems, achieving selective focusing, clutter rejection, and real-time tracking even in non-line-of-sight and highly scattering environments, while reducing system cost and complexity. The reflection-matrix paradigm realized by RIPA connects microwave imaging, optical imaging, and wavefront shaping in a unified framework, facilitating advanced computational techniques and new modalities in computational imaging (Ghamsari et al., 27 Jan 2025, Patole et al., 2013, Goïcoechea et al., 13 Dec 2025).