Holographic Interference Surfaces (HIS)

• HIS are engineered surfaces that use wave interference to encode both amplitude and phase information, providing a foundation for advanced imaging, metrology, and communications.
• They employ phase-shifting interferometry and analog power measurements to reconstruct complex field data, reducing hardware complexity in RF and optical systems.
• HIS technologies enable cost-effective, scalable architectures with applications in ultra-massive MIMO, programmable surfaces, and nanoscale materials processing.

A holographic interference surface (HIS) is an engineered structure that exploits the principle of wave interference—historically foundational in both classical optics and RF electromagnetism—to generate, encode, and reconstruct information-rich patterns for metrology, imaging, communications, and materials engineering. In its various physical manifestations, an HIS enables direct encoding of spatial amplitude and phase information, often by replacing complex signal chains with analog interference or by physical patterning at subwavelength or nanoscale resolution. HISs are now a central paradigm in scalable optical and wireless systems, high-resolution metrology, programmable surfaces, and advanced lithographic and materials processes.

1. Principles of Interferometric Holography in HIS

The unifying principle behind all HISs is the exploitation of interference between two waves—termed the “object” and “reference” waves—on a material or antenna surface. The fundamental formula encapsulating this effect is:

$$E_I(\mathbf{r}, t) = \left| E_o(\mathbf{r}, t) + E_r(\mathbf{r}, t) \right|^2 = |E_o|^2 + |E_r|^2 + E_o E_r^* + E_o^* E_r$$

where $E_o$ and $E_r$ denote the complex-valued object and reference waves, respectively. The interference (hologram) encodes both amplitude and phase information of the object wave, captured either as an optical intensity pattern, RF envelope, or spatial modulation on a physical surface.

In RF and optical HIS implementations, the phase information “hidden” in the cross-terms can be recovered using phase-shifting techniques—most commonly phase-shifting interferometry (PSI)—where the reference is shifted in phase (typically 0, π/2, π) and the resulting power/intensity samples are algebraically combined to eliminate DC and conjugate image terms:

$$\hat{E}_o = \frac{1-j}{4E_r^*} \big\{ I(0) - I(\pi/2) + j [I(\pi/2) - I(\pi)] \big\}$$

This allows full complex channel state or field information to be extracted using only analog power measurements (Yin et al., 14 Sep 2025, Huang et al., 2023).

2. Physical Implementations and System Architectures

HIS architectures span diverse application spaces:

• Electromagnetic Communications: HIS replaces traditional multi-antenna RF front-ends with a surface of low-cost sensors (e.g., power detectors or envelope detectors) operating purely in the RF power domain. The reference wave is introduced by a microstrip-fed oscillator, and object wave(s) arrive from users or external sources. All analog-to-digital conversion, down-conversion, and filtering in each antenna chain are rendered unnecessary, with a single control board performing global signal recovery via the interferograms (Yin et al., 14 Sep 2025).
• Metrology and Imaging: Optical HISs are realized by fabricating surfaces or elements that physically encode complex field or spatial interference patterns, often using multilayer semitransparent films, wavelike films, or Fourier-engineered profiles. These can function as compact, self-referencing interferometers, enhancing information content for phase measurement or high-resolution imaging in microscopy (Berz et al., 2016, Smolovich et al., 2017).
• Programmable and Reconfigurable Surfaces: Densely packed HISs (sometimes called “reconfigurable holographic surfaces”) use arrays of metamaterial or leaky-wave antenna elements to flexibly shape far-field beams by analog or amplitude-only programming, enabling low-power, multi-beam, and integrated sensing/communications functionality (Zhang et al., 2022).
• Materials and Nanofabrication: In materials processing, HISs manifest as directly written 2D or 3D surface patterns exploiting the interference of molecular beams with engineered nanoapertures (“Molecular-Beam Holographic Lithography”), enabling nanometric accuracy and material-agnostic nanofabrication (Zeng et al., 17 Jul 2024).

3. Mathematical Models and Information Recovery

Channel Estimation and Sensing

The essential innovation in HIS-based communications is channel state information (CSI) estimation from analog power (interference) measurements, rather than from time-/frequency-multiplexed pilots and full RF chains. The process hinges on two key mathematical steps:

1. Phase Demodulation of the Hologram: Using phase-shifted interferograms and known reference, the full object wave $E_o$ (amplitude and phase) is algebraically reconstructed, for each sensor.
2. Spatial and Spectral Analysis: The vector of reconstructed signals can be processed with classical algorithms (e.g., Bartlett DOA estimator, DFT) or with Prony-based segmentation methods for multi-user/channel discrimination, directly yielding quantities like spatial direction of arrival (DOA), CSI maps, or multi-user channel separation (Huang et al., 2023, Yin et al., 14 Sep 2025).

For wideband signals, the nonlinear structure of the hologram introduces strong cross-frequency self-interference (arising from quadratic combinations of subcarrier terms), which precludes standard DFT-based processing. HIS systems address this by designing geometric recovery maps (e.g., intersection of circles in the complex plane) or using ML estimation methods (with Wirtinger derivatives and noncentral chi-squared likelihoods) for unbiased CSI estimation. The performance is benchmarked against the Cramér–Rao lower bound (CRLB), and simulation confirms that accurate CSI can be achieved even in wideband settings (Huang et al., 30 May 2025).

Sensing and Localization

In multi-surface (e.g., multi-RIS or HMIMO) settings, HIS enables localization that seamlessly handles both near-field and far-field propagation physics. By sampling both spherical (near-field) and planar (far-field) steering vectors and fusing estimates across multiple surfaces, high-precision 3D localization is achieved. Interference management between surfaces is formulated as a constrained optimization minimizing the Fisher information bound and sidelobe emissions, typically solved via ADMM and manifold optimization (Cao, 5 Feb 2025).

4. Experimental Validation and Performance

A prototype system (Yin et al., 14 Sep 2025) consisted of a 32-unit array of patch antennas, each coupled to a reference wave and envelope detector. Experiments in an anechoic chamber with a horn antenna as object source demonstrated:

• Accurate Recovery of DOA: Bartlett processing of the reconstructed holograms matched theoretical DOA predictions across a range of angles.
• Phase Consistency: Phase distributions across the array, extracted solely from power domain interferograms, agreed with those from conventional digital receivers.
• Hardware Simplicity: Elimination of the requirement for one RF chain per element reduced system cost, power consumption, and design complexity, confirming the fundamental scalability rationales claimed for HIS-based architectures.

5. Efficiency, Scalability, and Impact on Communications Design

The adoption of HIS-based approaches gives several distinctive advantages:

• Power and Cost Reduction: By replacing phase shifters, mixers, and ADCs with passive envelope detectors, power consumption per array element drops by more than an order of magnitude in experimental systems (Zhang et al., 2022, Yin et al., 14 Sep 2025).
• Time/Frequency Resource Minimization: Since phase and amplitude are inferred directly via interference with a known reference (as in optical holography), there is a substantial reduction in pilot signal overhead and elimination of time-division multiplexed training (Huang et al., 2023).
• Green Communications and Ultra-Large-Scale Arrays: Unlike massively parallel digital arrays, the analog nature and simple hardware of HIS allow economic scaling to thousands or millions of elements, essential for next-generation 6G ultra-massive MIMO.
• Compatibility with Programmable and Intelligent Surfaces: HISs can function as passive, reflective, or transmitting surfaces, absorb or sense multi-user signals, and adapt their patterns dynamically, enhancing integration with RIS, ISAC, and other paradigms (Liu et al., 7 Jun 2024).

6. Extensions and Applications Beyond Wireless

HISs serve as foundational tools in multiple advanced areas:

• Integrated Sensing and Communication (ISAC): HIS supports joint radar/communication tasks via true multi-mode analog beamforming, maintaining low-power constraints and dense integration (Zhang et al., 2022, Liu et al., 7 Jun 2024).
• Photonic/Plasmonic Devices and Metrology: Self-referencing interferometers and surfaces with engineered Fourier spectra precisely manipulate light for metrological and imaging applications; noise-resilience and self-calibration are achieved by geometric field parallel transport and k-flip/U-unitary field rotations, enabling phase retrieval even in incoherent or discontinuous environments (Berz et al., 2016, Lassaline et al., 2019).
• Materials Science and Nanofabrication: MBHL and related methods exploit interference (notably via angular control of molecular beams) for direct, high-precision patterning, opening new regimes for device physics, 3D superlattice construction, and integration of organic and inorganic materials at the nanometer scale (Zeng et al., 17 Jul 2024).

7. Challenges and Future Directions

Critical research challenges remain, including:

• Error Analysis and Performance Bounds: Extension of CRLB-type performance benchmarks to non-Gaussian, nonlinear, and spatially structured HIS signals, especially under hardware non-idealities or high-multipath, multi-user interference (Huang et al., 30 May 2025).
• Hybrid Analog-Digital Architectures: Optimization of hybrid HIS-based transceivers that incorporate both analog (holographic) and digital (baseband) signal paths, especially in high-frequency, mmWave, and sub-THz bands (Zhang et al., 2022).
• Interference and Mutual Coupling: Management of mutual coupling in extremely densified arrays, tradeoffs in array aperture utilization, and design of interference-robust algorithms for multi-surface environments (Wang et al., 2023, Cao, 5 Feb 2025).
• Scalable Fabrication for Optical/Photonic HIS: Achieving subwavelength depth precision and overlay accuracy in patterned surfaces—bridging Fourier-optic designs with scalable thermal and molecular-beam lithographic techniques (Lassaline et al., 2019, Zeng et al., 17 Jul 2024).
• Entropic and Fundamental Physical Limits: Exploration of the role of HIS-related concepts in high-energy physics and cosmology, including holographic screens, entropy bounds, and extremal surface sequestration in AdS/CFT and quantum gravity (Chatwin-Davies et al., 2023).

• (Berz et al., 2016) — Twisted 3D holograms for self-referencing interferometers in metrology and imaging
• (Smolovich et al., 2017) — Optical elements containing semitrasparent wavelike films
• (Lassaline et al., 2019) — Optical Fourier surfaces
• (Huang et al., 2023) — Channel sensing for holographic interference surfaces based on the principle of interferometry
• (Wang et al., 2023) — Beamforming Performances of Holographic Surfaces
• (Liu et al., 7 Jun 2024) — Holographic Intelligence Surface Assisted Integrated Sensing and Communication
• (Zeng et al., 17 Jul 2024) — Direct Nanopatterning of Complex 3D Surfaces and Self-Aligned Superlattices via Molecular-Beam Holographic Lithography
• (Cao, 5 Feb 2025) — Hybrid Near-Field and Far-Field Localization with Multiple Holographic MIMO Surfaces
• (Huang et al., 30 May 2025) — Wideband channel sensing with holographic interference surfaces
• (Yin et al., 14 Sep 2025) — Holographic interference surface: A proof of concept based on the principle of interferometry

HIS represents a foundational shift in the encoding, transformation, and recovery of electromagnetic field information, and is emerging as a universal building block in next-generation communications, photonics, sensing, and materials engineering.