Spiral Phase Masks Turn a Simple Camera into a Five-Dimensional Optical Encoder, Study Shows

A camera that records a single blurred, seemingly meaningless pattern and still tells you where an object sits in three-dimensional space, what wavelength lit it, and which orbital angular momentum state the system stamped onto the light has been demonstrated by researchers working on a computational imaging technique called interferenceless coded aperture correlation holography, or I-COACH. In a study published in the journal Discover Imaging, the team showed that spiral phase masks, which imprint a helical phase structure onto light passing through an imaging system, can serve as an independent fifth encoding channel alongside the three spatial coordinates and the wavelength. The work was led by Eulàlia Puig Vilardell and colleagues, with Vijayakumar Anand as senior author, and combines numerical simulations with optical experiments using a spatial light modulator and a CMOS camera.

The key conceptual move in the study is a shift in where the orbital angular momentum lives. In earlier work by the same group on vortex speckles generated through self-interference of orbital angular momentum beams, the angular momentum influenced the correlation properties of the recorded intensity but did not act as a separately controlled encoding dimension. In the new framework, the orbital angular momentum states are deterministically introduced by the imaging system itself and embedded directly into the point spread function, the characteristic blur pattern a point source produces in the system. The researchers are explicit that orbital angular momentum is neither a property of the object nor of the light emitted by it; the system’s phase masks create the vortex beams. Four dimensions, the lateral position, depth and wavelength, remain object properties, while the fifth, the topological charge of the spiral phase mask, is set by the system.

The optical layout is deliberately simple. Light diffracted from the object is collected by a refractive lens and directed toward a spiral phase mask, implemented on a spatial light modulator, which imparts a chosen orbital angular momentum value onto the beam. The modulated field is then recorded by an image sensor as an intensity-only hologram. Because the technique is interferenceless, it avoids the stringent requirements of conventional holography, such as vibration isolation, intensity matching between interfering beams and phase-shifted hologram acquisition, while retaining three-dimensional recording capability. The recorded intensity does not look like a picture of the object; the information is encoded in the point spread function, and a computational reconstruction step is needed to recover the image.

For reconstruction, the team used the Lucy–Richardson–Rosen algorithm, an iterative deconvolution method that the authors describe as fast-converging and robust to noise for point-spread-function-based incoherent holographic imaging. During calibration, a library of point spread functions is recorded for each combination of depth, wavelength and topological charge of interest. Reconstruction then works by processing the recorded object intensity with a candidate point spread function from the library. When the point spread function matches the state that actually produced the recording, the object image emerges; when it does not, the reconstruction fails in a measurable way. This matching behavior is what allows the system to identify which spatial, spectral and angular momentum state was present.

Before building hardware, the researchers ran simulations in MATLAB on a 500 by 500 pixel grid with 8 micrometer pixels, using a refractive lens of 5 centimeter focal length and a spiral phase mask designed with a diffractive lens function of 20 centimeter focal length at 660 nanometers. They swept the orbital angular momentum states from just above zero to 30 in steps of roughly 0.15, wavelengths from 450 to 870 nanometers, and object depths over a range of 8 millimeters around the lens focal plane. A reference state was fixed at a depth of 5 centimeters, a wavelength of 660 nanometers and a topological charge of 15, and the team computed normalized cross-correlations between this reference point spread function and all others, using a phase-only matched filtering condition as the similarity metric.

The correlation maps revealed structured and somewhat counterintuitive patterns. In the depth-wavelength plane, high correlation values ran along a diagonal band: an increase in wavelength could be compensated by a decrease in axial distance, a reciprocity the authors trace to the propagation term that depends on the product of wavelength and depth in the quadratic phase of the field. In the planes involving topological charge, the structure was symmetric around the reference state, with strong correlation peaks appearing for decreasing topological charge whether depth or wavelength was increased or decreased. The researchers observed a many-to-one mapping, with recurring point spread structures at multiple parameter combinations, and noted that the spacing of these recurrences was not uniform. They emphasized that these multiple peaks arise from the intrinsic physics of vortex-modulated point spread functions during Fresnel propagation, not from sampling limitations or aliasing of the spatial light modulator or detector.

Armed with the correlation analysis, the team selected states that were well differentiated from the reference and simulated the full system response for eight spatial-spectral-angular momentum states, using two values of each parameter: depths of 5 and 5.2 centimeters, wavelengths of 660 and 450 nanometers, and topological charges of 15 and 25. Two different test objects, the digits 2 and 4, marked the two depths. When all eight simulated recordings were reconstructed with the reference point spread function, only the matching state produced a successful reconstruction. When the complementary point spread function was used instead, three high-fidelity reconstructions appeared, revealing cross-talk between correlated states. Quantitatively, simulated reconstructions under matching conditions achieved a root-mean-square error of 0.05 and a maximum normalized cross-correlation above 0.95, while non-matching reconstructions fell below 0.53 in cross-correlation, with the two cross-talk cases reaching 0.72 and 0.91.

The optical experiments closely mirrored the simulations. A spatially incoherent high-power LED at 660 nanometers provided red illumination and another at 455 nanometers provided blue light, with a ground glass diffuser removing grating lines from the sources and bandpass filters sharpening the spectral bands before detection. The objects were a 50 micrometer pinhole and transmissive digits from a negative USAF resolution test target, positioned at 5 and 5.2 centimeters to encode depth. Grayscale spiral phase masks with topological charges 15 and 25 were displayed on a Thorlabs Exulus HD2 spatial light modulator, and the modulated field was imaged onto a CMOS sensor. Because the spatial light modulator is not achromatic, changing the illumination wavelength distorts the vortex beam, but since the mask was kept invariant and the point spread function of each state was recorded under the same conditions, the chromatic distortion cancels out during reconstruction, becoming part of each state’s characteristic point spread function.

The experimental results reproduced the simulated behavior with moderate degradation attributed to detector noise, slight optical misalignments and unmodeled aberrations. Under matching conditions, the optical reconstructions achieved root-mean-square errors of 0.10 to 0.12 and maximum normalized cross-correlations between 0.89 and 0.95, while non-matching reconstructions ranged from 0.11 to 0.20 in error and 0.38 to 0.93 in cross-correlation. The same subset of states that reconstructed successfully in simulation also produced recognizable images experimentally, and the remaining states did not, which the authors interpret as evidence that the discrimination capability observed numerically survives realistic experimental perturbations. They also caution that the two quality metrics probe different things: root-mean-square error is sensitive to absolute intensity differences and noise, while the normalized cross-correlation measures structural similarity, so the two should be read as complementary indicators rather than equivalent scores.

The study stops short of claiming applications that have not yet been demonstrated. The experiments used flat, two-dimensional test objects, and the authors state that future work will extend the approach to fully three-dimensional objects, test the framework with coherent light, and explore advanced computational methods, including artificial intelligence based algorithms, to improve discrimination in strongly cross-correlated regimes. Within those limits, the demonstration establishes that orbital angular momentum can be incorporated as an independently controlled, system-defined encoding dimension in interferenceless coded aperture correlation holography, enabling discrimination of optical states across spatial, spectral and angular momentum domains and suggesting a route toward uses in optical communication, beam diagnostics and precision metrology.

Subject of Research: Five-dimensional optical encoding of spatial, spectral and orbital angular momentum information in interferenceless coded aperture correlation holography

Article Title: Five dimensional information encoding using spiral phase masks in coded aperture imaging

Article References: Vilardell, E. P., Joshi, N., Kahro, T., Rosen, J., Kukli, K., Gailevičius, D., Juodkazis, S., & Anand, V. (2026). Five dimensional information encoding using spiral phase masks in coded aperture imaging. Discover Imaging, 3(1), Article 8. https://doi.org/10.1007/s44352-026-00026-5

Image Credits: AI Generated

DOI: 10.1007/s44352-026-00026-5

Keywords: coded aperture imaging, computational imaging, orbital angular momentum, spiral phase mask, point spread function, incoherent holography, spatial-spectral-OAM states, cross-correlation, image reconstruction, optical communication, beam diagnostics, precision metrology