Monocentric Lens Assembly

• Monocentric lens assembly is an optical design where multiple lens elements share a common center to suppress aberrations like coma and astigmatism.
• The design strategically manages air gaps and employs advanced anti-reflective coatings or metasurfaces to optimize transmission, stability, and thermal performance.
• Applications range from LWIR imaging to X-ray and gamma-ray focusing, illustrating diverse assembly strategies and trade-offs in optical engineering.

Monocentric lens assembly denotes, in the literature summarized here, several closely related optical constructions built around either a common center of curvature or a rigidly stabilized alignment geometry. The most explicit recent example is a two-glass monocentric lens assembly for long-wave infrared imaging over $8\text{–}12~\mu\mathrm{m}$, composed of a central IG6 ball lens and two concentric Ge hemispherical shell lenses, with the three elements sharing a common center so that the optical center, principal points, and nodal points coincide; in that configuration, coma and astigmatism are suppressed and wide-field imaging is supported (Kala et al., 18 Aug 2025). Closely related developments include a bio-inspired all-spherical monocentric fisheye lens with a curved sensor for single-shot RGBD imaging (Yu et al., 29 Oct 2025), a “monocentric-like” all-COTS compound objective (Cui et al., 21 Jul 2025), a parabolic monocapillary X-ray lens treated by its authors as a monocentric lens assembly (Zhou et al., 2020), quasi-monolithic fiber collimators (Carter et al., 2024), edge-centered oil-coupled lens groups (O'Brien et al., 2014), and crystal-by-crystal Laue lens assembly and calibration workflows (Barrière et al., 2013).

1. Common-center geometry and canonical refractive layouts

In the LWIR study, the monocentric lens assembly is a two-glass architecture consisting of L2, a central spherical ball lens made of IG6, and L1 and L3, two concentric hemispherical shell lenses made of Ge. The reported radii of curvature are 88.75 mm and 28.35 mm for L1, 28.35 mm and 28.35 mm for L2, and 28.35 mm and 73.05 mm for L3. The reported diameters are 56.7 mm for L2 and 108.3 mm for L3. Rays are focused onto a spherical image plane at about 91.7 mm from the center. The source/detector pupil diameter used in simulation is 52 mm, while the overlapping angular position uses an entrance pupil size of 91.7 mm (Kala et al., 18 Aug 2025).

The same source describes the defining optical consequence of monocentricity in explicitly geometric terms: the three elements share a common center, so the optical center, principal points, and nodal points coincide. In that arrangement, coma and astigmatism are suppressed. The paper situates this architecture in hemispherical image surface scenarios, particularly in the LWIR region, where minimal aberration, larger field-of-view, and high resolution are emphasized (Kala et al., 18 Aug 2025).

A different realization appears in the Bionic Monocentric Imaging framework, which uses a novel bio-inspired monocentric lens or monocentric fisheye lens group. That system is all-spherical, symmetric about the stop, and coupled to a curved sensor. Its tabulated optical layout uses H-ZLAF3 and H-ZPK5, with a sensor radius of $-7.199~\mathrm{mm}$, and the reported effective parameters are F/# = 1.8, FoV = 120°, and EFFL = 7.16 mm (Yu et al., 29 Oct 2025).

2. Air gaps as an optical and mechanical control parameter

In the LWIR monocentric assembly, the lenses are separated by air gaps because IR optical glues are unavailable. The two internal gaps lie between the IG6 ball lens and the inner surfaces of L1 and L3. All internal and external surfaces are assumed to carry anti-reflecting coatings, and the baseline internal air gap is initially taken as 10 $\mu\mathrm{m}$ (Kala et al., 18 Aug 2025).

The optimization objective is to maximize transmission through the lens assembly over the LWIR band while maintaining mechanical stability and acceptable imaging performance. The reported method is numerical simulation in COMSOL Multiphysics, using the finite element method on a 3D geometry. The optical performance is evaluated by varying air gap, incidence angle, temperature, and wavelength in the $8\text{–}12~\mu\mathrm{m}$ range, with transmittance, focal length, and spot size / RMS spot radius as the key output metrics (Kala et al., 18 Aug 2025).

At normal incidence, the transmission at $10~\mu\mathrm{m}$ rises to a maximum of about 58% when the air gap is 2.5 $\mu\mathrm{m}$. Beyond that point, transmission oscillates with further air-gap increase due to interference effects. When averaged across the $8\text{–}12~\mu\mathrm{m}$ band, the transmittance remains fairly constant and peaks at about 53.7% at around 2 $\mu\mathrm{m}$ air gap. These two values are therefore the main optical optima identified in the study: 2.5 $\mu\mathrm{m}$ for highest $10~\mu\mathrm{m}$ transmittance at normal incidence, and 2 $-7.199~\mathrm{mm}$0 for best average LWIR-band transmittance at normal incidence (Kala et al., 18 Aug 2025).

Angular dependence changes that conclusion in practice. As the incidence angle increases from $-7.199~\mathrm{mm}$1 to $-7.199~\mathrm{mm}$2, average transmittance decreases. The reported values include 52.7% angle-averaged transmittance at $-7.199~\mathrm{mm}$3 for 2.5 $-7.199~\mathrm{mm}$4 air gap, and 48.3% wavelength-averaged transmittance over $-7.199~\mathrm{mm}$5 at 2 $-7.199~\mathrm{mm}$6 air gap. The same study therefore treats air-gap selection as a trade-off among high transmission, wide-angle performance, thermal and mechanical stability, and stable focal plane with acceptable spot size (Kala et al., 18 Aug 2025).

An important design tension appears here. Although the optical maxima occur near $-7.199~\mathrm{mm}$7, the preferred initial gap for real operation is $-7.199~\mathrm{mm}$8, because that value preserves stability under heating and helps avoid collapse or contact of the internal ARCs at elevated temperature (Kala et al., 18 Aug 2025).

3. Thermal dependence, focal behavior, and spot formation

The LWIR paper treats temperature as a coupled optical and mechanical variable. It reports that the refractive indices of Ge and IG6 increase linearly with temperature, while thermal expansion changes lens thickness and reduces the air gap. Thickness expansion is modeled as

$-7.199~\mathrm{mm}$9

where $\mu\mathrm{m}$0 is the expanded thickness, $\mu\mathrm{m}$1 is the reference thickness, $\mu\mathrm{m}$2 is the coefficient of thermal expansion, $\mu\mathrm{m}$3 is the operating temperature, and $\mu\mathrm{m}$4 is the reference temperature (Kala et al., 18 Aug 2025).

Using that model, the study reports that as temperature rises from $\mu\mathrm{m}$5 to $\mu\mathrm{m}$6, the air gap shrinks from about 18 $\mu\mathrm{m}$7 to 1.55 $\mu\mathrm{m}$8 if it starts at 10 $\mu\mathrm{m}$9 at room temperature. This is operationally significant because the gap must remain large enough to avoid contact or collapse of the internal ARCs. Over all wavelengths and angles, the average transmittance is about 37% overall, and it rises to about 45% at $8\text{–}12~\mu\mathrm{m}$0. The reported explanation is that above about $8\text{–}12~\mu\mathrm{m}$1 the effective optical path for wide-angle rays becomes larger and the changed gap geometry increases transmission (Kala et al., 18 Aug 2025).

Focal length and spot size also change systematically with temperature and angle. The paper reports that focal length increases with temperature, decreases with incidence angle, and remains near 91 mm overall. At $8\text{–}12~\mu\mathrm{m}$2, the focal length is about 91.28 mm to 91.55 mm at $8\text{–}12~\mu\mathrm{m}$3, 91.08 mm to 91.36 mm at $8\text{–}12~\mu\mathrm{m}$4, and 90.57 mm to 90.82 mm at $8\text{–}12~\mu\mathrm{m}$5. Over the same conditions, RMS spot size increases with both temperature and incidence angle: about 35.89 $8\text{–}12~\mu\mathrm{m}$6 to 36.33 $8\text{–}12~\mu\mathrm{m}$7 at $8\text{–}12~\mu\mathrm{m}$8, about 35.76 $8\text{–}12~\mu\mathrm{m}$9 to 35.88 $10~\mu\mathrm{m}$0 at $10~\mu\mathrm{m}$1, and about 47.05 $10~\mu\mathrm{m}$2 to 48.23 $10~\mu\mathrm{m}$3 at $10~\mu\mathrm{m}$4 (Kala et al., 18 Aug 2025).

These results establish a recurrent feature of monocentric assemblies in the LWIR regime: air gap is not a passive tolerance, but a parameter that co-determines throughput, focal stability, and thermal survivability. A plausible implication is that any operational specification based only on room-temperature peak transmittance would be incomplete (Kala et al., 18 Aug 2025).

4. Interface engineering: conventional ARCs and metasurface replacements

The LWIR regime imposes unusually strong interface constraints. The paper states that only a few materials are transparent in LWIR, Fresnel losses are severe because of high index contrast, and internal gaps are unavoidable in IR because bonding or gluing is problematic. For that reason, the baseline lens analysis assumes 97% transmitting ARCs on all surfaces, with ARC layers taken as 1.25 $10~\mu\mathrm{m}$5 thick (Kala et al., 18 Aug 2025).

The same work proposes a metasurface-based replacement for conventional multilayer ARCs. The proposed structure is a subwavelength cone-shaped metasurface fabricated directly from the lens material. Its generic geometry uses $10~\mu\mathrm{m}$6 and $10~\mu\mathrm{m}$7. For air $10~\mu\mathrm{m}$8 Ge, the optimized values are $10~\mu\mathrm{m}$9, $\mu\mathrm{m}$0, and $\mu\mathrm{m}$1. For air $\mu\mathrm{m}$2 IG6, the optimized values are $\mu\mathrm{m}$3, $\mu\mathrm{m}$4, and $\mu\mathrm{m}$5 (Kala et al., 18 Aug 2025).

The reported performance is angle-robust and interface-specific. For air–Ge, transmittance stays above 95% up to $\mu\mathrm{m}$6 for both TE and TM. For air–IG6, transmittance stays above 96% over wide field angles. For the Ge–IG6 interface with air gaps from 1 to 5 $\mu\mathrm{m}$7, transmittance remains above 90% over the whole LWIR band. The paper attributes this transmission improvement to the Kerker effect, described as constructive interference between electric and magnetic dipole resonances (Kala et al., 18 Aug 2025).

The comparison with conventional multilayer ARC is explicit. Metasurface ARCs are described as more thermally stable, able to be grown on the lens surface, more robust against environmental fluctuations, and capable of much higher interface transmission than the assumed 97% multilayer coating baseline. In the context of monocentric LWIR assemblies, this shifts interface design from a secondary coating choice to a principal determinant of system throughput (Kala et al., 18 Aug 2025).

5. Assembly strategies in related monocentric and monocentric-like systems

A broader review of recent arXiv work shows that monocentric performance is strongly conditioned by assembly methodology. In the all-COTS robust objective, the optical train is a compound lens assembly built from five 2-inch-diameter fused-silica singlets and custom-machined brass spacer rings. The first element is a meniscus lens, the following lenses are mainly plano-convex, and the final element is a plano-concave lens. The spacer rings control spacing accurately, help align optical centers, maximize contact area, and prevent lens damage. Unlike older long-working-distance COTS objectives that form a collimated intermediate image and then require additional optics to refocus it, this design directly converges imaged light to the back focal plane. The demonstrated system has 61 mm front working distance, 0.30 clipped NA, 0.37 unclipped NA, diffraction-limited performance from 375 nm to 866 nm, and a 540 $\mu\mathrm{m}$8 FOV at 397 nm (Cui et al., 21 Jul 2025).

The quasi-monolithic fiber collimator adopts a different rigid-body solution. It consists of only three optical/mechanical parts: a single-mode polarization-maintaining optical fiber, a fused-silica glass cuboid or spacer, and an aspheric collimating lens. The lens is bonded to the cuboid, the optical axis is actively aligned to the fiber axis using a Shack-Hartmann wavefront sensor, and the fiber is then CO$\mu\mathrm{m}$9-laser welded to the cuboid. In this design, the cuboid length $8\text{–}12~\mu\mathrm{m}$0 is the critical spacing parameter, with 19.80 mm required for ideal collimation, 19.84 mm as the intended fabricated length, and 20 $8\text{–}12~\mu\mathrm{m}$1 as the standard manufacturing tolerance on total length. The reported mean beam-quality factor is $8\text{–}12~\mu\mathrm{m}$2, with a range from 1.125 to 1.474 (Carter et al., 2024).

The KOSMOS oil-coupled spectrograph camera presents a near-monocentric or circumferentially centered assembly concept. Lens elements are centered by their outside circular edges against silicone rubber O-rings, which simultaneously provide radial centering, axial and radial stiffness, and oil sealing. The key procedure is post-assembly compression: the group is assembled with essentially zero O-ring crush, then the cell is closed and the rings are compressed to about 15% of cross-section diameter. In test results, the dummy lens showed 16–36 microns TIR, corresponding to 8–18 microns of lens decenter, and at nominal 15% crush the two O-rings together provide about 2 lbf/micron radial stiffness. The same architecture uses Kapton tape shims with measured effective thickness 85 $8\text{–}12~\mu\mathrm{m}$3 and silicone-rubber diaphragms with about 1.2 cc total working volume to absorb oil-volume change (O'Brien et al., 2014).

The Laue lens assembly station extends the problem into soft gamma-ray focusing. There, the issue is not common-center refractive geometry but the assembly of thousands of diffracting crystals with arcsecond-level precision. The reported breadboard lens contains 15 crystals arranged in 3 concentric-ring sections on an aluminum substrate. The station uses a 12-m-long beamline, a thermally insulated enclosure maintained around $8\text{–}12~\mu\mathrm{m}$4 with stability within $8\text{–}12~\mu\mathrm{m}$5 during gluing, and a Davidson Optronics D-656 autocollimator. For the Bragg-angle misalignment standard deviation $8\text{–}12~\mu\mathrm{m}$6, the requirement derived from simulation is $8\text{–}12~\mu\mathrm{m}$7; the measured values are 25.7'' for ring 0, 5.7'' for ring 1, and 4.8'' for ring 2. The paper identifies substrate orientation as being as critical as crystal orientation (Barrière et al., 2013).

Taken together, these systems indicate that “monocentric lens assembly” is not restricted to one mechanical embodiment. It includes common-center refractive stacks, circumferentially centered oil-coupled groups, quasi-monolithic bonded heads, spacer-ring-stabilized compound objectives, and crystal-by-crystal focusing structures. This suggests that assembly fidelity is often as consequential as nominal optical prescription.

6. Cross-spectral extensions, optical encoding, and recurring limitations

The term also appears outside visible and infrared refractive imaging. In the parabolic monocapillary X-ray lens paper, the authors describe a parabolic monocapillary X-ray lens (PMXRL) as a monocentric lens assembly because the source is placed at the lens focus and the parabolic inner wall guides rays by total external reflection so that reflected rays emerge nearly parallel to the optical axis. The profile is written as

$8\text{–}12~\mu\mathrm{m}$8

with design value $8\text{–}12~\mu\mathrm{m}$9 in simulation and fitted value $\mu\mathrm{m}$0 after fabrication. The fabricated intercepted lens length is 60.8 mm. With an embedded square-shaped lead occluder, the measured outgoing beam divergence is 0.36 mrad, summarized as less than 0.4 mrad over 15–45 mm of the lens outlet, with 2–3 times gain. The central direct-ray component is eliminated, but the output is not perfectly symmetric because the soft lead occluder deforms during insertion (Zhou et al., 2020).

At the opposite end of the spectrum, the BMI system uses a monocentric fisheye lens as a physical encoder for joint image restoration and depth estimation. The reported principle is that the point spread functions vary strongly with object depth, changing from large ring-like structures at close range to compact point-like patterns for distant objects. The forward model discretizes depth from 0.7 m to 10.0 m into 94 layers at 0.1 m interval, uses RGB wavelengths 656.3 nm, 587.6 nm, and 486.1 nm, and accelerates convolutions by FFT on 40×40 sub-images. The reconstruction network is adapted from MIMOUNet into a dual-head architecture. In the reported comparison, the full system achieves Abs Rel = 0.026, RMSE = 0.130, SSIM = 0.960, LPIPS = 0.082, and PSNR = 31.36 dB; in downstream RGBD semantic segmentation it achieves mIoU = 41.17% with 10.08M parameters (Yu et al., 29 Oct 2025).

Several recurrent limitations appear across these studies. In the LWIR monocentric assembly, peak-transmission air gaps near $\mu\mathrm{m}$1 are not the preferred operational gaps because thermal contraction can collapse the spacing (Kala et al., 18 Aug 2025). In the X-ray PMXRL, the beam stop successfully removes direct rays, but soft lead deformation perturbs symmetry (Zhou et al., 2020). In the quasi-monolithic fiber collimator, the design simplifies tolerance management and performs at least as well as a commercial fiber collimator, but the reported back-reflection ratios are 36.4 ± 1.4 dB for optically contacted samples and 29.2 ± 1.0 dB for hydroxide-catalysis-bonded samples, compared with 44 dB for the commercial reference (Carter et al., 2024). In the Laue lens breadboard, two rings meet the $\mu\mathrm{m}$2 Bragg-angle dispersion target, but substrate placement errors on the order of 1 mm can produce angular error of order 16.5'' (Barrière et al., 2013).

The overall record therefore presents monocentric lens assembly less as a single fixed instrument class than as a family of optical-engineering strategies. Common-center geometry, rigid fixation of alignment-critical parts, controlled inter-element spacing, and explicit management of interface losses recur from LWIR imaging to X-ray collimation, gamma-ray focusing, fiber-to-free-space conversion, and coded RGBD acquisition. The literature further suggests that, in these systems, assembly details are inseparable from optical function.