1D Diffraction-Limited Coronagraph (1DDLC)

• The 1DDLC is a Lyot-style coronagraph with a focal-plane mask that depends only on one coordinate, enabling one-dimensional nulling and high-contrast imaging.
• Experimental studies demonstrate nearly diffraction-limited performance at an inner working angle of 1λ/D with raw contrast suppression down to 10⁻⁵.
• Its design is optimized for rectangular apertures and fiber-fed observations, making it suitable for binary-star nulling and exoplanet spectroscopy via serial nulling.

Searching arXiv for the most relevant 1DDLC papers and closely related work. arXiv search query: "One-Dimensional Diffraction-Limited Coronagraph" One-Dimensional Diffraction-Limited Coronagraph (1DDLC) is a Lyot-style coronagraph whose focal-plane mask depends on only one focal coordinate, enabling diffraction-limited high-contrast imaging with an inner working angle of order $1\,\lambda/D$ while preserving a distinctly one-dimensional nulling geometry. It is especially suited to rectangular pupils or apertures well approximated by an inscribed rectangle, can suppress point sources on a line in the sky, and has therefore been presented as a binary-star nuller as well as a small-IWA coronagraph for fiber-fed exoplanet observations. Experimental studies have verified $10^{-5}$-level raw contrast mitigation at $1\,\lambda/D$, and later work has shown that its off-design chromatic leakage can be exploited by a downstream fiber nuller because that leakage remains on-axis-like at the Lyot plane (Itoh et al., 2023, Itoh et al., 30 Jun 2026).

1. Conceptual definition and scope

The defining property of the 1DDLC is that its focal-plane mask is one-dimensional: if the focal-plane Cartesian coordinates are $(x,y)$, normalized by $\lambda_c/D$, the mask depends only on $x$ and is invariant along $y$. This one-dimensionality is not merely geometric. In the formalism used for the first experimental verification, the coronagraph removes point sources on a line in the sky rather than suppressing the entire two-dimensional field, and the authors state explicitly that it “can remove point sources on a line in the sky,” which is why it has been proposed for high-contrast imaging of exoplanets in binary systems (Itoh et al., 2023).

The later serial-nulling work further sharpened this interpretation. There the 1DDLC is described as a binary nuller, with “binary” referring to the instrument’s ability to null a binary stellar system simultaneously because of the mask’s one-dimensional structure. The same work emphasizes that the mask’s invariance in one direction extends the nulling action naturally to line sources and therefore allows simultaneous suppression of double stars when aligned with the nulling direction (Itoh et al., 30 Jun 2026).

Within the broader coronagraphic landscape, the 1DDLC occupies an unusual design point. Compared with the one-dimensional band-limited mask coronagraph, it retains a diffraction-limited inner working angle. Compared with PIAA complex-mask coronagraphs, it preserves a diffraction-limited IWA while also retaining the one-dimensional property that is central to multi-star nulling and rectangular-pupil compatibility. This suggests that the 1DDLC is best understood not as a generic small-angle coronagraph, but as a specific one-dimensional Lyot architecture designed to combine small IWA, simple analytic structure, and favorable symmetry properties for rectangular apertures and line-aligned multi-source suppression (Itoh et al., 30 Jun 2026).

2. Mathematical formulation and diffraction-limited action

In the formulation used for the 1DDLC, the rectangular entrance pupil is written as

$$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$

with normalized pupil coordinates $\vec{\alpha}=(\alpha,\beta)$. A convenient pupil basis is

$$b_{kl}\left(\vec{\alpha}\right)=P\left(\vec{\alpha}\right)e^{2\pi i \left(k \alpha +l\beta\right)},$$

whose Fourier transforms are

$10^{-5}$0

with

$10^{-5}$1

In this basis the 1DDLC acts as a linear filter that removes all $10^{-5}$2 components and transmits the others up to a global factor, which is the precise sense in which it is diffraction-limited along one direction (Itoh et al., 2023).

The focal-plane mask is written as

$10^{-5}$3

with

$10^{-5}$4

chosen so that $10^{-5}$5. Because $10^{-5}$6 depends only on $10^{-5}$7, the mask is constant in the orthogonal coordinate and therefore implements one-dimensional nulling (Itoh et al., 30 Jun 2026).

The experimentally verified theory gives the corresponding filter tensor as

$10^{-5}$8

so the $10^{-5}$9 sector is perfectly removed while the $1\,\lambda/D$0 sector is transmitted up to the global factor $1\,\lambda/D$1. This is the key formal statement that the coronagraph nulls one specific one-dimensional subset of the diffraction-limited basis (Itoh et al., 2023).

A particularly important corollary is the preservation of the off-axis point-spread function at $1\,\lambda/D$2. For a source displaced by exactly $1\,\lambda/D$3, the derivation reduces to the vanishing of $1\,\lambda/D$4, so the off-axis amplitude is transmitted with unchanged shape apart from global attenuation. This is the mathematical basis of the experimentally observed statement that the output PSF at $1\,\lambda/D$5 is nearly completely the same as before the coronagraph (Itoh et al., 2023).

3. Optical architecture and physical implementation

Optically, the 1DDLC follows the standard Lyot sequence but with a specialized one-dimensional focal-plane mask. The entrance pupil is imaged to a focal plane, the mask $1\,\lambda/D$6 modulates the stellar field there, and the field then propagates to a downstream pupil plane where a Lyot stop rejects diffracted on-axis starlight. In the standalone 1DDLC this is followed by formation of the final science focal plane; in the serially coupled architecture, the Lyot-stop plane is instead used as the entrance pupil for a second nuller (Itoh et al., 30 Jun 2026).

The focal-plane mask is realized experimentally with polarization optics. A custom-patterned half-wave plate is placed between two linear polarizers, enabling real mask values in the interval $1\,\lambda/D$7. In this implementation the negative part of the mask corresponds to a $1\,\lambda/D$8-phase shift because

$1\,\lambda/D$9

The later experimental serial-conjunction paper states explicitly that the 1DDLC mask therefore combines amplitude modulation and $(x,y)$0-phase modulation, while the conference paper contrasts this linear-polarizer realization with the vector vortex, which uses a patterned half-wave plate between circular polarizers to trace unit-modulus complex values (Itoh et al., 24 Jul 2025, Itoh et al., 30 Jun 2026).

The first experimental verification used a He-Ne laser at $(x,y)$1, a square pupil of width $(x,y)$2, and an optical system with $(x,y)$3. Because the focal-plane mask had a finite clear aperture of about $(x,y)$4, corresponding to roughly $(x,y)$5, some undersizing of the Lyot stop was required; the Lyot stop width was set to about $(x,y)$6 rather than the $(x,y)$7 entrance-pupil width (Itoh et al., 2023).

The same experimental lineage later served as the front end for serial conjunction with a fiber nuller. In that work the 1DDLC was followed by a Lyot-plane phase mask, relay optics with $(x,y)$8 scaling, and a single-mode fiber, with sub-micron fiber positioning performed on a closed-loop piezo stage to manage mode matching and null-depth optimization (Itoh et al., 24 Jul 2025, Itoh et al., 30 Jun 2026).

4. Verified performance, throughput, and fiber compatibility

The central experimental result of the first dedicated 1DDLC demonstration was that the coronagraph mitigates the raw contrast of a star-planet system by at least

$(x,y)$9

even for a $\lambda_c/D$0 star-planet separation. At the same separation, the off-axis PSF was found to retain nearly completely the same profile as before the coronagraph, providing an experimental confirmation of the diffraction-limit argument based on $\lambda_c/D$1 (Itoh et al., 2023).

The behavior below the nominal diffraction scale is also distinctive. Measurements from $\lambda_c/D$2 to $\lambda_c/D$3 showed that sub-$\lambda_c/D$4 sources still produce relatively sharp transmitted PSFs rather than strongly smeared residuals. This was presented as particularly promising for fiber-based exoplanet spectroscopy. At the same time, the transmitted PSF peak is not astrometrically faithful at very small separations: the Gaussian-fitted output peak moved from about $\lambda_c/D$5 to $\lambda_c/D$6 as the true source separation varied from $\lambda_c/D$7 to $\lambda_c/D$8, so the peak location requires calibration if it is used as an estimator of angular separation (Itoh et al., 2023).

The same experiment quantified single-mode-fiber compatibility. The coupling efficiency exceeds $\lambda_c/D$9 when separation is greater than $x$0, and exceeds $x$1 when separation is greater than about $x$2. Under the convention used there—relative to the no-focal-plane-mask case, assuming linearly polarized-light injection, and excluding the factor due to the ratio of pupil width to Lyot-stop width—the off-axis throughput including fiber coupling is about $x$3 for a $x$4 source and about $x$5 for a $x$6 source (Itoh et al., 2023).

These experimentally verified properties explain why the 1DDLC has been repeatedly associated with fiber-fed observations. The combination of a sharp off-axis response near the diffraction limit, retention of PSF morphology at $x$7, and substantial coupling efficiency above roughly $x$8 makes the architecture unusually compatible with downstream mode filtering and spectroscopy (Itoh et al., 2023).

5. Chromaticity, tilt sensitivity, and higher-order variants

The main weakness of the single 1DDLC is sensitivity to wavelength detuning and tilt. Writing the normalized wavelength offset as

$x$9

the stellar leakage scales as

$y$0

Similarly, for angular offset $y$1, normalized by $y$2, the leakage scales as

$y$3

This is what the later work summarizes as second-order sensitivity to both spectral bandwidth and tilt aberrations (Itoh et al., 30 Jun 2026).

A crossed-double architecture raises both sensitivities to fourth order. Its focal-plane mask is the separable product

$y$4

and the corresponding leakage laws become

$y$5

The experimental serial-coupling papers, however, focus on the single 1DDLC and on the use of a second nulling stage rather than on an experimental demonstration of the crossed-double variant (Itoh et al., 30 Jun 2026).

The most important chromatic property of the single 1DDLC is not only the second-order leak amplitude, but the structure of that leak. The conference paper states that stellar leakage caused by wavelengths other than the design wavelength emerges on the Lyot-stop plane as a flat wavefront and therefore reaches the downstream focal plane with the same complex amplitude profile as an on-axis point source. The related experimental report describes the same effect as a “clean” stellar leak, meaning constant amplitude and phase on the Lyot-stop aperture and therefore the same functional profile as the amplitude of the on-axis point source before the coronagraph focal-plane mask except for a constant multiplication (Itoh et al., 30 Jun 2026, Itoh et al., 24 Jul 2025).

This chromatic structure is central to the subsequent development of the concept. Rather than treating bandwidth sensitivity as only a failure mode, the later literature treats the on-axis-like residual as a mode that can be rejected by a second nuller. A plausible implication is that the 1DDLC’s practical value lies not only in its standalone small-IWA behavior, but also in the regularity of the residual field it produces when operated away from the exact design condition (Itoh et al., 30 Jun 2026).

A separate but related one-directional coronagraphic development is the “spectroscopic fourth-order coronagraph,” which is built on a focal-plane mask that modulates the complex amplitude of the Airy disk along one direction and then uses two spectrographs to optimize the mask for each spectral element. That work reports $y$6 contrast at $y$7–$y$8 over $y$9–$$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$0 for the entrance pupil of the LUVOIR telescope. It is not identified there as a 1DDLC, but it belongs to the same broader family of one-dimensional, diffraction-limit coronagraphic strategies for overcoming the bandwidth limits of focal-plane complex masks (Matsuo et al., 2020).

6. Serial nulling, parity filtering, and current status

The most consequential recent extension of the 1DDLC is its serial coupling to a downstream fiber nuller, specifically a Parity Fiber Nuller (PFN). In this architecture the 1DDLC acts as the first nulling stage and the PFN as the second. The stages are deliberately non-redundant: the 1DDLC provides small-IWA access and produces a structured residual, while the PFN rejects that residual on the basis of parity and fiber-mode overlap (Itoh et al., 30 Jun 2026).

The PFN relies on the parity-selection property of single-mode-fiber coupling. The conference paper states that only the $$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$1 component of the input field can couple into the fiber mode. The Lyot-plane phase mask used in the PFN is

$$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$2

where $$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$3 are pupil-plane Cartesian coordinates normalized by the rectangular pupil dimensions. This low-spatial-frequency sign pattern produces four diffraction peaks separated by $$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$4 from the optical axis and is chosen so that the residual stellar field from the first stage is shifted into parity sectors that the centered single-mode fiber does not accept (Itoh et al., 30 Jun 2026).

The associated experimental report describes the same second stage somewhat differently but compatibly: the Lyot-plane mask splits the incoming beam into four beams so that, in principle, the on-axis single-mode fiber does not couple with the on-axis leak from the 1DDLC. That report gives the theoretical coupling efficiency for off-axis sources as $$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$5 at diffraction-limited separation angles and identifies $$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$6 as the tested off-axis operating point (Itoh et al., 24 Jul 2025).

Experimentally, the serial architecture has already demonstrated substantial mitigation of off-design leakage. One reported result gives a contrast-mitigation ability of

$$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$7

for a wavelength $$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$8 shorter than the coronagraph’s design-center wavelength, about $$P\left(\vec{\alpha}\right)=\mathrm{rect}\left[\alpha\right]\mathrm{rect}\left[\beta\right],$$9 of the value obtained with only the 1DDLC. The conference paper reports the same $\vec{\alpha}=(\alpha,\beta)$0 mitigation and likewise states a factor-of-20 improvement, while also noting a wording inconsistency concerning whether the detuned wavelength was “6-% less” than the design wavelength or “6.5% longer” in the body text and figure caption. The common substantive point is that the combined system removed much of the 1DDLC’s off-design leak and approximately recovered the center-wavelength suppression scale of the standalone 1DDLC (Itoh et al., 24 Jul 2025, Itoh et al., 30 Jun 2026).

The present limitations are explicitly described as experimental rather than fundamental. The serial demonstrations included no active wavefront correction, were affected by thermal instability, and required extremely precise fiber alignment and mode matching. The reported conclusion is therefore cautious: future work must demonstrate the anticipated broadband robustness for contrast levels below about $\vec{\alpha}=(\alpha,\beta)$1 (Itoh et al., 30 Jun 2026).

Parallel numerical work on a wide-spectral-band nuller built around the 1DDLC pursues the same objective from a different angle. By adding a Lyot-plane phase mask and an on-axis single-mode fiber, that study reports simulated planetary throughput of about $\vec{\alpha}=(\alpha,\beta)$2 for about $\vec{\alpha}=(\alpha,\beta)$3 planetary separation almost independently of spectral bandwidth, together with raw contrast of about $\vec{\alpha}=(\alpha,\beta)$4 for $\vec{\alpha}=(\alpha,\beta)$5 bandwidth and $\vec{\alpha}=(\alpha,\beta)$6 for $\vec{\alpha}=(\alpha,\beta)$7 bandwidth for a stellar angular diameter of $\vec{\alpha}=(\alpha,\beta)$8. The caveat there is strong azimuthal throughput dependence, which the authors note may degrade exploration efficiency compared to an isotropic throughput even though the wide spectral band partly offsets that penalty (Itoh et al., 2024).

Taken together, these results define the present status of the 1DDLC. As a standalone device it is a small-IWA, rectangular-pupil-compatible, one-dimensional Lyot coronagraph with verified $\vec{\alpha}=(\alpha,\beta)$9-scale operation, preserved off-axis PSF shape at that separation, and distinctive usefulness for binary-star nulling. As an evolving architecture it has increasingly been treated as the front end of a serial nulling system, where the regularity of its chromatic and tilt-induced leakage is not merely a limitation but also the reason that downstream parity-selective fiber nullers can remove that leakage efficiently (Itoh et al., 2023, Itoh et al., 30 Jun 2026).