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J. Eur. Opt. Society-Rapid Publ. 22, 35( 2026)
motivate a class of space telescope designs that extend established architectures toward larger photon collecting area and instantaneous FoV, while delivering high angular resolution, high photon throughput, and stable, spatially uniform Point Spread Functions( PSFs). Within this design space, optical performance, survey efficiency, and information yield are more tightly coupled. In this work, we introduce a practical metric for quantitative comparisons of information collection rates across facilities, and examine two illustrative optical system architectures and the science opportunities they enable.
2 Resolution-weighted étendue for spacebased astronomy
Conventional étendue, AX, has been adopted as a firstorder figure of merit for survey efficiency( often quantified as survey speed), particularly in the sky-noise-limited regime, where the sky area surveyed to a given depth per unit time scales with the photon collecting area A and the FoV X. However, AX alone does not reflect the rate at which independent information is acquired at finite angular resolution. In particular, source blending and crowding impose a resolution-dependent limit on source detection and measurement such that increases in exposure time or étendue do not translate linearly into gains in effective depth or information acquisition efficiency.
Previous studies in survey telescope design and optimization have shown that survey efficiency depends not only on photon throughput but also on the PSF footprint( e. g., [ 11 ]). Building on this physical insight, we introduce a Resolution-Weighted Étendue( RWE) as a practical comparative metric. The RWE quantifies differences in the rate at which independent information is collected across telescopes by capturing both the light-gathering power per pointing and the delivered angular resolution.
In its most general form, the RWE may be written as
E RW; k ¼ A FoV; ð1Þ
PSF; k
where Ω FoV denotes the instantaneous FoV. To ensure RWE serves as a practical diagnostic tool of effective information throughput on an equivalent basis, we define Ω PSF, λ as the solid angle of the delivered system-level PSF measured at a chosen wavelength λ. Since the PSF size is intrinsically tied to the observing wavelength, the resulting RWE is a band-specific metric. Consequently, a meaningful crosscomparison of different facilities requires evaluating them at consistent or closely overlapping spectral bands. For Gaussian, near-circular PSFs, Ω PSF, λ ∝ θ 2 PSF, λ, allowing the metric to be equivalently expressed in terms of the PSF Full Width at Half Maximum( FWHM) at the specified wavelength λ, θ PSF, λ( typically in arcseconds).
In contrast to an idealized diffraction limited PSF such as Airy pattern for a circular aperture, X PSF, k accounts for the end-to-end performance of the actual optical train and
Figure 1. Étendue comparison for two distinct groups: optical / near-IR( filled symbols) and far-IR( open symbols) telescopes. The sample includes ground-based( orange) and space-based( blue and green) telescopes, selected to span a wide range of aperture sizes and FoVs, reflecting the diverse capabilities of current and next-generation facilities. Collecting area is evaluated assuming no field vignetting and excluding wavelengthdependent transmission, enabling a uniform, geometry-based comparison. The dotted gray contour lines show loci of constant étendue and serve as a visual reference for comparison. Standard étendue( squares) and RWE( stars) are projected onto a common FoV-based representation, enabling direct comparison on the same A – X plane. Specifically, the square symbols are plotted at( A, X FoV), while the star symbols are plotted using an effective, resolution-weighted FoV, X eff, FoV X FoV / X PSF, k. The Kim TMS Type-I space telescope and the gigantic ground-based telescope E-ELT [ 12 – 14 ] exhibit substantially larger RWE, corresponding to greater depth and more resolved detail per pointing despite its smaller geometric FoV.
its operational environment 1. ThisallowsRWEtoquantify the realistic information yield of a system and to penalize designs where theoretical resolution is degraded by practical constraints such as wavefront errors, pointing jitter, and detector-level sampling effects.
For consistent numerical comparisons across facilities, we further define a dimensionless RWE using a per-unit normalization as
1 For operational facilities( e. g., JWST), X PSF, k refers to the
measured on-sky PSF. For facilities that are in the design, development, or construction phase, it represents the predicted“ delivered” PSF, which incorporates the nominal optical performance combined with field-dependent aberration balancing tradeoff and expected system-level error budgets to reflect realistic performance once operational. Thus, even for space telescopes, achieving a large X FoV while maintaining a small X PSF, k is a challenging optical design optimization.