Authors
Xiao Wang, Kongo Lai, Shengtai Zhu, R John Koshel, José Sasián
Published in
Journal of the Optical Society of America. A, Optics, image science, and vision. Volume 43. Issue 10. Pages 1551-1557. Oct 01, 2026.
Abstract
Astigmatic focal loci govern field-dependent imaging behavior in optical systems. We derive the spatial loci of the local tangential and sagittal focal positions as the object point varies continuously along a meridional field line in a flat object plane. We show that, within the Coddington formulation, these loci range from simple low-order geometries-including lines, planes, and conic sections-to higher-order algebraic curves, depending on the physical interaction at the interface and the object position. For a real object and a concave non-diffractive spherical mirror, the tangential locus is an exact conic whose eccentricity is determined by the normalized object coordinate L/R, with e=R/(2L), where R is the algebraic radius of curvature of the surface and L is the algebraic axial coordinate of the object plane. In contrast, the refractive spherical surface retains a quadratic sagittal locus but generally produces a higher-order tangential locus, while the one-dimensional spherical gratings considered here generically give rise to higher-order field-dependent loci. Under the separate Rowland object-space condition, the tangential focal locus reduces to the same circular form for spherical mirrors, refractive spherical surfaces, and the spherical gratings considered here. These results extend the Coddington framework from a local description of astigmatism to a field-wide geometric characterization of the focal structure.
PMID:
42837592
Bibliographic data and abstract were imported from PubMed on 07 Oct 2026.
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