Pupil function¶
A complex-valued aperture-plane function describing the amplitude transmission and phase shift imposed by an optical imaging system.
Core Idea¶
The pupil function combines aperture support, apodization, obscuration, aberration phase, and sometimes polarization conventions; its Fourier transform governs coherent point-spread behavior. Each pupil coordinate multiplies the incident field by a complex transmission; propagation then superposes those contributions in the image plane, converting aperture and phase structure into blur and transfer response. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Pupil function belongs to fourier optics and is useful where the analyst can specify the typed fourier optics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate wavelength, pupil coordinates and normalization, aperture support, amplitude, phase and aberration convention, coherence model, and propagation relation are explicit. The scope is broad within that domain but bounded by the need for wavelength, pupil coordinates and normalization, aperture support, amplitude, phase and aberration convention, coherence model, and propagation relation are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making wavelength, pupil coordinates and normalization, aperture support, amplitude, phase and aberration convention, coherence model, and propagation relation are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Pupil function can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Pupil function. Pupil function compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed fourier optics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express wavelength, pupil coordinates and normalization, aperture support, amplitude, phase and aberration convention, coherence model, and propagation relation are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of fourier optics because they reuse the typed fourier optics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Each pupil coordinate multiplies the incident field by a complex transmission; propagation then superposes those contributions in the image plane, converting aperture and phase structure into blur and transfer response., and type the carrier, state every parameter and convention in the definition, test that wavelength, pupil coordinates and normalization, aperture support, amplitude, phase and aberration convention, coherence model, and propagation relation are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Pupil function Domain-specific
Parents (1) — more general patterns this builds on
-
Pupil function is a kind of Structural Filtering Prime
The proposed strict upward parent is
prime:structural_filtering.
Hierarchy path (1) — routes to 1 parentless root
- Pupil function → Structural Filtering → Selection
Neighborhood in Abstraction Space¶
Pupil function sits in a moderately populated region (42nd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Physical Optics & Wave Propagation (21 abstractions)
Nearest neighbors
- Physical optics — 0.92
- Optical space — 0.89
- Jones calculus — 0.89
- Spatial frequency — 0.89
- Jones diagram — 0.89
Computed from structural-signature embeddings · 2026-09-08