Schwarzschild criterion in optics
E350919
The Schwarzschild criterion in optics is a condition that determines when an optical system is free from spherical aberration by relating the geometry of the system’s mirrors or lenses to the paths of incoming light rays.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Schwarzschild aplanatic systems | 1 |
| Schwarzschild criterion in optics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3345038 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Schwarzschild criterion in optics Context triple: [Karl Schwarzschild, knownFor, Schwarzschild criterion in optics]
-
A.
Schwarzschild criterion
The Schwarzschild criterion is a condition in astrophysics that determines when a star’s interior becomes convectively unstable, leading to energy transport by bulk motion of stellar material.
-
B.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
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C.
Rayleigh criterion
The Rayleigh criterion is a fundamental limit in optics that defines the minimum angular separation at which two point sources can be distinguished as separate due to diffraction.
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D.
Principles of Optics
Principles of Optics is a seminal textbook that rigorously develops the theory of electromagnetic waves and optical phenomena, profoundly shaping modern physical optics.
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E.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Schwarzschild criterion in optics Target entity description: The Schwarzschild criterion in optics is a condition that determines when an optical system is free from spherical aberration by relating the geometry of the system’s mirrors or lenses to the paths of incoming light rays.
-
A.
Schwarzschild criterion
The Schwarzschild criterion is a condition in astrophysics that determines when a star’s interior becomes convectively unstable, leading to energy transport by bulk motion of stellar material.
-
B.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
-
C.
Rayleigh criterion
The Rayleigh criterion is a fundamental limit in optics that defines the minimum angular separation at which two point sources can be distinguished as separate due to diffraction.
-
D.
Principles of Optics
Principles of Optics is a seminal textbook that rigorously develops the theory of electromagnetic waves and optical phenomena, profoundly shaping modern physical optics.
-
E.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
- F. None of above. chosen
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
aberration-free condition
ⓘ
optical criterion ⓘ |
| aimsAt | stigmatic imaging for selected field points ⓘ |
| appliesTo |
lens systems
ⓘ
mirror systems ⓘ optical systems with spherical aberration ⓘ |
| assumes | paraxial approximation in many derivations ⓘ |
| basedOn | geometrical ray tracing ⓘ |
| category |
aberration theory
ⓘ
optical design principle ⓘ |
| concerns |
ray geometry
ⓘ
spherical aberration ⓘ |
| contrastsWith | numerical optimization methods in modern optical design ⓘ |
| describes | condition for zero spherical aberration ⓘ |
| ensures | coincidence of marginal and paraxial focus for spherical aberration-free design ⓘ |
| field |
geometrical optics
ⓘ
optics ⓘ |
| goal | elimination of spherical aberration ⓘ |
| historicalContext | early 20th century optical aberration theory ⓘ |
| influenced | development of aplanatic telescope designs ⓘ |
| involves |
conditions on incidence angles of rays
ⓘ
conditions on mirror or lens curvature distribution ⓘ conditions on object and image distances ⓘ |
| namedAfter | Karl Schwarzschild ⓘ |
| partOf | classical aberration correction methods ⓘ |
| relatedTo |
Schwarzschild criterion in optics
self-linksurface differs
ⓘ
surface form:
Schwarzschild aplanatic systems
Seidel aberrations ⓘ aplanatic condition ⓘ |
| relates |
geometry of optical surfaces to ray paths
ⓘ
mirror or lens shape to spherical aberration ⓘ |
| requires | specific relationships between surface curvatures and conjugate distances ⓘ |
| usedFor |
design of aberration-corrected imaging systems
ⓘ
design of aplanatic optical systems ⓘ |
| usedIn |
high-resolution imaging systems
ⓘ
microscope objective design ⓘ telescope mirror design ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Schwarzschild criterion in optics Description of subject: The Schwarzschild criterion in optics is a condition that determines when an optical system is free from spherical aberration by relating the geometry of the system’s mirrors or lenses to the paths of incoming light rays.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Karl Schwarzschild
Schwarzschild criterion in optics
→
relatedTo
→
Schwarzschild criterion in optics
self-linksurface differs
ⓘ
this entity surface form:
Schwarzschild aplanatic systems