conjugate planes (original) (raw)

Author: the photonics expert (RP)

Definition: pairs of planes where an optical system images one into the other and vice versa

Category: vision, displays and imaging

Related: image planesimaging with a lensadaptive opticsgeometrical opticsparaxial approximation

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DOI: 10.61835/pow Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

What are Conjugate Planes in Imaging Devices?

An optical imaging system often works such that all points in a certain plane are imaged into points of another plane. At least within geometrical optics, there is then a one-to-one correspondence between points in the two planes: One point in one of the planes is mapped onto a certain point on the other plane, and vice versa, as shown in Figure 1. The two planes are then called conjugate to each other.

Figure 1: Imaging of points from an object plane to an image plane, which are conjugate planes. (The light path for the correspondence of two pairs of points is indicated with different colors.) The plane of the lens, for example, is not conjugate to the object or image plane.

Conjugate planes usually exist only within the paraxial approximation. For larger ray angles relative to the optical axis, the image points corresponding to points in one plane are often found to lie on a curved surface. This phenomenon is related to image distortion, as explained in the article on optical aberrations.

Just like conjugate planes, there are also conjugate points — one point in a plane is conjugate to another point in the conjugate plane.

Conjugate Planes in Imaging Instruments

Conjugate planes do not only come in pairs; there can be subsequent imaging stages, e.g., in a microscope, creating multiple planes which are conjugate to each other. One may also distinguish different sets of conjugate planes in a microscope:

• An image-forming plane set has planes at the specimen, an intermediate image plane near the eyepiece, and the retina of the observing eye, and normally also a plane in the illumination beam path.
• There is also an illumination plane set with the lamp filament (typically of a halogen lamp), condenser diaphragm, objective back focal plane and eye iris.

Those two plane sets are usually separated such that the structure of the lamp filament does not significantly affect the image of the specimen (principle of Köhler illumination): the plane of the lamp filament must be far from being conjugate to the specimen plane.

The understanding of conjugate planes is also vital in the context of adaptive optics. Generally, it is preferable to place the wavefront corrector in a plane which is conjugate to the plane where the phase distortions to be compensated are generated.

Conjugate Planes at Infinity

In a generalization of the concept, one or both of the planes can lie at infinity (i.e., at infinite distance from the imaging system). This can be the case for a telescope in its basic afocal configuration, where objects at an infinite distance are mapped to an image which is also at infinite distance. In other words, parallel incoming light rays are transformed into parallel rays at the output, just with some angular magnification. In a modified configuration, there can be an image plane at a finite distance on one side, where an image sensor can be placed, for example. Further, a slight increase of the distance between objective and ocular lens can also bring the object plane to a finite distance.

Frequently Asked Questions

What are conjugate planes in optics?

Conjugate planes are pairs of planes in an optical system where an object in one plane is sharply imaged onto the other. There is a one-to-one correspondence between points in these two planes, at least within the paraxial approximation.

Can an optical instrument have more than two conjugate planes?

Yes, a system with multiple imaging stages, like a microscope, can have several planes that are all conjugate to each other. For example, the specimen plane, an intermediate image plane, and the observer's retina can form a single set of conjugate planes.

How are conjugate planes used in microscope illumination?

In Köhler illumination for microscopes, the illumination system is designed so that the light source plane is not conjugate to the specimen plane. This ensures uniform illumination of the specimen, without imaging the structure of the lamp filament.

What does it mean for a conjugate plane to be at infinity?

A conjugate plane is at infinity if parallel light rays are associated with it. For example, an afocal telescope can map an object at an infinite distance to an image that is also formed at an infinite distance.

Why is this concept important for adaptive optics?

In adaptive optics, a wavefront corrector is most effective when placed in a plane that is conjugate to the source of the optical distortions. This allows the corrector to apply a phase correction that directly cancels the aberrations.

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