aberration

Deviation of optical imaging results

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aberration^[1] (Full name: aberration) refers to the actual optics In the system result And paraxial ray tracing Gaussian optics (First order approximation theory or Paraxial ray ）Ideal deviation 。 Aberrations mainly include spherical aberration, coma, field curvature, astigmatism, distortion chromatic aberration And wave aberration. The above aberrations are detailed Introduction to.

Chinese name: aberration
Foreign name: aberration
Classification: Chromatic aberration and monochromatic aberration

Full name: Chromatic aberration
From: physics
Discipline: Physics

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nine Scientific research achievements

Aberration Introduction

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Aberrations generally fall into two categories: Chromatic aberration And monochromatic aberration. Color aberration chromatic aberration , due to the Refractive index Is a function of wavelength, and the resulting aberration. It can be divided into position color difference and magnification color difference. Monochromatic aberration means that even at height Monochromatic light According to the effect produced, the aberrations also produced in the image can be divided into two categories: blurring and distorting the image. The former category includes Spherical aberration , coma aberration and astigmatism. The latter type has image field bending and distortion.

In actual work optical system The image formed is similar to Paraxial optics (Paraxial Optics， Gaussian optics ）The results obtained are different, with certain deviation, Optical imaging relative Paraxial imaging The deviation of is called aberration.

Due to image aberration imaging It is different from the original shape. Polychromatic light Caused by Chromatic aberration abbreviation chromatic aberration ； Nonparaxial monochromatic light Will cause Monochromatic aberration 。 There are five kinds of primary aberrations: Spherical aberration 、 Coma aberration 、 Astigmatism 、 Image field curvature And distortion.

The photographic head cannot focus all the light emitted from a single point on the negative film due to imprecise production or man-made damage Photosensitive film At the same position on, the image is deformed, or out of focus and blurry.

There are various aberrations in practical optical systems. The image formed by one object point is the result of integrating various aberrations; in addition Actual optical system It is completely possible not to focus on the ideal image plane, and then the aberration (the image spot on the real image plane) will certainly change. In astronomy, the spot plot of ray tracing is often used to represent the actual aberration; Also available Wavefront aberration To represent the aberration. The light wave emitted by an object point is spherical wave , after passing through the optical system, Wavefront Generally, it is no longer spherical. The deviation from a spherical surface centered on a reference point multiplied by the refractive index of the medium at that point is called wave aberration.

Seidel's Five Aberrations In 1856, Seidel in Germany analyzed that five types of mirror head image differences were caused by a single color (a single wavelength). This is called Seidel five aberration^[2] 。

Spherical aberration

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concept

In coaxial spherical systems^[3] The on axis point and the off axis point have different aberrations. The on axis point has the simplest form of aberrations because it is in an axisymmetric position. When the object distance L of the object point on the axis is determined and imaged with a wide beam aperture, its image intercept changes with the change of the aperture angle U (or the aperture height h), so the concentric beam with a certain aperture emitted by the object point on the axis is no longer a concentric beam after being imaged by the optical system. The ideal position of object point imaging l 'can be obtained in the paraxial area where the aperture angle is very small. The position where the imaging ray of any aperture angle U deviates from the intersection of the ideal image point and the optical axis is L'. When an object point on the axis is imaged at a certain aperture angle U, the difference between its image intercept L 'and the ideal image point position l' is called the spherical aberration of the point on the axis, also called the axial spherical aberration.

It has nothing to do with the height incident light Aberration proportional to the third power of pupil aperture. It makes all the image points in the ideal image plane become circular spots of the same size. The object point on the axis has only spherical aberration. adopt Entrance pupil Light from different bands on the optical axis converge at different points after passing through the optical system. These points are the same as Paraxial light Of Iconography The difference is called longitudinal aberration 。

Qiming point of single refraction sphere

For a single refraction sphere, it can be proved that there are three object positions that can avoid the spherical aberration of points on the axis. The three locations are:

1. The object point is located at the center of the sphere, that is, all rays will be incident along the normal direction of the sphere, that is, the incidence angle is equal to 0;

2. The object point is located at the vertex of the sphere. At this time, no matter what the U angle is, all incident rays that hit this point will also leave through this point after being refracted, that is, the image point is also at the vertex.

3. The object point is located at

At this time, for any aperture angle, I '=U, U'=I.

Coma

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concept

Coma

The object point located outside the optical axis, due to deviation Coaxial spherical system After imaging, the beam focusing is much more complicated than the point on the axis.

The meridian plane is the symmetry plane of the system and also the symmetry plane of the light beam. The light beam in the plane is still in the plane after the system imaging. Therefore, the structure of the meridian beam can be represented by a plane figure.

The off-axis object point B emits a beam of light that is full of the entrance pupil. The beam of light takes the main light passing through the center of the entrance pupil as the symmetrical center. The main ray z and a pair of upper and lower rays a and b. Before refraction, the upper and lower rays are symmetrical to the main ray, but after refraction, the upper and lower rays are no longer symmetrical to the main ray, and their intersection points deviate from the main ray.

It is formed with the first power of object height and the second power of incident pupil aperture Proportional The aberration of. If there is only cometary aberration, the light emitted by the off-axis object point passing through the different bands of the incident pupil will form a radius change on the ideal image plane and along the field The image circle offset in the radial direction. Their combination will make the image of the object point become the same shape as comet alike Diffuse spot 。

The coma is a kind of asymmetric vertical aberration of off-axis object point imaging with wide beam. Except for meridian and sagittal sections, other sections also have different forms of asymmetry. If the entrance pupil is a circle, the light entering the system at an off-axis point is a cone beam with the object point as the vertex and the main light as the symmetrical center. Different apertures correspond to different cone sizes. After passing through the system, due to the existence of coma, this beam is no longer a cone beam symmetrical to the main beam, and no longer converges at a point. It intersects with the Gaussian image plane to form a closed complex curve, and the shape of the curve is symmetrical to the meridian plane. The larger the light cone angle, the greater the degree of asymmetry. The whole entrance pupil can be seen as composed of numerous rings of different sizes. All conical light beams passing through these rings sent by off-axis objects pass through the system and cut off closed curves of different sizes and shapes on the Gaussian image plane, and stagger each other in the vertical direction. Finally, they are superimposed into a diffuse spot of complex shape symmetrical to the meridian plane.

Influence of aperture aperture on coma

The coma is caused by the spherical aberration of the refraction sphere because the main ray of the off-axis point wide beam does not coincide with the spherical symmetry axis. If the entrance pupil is set at the center of the spherical surface, the main light passing through the entrance pupil coincides with the auxiliary optical axis. At this time, the point outside the axis is the same as the point on the same axis. The incoming upper and lower light pairs will be symmetrical to the auxiliary optical axis, and the outgoing light must also be symmetrical to the auxiliary axis. The spherical surface will not produce coma. The farther the entrance pupil deviates from the center of the ball, the more serious the asymmetry, and the greater the difference in intelligence.

Field music

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Image surface bending

Let the spherical object Q be concentric with the refractive sphere R. It can be seen from the analysis that the object on the vertical axis plane cannot be imaged on the ideal vertical axis image plane, and this deviation phenomenon gradually increases with the increase of the field of view, so that the plane object perpendicular to the optical axis becomes bent after spherical imaging^[4] 。

Aberration in direct proportion to the second power of the object height and the first power of the entrance pupil aperture. If there is only field curve, all points on the object plane have corresponding image points, but they are distributed on a sphere; If the negative is bent into this shape, clear images can be obtained everywhere. At this time, on the ideal image plane, the image points appear as round spots.

Astigmatism

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Astigmatism

When an off-axis object sends a very thin beam through the entrance pupil to enter the system, the asymmetry between the paired broad beam beams will be ignored, and the spherical aberration will not have a great impact on the thin beam^[5] 。 However, there is still asymmetry between the beam sections, which becomes more and more obvious with the increase of the field of view. The surface cut on the spherical surface by the thin beam emitted from the off-axis point B is obviously not a symmetrical rotary surface, it has different curvature in different section directions, and has the maximum or minimum curvature in the meridian and arc vector, which are perpendicular to each other, showing the largest curvature difference. Although the fine beams on the meridian and sagittal planes can converge at a point on the main optical line respectively, they do not coincide with each other, that is, an off-axis object point is imaged with a fine beam and is focused into two images, meridian and sagittal. This aberration is called fine beam astigmatism.

If there is only astigmatism, the light of the off-axis object point will focus into two focal points after passing through the optical system. At the midpoint of these two focal lines, light beam Minimum formation Mi scattered circular 。 If the negative is bent to such a position, it can be obtained that the dispersion of image points everywhere is the smallest Circular spot 。 At this time, on the ideal image plane, the image point is Elliptic spot 。

distortion

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Distorted aberration

Ideal optical system In, the vertical axis magnification on the conjugate plane of the object image is constant, so the image is always similar to the object. However, in practical optical systems, such properties only exist in the paraxial region. In general, the magnification on a pair of conjugate planes is not a constant and changes with the increase of the field of view, that is, the axial object point and the edge of the field of view have different magnification, so the object and image are no longer completely similar. This kind of distortion aberration of image to object is called distortion.

Aberrations that are only proportional to the third power of the object height. If there is only distortion, the image obtained is clear, but the shape of the image is not similar to the object.

The above monochromatic aberration is only proportional to the total third power of the object height and the incident pupil aperture, called Third-order aberration (also known as Primary aberration ）In addition, there is also an aberration that is proportional to the total power of the object height and the entrance pupil aperture higher than the third power, called Advanced aberration 。

chromatic aberration

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In most cases^[6] Objects are imaged with polychromatic light (such as white light). White light contains monochromatic light of different wavelengths, and optical materials have different refractive indexes for spectral lines of different wavelengths. The lens calculation given in Chapter 3 shows that the focal length of the lens depends on the radius of curvature of the two surfaces and the refractive index of the material. When the radius is determined, the focal length changes with the refractive index. When the white light passes through the optical system, the system has different focal lengths for different wavelengths, and each spectral line will form its own image points, resulting in one object point corresponding to many image point positions and magnifications of different wavelengths. This kind of imaging color difference is collectively referred to as color difference.

chromatic aberration

Because the refractive index of the transmission material changes with the wavelength, the light of different wavelengths emitted by the object point will not converge at one point after passing through the optical system, but become a colored diffuse spot. It only appears when Transmission element Of optical system Medium. According to the relationship between the line size of aberration on the ideal image plane and the object height, it can be divided into:

① Positional chromatic aberration (also known as Longitudinal chromatic aberration ）Aberration irrelevant to object height, that is, light of different wavelengths converge at different focuses after passing through the optical system.

② Transverse chromatic aberration (also known as Magnification chromatic aberration ）Aberration proportional to the first power of object height. It makes the image heights of light of different wavelengths different, and the image of a point on the ideal image plane becomes a small spectrum.

These are the two most basic chromatic aberrations. Due to different wavelengths, monochromatic aberration will also be different, which is called Chromatic aberration , such as Chromospheric aberration 、 Chromatic coma Etc. If the object plane is at infinity, the above object height shall be replaced by that of the object point visual angle (i.e. the angle between it and the optical axis).

Wavefront aberration

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After the wave surface emitted from the object point passes through the ideal optical system^[7] The outgoing wave surface should be spherical. However, there are aberrations in the actual optical system, so there is a deviation between the actual wavefront and the ideal wavefront. When the actual wavefront is tangent to the ideal wavefront at the exit pupil, the optical path difference between the two wavefronts is the wavefront difference.

Scientific research achievements

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In October 2022, the Tsinghua University team proposed a new path to break through the world problem of optical aberration. Relevant research papers were published in the latest issue of Nature upper^[8] 。

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