The ball error is due toElectromagnetic lensCenter area and edge area pairelectromagnetic waveIt is caused by different convergence ability.Off axis electromagnetic wave passing throughlensThe electromagnetic wave scattered by the same object point does not intersect at a point after passing through the lens, but becomes adiffuseRound spot.Spherical aberration is the limiting lensDiscriminative abilityThe most important factor.
When the object distance L of the object point on the axis is determined, its image point position L 'is a function of the aperture angle U (or h). The difference between the actual image point and the ideal image point is called spherical aberration.Spherical aberrationSpherical aberration。From the point on the shaftlight beamAfter passing through the optical system, the light at different angles with the optical axis intersects the optical axis at different positions. Therefore, a circular diffuse spot is formed on the image plane, which is called spherical aberration.Generally, the actual light is relative to the intersection of the image side and the optical axisParaxial rayIntersection point with optical axis (i.eGaussianIt is measured by the axial distance of the image point.
aboutMonochromatic lightIn terms of spherical aberration, it is the only one that exists when imaging on axis pointsaberration。There are many kinds of aberrations in off-axis point imaging, and spherical aberration is only one of them.In general, single spherical surfacelensThe spherical aberration cannot be corrected. The positive lens produces negative spherical aberration, and the negative lens produces positive spherical aberration.For a point at a certain position, when theapertureandfocal lengthThe spherical aberration varies with the shape of the lens.Therefore, the double lens group or double glued lens group composed of positive and negative lenses with proper shape is a simple structure that can eliminate spherical aberration.Changing the shape of the lens while keeping the focal length of the lens unchanged is like bending a soft object back and forth, so it is called the overall bending of the lens. It is an important technique for correcting image errors in optical design.[1]
Causes of spherical aberration
Announce
edit
The ray with different aperture angle U intersects the optical axis at different points, and has different deviations from the position of the ideal image point.
Spherical aberration is the only monochromatic aberration at the point on the axis.
Measurement of spherical aberration
Announce
edit
The beam on the Gaussian image plane does not converge on an image point, but a circular diffuse spot.
Spherical aberration on shaft:
Vertical axis spherical aberration:
Symbol rules: from ideal image point to actual ray intersection point
DL>0 --- positive spherical aberration:
DL<0 --- negative spherical aberration:
Spherical aberration curve
Announce
edit
Corresponding maximum aperture angle UmaxHeight of incident light hmaxIt is called full aperture (edge light spherical aberration).
if
, it is called 0.7 aperture or 0.7 light (with photosphere difference).
Insufficient spherical aberration correction
The curve in the following form is generated due to insufficient spherical aberration correction:
Insufficient spherical aberration correction
Spherical aberration overcorrection
The curve in the following form is generated due to the overcorrection of spherical aberration:
Spherical aberration overcorrection
Another Spherical Aberration Curve with Primary Spherical Aberration and Secondary Spherical Aberration
The first item is called primary ball difference, and the following items are called secondary ball difference, tertiary ball difference, etc. in turn.All items other than the primary ball difference are collectively referred to as the advanced ball difference.[2]
Influence of spherical aberration
Announce
edit
The vertical spherical aberration of the entire aperture beam forms a circular diffuse spot symmetrical to the optical axis on the image plane, which makes the image of the point on the axis blurred in serious cases.[3]
Correction of spherical aberration
Announce
edit
(1) Three positions without spherical aberration for a single sphere
(2) Ziming lens
(3) Spherical aberration of single lens
(4) Combination of positive and negative lenses
Antispherical aberration
Announce
edit
A、In general, the spherical aberration elimination system can only make the spherical aberration of one aperture zero;
B、Generally, spherical aberration is corrected for edge aperture;
C、The spherical aberration of all apertures cannot be zero;
Spherical aberration distribution and representation
The total spherical aberration of the system is the superposition of spherical aberration generated by each refraction surface and transferred to the image space. Each refraction surface contributes to spherical aberration, and the contribution value is the spherical aberration distribution.
The image square spherical aberration consists of two parts: one is the spherical aberration generated by the refracting surface itself, and the other is the spherical aberration obtained by multiplying the object square spherical aberration by the rotation plane magnification.
Elephant square spherical aberration:
Face turning magnification:
Spherical aberration distribution coefficient and formula
Spherical aberration distribution coefficient
：
Refracting surface
And
The product of is the contribution of the refractive surface to the total spherical difference of the optical system.
It is called spherical aberration coefficient.
Calculation of spherical aberration distribution coefficient:
Definition formula:
Calculation formula:
, where,
。
application
Announce
edit
Set single refractionsphereThe radius of curvature of is r, and the refractive index of the media on both sides is noneAnd ntwo, when the object point is at three positions, that is, the vertex of the sphere（Object distanceu=0)、The sum of spherical centers is determined by l=r+r * ntwo/noneThe determined point does not produce spherical aberration, and the latter two cases have important applications.spherereflectorThere is no spherical aberration only when the object point is at the vertex and the center of the sphere.
All rotating secondary aspherical mirrors have a pair of conjugate points that do not produce spherical aberration.Among them,Parabolic mirrorIs the point and focus on the infinite axis;Ellipsoidal mirror andHyperboloidThe mirror is their focus.They all have practical applications.
