Optical system refers to the optical systemlens、reflector、PrismandDiaphragmAnd other optical elements in a certain order.Usually usedimagingOr doOptical information processing。Center of curvatureTwo or more on the same linerefraction(orreflex）The optical system composed of spherical surfaces is calledCoaxial spherical systemThe line where the center of curvature is located is calledoptic axis。[1]
An optical system should considerGaussian opticsSuch as object image conjugate positionMagnification, image transformation and turning light path, etcImaging rangeThe size of, the size of the imaging beam aperture angle, the size ofWide and narrowAnd likedefinitionAnd illuminance.Satisfying a series of requirementsActual optical systemIt is often not a simple combination of several lenses, but a series of lenses, curved mirrorsPlane mirror、Reflecting prismandReticleEtcOptical partsComposition, and through reasonable setting of diaphragm and fine correctionaberrationOnly by means of properly determining the transverse dimensions of optical components can a high-quality system meet the requirements.[2]
Chinese name
optical system
Foreign name
optical system
Purpose
Usually used for imaging or optical information processing
The light beams whose lines all intersect at the same point are calledConcentric beam。After the incident concentric beam passes through an ideal optical system, the outgoing beam must also be concentric.The intersection points of incident and outgoing concentric beams are called object points andIconography。The ideal optical system has the following properties: ① After all the light rays passing through the object point pass through the optical system, the outgoing light rays all pass through the image point.vice versa.This pairvisible imageInterchangeable points are calledConjugate point。②Each line of the object side corresponds to a line of the image side, which is called the conjugate line;The corresponding face is called conjugate face. ③Any plane perpendicular to the optical axis, its conjugate plane is stilloptic axisVertical. ④A pair of conjugate planes perpendicular to the optical axis, transverseMagnificationIs a constant.ResearchIdeal optical systemBoth sides of the above objects and imagesOne-to-one correspondenceThe theory of relationship is calledGaussian optics。First, German scientist CGaussianIt was stated in the 1841 book.In fact, there is no real ideal optical system.Coaxial spherical systemUnder the paraxial condition, it can approximately meet the requirements of an ideal optical system.[1]
Base point and base plane
decisionIdeal optical systemSeveral pairs of special points and surfaces of object image conjugate relationship.[1]
Focus and focal plane
On the optical axis and at infinityIconographyconjugateThe point offocus(or the first focus), recorded asF；The point on the optical axis that is conjugate with the object point at infinity is called the image focus (or the second focus), which is recorded asF'。adoptFandFThe plane at 'and perpendicular to the optical axis is called object focal plane (first focal plane) and image focal plane (second focal plane).[1]
transverseMagnificationA pair of conjugate surfaces equal to 1 is called the principal surface, and the intersection of the two principal surfaces and the optical axis is calledMain point。From the object focusFAny light emitted will become a light parallel to the optical axis after passing through the optical system, and extend this pairConjugate rayGet its intersectionM, the collection of the intersection points constitutes the main surface of the object (the first main surface), and the intersection point of the main surface and the optical axisHIt is called the main point of the object side (the first main point).After the ray parallel to the optical axis enters, the outgoing ray intersects the image focusF', extend the intersection of the pair of conjugate raysM', the collection of the intersection points forms the main surface of the image square (the second main surface), which intersects with the optical axisH'It is called the main point of the image side (the second main point).Two principal surfaces are a pair of conjugate surfaces, and two principal points are a pairConjugate point。The height of any pair of conjugate points on the two main planes from the optical axis is equalMagnificationIs 1.[1]
Upper angle of optical axisMagnificationA pair of 1Conjugate pointcallnode, which passes through the node and is perpendicular to the optical axisNodal plane。[1]
Object image relationship
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Gaussian opticsThe specific optical system is abstractly summarized asthe base levelThe system composed of,Object distance、Image distanceandfocal lengthBoth in twoMain pointIs the benchmark calculation.Object pointQAnd the ownerfocusFTo the main point of the ownerHDistance ofsandfAre object distance and object square focal length respectively;Image square principal pointH'toIconographyQ'andImage focusF'The distance of is image distances'And image square focal lengthf'。The position relationship between objects and images is expressed by the following formula:
f'/s'+f/s=one
This formula is calledGauss formula。Object and image locations are also availablex、x'Indicates that the relationship between them is:
optic axisThe ratio of the longitudinal depth of the upper image along the optical axis to the longitudinal depth of the object, usingαexpress.αAndβThe relationship of is:
ThreeMagnificationThe relationship between them is as follows:
αγ=β[1]
Diaphragm
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For optical systemlight beamAn optical element that acts as a limiting element.It's an optical element（lens、reflectorThe frame itself can also be set with holesTransparent screen。DiaphragmThe center is usually on and perpendicular to the optical axis.[1]
Each part of the optical systemOptical partsBy their ownMirror frameIn most cases, the light through hole is round.Sometimes, fixed or variable special optical holes are added to the system.In all these optical holes, there must be one optical hole to limit the point imaging beam on the axisAperture angleThe role of;In addition, there is a light hole for restrictionImaging rangeRole of.Such optical holes are calledDiaphragm: The former is calledAperture diaphragmOr effective aperture;The latter is calledField aperture。Any optical system must have such two apertures.[2]
Aperture diaphragm
Among multiple apertures, the limiting effect on the beam is the largest, that is, the aperture that determines the size of the imaging beam, also known as the effective aperture.Aperture diaphragmCan block the deviation in the beamParaxial rayLargerlight, iconicaldefinition, accuracy, brightness andDepth of fieldAnd so on.[1]
Since the imaging beam of the point on the axis is limited by the aperture aperture, it is easy to imagine that when all the optical holes of the system are imaged into the object space through the optical parts in front of them, the image with the smallest opening angle of the object point on the axis, orPawnAt infinity, the aperture corresponding to the image with the smallest aperture must be an aperture.The image of aperture diaphragm in object space is calledEntrance pupil, and its angle to the object point is called the beam of the object sideAperture angle。Similarly, the aperture aperture is formed into an image in the image space by the optical parts behind it, which is calledExit pupil, it must also be on the opposite axisIconographyThe opening angle is the smallest optical hole image, and this opening angle is the beam aperture angle of the image square.Incident pupilAperture diaphragmAnd exit pupilconjugateOf.If the aperture is ignoredaberrationThe incident pupil is the common entrance of the imaging beam at each point on the object surface;The exit pupil is the common exit of the imaging beam.The light passing through the center of the aperture diaphragm is called the main light. Because of the conjugate relationship, it also passes through the center of the entrance pupil and the center of the exit pupil.Therefore, generally speaking, the main ray is the imaging beamCenterline。[2]
The position of the aperture diaphragm in an optical system is related to many factors.There are specific requirements in some systems, for example, the visual optical system must usePupilbe locatedeyepieceIn addition, so that the pupil of the eye can coincide with it;In the telecentric system, the aperture diaphragm shall be located atfocusOn.In addition, the position of the aperture diaphragm is also related to the aberration correction and the transverse dimensions of the optical components of the system, which should be reasonably determined during the design.[2]
Field aperture
An aperture that determines the range of objects to be viewed.Field apertureDeterminablefieldThe size of the range.The image scale formed by the optical system in front of the field apertureIncident windowThe image formed by the rear system is called the exit window.[1]
The field aperture is an optical hole in an optical system that determines its imaging range.In a system with an intermediate real image plane (e.gKepler telescopeAnd microscope) and systems with real image planes (e.gPhotography system）The field apertures are set on this image plane.The image of the field stop formed by the optical parts in front of it in the object space is called the incident windowEntrance pupilThe angle of the center is the smallest of all optical hole images. This angle is calledField angle。Similarly, the image formed by the optical part behind the field stop in the image space is called the exit window.The entrance window, field aperture and exit window are also conjugate.When the field aperture is set on the real image plane or the middle real image plane, the entrance window and exit window coincide with the object plane and image plane respectivelyfieldThere are clear boundaries.In NoneReal imageOr the middle real image plane, such as eyes passing throughmagnifierorGalileo telescopeWhen observing, there is always a part in the systemLuminous apertureIt limits the field of view. In the above two cases, the magnifying glass itselfapertureAnd telescopeobjective lenseThe aperture ofField aperture。Obviously, at this time, the incident window does not coincide with the object plane, and there is no clear field boundary.[2]
Relative aperture
Imaging instrumentinobjective lensediameterDAndfocal lengthfRatio of.Used to describe the light collecting ability of objective lensphysical quantity, because it looks likeLuminous flux densityAnd（D/f)twobecomeProportional。Relative apertureOfreciprocalcallAperture coefficient, orF number。Photographic lenses are equipped with adjustable apertures (commonly known asaperture）, used to adjust the size of the relative aperture, so as to adjustPhotosensitive filmThe luminous flux density on the.The lens is engraved with a series of F numbers, and the F number decreases by 2% of the original value－1/2The luminous flux density is increased by 2 times.The general F-number series values are
1，1.4，2，2.8，4，5.6，8，11，16，22,…
The above values are calculated by the following formula (afterrounding）：11
xbypositive integer, called the index of aperture coefficient, also called AV value.The difference between the values of two adjacent gears in the above F number series is 2 times, the corresponding luminous flux density is 2 times, and the AV value is one level different.[1]
vignetting phenomenon
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Ideally, thelight beamAll sufferAperture diaphragmWith basically the same beamAperture angle, iffieldNot too big, the whole field of viewImage illuminanceBasically even.However, in theActual optical systemIn the middle, the off-axis point imaging beam is often affected by otherOptical partsAs a result, the beam aperture angle of the off axis point is much smaller than that of the on axis point due to the limitation of the through hole.This is because the point outside the axis is also filled withEntrance pupilWhen the light beam is imaged, those far away from the aperture aperturelensIt needs to have a fairly large diameter andFull apertureThe off axis beam is correctedaberrationIt's also very difficult.Therefore, in order to improve the imaging quality of off-axis points and ensure that the transverse size of optical parts is not particularly large, it is often necessary to reduce the diameter of certain lenses to limit the off-axis beam.This phenomenon that the light beam full of the incident pupil emitted from the off-axis point is partially intercepted by some optical parts and cannot pass through the optical system completely is called the light beamVignetting。Off axis point separationoptic axisThe farther away, the more serious the interception phenomenon (i.e. vignetting) is, and the result isfieldPeripheral image planeilluminationGreatly reduced.Of course, most optical systems allow a certain degree of vignetting.[2]
Imaging beam
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The imaging beam of the object point is a beam with the object point as the vertexEntrance pupilBottom spaceLight cone。After the beam passes through the optical system, its structure will changeAxisymmetric optical system(The vast majority of systems belong to this category). The point beam on the axis always has symmetry, butOuter pointThe beam is out of symmetry after passing through the system.In order to understand the structure of this beam, the plane beam on its two characteristic planes is usually used to describe it.
The plane containing the off axis object point and the optical axis is called the meridian plane.Due to theaxial symmetryProperty: the off axis object points can always be located on the drawing plane, that is, the paper plane is the meridian plane.The beam on the meridian plane is called the meridian beam.Obviously, the main light must be one of the meridional beamslight。
The plane containing the main ray and perpendicular to the meridian plane is calledsagittal Plane.The beam on the sagittal plane is called sagittal beam.Obviously, the main ray is the intersection line between the meridian plane and the sagittal plane.Since the main light passes through therefraction、reflexAnd change its direction, so the sagittal plane also changes plane by plane rather than a unified plane.
Due to the axis of the optical systemSymmetryOn axis point beam does not need molecular noon beam and arc vector beam, and off axis point beam must be opposite to meridianPlane symmetryOf.[2]
aberration
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lensThe phenomenon that the image formed by (or lens group) is not exactly similar to the original appearance.Due to the light emitted by the object point and the main axis of the lensAngle of intersectionToo large, far away from the axis or the refractive index of the lens material varies withlightOfwavelengthAnd change.aberrationThe size reflects the quality of imaging.There are 7 kinds of aberrations;yesMonochromatic lightThere are 5 kinds, namelySpherical aberration、Coma、AstigmatismandImage surface bendinganddistortion。aboutPolychromatic lightThere are two morechromatic aberration, i.eaxialSum of chromatic aberrationVertical chromatic aberration。It is designed to eliminate or reduce these aberrations as much as possibleOptical setAn important task of.[2]
Symmetric coaxial drawing
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Properties of Symmetric Coaxial
①optic axisObject points on,IconographyAlso on the optical axis; ②The object point in the cross section of the optical axis, and its imageCoplanar；③The properties of any cross section of the optical axis are the same; ④The plane perpendicular to the axis, with the sameMagnification；⑤Two pairs are knownConjugate facePosition and magnification, or the position and magnification of a pair of conjugate planes are known, plus two pairs on the optical axisConjugate point, can determineIdeal optical systemOfimaging。
① Given the position and magnification of two pairs of conjugate faces, the drawing is proved as follows: ② Given the position and magnification of a pair of conjugate faces, and the position of two pairs of conjugate points on the axis, the drawing is proved as follows:
