Comparison of aberrations in__ different types of progressive power lenses[1]

第39卷第1期2018年1月应用光学Journal of Applied Optic;Vol. 39 No. 1 Jan. 2018文章编号！002-2082(2018)01-0088-05渐进多焦点镜片波前像差的扩束测量方法汪成立，禹静，华芳芳，李东升(中国计量大学计量测试工程学院，杭州310018):利用波前传感器测量自由曲面镜片时，由于自由曲面镜片的直径通常大于波前传感器的接收孔径，主要采用子孔径拼接技术测量镜片的波前像差。

针对子孔径拼接技术测量中存在着操作繁琐、数据处理量大等问题，提出渐进多焦点镜片波前像差的扩束测量方法，得到渐进多焦点镜片中央直径为22m m圆形区域内的波前像差。

为了验证试验的可靠性，将测量得到的波前像差泽尼克表述中的离焦项转换为球镜度，与条纹偏折法测量得到镜片的球镜度进行对比实验，实验结果证明了渐进多焦点镜片波前像差的扩束测量方法可以用于渐进多焦点镜片波前像差的测。

:光学技术与仪器；渐进多焦点镜片；波前像差；球镜度中图分类号：TN247 文献标志码：A doi：10. 5768/JAO201839. 0103002Method for measuring wavefront aberration of progressivemuilti-focus lens based on beam expanding systemW angCh e ngli,Yu Jing,HuaFangfang,LtDong s h e ng(College of Metrology i Measurement Engineering,University of China Jiliang，Hangzhou 310018, China)Abstract：In current measurement of the freeform spectacle lenses using wavefront sensor,the di­ameter of progressive addition lenses is usually larger than the receiving aperture of wavefront sensor，it is mainly used to measure the wavefront aberration of the lens by means of the sub-ap­erture stitching technique.In order to solve the problems of complicated operation and large a­mount of data p rocessing in the measurement of the sub-aperture stitching technology,a method of beam expanding-shrinking system measurement for wavefront aberration of progressive addi­tion lens was presented,through which the wavefront aberration within 22 mm diameter circular area of progressive addition l ens could be got.In order to verify the reliability of the test,the measured defocus co-efficients in Zernike representation of wavefront aberration were trans­formed into spherical mirror degree,and compared with the spherical mirror degree measured by fringe deflection method.Results prove that the method based on the beam expanding-shrinking system is feasible.Key words：optical technology and instruments；progressive addition lenses；wavefront aberra­tion；spherical mirror degree收稿日期！017-07-26 ; 修回日期！017-09-05基金项目：国家自然科学基金（6160031108)作者简介：汪成立（991 一"男，河南信阳人，硕士，主要从事精密仪器检测及光学精密测量方面的研究工作。

MAKING YOUR OWN TELESCOPEAllyn J.ThompsonPor to the timeof the telescope,man’s view of the celestial universe was woefully restricted when compared with what now can be enjoyed on any clear evening with ordinary binoculars.There were visible to him then only the naked-eye objects,the sun and the moon,five of rhe planets,and on a clear night stars down to about the 6th magnitude, some 2000 in all. A few hazy spots could also be seen,and there would be an occasional pletely unknown were the outer planets,satellites of the planets,Saturn’s rings,and infinite numbers of stars and galaxies.Y et,working without optical aid,early observers managed to make some amazingly accurate charts of the visible stars,and amassed the observations from which the laws of planetary motion were deduced.The principal instrument used in establishing star and planet positions was the quadrant,a device having a graduated arc,and a pointer that pivoted about its center.With it Tycho Brahe,Danish astrinimer,and one of the keenest of all observers,was able to record the positions of star to within one minute of arc----about 1/30 the diameter of the moon.This was an amazing feat,when it is considered that one minute of arc is about the limit of visual acuity.Then,in 1608,seven years after Tycho’s death,the telescope was brought upon the scene by a Dutch spectacle maker,Jan Lippershry,to whom its invention is credited.Theinvention marked one of the great progressive triumphs of man,enabling him to reach farther and eer farther out into space.It was not much of a telescope,this first refractor,consisting of two spectacle lenses perhaps an inch in diameter,one convex and the other concave,and magnifying possibly two or three times.Lippershey,whose name historians spell in various ways,managed to combine two such instruments into a unit,and thus also made the first binocular telescope.The Galilean Telescpoe.V ery soon,spectacle makers and scientists up and down Europe,learning of lippershey’s invention,were making similar instruments.Notable among the scientists was Gakukei Galilei,the great Italian physicist and astronomer,who fitted a plano-convex and a plano-concave spectacle lens into opposite ends of a lead tube,making a telescope that magnified three times.”They appeared three times nearer and nine times larger in surface than to the naked eye,”wrote Galileo.He experimented further and improved this erecting telescope as well as was possible with simple lenses,carrying the magnification up to 30 or more.This was about the limit of its usefulness,however,on account of the great reduction in the size of its field of view.The general arrangement of Galileo’s telescope is shown inFIg.2.Ordinarily,rays from a distant object AB would,after refraction through the objective lens O,meet to form an inverted image ba in the focal plane,but by interposing the concave eye lens E in front of that plane the rays are caused to become divergent,as though they had proceeded from the points A’B’,where a virtual image of the object is formed.This image is erect and magnified;the amount of magnification is the ratio of angle c’ to angle c.As the eye pupil can hardly embrace all of the rays emerging from lens E,only part of the actual field shown can be utilized.Also.the exit pupil is located inside the instrument.Tfield of view thus depends on the size of the eye oupil,and on the diameter of the objective lens.The Galilean telescope is found today in the form of opera and field glasses,but employing quite moderate magnification:2 to 3 power in the opera glass,and 3 to 6 power in the field glass.The Keplerian Telescope.An improvement on Galileo’s telescope was made in 1611 by Johannes Kepler,a German astronomer and former pupil of Tycho,who suggested that theconverging rays from the objective be allowed to come th a focus,and that the resultant image be magnified with a convex lens.Fig.3 shows the advantage of this new arrangement.T rats,upon emergence from the eye lens,are now converging;hence more of them and a wider field of view can be taken in by the eye.Projected backward through the eye lens,the rays appear to proceed from B’A’,where a virtual image,inverted and enlarged,is formed.As before,the amount of magnification is in the ratio of angle c’ to angle c.Considerably higher magnification can be had with this inverting telescope.But with increasing magnification,the inherent defects of a lens,notably chromatic and spherical aberration were likewise increased.The aberrations could be diminished to a considerable extent by lengthening the focus of the objective lens. Consequently,in efforts to reduce these aberrations,enormous proportions were reached,instruments of 130 and 150 feet in length being constructed.Lens diameters up to six inches and more were attained.Non-spherical surfaces were also attempted in an endeavor to overcome spherical aberration.With these extremely long telescopes,working fields of only two or three minutes of arc must have been the rule.For comparison,the angular diameter of the planrt Jupiter is almost one minute of arc,so the trials and patience of these 17th-century astronomers in aiming their exceedingly long instruments can be appreciared.Magnification is a secondary condary consideration of the telescope;its chief function is to collect light,The eye alone gathers a limited amount of light,hence the lununosity of an object determines its visibility;also,the unaided eye can resolve only a limited amount of detail.An objective lens of the same diameter as the pupil of the eye would not improve vision,regardless of the amount of magnification employed,except that thtough this enlargement the detail in an object would be made more apparent.A l-inch objective lens,assuming it to be about 3.5 times the diameter of the eye pupil,collects about 13times as much light,and correspondingly fainter objects become visible.The amoun of detail seen is also increased,due to the greater aperture.So it id evident that the early boservers needed larger objectives for greater light-gathering and resolving power.But since spherical aberration increases with the square of the aperture,the only way in which it could be kept under control was to lengthen the focus,but there was a practial limit to what lengths could be handled.Moreover,a larger field of view was greatly desired and this could acc rue only with the use of shorter focal lengths.While spherical aberration could be pretty well eliminated by the use of two suitably curved lenses of the same kind of glass,there still remained chromatic aberration to be contended with.In the hope of combining lense of different glasses in such a way as to overcome chromatic aberration,Sir Isaac Newton attempted to determine if refraction and dispersion were the same in all optical media.Although his experiment was inconclusive,from it New ton assumed that refraction and dispersion were proportional to each other,and he decided that nothing could be done to improve the refractor.He therefore directed his energies to the formation of images from concave reflecting surfaces,which are perfectly achromatic,Practical experments with reflectors had already begun in 1639,but it was not until 1663 that they gained any prominence.In that year a Scottish mathematician,James Gregory,at the age of 24,published a treatise entitled Optica Promota.In this he gave a description of a compound reflecting telescope employing two concave specula.The larger one was to be perforated,and to have a paraboloidal surface; the smaller was to be ellipsoidal. The arrangement is shown inFig.6.Notice that the ellipsoidal mirror s is place beyond the focal point F of the primary,which is also of the foci of the ellipsoid.From this position,the secondary mirror returns the rays to form an erect image at its other focus f. High magnification could be had with this instrument,the second reflection amplifying the focal length of the primary in the ratio of fs to Fs. Construction of the telescope was undertaken,but whatever chance it may have had of performing creditably was lost by polishing the polishing egent. The unyielding lap was an insurmountable barrier to parabolizing,interest apparently ebbed,and about 60 years were to elapse before a workable model was finally produced.制作自己的望远镜Allyn J.Thompson在望远镜出现之前的时间里，人们对于宇宙和天空的视野只能悲哀的被限制在用普通的肉眼可以看清天空的夜晚里。

Chapter V Field stop and aperture stop视场光阑与孔径光阑5.1Field stop and aperture stop 视场光阑与孔径光阑5.2Filed of view 视场5.3Vignetting and field lens 渐晕与场镜5.4T elecentric system 远心系统5.5Depth of focus and depth of field 焦深与景深5.6Stray light in lenses 透镜中的杂散光5.1 Field stop and aperture stop一、Field stop and aperture stopAperture stop:The stop close to lens limits the size of the bundles of rays of axis point. It determines the amount of light reaching any given point in the image, therefore controls the brightness of image (image plane).Field stop:Just front of the focal plane limits the angle at which the incident bundles can get through to this plane (image plane). It determines the extent of the object or the field. (Field stop is usually made to coincide with image.)二、Entrance pupil and exit pupilEP: The image of aperture stop formed by preceding it.'E P: The image of aperture stop formed by following it.The image of this stop, as formed by the lens is found to lie at the position PL.P L is inside the focal plane, its image PL lies in the object space and is virtual and erect, *Since ''PL called entrance pupil.P L lies in the image space, called exit pupil.*''`*'P P,'LL,'E E are pairs of conjugated points. Any ray in the object space directed through one of these points will after refraction pass through its conjugate point in the image space.三、Chief rayAny ray in the object space that passes through the center of entrance pupil is called chief ray. After refracting also pass through the center of the exit pupil.*Chief ray is a central ray of obl i que rays.l preliminary design of an optical instrument, must determine which one actually does the l i mi ti ng?nThe entrance pupil of the centric system is the image of the aperture stop formed by all lenses preceding it.The exit pupil is the image formed by all lenses following it.四、Stop between two lensesChief ray pass through the entrance pupil, the stop and the exit pupil.How to determine aperture stop?五、 Two lenses with no stopThe periphery of any lens in system is a potential stop.Object at infinity, 11M N : entrance pupil.Object at A, ''22P L : entrance pupilDetermination of the aperture stopThe system consists of tow lenses and a stop.'12P is the virtual image of the first1lens (1L )and a stop formed by 2lens (2L )'0P : Virtual image of the stop P formed by 2lens .0P : Virtual image of the stop formed by 1lens .21P : Virtual image of the second lens formed by 1lens .For all axial object points lying to the left of X, 0P limits the entrance bundle of rays to the smallestangle.0P constitutes the entrance pupil.'0P constitutes the exit pupil.For all axial object point lying to the right of Z,21P is the entrance pupil and '2P is the exi t pupi l .Nominal aperture stop: The aperture stop of any system may change with a change in the object position.General rule: the aperture stop of the system is determined by that stop or image of stop w hich subtends the smallest angle as seen from the object point.Telescope and microscope (low power): usually aperture stop is selected at the large-sized objective lens.5.2 Field of view一、Field of view2W: object field and image fieldLook out at landscape through a window.Fig 1: The field of view is limited by the size of window and by the position of the eye. Window is fieldstop.General speaking, field stop is at image plane. ( such as telescope, microscope) The margin of reticle orfilm is field stop or frame.二、Field of a plane mirrorThe field of view offered by a plane mirror is very similar to that of a simple window.''M N: observer’s eye, which constitutes the exit pupil.MN: The entrance pupil, virtual image of the eye pupil formed by mirror.Chief rays define the field of view.The object B and entrance pupil MN are in the object space.三、How can you define the field of view of a convex mirror?四、Field of a positive lensThe pupil of eye is an exit pupil and aperture stop.MN: the image of eye is an entrance pupil.The field stop in this case is the lens itself.Object AB is in a position inside the primary focal point F. Through each of three points P、E、L, rays are drawn from 'B to lens.Refracted rays are directed through 'P、'E、L, virtual image is located at 'B.*When converging lens is used as a magnifier, the eye should be placed close to the lens, since this widens the image-fieldangle.For visual visional optical instruments, the eye should be placed the exit pupil of optical system, such as telescopes and microscopes.五、Entrance window and exit windowEntrance window is the image of field stoop formed by all lenses preceding it.Exit window is the image of field stoop formed by all lenses following it.Both entrance and exit window are at infinity.六、Aperture angle and field angleAperture angleu: Aperture angle in the object space. On-axis point subtend to the margin of entrance pupil.'u: Aperture angle in the image space. On-axis image point subtend to the margi n of exi t pupi l.Field anglew: The center of entrance pupil subtended to the margin of entrance window.'w: The center of exit pupil subtended to the margin of exit window.5.3 Vignetting and Field lens一、VignettingAt small filed of view, the highest and lowest rays passing through the lens, strike the top and bottom ofAS ,EP ,'E P .At greater field of view, entrance upper and lower rays are often limited by the front and rear lens openings. The failure of an oblique beam is known as vignetting.The brightness of an image will be gradually decreased darken, when the field of view increased.Coefficient of vignettingw D k D=Chief ray (principal ray): passes through the middle of aperture stop from off-axis object point or theray that enters the lens midway between the highest and lowest rays of oblique beam.二、Field lens(1) In order to reduce the size of following optical system, field lens is usually at the image plane.'01l l β==⇒= (See chapter I)Free fromI S II S III S I C IICThere are only field curvatureIV S and distortion V S caused by IV S .(2)Field lens can be used to change the position of exit pupil to satisfy pupil connection.Exit pupil of preceding system should be coincide with entrance pupi l of fol l owi ng system.I Galilean telescopeAperture stop: rim of objective so is entrance pupilField stop: eye piece so is exit windowII Kepler telescopereticle is field stop.Entrance window and exit window are at infinity. Field angle:1'1'2'222D tgw f D tgw f ⎧=⎪⎪⎨⎪=⎪⎩ Exit pupil is close to'2F .if eye iris is less than exit pupil, iris is aperture stop.III Microscope with low magnificationAperture stop is the rim of objective so is entrance pupil.Field stop is the rim of reticle. Entrance window coincides with object plane.Exit window coincide with image plane (infinity).5.4 Telecentric systemI object space telecentric systemII image space telecentric systemIII double telecentric system*In most cases, the aperture stop is located somewhere inside the lens, such as photographic cameras.*eyepieces condenser are exceptions.一、Telecentric system1) Telecentric system in the object space:The aperture stop is at the rear focal plane 'F.The entering principal ray is parallel to axis.2) Telecentric system in the image space:The aperture stop is at the front focus F.The entering beam come from infinity, and exiting principal ray is parallel to axis.3)Telecentric system at the both ends:The aperture stop is at'12F F . '1F and 2F are coincided.The system usually used as inverting system and relay lens.二、 Contour projectorContour or profile projector is a instrument for projecting a magnified image of a small mechanical partsto check its dimensions.5⨯ 10⨯ 20⨯ 50⨯The optical system is invariable telecentric, the virtual of a telecentric system is that the size of the projected image does not alter, if the image is slightly out of focus.The diameter of the lens aperture must be greater than the diameter of the object.Condenser lens near the lamp, providing collimated light, must also be larger than the largest object to be projected.Final image is generally projected on a ground glass screen, sometimes equipped with Fresnel lens to brighten up the outer parts of screen.5.5 Depth of focus and depth of field一、conceptAssuming the lens is free from all aberrations.1) There will be a ceitain plane in the object space that is precisely conjugate to the film plane in theimage space. This is known as the focused plane in the object.2) The observer ’s eyes have a limited acuity.There will be a small amount of tolerable blur in a photograph that observer will be unable to distinguish it from sharp image.⇒a point object may be imaged as a small circle of confusion on the film.The depth of focus of lens is the distance along the of sharp definition to the plane where the image of apoint source just reaches this circle of confusion.The depth of field of lens is the corresponding distance of an object point from the focused plane inobject space to the plane where its image reaches the permissible circle of confusion in the fi l m pl ane.二、calculation1. Depth of focus is obviously equal to the product of the diameter 'C of the permissible circle ofconfusion on the film and the F-Number F of the lens.Df C N C ''''**==∆The distance is the same whether the image is just within or just beyond thefilm plane.'?C = how large?When a picture is viewed by an observer, most people are incapable of distinguishing between a perfectpoint and a small circle of confusion that subtends about 2 arc-min.2. The depth of fieldThe diagram is based on the fact that everything lying in the focused plane will be imaged sharply on the film.C is the object of 'C (circle of confusion in image space) or C the diameter of the acceptablecircle of confusion in the focused plane.1A and 2A are the far and near object point which is imaged and forms a circle of confusi on 'C .1∆is far depth of field.2∆is near depth of field.22112C∆--∆=∆+-∆=p p⇒a C Cp 21-=∆; aC Cp22+-=∆,1∆ is larger than 2∆.(1∆>2∆)If2a c =, entrance pupil equal to circle of confusion in object space.1∆ becomes infinity.(∞=∆1， aC app 2222+=∆=)if 2a is reduced, the depth of field 1∆2∆ increased.Far object point a C app p 2211-=∆-= Near object point aC apa p p 2222+=+=The diameter of aperture stop controls five separate performance of system.1) System field of view determined by vignetting.2) Photometric speed of system or light collecting ability.3) Depth of focus and depth of field.4) Amount of aberration degrading image quality. 5) Diffraction based performance of system.5.6 stray light in lensesStray light does not form any recognizable ghost or flare spots, it is generally referred to as veiling glare.This has the effect of lowering the overall contrast of the image.How come (arise)?1) Arise from mechanical scattering on the inside of the lens barrel and ground ri ms of the l enses.2) Arise from interreflection between pairs of lens surfaces.Since the surface is spherical and polished a series of image of a bright source is formed, even if the source is outside the picture.These so called ghost image are often seen in motion picture, mast of the ghost image will be out of focus, and appears as irregular.3)Stop of limiting stray light4)Lens coating untireflection film。

ZCB00非球面人工晶体植入术后视觉质量分析目的比较Tecnis ZCB00非球面人工晶状体（IOL）和球面AR40e IOL植入术后的视觉质量。

方法选取2015年1～7月在保定市第一中心医院接受治疗的白内障患者60例（60眼）。

按随机数字表法将其分为观察组与对照组，每组各30例。

两组患者均行超声乳化白内障吸除联合IOL植入术，观察组植入ZCB00 IOL，对照组植入AR40e IOL。

术后3个月观察患者的裸眼视力、最佳矫正视力（BCV A）、对比敏感度（CSF）及5 mm瞳孔直径下的全眼及内眼像差及调制传递函数（MTF）。

结果两组患者的裸眼视力及BCV A比较，差异无统计学意义（P > 0.05）。

在5 mm瞳孔直径下，观察组术后全眼及眼内高阶像差均低于对照组，差异有高度统计学意义（P 0.05）.The postoperative high order aberration of the eye at 5 mm pupil diameter in the observation group was less than that in the control group （P 0.05），具有可比性（表1）。

纳入标准：单纯老年性白内障[5]，角膜散光0.05）。

临床上，经常会有部分病人虽然视力检查结果较好，但常常抱怨视物模糊，尤其是眩光、夜间视力差等问题。

视力表测定是视觉敏锐度，不能测出日常生活中辨别“真实世界”的不同对比度的能力，而CSF反映了人眼分辨不同对比度的能力，比视力更能反映视功能情况[14]，是目前评价IOL眼的视觉质量的一个重要监测指标。

本研究得出观察组的CSF优于对照组，尤其是中低空间频率（P 0.05）。

这说明，非球面IOL改善了患者夜视力，避免发生眩光失能，对夜间开车患者尤为适用。

本研究与国外报道之间的差异，可能来自于统计样本的选择偏倚，另外，CSF是一项针对视觉成像质量综合因素的主观评价指标，其他因素如年龄、视网膜神经节细胞的功能、视觉神经系统情况及患者的理解力等均会对CSF的结果造成影响。