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The Prentice Medal is alleged afterwards Charles F. Prentice, a founding ancestor of able Optometry. In the added copy of his argument on ophthalmic lenses, arise in 1907, Prentice said:1
“The prism diopter stands advisedly in its altered adeptness to accord all of the refracting elements in the optometrical lens-case by establishing a complete and inseparable accord amid prisms and lenses.”
What is this “complete and inseparable relationship” that plays such a axiological role in optometric eyes and makes the Prentice aphorism alike added important today than it was in Prentice’s time a aeon ago?
As every apprentice of optometry knows, the Prentice aphorism describes how lenses refract appliance of light. Fig. 1 shows a arrangement of alongside appliance from a abroad point of light, like a brilliant in the sky, entering a lens alongside to the optical arbor of the lens. For an ideal all-around lens, all of these ablaze appliance arise to focus at a distinct point at a ambit d from the lens. The attribute F in the Prentice blueprint is the dioptric adeptness of the lens, which is according to the changed of ambit d. The letter c in the Prentice blueprint refers to the displacement of an admission ray from the optical axis. If we abstract any ray for inspection, we see from the geometry of adapted triangles that the bend Δ with which the refracted ray strikes the optical arbor is according to c/d, but because 1/d is the lens power, the bend Δ is the artefact of ray displacement and lens power. That is the Prentice rule: Δ = c F.
To affix the Prentice aphorism with wavefronts, we draw a connected apparent that is erect to every ray of light. Now draw a departure band to this wavefront apparent at the basal of our abandoned ray so we can see how the abruptness of the departure band (which is additionally the abruptness of the wavefront) makes the aforementioned bend Δ with a advertence alike erect to the optical axis. That agency the Prentice aphorism additionally tells us the abruptness of the wavefront at every point on the wavefront. Moreover, if we adapt the Prentice blueprint to anatomy a arrangement of wavefront abruptness Δ to the displacement c, the aftereffect is 1/d, which is the vergence of the arising ray and additionally the wavefront vergence at anniversary ray area on the wavefront.
This way of interpreting the Prentice blueprint is an important change in viewpoint. We are no best talking about the lens itself, but the wavefront produced by that lens. This focuses our absorption on the wavefront of ablaze rather than the lens that shaped the wavefront. Moreover, the diagram in Fig. 1 defines a absolute wavefront, the gold accustomed for wavefront analysis. Rearranging the Prentice blueprint showed that, if the arrangement of Δ/c is constant, again all of the appliance accept the aforementioned vergence, which agency that they all cantankerous the optical arbor at absolutely the aforementioned focus point. That is what makes a wavefront perfect.
Of course, no lens is perfect, and that goes for eyes as well. Fig. 2 shows an aberrated lens basal an aberrated wavefront from a abroad point source. The diagram is ambiguous (yet frequently activate in textbooks) because abounding of the appliance are not alike in the alike of the diagram—it’s alone our acuteness that is in the alike of the diagram. The appliance advancing out of the alike of the diagram are alleged “skew rays.” Because skew appliance don’t bisect the optical axis, the acceptation of bend Δ as an bend of circle amid the ray and optical arbor ceases to be useful. Nevertheless, we can consistently draw a departure alike erect to the ray (even if the ray is skew) so we can admeasurement the bend Δ amid a ray and a plane. That bend tells us the abruptness of the wavefront at a specific point on the wavefront. If we can admeasurement wavefront abruptness at abounding ray locations, again we can use calculus to board those wavefront abruptness abstracts to accede the wavefront’s shape.
This generalization of the Prentice aphorism to become a annual about wavefront abruptness is the foundation of avant-garde wavefront aberrometry. The aphorism applies alike if the wavefront is not a absolute sphere, so the appliance do not accept the aforementioned vergence and do not cantankerous the arbor at the aforementioned place. As illustrated in Fig. 3, the Prentice aphorism works additionally for skew appliance associated with nonprincipal meridia of an astigmatic wavefront. For such rays, wavefront abruptness has two components, the accustomed meridional basal associated with wavefront adorable vergence and the borderline basal amenable for skewness that prevents the ray from intersecting the optical axis. Behindhand of the appearance of the wavefront, the meridional abruptness is acceptable to reconstruct wavefront appearance by algebraic integration.
What does this wavefront access of geometrical eyes accept to do with the eye? Instead of ablaze accession at a lens from a star, brainstorm a point antecedent of ablaze reflected from the retina and arising from the eye’s optical arrangement as a wavefront (Fig. 4). As ahead shown, if we can admeasurement the abruptness of the arising wavefront at abounding credibility on the wavefront, again we accept all of the advice bare to reconstruct the appearance of that wavefront, thereby accepting a absolute description of the eye’s optical aberrations. Although it is accessible to accomplish the aforementioned aftereffect by barometer the circle point of ablaze appliance with an angel alike abreast the focus point, that access is added difficult because the appliance overlap and get abashed abreast the focus point, so they charge be abandoned and abstinent sequentially. By barometer wavefront abruptness abreast the eye, area alone appliance are able-bodied separated, it becomes accessible to accomplish abounding abstracts simultaneously.
If Prentice were animate today, I’m abiding he would anon accept the assumption of avant-garde wavefront assay because this 21st aeon alignment is aloof a analytic appliance of his 20th aeon aphorism apropos wavefront abruptness to wavefront shape. However, Prentice wasn’t the aboriginal actuality to anticipate this way. The basal abstraction for isolating appliance of ablaze to admeasurement wavefront slopes to actuate refractive errors is at atomic 400 years old. The ancient advertence I apperceive is the Scheiner treatise2 on physiological eyes arise in 1619. Scheiner was a abreast of Galileo and Kepler, and he devised a simple accessory now alleged Scheiner deejay apparent in Fig. 5 to abstract a brace of appliance to actuate the eye’s refractive error. Some 200 years later, Thomas Young acclimated the Scheiner assumption to body an optometer that he acclimated to admeasurement the amaurosis of the animal eye for the aboriginal time.
Workers in added areas of eyes are conceivably added accustomed with Hartmann’s rediscovery of the Scheiner deejay in the aboriginal 20th aeon as a way to admeasurement the affection of appliance and lenses. In fact, Hartmann and Prentice were aeon so we adeptness brainstorm that if they had accustomed of anniversary other’s work, we would be adulatory the 100th altogether of wavefront aberrometry today. The schematic diagram in Fig. 6 shows how the Scheiner-Hartmann awning isolates abounding alone appliance accompanying as they arise from an eye. The circle of anniversary abandoned ray with a ablaze detector tells us the administration of the ray and appropriately the abruptness of the wavefront in the alike of the Hartmann screen.
The avant-garde adaptation of the Scheiner deejay assumption adapted by Dr. Roland Shack and Ben Platt replaces the Hartmann awning with an arrangement of tiny lenses, which are added able at capturing ablaze and absorption it assimilate a video sensor. As apparent in Fig. 7, a broadcast telescope images the eye’s access adherent assimilate the lenslet arrangement so that the wavefront abstracts board corneal refraction but is conceptually agnate to agreement the lenslets in the adherent plane. This schematic diagram of a avant-garde wavefront aberrometer shows a laser axle actuality acclimated to abode a baby atom of ablaze on the retina. The atom would be placed on the fovea to admeasurement ocular aberrations forth the arch band of afterimage but could be instead placed anywhere on the borderline retina to admeasurement aberrations forth accessory curve of afterimage associated with borderline vision. Aback ablaze from this retinal “beacon” reflects aback out of the eye, it is captured by a brace of broadcast lenses that focus the eye’s adherent alike assimilate an arrangement of lenses that bisect the ablaze into abounding baby beams. Depending on how anniversary little axle is deflected as propagates to anatomy a atom angel on the sensor, we can bulk out the abruptness of the wavefront over anniversary lenslet. Although this accessory is frequently accustomed as a “Shack-Hartmann” aberrometer, the absolute absolute bearing is: Scheiner, Young, Hartmann, Prentice, Shack, Liang (who patented the idea!).
The apparatus of technology for barometer wavefront appearance opens up a accomplished new apple of ocular wavefront aberrometry: the analytical allocation of refractive errors according to wavefront shape. Basal wavefront shapes can be classified by extending the 20th aeon convenance of decomposing refractive errors into focus errors (associated with amaurosis and hyperopia) and astigmatic errors, as illustrated in the top bisected of Fig. 8. In the 21st century, acknowledgment to wavefront technology, abounding added basal shapes are bare to call eyes. Coma and trefoil are two examples of abounding basal shapes declared mathematically by Zernike polynomials.
Frits Zernike (1888–1966) is a Nobel laureate acclaimed for his apparatus of appearance microscopy. In the process, he invented a set of eponymous algebraic functions and again attentive donated them to eyes science for anecdotic the optical backdrop of eyes. The aboriginal 21 Zernike base functions, or “modes” as they are generally called, are apparent in Fig. 9. This pyramid of shapes is logically organized into rows and columns, rather like the alternate table of the elements. Anniversary row of the pyramid corresponds to a accustomed adjustment of the polynomial basal of the function, and anniversary cavalcade corresponds to a altered meridional abundance of the sinusoidal component. The basal abstraction of Zernike wavefront assay is to mathematically decompose a wavefront into a abounding sum of basal shapes. The weights, or bulk of anniversary component, are alleged Zernike coefficients Cnm, area n is the pyramid row cardinal and m is the cavalcade number. The six modes in the top three rows are the base of 20th aeon optometry but are now accustomed as aloof the tip of the Zernike pyramid. An absolute cardinal of modes beneath the tip represent the accretion ambit of optometry and ophthalmology into the 21st century. From this perspective, the second-order adeptness agent apparatus M, J0, and J45 are history. They accord to the 20th aeon afore we grasped the beyond mural arise by Zernike analysis.
The above-mentioned diagrams accord abounding affirmation of the three-dimensional attributes of optical wavefront analysis. Unfortunately, best eyes textbooks board alone two-dimensional assets that attack to explain three-dimentional concepts. Brainstorm instead a arbiter complete like a child’s aerial that reveals Cinderella’s alcazar aback the book opens! An archetype of advance optical origami advantageous for envisioning the geometry of appliance and wavefronts is illustrated in Fig. 10 (see cyberbanking addendum online for a alive model, accessible at http://links.lww.com/OPX/A136). Follow the instructions to bend the aeroplane to accede the optical axis, the arch ray abutting adherent centermost to an off-axis article point, the meridional plane, the sagittal plane, and the AIRPLANE!
Looking aback in time, I would say 1997 was the year our optical mind-set began to change because of wavefront aberrometry. That was the year Optometry and Eyes Science arise a brace of affection issues highlighting basic assignment actuality done application the new wavefront abstraction for anecdotic the optical aberrations of the eyes and their correction. To acquaint one of those issues, I wrote an beat advantaged “The New Beheld Optics,” which said, in part3:
“Contemporary beheld eyes assay is alteration our mindset, our way of cerebration about the optical arrangement of the eye, and in the action is re-defining the acreage of beheld optics. All of the eye’s optical imperfections will one day be represented assiduously by a two-dimensional map in the alike of the pupil. This adherent map will attending abundant like the corneal topographic maps currently acclimated to call the appearance of the corneal surface. Interpretation of the two maps will be absolutely different, however, because the adherent map describes how wavefronts entering the eye from anniversary point in the beheld apple become adulterated from the absolute all-around appearance bare to anatomy the ideal retinal image.”
The approaching accustomed abundant eventually than anyone anticipated. Aloof 3 years afterwards that editorial, the avant-garde era of analytic wavefront aberrometry began with the bearing of the 21st aeon and the accession of the aboriginal bartering aberrometer for assuming wavefront refraction based on the Hartmann-Shack wavefront sensor. This accession of aberrometry technology into the dispensary additionally alien a change in attitude: college adjustment aberrations were no best a nuisance to be avoided. Instead, aberrations will be taken into annual aback prescribing the best accessible acclimation lens based on a key principle: the best decree is the one that optimizes retinal angel quality.
But how can a analyst apperceive if angel affection is optimized aback the alone actuality in the apple who can see the retinal angel is the patient? The analyst can’t attending central the eye to see if the angel is able-bodied focused, so how can he or she apperceive that angel affection has been maximized by a authentic aggregate of acclimation lenses? The acknowledgment is that we can annual the retinal angel alike admitting we cannot beam it. Optical access tells us that the wavefront abnormality map is acceptable to accredit an authentic abacus of retinal images, including the furnishings of diffraction and interference, application the attempt of concrete optics. As illustrated in Fig. 11, the aboriginal footfall uses the abstinent wavefront abnormality map of an eye to compute the retinal angel of a distinct point of light. Because any article in the apple is a accumulating of point sources, anniversary of which is blurred the aforementioned way, we can add these partially overlapping images of all the article credibility application a algebraic abacus alleged “convolution.” The aftereffect is a apprehension of the retinal angel of any object, for example, an eye chart. In this way, clinicians are empowered with a apparatus able of accouterment acumen into the patient’s botheration aback faced with the assignment of chief which acclimation lens is better, cardinal 1 or cardinal 2?
Given an adeptness to compute images from wavefront measurements, we can activate to abode the simplest and best axiological of optometric questions: area is the far point of an aberrated eye? According to the wavefront refraction assumption ahead given, the far point is the axial area for the article that optimizes the affection of the retinal angel aback adaptation is relaxed. This analogue leaves unstated the archetype by which retinal angel affection should be judged. Award a advantageous metric of angel affection is arduous because, alike for a simple point of light, appliance casual through altered genitalia of the adherent arise to focus at altered axial distances. An archetype is apparent in Fig. 12 for an eye with absolute all-around aberration. If the beheld article is amid at the ambit area paraxial appliance arise into focus, the retinal angel is bright and aciculate but has almost low contrast. Alternatively, if the article is amid at the ambit area bordering appliance focus, the angel will arise darker with added adverse but is not as clear or sharp. These adverse belief of “sharper” against “darker” are able-bodied accustomed to clinicians, but alone by demography into annual the furnishings of all-around abnormality does an optical annual arise and an compassionate advance of how this authentic abnormality affects vision.
An important acumen acquired by wavefront assay is that the optometrist’s assiduous question, “which is better?” does not accept a distinct absolute acknowledgment because abounding criteria, in accession to “sharper” or “darker,” can be acclimated for anticipation angel quality. For example, the all-around may adjudicator perceived affection based on some centralized angle of claimed esthetics, a faculty of adorableness that makes one antidotal lens bigger to another. Or affection may be based on the allegiance of the image—whether it meets some apprehension or ideal angle of what the article affliction to attending like. Both of these belief are internal, subjective, and difficult to assimilate for reliable and constant use in a accurate or analytic setting.
An cold access to the altitude of angel affection defines anatomic optical affection in agreement of measureable beheld performance. This access leads to the conception of a axiological antecedent that links the apple of the anima (mind) to the concrete apple of appreciable events. That psychophysical bond antecedent is bigger images crop bigger beheld performance. Conversely, bigger achievement indicates bigger images. Thus, for the angel illustrated in Fig. 13, if beheld achievement on a specific assignment (such as letter identification) is bigger aback examination through the lens instead of about it, again the lens is accouterment above angel affection behindhand of the artful address or allegiance of the angel to the aboriginal object.
An cold archetype for chief which acclimation lens is bigger begins by application a abstinent wavefront map to annual the retinal angel of a distinct point of ablaze (called the point-spread action [PSF]). The angel of a point is about too complicated for absolute evaluation, as illustrated in Fig. 14, but it can be bargain to a distinct cardinal application an angel affection calculator. This metric amount is again acclimated to adjudge which acclimation lens is optimum. Some metrics of angel affection are added calmly defined in the spatial abundance domain, in which case the calculator would be based on the eye’s optical alteration action (OTF), which can additionally be computed from the wavefront map.
The ability of angel affection calculations can be bigger by demography into annual the aboriginal stages of neural processing of the retinal image. For example, Fig. 15 illustrates coil of the optical PSF (which describes how ablaze from a point antecedent spreads laterally) with a neural PSF (which describes how the neural acknowledgment to a point bang on the retina spreads laterally) yields a beheld PSF (which describes the neural acknowledgment to a distinct point of ablaze in the object). The arrangement of the best amount of this beheld PSF for the patient’s eye to the best amount accomplished for an optically absolute eye is a metric of angel affection alleged the beheld Strehl arrangement that is advantageous for admiration beheld acuity. This metric may additionally be computed in the spatial abundance area by abacus the OTF by the neural adverse acuteness action of the eyewitness to accomplish a beheld alteration function. The aggregate beneath this beheld alteration function, compared with that acquired for an optically absolute eye, is an agnate admeasurement of the beheld Strehl ratio.
Fig. 16 summarizes the computational action of wavefront refraction, which is the action of award the optimum spherocylindrical acclimation lens that maximizes the affection of the retinal image.4 Conceptually, the abstraction is agnate to accepting a tiny OD central the eye to appraise retinal angel affection application the angel affection calculator. A basic lens is again adapted by mathematically abacus a all-around wavefront to absolute defocus (and/or an astigmatic wavefront to absolute astigmatism) to the eye’s wavefront to aerate the affection of the computed retinal image.
Only a baby footfall of acuteness is bare to augment the abstraction of wavefront refraction to considerately actuate the refractive accompaniment of an aberrated all-around eye. As adumbrated in Fig. 17 (see activated adaptation online), all ocular aberrations change aback the apparent lens accommodates, but the primary change is for Zernike defocus (C20). The aforementioned computational action acclimated to actuate the optimum acclimation lens of the airy eye applies additionally to the all-around eye by optimizing an adapted metric of angel quality.
A academic archetype of wavefront altitude of refractive accompaniment of an all-around eye is illustrated in Fig. 18. The archetypal animal eye has absolute all-around abnormality aback adaptation is relaxed, in which case the optimum focus alike is afterpiece to the eye for bordering appliance than for paraxial rays. Aback eyes board to a abreast target, all-around abnormality about changes assurance to become negative. Consequently, the about locations of focal planes for paraxial and bordering appliance become reversed, as illustrated in the basal console of the figure. That expands the ambit of adaptation if the ambition is to aftermath a bluff angel but compresses the ambit of adaptation if the ambition is to aftermath an angel with best contrast. That acumen would not accept been accomplished after demography aberrations into annual aback analytical retinal angel quality.
Fig. 19 summarizes the wavefront adjustment for accretion the refractive accompaniment of an all-around eye. The all-around angle a bang that evokes adaptation while the analyst accompanying measures the eye’s wavefront abnormality and measures angel quality. The catechism is was the ambition in the optimum location? Or would retinal angel affection accept been greater if the ambition were hardly afterpiece or further away? If angel affection can be bigger by defocusing the abstinent wavefront, that indicates the attendance of an accommodative absurdity that can be quantified as the abnormality amid the optimum ambition vergence and the absolute ambition vergence.
Given this wavefront access to barometer refractive state, a new angle emerges on abounding accustomed issues in adaptation research. For example, is retinal angel affection best for all states of accommodation? Or are we all abiding laggards who don’t board abundant to aerate the affection of our retinal images? How do changes in college adjustment aberrations and adherent admeasurement during adaptation affect refractive state? The angle that the adherent plays a role in free refractive accompaniment is a abolitionist abstraction that arises alone aback aberrations are taken into account. How do age-related changes in adaptation affect retinal angel quality? That affair is acceptable added accordant with the crumbling citizenry and our charge to bigger accept the beheld after-effects of presbyopia. Do amaurosis therapies based on abnormality concepts work? If not, why not?
Wavefront aberrometry is everywhere in optometry, ophthalmology, and beheld optics; it is absolutely the “wave” of the future, and the approaching has arrived. In this lecture, I’ve commented alone on cold refraction of the airy eye and the altitude of refractive accompaniment during accommodation. In addition, wavefront technology is actuality acclimated to abstraction breach blur eyes and the ocular surface. Wavefront sensors are the key basal of adaptive eyes systems for high-resolution imaging of the fundus. Wavefront aberrometers advice appraise analysis strategies application acquaintance lenses or refractive anaplasty for correcting, or exploiting, college adjustment aberrations. Wavefront account may alike advice alleviate the mysteries of amaurosis development by absolute the optical altitude that ascendancy ocular growth.
These are agitative times for beheld eyes assay and its analytic applications. The American Academy of Optometry plays a analytical role in advice advances in ability acquired by assay into all-around care. By giving articulation to optometric research, this Academy makes its greatest contribution, by way of the practitioner, to the public’s well-being.
Larry N. Thibos
School of Optometry Indiana University
800 E. Atwater Ave.
Bloomington, IN 47405-3680
e-mail: [email protected]
Numerous colleagues and acceptance from Indiana University and added assay institutions about the apple accept contributed to the account abbreviated in this lecture. I acquiescently accede 30 years of connected banking abutment (grant R01-EY05109) from the National Eye Institute of the US National Institutes of Health added additional abutment from the ophthalmic eyes industry beneath the advocacy of the Borish Centermost for Ophthalmic Assay at Indiana University.
Received March 9, 2013; accustomed May 29, 2013.
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