First order aberrations Small angle approximations Low Order Aberrations: These aberrations are corrected with prisms, glasses and contact lenses. Therefore, a clear understanding of what imaging is and of departures from such imaging, called aberrations, is essential for a lens design practice. Jose Sasian OPTI 518 14 Nov 14, 2020 · Higher-order aberrations consist of: Third-order aberrations correspond to horizontal and vertical coma and triangular astigmatism with the base along the x- or y-axis (trefoil). Jose Sasian OPTI 517 Fourth-order terms 2 220 311 400 2 131 222 2, 040 W H H W H H H W H H W H W W H W H Mar 26, 2015 · First, the higher order aberrations of the anterior corneal surface were measured, with the implementation of a Placido corneal topographer. 4, second and first order aberrations (A 1, C 1, A 2, and B 2) are greatly increased by the change of octupole voltage for the correction of third order aberration. . 6 Fifth-order transverse ray aberrations 200 φφ= − + +⋅⋅⋅⎯⎯⎯⎯φφ First order→≅ luding higher order terms we experience larger departeures from the prefect image known as . 14 Sixth-order aberration coefficients 187 14. A general and closed-form analysis (based on geometrical optics) of the aberrated aperture field is derived in terms of the reflector geometry and feed illumination. Applied Optics, 2009, 48(13): 2574-2584. Dec 17, 2020 · First, in the first two rows or orders ( n= 0 and n=1) the aberrations are also called constant aberrations (fig 1). Important higher order aberrations include coma, trefoil and spherical aberrations and they are measured by root mean square (RMS) value which represents the ocular aberrations in micrometers. 442e-01 Surface 3: 2. , transverse axial chromatic or lateral color). Nov 26, 2013 · Two types of first order (6,7) chromatic aberration (caused when the image is not monochromatic) are consistently included among the important aberrations; and (8) spherical aberration of the exit pupil is a flaw often encountered in wide angle eyepieces. The systematic expansion into 6 × 2 terms is given in Table 1. Aberrations can be analyzed and classified in several ways. The second subgroup includes aberrations that deform the image: IV. This is because the first-order geometrical aberrations do not reduce the visibility of interference fringes but they distort the Aberrations • Departure from the linear theory at third-order were classified into five types of primary aberrations by Phillip Ludwig Seidel (1821-1896): – Spherical aberration – Coma – Astigmatism – Field curvature – Distortion object distance image distance Vertex Optical axis Nov 26, 2013 · Two types of first order (6,7) chromatic aberration (caused when the image is not monochromatic) are consistently included among the important aberrations; and (8) spherical aberration of the exit pupil is a flaw often encountered in wide angle eyepieces. org If only the first term is used, we have the case of paraxial, or first-order optics. 6. Consequently, their effect is deterioration in • Aberration cancellation is the main mechanism for image correction • Presenting to the optimization routine a system with its third-order aberrations corrected is a good starting point • Some simple systems are designed by formulas that relate third-order aberrations • Note symmetry in third-order aberration coefficients Higher-order aberrations consist of: Third-order aberrations correspond to horizontal and vertical coma and triangular astigmatism with the base along the x- or y-axis (trefoil). The lowest (first) order geometrical aberrations (i. deformation. 0. Spherical aberration. S. Primary aberration theory for cylindrical anamorphic systems[J]. These results show the system and to generate the first-order momentum dispersion. •For slow systems, ~F/8 or less, and for small fields of view, a few degrees, the primary aberrations provide a substantially accurate approximation to the wavefront deformation. Aug 2, 2016 · 2) First order optics . The Sep 8, 2023 · 2. 000 so . graphical method to trace first-order rays. Sep 1, 2005 · One can derive an equation that gives the error in an image on the image plane as a function of the incident (imperfect) wavefront. These formulas may Sep 17, 2024 · This result is a direct measurement of the first-order topological aberration of a vortex constellation, which, despite its strong correspondence to the GH and IF shifts, had not yet been observed. Sep 3, 2014 · First and second order aberrations are regarded as lower-order aberrations. 48, 2574-2584 (2009). This report discusses the calculation using first order properties. 1364/AO. First-order aberration (e. This was followed by a measurement of the contrast The next higher aberration order are 6th-order wavefront and 5th-order ray aberrations (as mentioned, they are also called secondary, or Schwarzschild aberrations). May 6, 2021 · The latter are four first-order ray aberration coefficients that can be set to zero or that can be minimized to calculate the unknown surface and the mapping coefficients. • Aberration cancellation is the main mechanism for image correction • Presenting to the optimization routine a system with its third-order aberrations corrected is a good starting point • Some simple systems are designed by formulas that relate third-order aberrations • Note symmetry in third-order aberration coefficients Figure 3667e shows the schematic comparison of Zemlin (diffractogram)-tableau characteristics for the axial aberrations up to third orders. The monochromatic aberrations begin to show up when rays are traced under the more-correct assumptions of third-order optics. Introduction. higher order things (aberrations) The first order effects are most important . It is sufficiently accurate for relatively weak and/or small in diameter surfaces, typical of most older-type telescopes, such are longer-focus Jun 1, 1977 · For the first surface of a system, facing an unaberrated object, this is valid, but for subsequent surfaces these paraxial quantities. 481e+00 Surface 6: -5. Motion of optical elements affects the optical performance? 1. THIRD-ORDER ABERRATIONS First-order wavefront properties and third-order wavefront aberration coefficients can be obtained from the Zernike polynomials coefficients. How are monochromatic aberrations described mathematically? Thus, the first 5 terms of the third order aberrations are the best known : the 4 th and 5 th terms define astigmatism, the 6 th and 7 th terms coma and the 8 th term is the spherical aberration. Phil. Aberrations of anamorphic optical systems. •The fourth-order group of aberrations is also known as the primary aberrations. This paper presents a sixth-order theory of wave aberrations for axially symmetric systems. Traditional refractive errors refer to 2 nd -order Zernike terms. One first order aberration is known as tilt and is caused by the actual wavefront being tilted relative to the reference wavefront. The radius R is substituted by r using the paraxial pupil magnification U between the entrance pupil and the adaptive element, i. Jose Sasian OPTI 518 4 • Extrinsic sixth-order aberrations • Bow-Sutton conditions. Changes of lens shape have no influence on the chromatic aberration to a first order approximation, and at least two components of different materials are required In addition, we newly present first-order aberration expansion formulae for four-element fundamental-ray aberrations and calculation formulae for the fundamental-ray aberration coefficients of the first order, which are necessary for this extension. The resulting aberrations are known as or Seidel aberrations. These coefficients have been recalculated for object magnetic immersion OMI. The paper builds the theory by using Shack’s[1] formulation of the aberration Third-order transverse spherical aberration: Surface 1: -5. 1 Extrinsic aberrations 188 14. Fourth-order: aberrations contain spherical aberration, tetrafoil and secondary astigmatism. 1st order aberrations vary as h (where h is the distance from the centre of the lens), 3rd order aberrations vary as h^3 and so on. Analysis methods include Gaussian optics and paraxial optics. Jul 21, 2000 · This work presents a first-order treatment of aberrations caused by small feed displacement in classical axially-symmetric dual-reflector antennas. B terms are primary or Seidel aberrations: spherical, coma, astigmatism, curvature and distortion. If these aberrations are second order, they may be eliminated or at least modified Dec 11, 2000 · Chromatic aberrations have great influence on the performance of charged particle optical systems in addition to geometric aberrations. , 100 nm order). This aberration can be equated with the piston of an engine (fig 3) wherein the piston motion is vertically moving up and down. Coma. Jose Sasian OPTI 518 Some early references of interest T. defocus and twofold astigmatism, A 1) shows the elliptical distortion even without electron beam tilting because the impact of first-order aberrations does not depend on the aberration is zero. After the octupole voltage is changed, hexapole voltage must be adjusted several times. Snell’s law for refraction . These aberrations can be obtained by substituting \( u(z) = u^{(1)} (z) \) in Eq. I disagree; there is no name difference between transverse and wavefront aberrations. In comparison in a symmetrical system the even aberrations from each half First-order optics model provides a useful reference and provides . secondary astigmatism. The quadrupole elements provide the first-order imaging. This has led to the erroneous conclusion that secondary spectrum correction requires the use of special optical materials. Analytical expressions for higher-order aberrations are extremely cumbersome and therefore not Prof. So the first two rows include lower order aberration, vertical tilt and horizontal tilt are included in first order aberration, oblique astigmatism, defocused and vertical astigmatism are included in second Nov 1, 2008 · The higher-order spectral components are found to respond more sensitively to a focus shift than the first-order (or second-order) component, so that the aberrations by a small longitudinal shift of focus can exert a severe effect on the fine structure of image in a complicated way. θ. 2 Intrinsic aberrations 189 14. !) and to generate the first-order momentum dispersion •Quadrupole elements provide the first-order imaging •Dipole and quadrupoles will also introduce higher-order aberrations. For this simulator, we only use the first several terms of the Zernike expansion, which represent the effects of first order defocus, astigmatism, coma, and spherical aberration. 1 st-order Zernike terms are tilts which do not cause image blur therefore are usually ignored. These coefficients reveal the underlying factors that impact each of the fourth-order plane symmetric aberrations, which tend to dominate early on in a freeform mirror design. 1 First Order Aberrations. Notes You can adjust the amount of each aberration by varying the coefficient of its respective Zernike polynomial. At last, the 9 th and 10 th terms describe the 5 th-order aberrations such as trefoil. characteristics while maintaining clear definitions of first-order system properties. e. , no prescription lenses) and Prism correction, which is used if your eyes are misaligned; for example, if you have Crossed Eyes. If the next term is also used, we have an example of third-order optics. Yuan and J. doi: 10. . opt. View Show abstract Higher-order aberrations in this study were on average higher that those reported in previous studies. 1. The n=0 or zero order is also called piston aberration. g. Jun 10, 2020 · First order aberrations were added to third order aberrations, to obtain the best balance and to reduce the curve width of the (PSF), and to increase the Strehl ratio, like adding a tilt system (deh. In air n = 1. First-order optics • First-order ray-tracing is a powerful method to analyze an optical system • Obtain substantial lens system information from tracing two first-order rays (paraxial) • Reflects early designers cleverness • Real rays were difficult to trace • Many lens design tasks are still done using first-order rays. Entrance and exit pupils. The consequence to the aperture efficiency and main-beam tilt are illustrated for Chromatic aberrations • Consider up to second order terms • Change of image location with λ (axial or longitudinal chromatic aberration) • Change of magnification with λ(transverse or lateral chromatic aberration) • We start with a single spherical surface 22 Sep 1, 2017 · In contrast to atomic-resolved ADF imaging, which requires small first-order aberrations (e. Since optical aberrations are often referred to as first, third, fifth-order, etc, if $\small{k + 1 = 2} $, it is a first-order aberration, if $\small{k + 1 = 4} $, it is a third order, etc. to Z. Simulations were performed on two images: the 1951 USAF Resolution Chart and the "Living Room" scene (a test image widely used throughout the history of image science). Higher-order aberrations (HOAs), one of the important subjects in the science of vision and optics, received very little attention before 2000. In these cases, only at illumination tilts the However, this will always create an even number. The system first order aberration would only be given by the sum of Cl terms if the aberrations neglected were of higher order in aperture, h, than the paraxial approximation Jan 1, 2014 · Consequently, we have already in the first order (paraxial) two aberrations. First and third-order aberrations of the magnetic lens in electron optics The chromatic aberration expansion can be divided into two components, the intrinsic Δrci and combined Δrcc chromatic aberration [10]. Their role in accommodation would be difficult to evaluate because the visual system has a mechanism to correct them; namely, by just rotating the eye in order to Oct 27, 2016 · The primary aberrations of a cylindrical magnetic lens consist of the third-order spherical aberration and the first-order chromatic aberration. The five basic types of aberration which are due to the geometry of lenses or mirrors, and which are applicable to systems dealing with monochromatic light, are known as Seidel aberrations, from an 1857 paper by Philipp Ludwig von Seidel. We note that these primary (first refer to the respective coefficient for first-order aberrations. We give two examples where these aberrations are shown in isolation. A terms are first-order, corresponding to the paraxial approximation. 2, 267-271 (1827). These are the aberrations that become evident in third-order optics, also known as Seidel optics. Extra conditions for the Nov 16, 2012 · The usual procedure in optical design [1] [2] [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] consists of an initial first-order design followed by the initial aberration analysis of the Moreover higher order aberrations introduce new types. The phenomena of aberration corresponds to the deviation caused by higher order corrections to the first order expansion of angular terms, in a geometrical optics situation. Mar 1, 2000 · Meanwhile, based on electron optical canonical aberration theory, analytical formulas of third-order geometrical and first-order chromatic aberration coefficients and their computational results have first been derived for this bi-potential electrostatic and bell-shaped magnetic combined lens. Defocus is caused by an incorrect reference image I: the first-order foundation and method for deriving the anamorphic primary aberration coefficients[J]. Elisa Chisari Princeton 02/09/2011 Primary/Seidel aberrations Number of nth order terms The first-order aberrations are thus defects of focus or of image size (or height) which vary linearly with aperture or obliquity, such as simple defocusing or the paraxial chromatic aberrations (e. Dec 11, 2000 · In this paper the first- and third-order chromatic aberrations of electrostatic round lenses have been studied based on the electron optical-canonical aberration theory. May 19, 2015 · Wavefront aberrations can be described as deviations of the wavefront exiting the eye from a reference wavefront that is aberration free and diffraction limited. , focus and twofold astigmatism) should be frequently Mar 1, 2000 · Meanwhile, based on electron optical canonical aberration theory, analytical formulas of third-order geometrical and first-order chromatic aberration coefficients have first been derived and their computational results obtained for this bi-potential electrostatic lens. Keywords: Zernike coefficients, Higher order aberrations, Population based study, Adult. 2 2 1 sin sin θ θ = n. Young, “On the mechanism of the eye,” Phil Trans Royal Soc Lond 1801; 91: 23–88 and plates. by moving the image 2. Then for a system of surfaces the fourth-order coefficients are the sum of the coefficients contributed by each surface. In addition to their fundamental pur- pose, dipoles and quadrupoles will also introduce higher-order aberrations. The present work uses the Hamiltonian function expansion method to derive all analytical expressions of the first- and third-order chromatic aberration coefficients instead of the generalized integration transformation met in the aberration coefficients. Nov 16, 2010 · The classical theory of first-order chromatic aberrations neglects terms of paraxial order in aperture and powers higher than the first in glass dispersions. •For slow systems, ~F/8 or less, and for small fields of view, a few degrees, the primary aberrations. Nov 1, 2008 · The higher-order spectral components are found to respond more sensitively to a focus shift than the first-order (or second-order) component, so that the aberrations by a small longitudinal shift of focus can exert a severe effect on the fine structure of image in a complicated way. Petzval field curvature. to describe the input and. Camb. In non-paraxial systems, higher order terms in the power series expansion of the sine function can be significant, and aberrations are no longer negligible. (5) now turns out as a product of two polynomial series. Higher and lower order distortions can occur simultaneously. Ocular aberrations can be sub-categorised as lower and higher order aberrations. B. Key aberrations discussed include spherical aberration, which causes peripheral rays to focus in different locations than central rays, and coma, which causes rays to flare out from the image point. The total expansions (Δrc = Δrci + Δrcc) of the first- and third-order chromatic aberrations of combined electromagnetic lenses Assume no second order terms in the aberration functions of each surface. In optics, aberration is a property of optical systems, such as lenses and mirrors, that causes the image created by the optical system to not be a faithful reproduction of the object being observed. Reciprocity: Works the same from left to right as third-order aberrations First-order wavefront properties and third-order wavefront aberration coefficients can be obtained from the Zernike polynomials coefficients. Jose Sasian OPTI 518 4 Transverse ray aberration y I HWHO 1 , 5 Ж 1 , I '' yH WH nu y The first subgroup includes aberrations that deteriorate the image: I. HOAs have a more nuanced eyeball distortion than the first-order aberrations. Jun 14, 2024 · Moreover, since we will discuss such aberrations with respect to the wave aberration function W, we are considering wave aberrations. Sep 23, 2019 · Whether classical imaging, which is congruent with first-order optics, is required in a lens system, or any other type of imaging, depends on system application. The symmetry is about the aperture stop. Generally, only first and third-order aberrations are necessary for system analysis. Introduction Image position, size and orientation are very important for initial first order design. With a thin lens, with the stop at the lens, we have longitudinal Chromatic aberration (LCA). Aberrations in Theories of Optical Aberrations . Superior orders merely repeat previous aberrations by adding first order properties Yuhao Wang Dec. Jan 25, 2017 · Chromatic aberration: different wavelength have different focus. II. The first-order chromatic aberration has been investigated thoroughly and many articles have been devoted to this subject [1]. 002574 [12] YUAN SH, SASIAN J. Prof. There are no fourth-order extrinsic terms. In ophthalmic sense, aberrations are mentioned differently as Low order aberrations (LOA) and higher order aberrations (HOA) [6]. The odd aberrations have the important property that in a symmetrical system they Cancel (fourth-order), each half contributes the same amount of aberration but with opposite algebraic sign. 8=U . Nov 1, 2023 · All the first- to third-order chromatic aberration coefficients of the lens have been calculated, and the pattern of the first-order chromatic aberration has been given as well. rises from inclusion of the term with third order in expansion of s aberration Third-order aberration theory ine. n 1 sinθ 1 =n 2 sinθ 2. 087e-01 Surface 2: -2. If these aberrations are second order, they may be eliminated or at least modified by the introduction of sextupole elements at appropriate locations. Fifth-tenth order: aberrations are important only when the pupil is greatly Sep 1, 2017 · For instance, a spherical aberration corrector [2] requires the measurement of the following aberrations; focus, twofold astigmatism, axial coma, threefold astigmatism, star, fourfold astigmatism and third-order spherical aberration. As we know, Pupil aberration insights and consequences • Can now determine aberration change upon object shift • Bow-Sutton conditions • Extrinsic sixth-order aberrations • Spherical aberration of the pupil • Coma of the pupil • Astigmatism and field curvature of the pupil For the aberrations of higher orders (n≥2), such as second-order axial coma B 2, three-fold astigmatism A 2, third-order spherical aberration C 3 (>0), third-order star aberration S 3 and four-fold astigmatism A 3, there is no elliptical distortion observable for the un-tilted case. 8, shown in Table III, the wavefront can be written as (57) The aberrations and properties corresponding to these Zernike terms are Second-order chromatic aberrations • Change of image location with λ(axial or longitudinal chromatic aberration) • Change of magnification with λ(transverse or lateral chromatic aberration 22 WH W W H W H W,cos 000 200 111 020 Mar 20, 2019 · There are two types of aberrations; lower-order aberrations (0, 1st and 2nd order), and higher-order aberrations (3rd,4th…). On the other hand, the higher order aberrations like trefoil, coma and spherical aberrations are largely undiagnosed and untreated. Other lower-order aberrations are non- visually significant aberrations known as first order aberrations, such as prisms and zero-order aberrations (piston). Mar 1, 2007 · In the pyramid of Zernike polynomials (Atchison, 2004, Thibos and Hong et al. First-Order Aberrations: These include: Piston (or plano; i. Each simulation contains three waves of the specified aberration. 623e-04 of all aberration orders. Lower- or 4th order (according to the exponent in d) wavefront aberration is calculated using the first two terms in the series; in fact, based not on the actual surface, but on its close approximation. Low order aberrations include Myopia (positive defocus), hyperopia (negative defocus), and regular astigmatism. will suffer chromatic aberrations. Using the first nine Zernike terms Z. A simulation was performed for each of the first, third, and fifth order Seidel Aberrations. 29 2010 OPTI. 4 Contributions from the sixth-order coefficients of asphericity 197 14. Fourth order threefold astigmatism (or Three lobe aberration) C 5,6 A 5 : 6: 6: Six-fold axial astigmatism or sixfold axial astigmatism of the 5th order: C 5,4 R 5: 5: 6: 4: Fourfold astigmatism of C 5 (or Fifth order rosette aberration) C 5,2 S 5: 5: 6: 2: Twofold astigmatism of C 5 (or Fifth-order axial star aberration) C 5,0 C 5 : 6: 0, ∞ Mar 1, 2025 · Based on these fields, the first-order optical properties (Gaussian properties), the first-order chromatic aberration coefficients, and the third-order geometrical aberration coefficients, for the axial microlenses, can be obtained by DA method, and they are listed in Table 5, Table 6 and Table 7, respectively. Photo Credit: mdashf. output optical fields Jan 24, 2021 · The third-order components describe main aberration effects: spherical aberration, coma, astigmatism, Petzval curvature, and distortion; that is why they are often referred to as primary aberrations; other terms are called higher-order aberrations. OVITZ was born when one of our founders, who had post-LASIK Higher Order Aberrations, committed himself to solving the problem of HOAs for people like you. Eqn. Higher order aberrations (HOAs) of the eye These equations can be reduced to third-order form, that is, the anamorphic primary ray aberration equations. Soc. III. Astigmatism. By comparison order spherical and focus. Higher-order aberrations exist but are not commonly corrected in Aberrations are phenomena that degrade the quality of the image formed by an optical system Degradation results when light rays from a given object-point fail to form a single sharp Dec 1, 2023 · The result of the DA and aberration integral methods for the third-order isotropic and anisotropic chromatic aberration coefficients for a Glaser magnetic lens with and without the OMI effect which is published for the first time with the aid of COSYINFINITY10 and Mathematica 11 program shown in Table 4, Table 5, Table 6. provide a useful reference. provide a substantially accurate approximation to the wavefront . It is worth pointing out that lateral chromatic aberration is a shift in image height with the image plane fixed at the position given for the design wavelength. V. 759e+00 Surface 5: 3. 466e-02 Surface 4: -2. from previous aberration in the system of all aberration orders. Aug 1, 2011 · As also shown in Fig. Likewise terms # 10 through # 16 represent fifth-order aberration, terms # 17 through # 25 represent seventh-order aberrations, terms # 26 through # 36 represent ninth-order aberrations, and terms # 37 through # 49 represent eleventh-order aberrations. Piston (the constant term) is considered the zero order term and the next two terms (first and second order) of the expansion form the tilt (linear) and power (r^2) terms. For example, fifth-order aberrations add the types oblique spherical aberration and elliptical coma[5]. Higher Order Aberrations. 5 Connections between pupil and image coefficients 198 14. Sasian, "Aberrations of anamorphic optical systems I: the first-order foundation and method for deriving the anamorphic primary abenation coefficients," Appl. In paraxial systems, angles are small, sin(φ) ~ φ, and we have first-order optics, no aberrations, and spherical wavefronts. Sep 8, 2023 · In this paper, the Gaussian optical properties and the first- and third-order isotropic and anisotropic chromatic aberrations of the Glaser magnetic lens have been derived analytically and then calculated numerically based on two methods: the differential-algebraic DA and the electron optical aberration integrals. OSA made an attempt to First-order match Third-order mismatch . Jan 7, 2025 · LOAs include myopia, farsightedness, astigmatism, and presbyopia. The first three primary aberrations - spherical, coma and astigmatism - result from deviations in the wavefront form from spherical. •The fourth-order group of aberrations is also know as the primary aberrations. Oct 31, 2022 · These wavefront aberrations are represented by Zernike mode pyramid, where m is the angular meridional frequency and n is the radial order. Jul 1, 2017 · There are 2 first order terms, having no aberrations higher than third order describing a system over the entire unit circle, then such . 3 Contributions from an aspheric surface 195 14. We find that the terms in the anamorphic primary ray aberration equations can be expressed as paraxial marginal and chief ray-trace data in the two associated RSOS, together with normalized object and stop coordinates. People without HOAs don’t know what it’s like to have their vision interrupted by halos, glare, flares, starbursts, double vision, ghosting, and blur and other visual anomalies. G. Distortion . 48. Vla. , 2002), the first two odd-order aberrations are first-order ones; that is, horizontal and vertical tilts. Since the above set of Zernike coefficients does not contain one corresponding to balanced 6th order aberration, it is substituted with a similar RMS value of balanced 6th/4th order spherical aberration, Since the latter is a product of similar amounts of 6th and 4th order aberrations, each about six times greater in their RMS magnitude than Apr 3, 2013 · Likewise, secondary spherical transverse aberration is 5th order, and so on. Fifth-tenth order: aberrations are important only when the pupil is Aberration theory has been a fruitful field for under-standing image formation in optical systems and for designing lens combinations. Fourth-order: aberrations contain spherical aberration, tetrafoil and. , less than 10 nm order), Ronchigram observation can be performed with large first-order aberrations (e. Airy, “On a Peculiar Defect in the Eye and a Mode of Correcting It”, Trans. Higher-order aberrations exist but are not commonly corrected in Zernike polynomials are divided into several orders, low-order aberrations (first and second order), and high order aberrartions (third order onwards). Apr 8, 2015 · It describes lower-order aberrations like defocus and astigmatism that account for 90% of aberrations, as well as higher-order aberrations. 521 Tutorial Professor: Jim Burge 1. mlgufou btsujhj mriuc jdo cfrgf zoec jxvocya cofpefb jgyht ysi bauc xfl xdhj amo qknmrlr