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WO2014077669A1 - Lentilles correctrices et procédé pour les produire avec une aberration sphérique nulle - Google Patents

Lentilles correctrices et procédé pour les produire avec une aberration sphérique nulle Download PDF

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Publication number
WO2014077669A1
WO2014077669A1 PCT/MX2013/000141 MX2013000141W WO2014077669A1 WO 2014077669 A1 WO2014077669 A1 WO 2014077669A1 MX 2013000141 W MX2013000141 W MX 2013000141W WO 2014077669 A1 WO2014077669 A1 WO 2014077669A1
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WIPO (PCT)
Prior art keywords
sign
lenses
spherical aberration
calculated
variables
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PCT/MX2013/000141
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English (en)
Spanish (es)
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WO2014077669A8 (fr
Inventor
Juan Camilo VALENCIA ESTRADA
Ricardo Benjamín FLORES HERNÁNDEZ
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CENTRO DE INVESTIGACION EN OPTICA AC
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CENTRO DE INVESTIGACION EN OPTICA AC
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Publication of WO2014077669A1 publication Critical patent/WO2014077669A1/fr
Publication of WO2014077669A8 publication Critical patent/WO2014077669A8/fr
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/02—Simple or compound lenses with non-spherical faces
    • G02B3/04—Simple or compound lenses with non-spherical faces with continuous faces that are rotationally symmetrical but deviate from a true sphere, e.g. so called "aspheric" lenses

Definitions

  • the present invention is located in the field of optics and ophthalmic. Specifically, the present invention relates to a method and set of aspherical lenses without spherical aberration (Zero spherical aberration), with various industrial applications.
  • the classic centered refractive geometric optics is based on the refraction of light on spherical and aspherical surfaces of revolution, which are normally specified in a cylindrical coordinate system ⁇ r, z).
  • EP0472291B1 a lens production method is shown, showing the stages required for its design, as it is intended to do in this application.
  • Another objective of the invention is to have a set of aspherical lenses with "zero spherical aberration" which can be represented by means of parametric mathematical functions which allow to calculate the thicknesses of the lenses in an exact manner, thus avoiding the use of approximate series that are used until this work in the optical industry for the design of lenses.
  • Another objective of the invention is to have a set of aspherical lenses with "zero spherical aberration" that improve the health of many people and increase the resolution of machines, devices and optical instruments.
  • R a Radius of a spherical anterior interface.
  • R b Apical radius of a corrective posterior interface. Radius of a spherical posterior surface.
  • the thicknesses on the edge cannot be diametral, since the posterior surface is oblate, so these lenses should be lenticularly designed.
  • Auxiliary rays are shown to indicate virtual caustic.
  • the loss of continuity in the vertex of the solution is observed in the last lens (c) by the commutation of the sign s before a small decrease in the absolute distance-object.
  • the other variables were X2013 / 000141
  • Fig. 13 Sphero-aspherical lenses with negative or positive designs, it is observed that there is no diametral thickness at the edge for the maximum diameter according to (112) in any of the lenses (a, b, c, d, e and f ), and that there is re-entry of the refracted rays in the anomalous region of the first two lenses with negative design (Sectors with a more saturated gray tone in a and b), whose subsequent refraction is not indicated. Auxiliary lines are included to indicate the position of the virtual focus that is not shown on the last two lenses (e and f).
  • the notable reduction in volume of the last lens (c) is observed as the index increases. The position of the virtual image point with two auxiliary rays is indicated.
  • Abnormal sectors are observed with a more saturated gray tone (In b, c and d), which require polishing and coating the edge of the lens with an absorbent material. The position of the virtual image point with two auxiliary rays is indicated.
  • the position of the virtual image point with two auxiliary rays is indicated, which is not visible on the first lens (a).
  • Fig. 19 Simple spherical-aspherical lenses with virtual object and image in the same place with prescribed diameter and negative design, four lenses (a, b, c and d) spherical-aspherical are shown
  • Lenticular designs with incident angular field of 180 degrees or more have many uses in remote sensing and in the design of solar collectors.
  • Axi conical designs similar to the right lens have numerous technological uses, which merit the production of a technical document that is not the subject of this work.
  • Fig. 22 Convex-Inflex simple spherical-aspherical lenses with positive design and blade edge, four lenses (a, b, c and d) are shown with the same vertex-anterior point-image distance.
  • the dependence of the positive design as a function of the distance object-image point / y -80, -20, - 10 and - 1 is clearly observed.
  • Four auxiliary rays are included in each lens to indicate the position of the virtual object and image points.
  • Fig. 25 Simple spherical-aspherical lenses with virtual object in the center of the sphere of the first surface and virtual image, several lenses are shown (a, b and ⁇ c).
  • Auxiliary rays are used to indicate the virtual positions of the object and the image on each lens.
  • Four auxiliary rays are used to indicate the virtual positions of the object and the image. It is observed in the posterior vertex (Valley) that the rays are close to the quadrant inversion. If the distance-object is reduced further, the inversion phenomenon will occur.
  • the designs were made with different diameters, indicating the circle of apical curvature with a tangent arc with gray color.
  • the radii of curvature were calculated using (136).
  • the present invention describes an analytical method for designing a set of aspherical lenses which are characterized by having a perfect central image (Zero spherical aberration) and not "reduced spherical aberration".
  • Said set of lenses is obtained from performing an analytical method applicable to any anterior or complementary surface of a rotationally symmetric lens.
  • a lens is made up of a pair of surfaces; a surface corresponding to the anterior interface of the lens and a surface corresponding to the posterior interface of the lens, which allows different types of anterior interfaces to be combined with subsequent interfaces depending on the characteristics that are desired to be obtained from the lens being designing, the design being reversible, that is, the anterior surface becomes posterior and the posterior surface becomes anterior if the lens is rotated 180 degrees while retaining the same optical axis, and exchanging the object and image distances.
  • lens and optical sense either: Biconvex, convex-flat, convex-concave, flat-convex, flat-concave, biconcave, concave-flat and concave-convex.
  • cut sections of the surfaces of revolution may have inflection points, that is, they are "inflexed.”
  • thin lenses can be designed with or without inversion of the light rays inside them, according to the "minimum thickness criterion", which is based on the fact that when obtaining lenses as much Thin possible light transmission is maximized and generally all other aberrations are minimized (Comatic, chromatic, field curvature (Petzval), astigmatism and distortion).
  • a single aspherical lens should be designed by presetting at minimum thickness t min "(either paraxial, that is, measured in the direction of the optical axis z, or not paraxial) and the diameter d ", choosing the geometry of the interfaces so that the expected refractive behavior is obtained. It should be noted that not always the minimum thickness is the central" ⁇ ", nor the diametral edge" 4 ", since which sometimes happens somewhere in between.
  • optical zone which is commonly used in the optical industry, serves to denote a regular or irregular edge sector of a monolithic, simple or composite object, which has refractive properties according to a specific function .
  • optical zone of a contact lens.
  • physical optics it is equivalent to specifying the entrance pupil of a lens or an optical system.
  • monolithic optical systems are those that are made up of a single piece of material (for example, a single lens), while simple optical systems consist of a single monolith, composite optical systems consist of two or more monoliths.
  • the composite optical systems also called “non-adhered lenses", which are made up of several simple systems where the lenses can be in contact with each other (not separated) without being attached or they can be separated maintaining a space between themselves.
  • the parametric solutions with parameter "r a " of the corrective surfaces of the spherical aberration are presented below, which guarantee “zero spherical aberration” and not “reduced spherical aberration", according to the type of geometry of the anterior surface "z a " , the thickness of the lens "t", the position of the object "4", the position of the image "” and the material of the lens immersed in the same medium with relative refractive index " « ", provided that both the object as the image are located at a finite distance: the.
  • the geometry of the anterior interface z a is preset, which can be any rotationally symmetrical surface that has spherical aberration, for example:
  • the expression obtained in the previous step 4a is simplified to the maximum.
  • a new recurring variable C is calculated using the results of steps 2a and 6a:
  • L K ⁇ Dr a -tt b + z a ) -J-
  • R B 2 (F 2 + K) -0 2
  • the radius of abscissa r b of the second surface is calculated using results from steps 6a, 8a, 9a, 10a, 12a and 13a.
  • the procedure can also be established to determine the geometry of the second surface of the lens that ensures that there is no spherical aberration, if the object is at infinity and Image is finite, for a first non-flat first surface:
  • the geometry of the previous interface z a is preset, which can be any non-flat rotationally symmetric surface that has spherical aberration, except for the vertex (if it exists), since it is an irregular point, using, for example, the expressions ( 2-6).
  • n which includes in the denominator the absolute value of the expression z a 'obtained in the previous step 2b.
  • R F 2 + K-0 2 where the sign s 4 is dichotomous, that is, it can only take the value 1 or -1 but never the value zero.
  • step Ib If the first surface is spherical convex (step Ib)
  • the parametric shape of the posterior surface can be obtained by evaluating the recurring variables according to the method described in the invention (Steps 2b-12b), with (32) in the first step, for all r to ⁇ 0:
  • the vertex distance must be prescribed anterior-focus f a , the index of refraction n, the diameter d ⁇ less than or equal to 2 R a and the thickness at the edge t e , which satisfy:
  • the maximum diameter of the lens is less than 2R a and can be determined by the numerical solution of:
  • the posterior central curvature of these spherical-aspherical lenses with an object in the infinite and real image is obtained by evaluating: which corresponds to a radius of relative central curvature Gaussian R ⁇
  • the posterior central curvature of these spherical-aspherical lenses with an object in the infinite and virtual image also satisfies the expression (70) and is also corresponding to a radius of central curvature R, according to (71) that also satisfies the Gaussian approximations (72) and (73).
  • Fig. 7 the ray tracing is presented in a bpherical lens, where spherical aberration and some anomalies can be appreciated.
  • R B 2 (F 2 + K) -0 2
  • the first factor in parentheses is an even and positive function
  • the right factor is even function of r ai (Since both the numerator and the denominator are even functions of r composer)
  • the recurring variable M is an even function of r a .
  • the value of the sign 53 must be dichotomous to ensure that (104) is even, that is:
  • the first discontinuity point (the farthest vertex in Fig.10) appears associated with the values of r satisfying:
  • the index must be prescribed of refraction n, the diameter di satisfying (112) and the minimum thickness t mm . If the design is negative, the image distance is also prescribed. If the design is positive, the distance point-object point-image / / , which satisfies (113) with tyt b as unknown variables, is prescribed.
  • the diametral thickness at the edge t e satisfies (114) with z ⁇ in an explicit and unknown way, if and only if no refracted ray relapses on the second surface in the same quadrant, or if the absolute maximum abscissa of the second surface is greater or equal to the half diameter.
  • the anomalous reentry phenomenon can occur more easily if the absolute distance-object is large in combination with a small absolute distance-image, a situation that must be verified by ray tracing, further reducing the upper dimension for the maximum diameter of the lens
  • the posterior central curvature of these sphero-aspherical lenses with real object and virtual image can be calculated according to
  • subsequent distance-vertex can be determined with the initial condition
  • the thickness at the edge t e of the lens can be determined by:
  • FIG. 15 An example of the positively designed ray tracing is shown in Fig. 15, varying the thickness at the edge.
  • Fig. 16 Some designs with maximum diameter and blade edge are presented in Fig. 16. The best bi-spherical approximation of the third lens of Fig. 16 is presented in Fig. 17.
  • the point-to-point-to-image-distance /, the refractive index n, the position of the lens with respect to the virtual object t must be prescribed a > 0 and the diameter d ⁇ .
  • the posterior vertex distance must be determined with the initial condition:
  • edge thickness t e of the lens can be determined by evaluating (142) the closest to the positive semi numerical solution for real and iámetro r in:
  • the reader can perform a comparative analysis of the general solution using (108-110) with an object distance close to R fl , versus the result obtained using the system (162) for a design lenticular, as shown in the first lens of Fig. 20, or with the axiconic design with maximum diameter and blade edge thickness, as shown in the second lens of the same figure.
  • the word axicone should be incorporated into the dictionary of the Royal Spanish Academy of the Spanish language. (Axicone: (Singular male substantive. Lens with one or more cone-shaped conical surfaces of revolution.)
  • the sign rule (169) is not consistent for all t a ⁇ R a .
  • Fig. 26 shows an example of this phenomenon.
  • Fig. 27 shows several lenses (without ray tracing), varying the object distance, and indicating at the vertex of the aspherical surface an arc of the oscillating tangent circle, corresponding to the section of the osculatrial sphere.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Lenses (AREA)

Abstract

La présente invention se rapporte à un procédé caractérisé en ce qu'il permet la conception de lentilles asphériques présentant une aberration sphérique nulle, qui peuvent être représentées au moyen de fonctions mathématiques paramétriques, par un procédé qui permet un calcul précis des épaisseurs des lentilles évitant ainsi l'utilisation des séries approximées qui sont utilisées dans l'industrie optique pour la conception des lentilles, supprimant ainsi le concept de "faible aberration sphérique". Lesdites lentilles permettent également d'améliorer la santé visuelle de nombreuses personnes du fait de l'absence d'aberration sphérique. Les surfaces correctrices antérieures ou postérieures (en tenant compte du fait que les formes sont réversibles) peuvent être réalisées facilement par différents processus de fabrication tels que l'usinage CNC et le moulage. Lorsqu'il est assumé que a) tout le rayonnement incident est entièrement réfracté, b) le matériau de la lentille est idéalement isotrope et homogène, c) la lentille est immergée dans un milieu également isotrope et homogène, d) les interfaces réfractrices sont idéalement continues, les lentilles à aberration sphérique nulle créées selon ce procédé possèdent une fonction d'étalement du point image (Point Spread Function ou PSF), pour un point objet situé dans l'axe, avec des ondes qui "convergent vers" ou "divergent depuis" le point image, comme sous-produit • des réflexions internes successives de la lumière non polarisée radialement, • de la résolution maximale de la surface à une échelle atomique, • de l'automodulation de phase et des effets non linéaires de dispersion en cas d'intensités lumineuses très élevées. Ces ondes peuvent également être réfractées dans le sens positif de l'axe z du fait que le champ électrique de l'onde oscille en permanence dans le plan r-z, porduisant ainsi une image du point objet avec un étalement, qui ne doit pas être confondu avec l'aberration sphérique ni avec les effets de diffraction. Une voie s'ouvre ainsi vers une nouvelle génération de lentilles et d'instruments optiques qui permettront un progrès dans de nombreuses disciplines humaines.
PCT/MX2013/000141 2012-11-16 2013-11-14 Lentilles correctrices et procédé pour les produire avec une aberration sphérique nulle Ceased WO2014077669A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
MXMX/A/2012/013376 2012-11-16
MX2012013376A MX2012013376A (es) 2012-11-16 2012-11-16 Lentes correctoras y metodo para producirlas con cero aberracion esferica.

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WO2014077669A1 true WO2014077669A1 (fr) 2014-05-22
WO2014077669A8 WO2014077669A8 (fr) 2014-07-10

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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4181409A (en) * 1978-10-16 1980-01-01 American Optical Corporation Aspheric lens series
US4504128A (en) * 1981-07-08 1985-03-12 Optische Werke G. Rodenstock Spectacle lens with high positive refractive power
JPS619601A (ja) * 1984-06-25 1986-01-17 Hitachi Ltd 光学レンズ
JPS63155102A (ja) * 1986-12-19 1988-06-28 Olympus Optical Co Ltd 非球面接合レンズ及びその製造方法
US5050981A (en) * 1990-07-24 1991-09-24 Johnson & Johnson Vision Products, Inc. Lens design method and resulting aspheric lens
US20090285079A1 (en) * 2008-05-16 2009-11-19 Toshiaki Katsuma Objective lens, optical pickup device, and optical recording/reproducing apparatus

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4181409A (en) * 1978-10-16 1980-01-01 American Optical Corporation Aspheric lens series
US4504128A (en) * 1981-07-08 1985-03-12 Optische Werke G. Rodenstock Spectacle lens with high positive refractive power
JPS619601A (ja) * 1984-06-25 1986-01-17 Hitachi Ltd 光学レンズ
JPS63155102A (ja) * 1986-12-19 1988-06-28 Olympus Optical Co Ltd 非球面接合レンズ及びその製造方法
US5050981A (en) * 1990-07-24 1991-09-24 Johnson & Johnson Vision Products, Inc. Lens design method and resulting aspheric lens
US20090285079A1 (en) * 2008-05-16 2009-11-19 Toshiaki Katsuma Objective lens, optical pickup device, and optical recording/reproducing apparatus

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WO2014077669A8 (fr) 2014-07-10
MX2012013376A (es) 2014-05-21

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