fig1 illustrates a toric surface configuration suitable for use as a contact lens , intraocular lens , single element lens or a multiple element lens . the optical axis coincides with z - axis and the shortest radius r y ( steepest curvature ) is along y - axis that coincides with tangential meridian and the longest radius r x ( flattest curvature ) is along x - axis that coincides with sagittal meridian . the toric surface 100 is characterized by the principle meridians along the steepest curvature , 110 , and flattest curvature , 120 . in a spheric toric lens , r y and r x are constant along the corresponding principle meridians and the in an aspheric toric lens r y and r x are variable , that is , the toric surface has an aspheric cross section at the tangential or y - axis and sagittal meridians or x - axis of the described configuration commonly used for analysis by an optical design software such as zemax for instance . toric surface cylinder is defined by the difference in dioptric power between the meridians . the toric surface spherical power is defined by the average dioptric power between the principle meridians . fig2 illustrates ray tracing through a toric surface . the point object p is located on the optical axis 130 . the transverse rays 140 and 150 are refracted by the toric surface 100 at the tangential meridian 110 to form tangential focal segment t . the sagittal rays 160 and 170 are refracted by the toric surface 100 at the sagittal meridian 120 to form sagittal focal segment s . the corresponding focal segments locate at different distances along the optic axis and are called the sagittal focus and the transverse focus , respectively . the distance between these foci is called interval of sturm , is . in between these two foci closely to the middle , a round but “ blurry ” image is formed . this is called the medial focus or “ circle of least confusion ”, 180 . this plane usually represents the best compromise image location in a system with astigmatism . fig3 illustrates an example of longitudinal spherical aberrations at y - and x - axes within 3 mm diameter of nominal astigmatic eye with 2 . 5 d cylinder corrected by spherical toric lens . both lsas are practically equivalent and demonstrate a common lsa shape with a negative magnitude that is similar to the eye with a spherical lens of the same power as power of the spherical toric lens averaged between both principle meridians . fig4 provides an example of contra - aspheric toric shape along the principle meridians per the lens specification provided in the table 1 below . the curve characteristics along y - axis are designated by “ y subscript ” and along x - axis are designated by “ x subscript ” and both are plotted as the deviations from the corresponding spherical shapes defined by the vertex radii in y - and x - meridians . aspheric toric surface of a toric lens can be described by the following equations along y - and x - axes : where “ y ” and “ x ” is the distance from the lens center along y - axis and x - axis correspondently , “ c y ” and “ c x ” are vertex curvatures along y - and x - axis correspondently , c y = 1 / r y and c x = 1 / r x with r y and r x being vertex radii along y - and x - axis correspondently . coefficients a y2 , a y4 , etc are aspheric coefficients along y - axis and a x2 , a x4 , etc are aspheric coefficients along x - axis . the term sphere ( y 2 ) is the first taint defined by the sphere of the vertex radius r y shifted by the second term a y2 and the term sphere ( x 2 ) is defined correspondently along the x - axis . aspherization along the principle meridians may change effective tangential and sagittal powers effective correction for conical cylinder and the second order aspheric confidents a y2 and a x2 play important role of adjusting the spherical powers of the principle meridians to maintain the correction for corneal cylinder . table 1 below lists the example of specifications of toric intraocular lens with toric aspheric surface according to the present invention . the astigmatic eye with spherical toric iol had the same specifications as with contra - aspheric toric iol except the absence of aspheric coefficients a y2 , a x2 , a y4 and a x4 . the fig4 demonstrates that the aspherization largely flattens the surface along the tangential plane ( y - axis ) and largely steepens the surface along the sagittal plane ( x - axis ). the planes coincide with the principle meridians to demonstrate maximum and minimum curvatures . fig5 illustrates an example of longitudinal spherical aberrations at y - and x - axes within 3 mm diameter of nominal astigmatic eye with 2 . 5 d cylinder corrected by contra - aspheric toric lens . the fig5 demonstrates the result of aspherization on the longitudinal aberrations in y - axis and x - axis . in order to collect lsa in x - axis , the toric surfaces were rotated by 90 degrees because zemax software plots lsa only in y - axis . the aspherization results in the lsas of opposite signs for tangential ( t ) and sagittal ( s ) planes . this is the origin of the term used in describing aspherization of the present invention : “ contra - aspherization ” as being the reference to the opposite signs of the lsas . fig6 a and 6b demonstrate depth - of - foci of resultant tangential and sagittal focal segments in the nominal astigmatic eye at 5 and 10 degrees meridional misalignments of spherical toric lens . to analyze depth - of - focus and image quality at 5 degrees of meridional misalignment between corneal toric lens and toric iol , one of the principle meridians of the corneal lens was placed at 42 . 5 degrees orientation and corresponding principle meridian of the toric iol was placed at 47 . 5 degrees orientation . this lead for the resultant principle meridians of the astigmatic eye with toric iol to be at y - axis and x - axis correspondently and enable to use zemax optical design software to calculate through focus responses ( tfrs ) at 50 lp / mm defining the depth - of - focus for the resultant tangential and sagittal images at 50 lp / mm ( 20 / 40 va level ) and their modulation transfer functions ( mtfs ) at the circle of least confusion . the mtfs define the resultant image quality at the best focus defined by the position of circle of least confusion . to analyze depth - of - focus and image quality for 10 degrees of meridional misalignment between corneal toric lens and toric iol , the principle meridian of the corneal lens was placed at 40 degrees orientation and the principle meridian of the toric iol was placed at 50 degrees orientation . again , zemax optical design software was used to calculate corresponding tfrs and mtfs ( fig8 a and 8b ) by the method described above for 5 degrees of meridional misalignment . tangential focal segment is referenced by the letter t and sagittal by the letter s in the figures . a distance between tangential and sagittal peaks increase with the meridional misalignment thus reducing their overlap and therefore , reducing the image quality at the best focus position defined by the position of the circle of least confusion . fig7 a and 7b demonstrate depth - of - foci of resultant tangential and sagittal focal segments in nominal astigmatism eye at 5 and 10 degrees meridional misalignments of contra - aspheric toric lens per fig4 . to analyze depth - of - focus in terms of tfrs and image quality in terms of mtfs for 5 and 10 degrees ( fig8 a and 8b ) of meridional misalignments between corneal toric lens and toric iol , the principle meridian of the corneal lens was placed according to the method used for spherical toric lens analysis per the description under the fig6 a . tangential focal segment is referenced by the letter t and sagittal by the letter s in the figures . a distance between tangential and sagittal peaks increase with the meridional misalignment similar to the specification with spherical toric iol but contra - aspherization increases the width of tangential and sagittal tfrs thus increasing their overlap at the position of the circle of least confusion that defines the best focus position . the contra - aspherization shifts the width of each focal segments more towards the best focus position — in this case , positive lsa in the tangential plane directs more light beyond the tangential focal segment towards the position of the circle of least confusion thus increase its contribution at the best focus position ; negative lsa in the sagittal plane directs more light towards the lens in front of the sagittal focal segment also towards the position of circle of least confusion thus also increasing its contribution at the best focus position . together they improve the image at the best focus position in tangential and sagittal orientations at the best focus as compare with the spherical toric lens at the same meridional misalignment . there is another advantage of the a contra - aspheric design of toric lens . in case of a defocus from the position of circle of least confusion located at the middle between tangential and sagittal focal segments , the difference in image quality between tangential and sagittal orientations doesn &# 39 ; t increase as drastically as in case of the corresponding spherical toric lens where tangential and sagittal peak are much more pronounced and therefore a difference in image quality between tangential and sagittal orientations increases much more drastically . it means that for the same amount of eye astigmatism and meridional misalignment the impact of spherical refraction error on image quality is much higher with spherical toric iol than with contra - aspheric toric iol . fig8 a and 8b demonstrate the examples of modulation transfer functions ( mtfs ) of nominal astigmatic eye with spherical toric lens and contra - aspheric toric lens per fig4 in aligned condition and 10 degrees meridional misalignment condition at the position of circle of least confusion . the method of calculation of the mtfs has been described under the fig6 a . at best focus position defined by the position of the circle of least confusion , both tangential and sagittal mtfs of the eye with each toric iol at different meridional misalignment are practically equivalent . at the condition of a perfect alignment the mtf ( t and s ) of the eye with spherical toric iol if better that the mtf ( t and s ) of the eye with contra - aspheric toric iol but contra - aspheric toric lens still provides high quality mtf that highly unlikely may impact the image quality . the mtf ( t and s ) of the eye with spherical toric iol is substantially reduced in the case of 10 degrees meridional misalignment that the image quality can only reach about 20 / 40 of visual acuity ( 50 lp / mm of spatial frequency ). the mtf ( t and s ) of eye with contra - aspheric toric iol , on the other hand , is substantially higher and the image quality still reaches 20 / 20 of visual acuity ( 100 lp / mm of spatial frequency ). fig9 demonstrate shapes of lsas of the eye in y - and x - axes coinciding with the principle meridians of a toric surface , not only within 3 mm diameter but at 5 mm diameter that is important for scotopic condition of low illuminance and where the surface profile along each principle meridian takes bi - sign asphericity . both lsa shapes take a configurations of a bi - sign aspheric where each tangential lsa or sagittal lsa includes the lsa regions of one sign within about 3 mm diameter and the opposite sign outside about 3 mm diameter in order to include aberration compensation at large pupils . in terms of general specification , the shape of one of the principle meridians comprises non - spherical profile with at least two regions within optical zone and one of these two regions being configured to produce a longitudinal ray aberration of a different sign the one produced by the other region . a description of a bi - sign lens and its benefits were provided in the u . s . patent application ser . no . 12 / 415 , 742 ; “ bi - sign aspheric intraocular lens ”, filed on mar . 31 , 2009 . the contra - aspheric toric lens with lsas of the eye model depicted on the fig9 meets the bi - sign aspheric lens description as applied to a toric lens and thus is designed to improve image quality at large pupils as compare with a spherical toric lens of similar power . the same specification is defined for base surface of a toric multifocal diffractive surface . fig1 demonstrate shapes of lsas of the eye in y - and x - axes coinciding with the principle meridians of a toric surface , not only within 3 mm diameter but at 5 mm diameter that is important for scotopic condition of low illuminance and where the surface profile along each principle meridian takes one - sign asphericity . both lsa shapes take a configurations of a one - sign aspheric where each tangential lsa and sagittal lsa includes the lsa regions of the same sign within about 3 mm diameter and outside about 3 mm diameter in order to include aberration compensation at large pupils . the same specification is defined for base surface of a toric multifocal diffractive surface . fig1 demonstrate shapes of lsas of the eye in y - and x - axes coinciding with the principle meridians of a toric surface , not only within 3 mm diameter but at 5 mm diameter that is important for scotopic condition of low illuminance and where the surface profile along sagittal principle meridian takes one - sign asphericity and tangential — bi - sign asphericity . tangential lsa and sagittal lsa shapes are opposite signs within about 3 mm diameter and the same signs outside about 3 mm diameter . a selection which asphericity belongs to tangential and sagittal orientation is arbitrary and determined by lens orientation . the same specification is defined for base surface of a toric multifocal diffractive surface . fig1 demonstrate shapes of lsas of the eye in y - and x - axes coinciding with the principle meridians of a toric surface , not only within 3 mm diameter but at 5 mm diameter that is important for scotopic condition of low illuminance and where the surface profile along sagittal principle meridians takes one - sign asphericity and tangential — bi - sign asphericity . tangential lsa and sagittal lsa shapes are the sane signs within about 3 mm diameter and opposite signs outside about 3 mm diameter . a selection which asphericity belongs to tangential and sagittal orientation is arbitrary and determined by lens orientation . the same specification is defined for base surface of a toric multifocal diffractive surface . although there has been hereinabove described a specific contra - aspheric toric ophthalmic lens in accordance with the present invention for the purpose of illustrating the manner in which the invention may be used to advantage , it should be appreciated that the invention is not limited thereto . that is , the present invention may suitably comprise , consist of , or consist essentially of the recited elements . further , the invention illustratively disclosed herein suitably may be practiced in the absence of any element which is not specifically disclosed herein . accordingly , any and all modifications , variations or equivalent arrangements which may occur to those skilled in the art , should be considered to be within the scope of the present invention as defined in the appended claims .
an ophthalmic toric lens to be worn on an eye or implanted inside of an eye , the lens includes an anterior surface , a posterior surface , and a toric shape formed into one of the anterior and posterior surfaces , the toric shape comprising two non - spherical principle meridians each having a region within an annular area of optical zone and the region of one principle meridian being configured for producing a longitudinal ray aberration of a different sign than a longitudinal ray aberration sign from the region of another principle meridian .