Multifocal optical device.

Brief Description Of The Invention

A diffractive multifocal optical element comprising a phase zone plate containing annular concentric zones in which the zones are spaced substantial­ly proportional to √n, the zones possess stepped facets that introduce a discon­tinuity in optical path length of less than λ/2. The invention also embraces a phase zone plate containing annular concentric zones possessing facets which provide an alternating stepped repetitive pattern in accordance with √n spacing in the optical element and wherein the depth of the steps of the facets are less than λ/2(η′-η), where η′ and η are the indices of refraction of the lens and the medium in which the lens is interacting and λ is the design wavelength.

Background To The Invention

This invention relates to an improvement in phase zone plate optics embracing contact and intraocular lenses. A "phase zone plate", as employed herein and in the claims, is a unitary optical region of a lens utilizing the combination of a zone plate and optical facets (such as in the form of echelet­tes) in the zones of the zone plate, and the combined facets in the zones diffract light to produce a specific wavefront which results in a specific inten­sity distribution of light at a variety of orders (e.g., 0^th, 1^st, etc.) of the zone plate. The orders constitute the foci of the zone plate. In a restrictive sense and also in the most utilitarian sense, the phase zone plate is designed for general lens applications where the distribution of light at effective intensities is dependent upon zone spacing for yellow light. Yellow light, as employed herein, is that portion of the visible spectrum at 530-570 manometers.

This invention relates <i>inter alias</i> to contact lenses. Contact lenses are classical vergence type lenses. They possess a concave corneal bowl (the posterior surface) that allows fitting to the eye and the outer surface (the anterior surface) is smooth and shaped to allow the eyelid to slide over the eye and to provide proper vergence of light (taking the lens material's refractive index into consideration) to a focal point accommodating to the eye. The majority of the commercial contact lenses are shaped such that the lenses are thinnest about the optical axis and the depth of the lenses gradually increases along a sloped radial length extending in the direction of the lens perimeter. Owing to the difference in depth extending from the optical axis, light passing through the optical axis has to pass through less of the lens material. Because light travels faster in air, the light passing through greater depths relative to light passing through lesser depths will be shifted, hence be retarded in time.¹ Consequently, the shape of the lens is selected to accommodate this progres­sive retardation of the light so that the lightwaves emanating from the posterior surface are in synchronization in reaching a desired focal point.

(1. See Fincham, et al., <u style="single">Optics</u>, Published by Butterworths, London, 9^th edition, 1980, 1981, pages 72-75.)

This invention concerns contact lenses utilizing phase zone plate optics, such as phase zone plate bifocals and "tuned" Fresnel lenses making use of concentric annular zones. Such lenses generally follow the designs described, for example, by Allen L. Cohen in U.S. 4,210,391; 4,338,005; and 4,340,283 ("Cohen patents"). A Cohen lens design provides that the radii "r_n" of the annular and concentric zones are substantially proportional to √n and that the zones are cut so as to direct light to more than one focal point.

The Cohen lens design with phase zone plate optics allows bifocal lens constructions which are exceptionally thin. Contact lenses may be designed with phase zone plate optics in order to achieve a bifocal or other multifocal effects. The specific chromatic properties of a phase zone plate may be incorporated in the design of a contact lens including a contact lens having multifocal properties. All phase zone plate optical elements which are desig­nated bifocals are possessed inherently with the ability to focus light to more than two focal points. They are designated bifocals because the intensity levels of the light to any two orders, e.g., the 0^th and 1^st order focal points are adequate for bifocal applications. In that sense, every bifocal distributes light to a third, and possibly more, focus. The judgment of whether a lens is a bifocal or trifocal is not based on any strict rule. If the wearer of the lens does not find objectionable the presence of the third or more focuses, then the lens is probably adequate as a bifocal. (See Klein and Ho, <u style="single">SPIE</u>, August 1986, Table 2 and the comments about Table 2.)

Other references mentioning or suggesting phase zone plate optics in regards to contact lenses are G. Forst, "Research into the Usability of Circular Grids as Aid to Vision,"<b>Der Augenoptiker,</b> 1966 (12), pages 9-19; Ziegler, "Fabrication or Correction of Optical Lenses," as modified by Cohen, see column 4, lines 27-36 of Cohen, U.S. Patent No, 4,339,005, and column 5, line 63 to column 6, line 68, of Cohen, U.S. Patent No, 4,210,391; Freeman, U.S. 4,637,697; and Freeman, U.S. 4,642,112 (to the extent that holography embraces phase zone plate optics).

Bifocal contact lenses utilizing the above principles of phase zone plate optics are commercially available. Such lenses are believed to utilize stepped annular facets each comprising a full-period zone where each zone has a depth of an optical path length of λ/2, providing a physical depth of λ/2(η′-η). η′andη are the indices of refraction of the lens and the medium (e.g., lachrymal layer) in which the lens is interacting and λ is the design wavelength, in this case that of yellow light. This results in a bifocal contact lens where the 0^th and 1^st orders have an equal split of yellow light intensity at about 40.1%.

A full-period zone, for purposes of this invention, is defined as the smallest repetitive sequence of facets within a phase zone plate which are spaced substantially proportional to √n. Such spacing is characterized by the formula: r_n≃√<o ostyle="single">2 n d λ</o> where d represents the 1^st order focal length. A half-period zone, for the purposes of this invention, is characterized by the formula: r_n≃√<o ostyle="single">n d λ</o> where d represents the 1^st order focal length.

Though the non-refractive step wall or riser to the plateau of the step is cylindrical or nearly cylindrical in the planar direction of the optical axis of the lens, and thereby occupies a small fraction of the lens phase zone plate surface area, it is regarded to be sufficiently large to contribute to a number of problems. Image shadowing and debris trapping are some of the problems that could be made less acute by reducing depth of the step wall or riser.

However, if such a lens were altered to reduce the depth of the facet³ to a value less than λ/2, λ being the design wavelength, the optical qualities of the lens quickly becomes very poor. Though one is dealing with very small values when working at λ/2, a few millimicrons change in dimension seriously impacts on lens performance. For example, a 10% reduction in the depth of the depth of the facets yields a significant loss of effective bifocality in such a lens. It should be appreciated that all other values relating to the phase zone plate's dimensions are commensurately small. The plateau of the facet extending from the non-refractive step to the nadir of an adjacent non-­refractive step, loses thickness from the λ/2 depth to a zero depth at the nadir of the adjacent step. These facts suggest that there is little one can do to avoid the loss in bifocality when reducing the depth of the step below λ/2.

(3. The terms "depth of a facet," "depth of the steps of the facet," "depth of the step" and words to that effect, as used herein, means in relation to the design wavelength of the lens, the degree of discontinuity in optical path length generated by the step.)

It has been discovered that small changes (in some embodiments exceptionally small changes) in the configuration of the shape of inclination of the plateaus of the facets within the framework of √n spacing provides that one can generate an effective bifocal lens based on phase zone plate optics where the depth of the step is less than λ/2. Through the alternating inclinations of facets embodied in the Cohen patents and the Cohen lens design, one can provide excellent bifocality in a contact lens where the facets have a depth less than about λ/2.

There is characterized herein a novel bifocal lens construction which provides the advantages of r_n zone spacing and stepped facets that introduce a discontinuity in optical path length of less than λ/2.

There is characterized herein a novel bifocal lens construction which reduces image shadowing attendant with conventional bifocal lenses contain­ing stepped facets having a depth greater or equal to λ/2.

There is characterized herein a novel bifocal contact lens having a phase zone plate which possesses less volume for tear collection than a bifocal contact lens having a conventional λ/2 parabolic echelette configuration. This means that the contact lenses of the invention have less volume for the trapping of debris on the eye and between the eye and the lens.

There are lens constructions according to this invention which provide surface contact with the cornea in a manner such that facet curves of the phase zone plate tangentially touch the cornea's surface. This causes the novel lens of the invention to rest more comfortably on the eye.

There is described herein a bifocal contact lens utilizing phase zone plate optics and a facet depth less than one-half the wavelength of the designed wavelength, where the primary focal points are at two orders, such as the 0^th and 1^st orders, the 0^th and 2^nd orders, or any other combination of two orders.

The Invention

The invention relates to a diffractive multifocal optical element comprising a phase zone plate containing annular concentric zones in which the zones are spaced substantially proportional to √n and the zones possess stepped facets that introduce a discontinuity in optical path length of less than λ/2 where λ is the design wavelength.

The invention encompasses a phase zone plate containing annular concentric zones possessing facets which provide an alternating stepped repetitive pattern in accordance with √n spacing in the optical element and wherein the depth of the steps of the facets are less than λ/2(η′-η), where η′and η are the indices of refraction of the lens and the medium in which the lens is interacting and λ is the design wavelength.

In a particular embodiment of the invention, the optical element comprises facets within the annular concentric zones providing an alternating stepped repetitive pattern wherein: <ul id="ul0001" list-style="none"><li>1. the facet of one of the alternating zones has an inclined curved profile that is interrupted at the zone boundary by another curved profile providing the differently inclined curved facet of the other alternating zone,</li><li>2. the zones are spaced substantially proportional to √n,</li><li>3. the depth of the facets are less than λ/2,</li><li>4. the zones are cut so as to direct yellow light to at least two primary focal points in at least adequate intensities for visual usage at each such primary focal point, and,</li><li>5. but for the alternating pattern, the element would not have such intensity.</li></ul>

The invention encompasses a bifocal optical element of the Cohen lens design wherein the odd and even zones of the phase zone plate <ul id="ul0002" list-style="none"><li>a. conform to r_n≃√<o ostyle="single">n d λ</o> spacing,</li><li>b. are contiguous and free of a non-refractive step interface at at least every other zone boundary, and leave a sloped profile at such contiguous interface,</li><li>c. the cross-section of each odd zone has the same general profile and the cross-section of each even zone has the same general profile,</li><li>d. the general profile of the odd zones is different from that of the even zones, and</li><li>e. the depth of steps for the zones are less than λ/2.</li></ul>

Preferably, the slope profile provides a smooth transsition from zone to zone.

In another aspect, the invention encompasses a bifocal optical element of the Cohen design comprising a faceted step phase zone plate containing an alternating profile wherein: <ul id="ul0003" list-style="none"><li>a. the phase zone plate conforms to r_n≃√<o ostyle="single">2 n d λ</o>;</li><li>b. the alternating profile occurs within the full-period spacing;</li><li>c. the facets have a depth less than about λ/2;</li><li>d. the zones are cut so as to direct yellow light to at least two primary focal points in at least adequate intensity for visual usage at each such primary focal point, and</li><li>e. but for such alternating profile the zones would not have such intensity for visual usage.</li></ul>

In a preferred embodiment, the optical element of the invention comprises optically diffractive facets providing two different curved profiles that are joined at radii r_n through transition profiles located about such radii, which transition profiles have profile curvatures that are different from said two different curved profiles whereby to form annular and concentric zones at such transition profiles which zones are spaced substantially proportional to √n and the zones are cut so as to direct yellow light to at least two primary focal points in at least adequate intensity for visual usage at each such primary focal point, which element but for the curved profiles would not have such intensity for visual usage.

This invention relates to an ophthalmic lens such as contact and intraocular lenses containing such optical elements. In a preferred embodi­ment of the invention, the ophthalmic lens is a bifocal lens that splits the light to two focal points in essentially equal intensities. In a most preferred embodi­ment of the invention, the optical element of the lens comprises a repetitive pattern of zones having a profile embraced by the equation d = D_o^· {1/2 + 1/2 ^· cos (π ^· r²/b²)} where <b>d</b> is the depth of the repetitive profile, <b>r</b> is the radial position of the zone, <b>b</b> is the radius of the 1^st zone, and <b>D</b>_o is the facet depth for the design wavelength.

One embodiment of the invention is directed to an ophthalmic contact lens containing at least two phase zone plates within its optic zone, at least one of which embraces the features of the aforementioned optical elements.

Another embodiment of the invention is directed to an ophthalmic contact lens having within its optic zone, (1) a phase zone plate embracing the features of the aforementioned optical elements and (2) a pure refractive portion, pre­ferably in the form of one or more channels.

Brief Description of the Drawings

<ul id="ul0004" list-style="none"><li>Figure 1 illustrates an incident plane wave striking a diffractive bifocal optical element illustrating the typical parabolic shaped echelettes, having the √n spacing pattern of the Cohen lens design, whereupon it is transformed into two (2) emergent spherical waves directed to different foci, thus depicting the general principles of multifocal diffraction.</li><li>Figure 2 is a curve illustrating the echelette profile cut from a typical prior art diffractive bifocal optical element, such as in a lens according to Ziegler, <i>supra</i>. The axis labeled <b>d</b> represents the echelette thickness and the axis labeled <b>r</b> represents the radial distance along the echelette.</li><li>Figure 3 is a cross-section of one embodiment of optical element in accordance with the invention, the facets of which are depicted graphically in Figure 4.</li><li>Figure 4 is a curve illustrating a facet profile of one embodiment of the inven­tion. The axis labeled <b>d</b> represents facet thicknesses and the axis labeled <b>r</b> represents the radial distance along the facets.</li><li>Figure 5 compares the graphical profiles of the full-period spaced echelette zone of the prior art possessing the conventional parabolic profile and the half-period spaced facet zones containing a multi-profile interrupted structure.</li><li>Figures 6 through 12 provide graphical depictions of cross-sectional views of a variety of facet arrangements for optical elements within the scope of this invention.</li></ul>

Details Of The Invention

This invention concerns <i>inter alia</i> bifocal optical lenses comprising an optic zone section which uses diffractive means for achieving multifocal properties. The diffractive means incorporates a repetitive pattern with shallow facet depths and a new profile. The use of a profile with shallow facet depths reduces shadowing of images, debris collection between the phase plate and the eye (in the case with contact lenses), and enhances wearer comfort in the case with contact lenses.

The invention finds its most favored employment in contact lenses. The invention involves incorporating the optical elements on the anterior or posterior portion, or both, of a contact lens. The optical elements may be provided on contact lenses by lathing or molding. The invention is favorably employed in multifocal (especially bifocal) intraocular lens.

The present invention relates to a diffraction bifocal optical element. It utilizes a circularly blazed diffraction grating to achieve its multifocal proper­ties as taught by Cohen. The blazed grating allows for adjusting the split of light between two focal points by adjusting both the facet depth D_o and the profile of the blazed facet itself. The invention utilizes novel profiles for the facets of the optical element.

The present invention relates to a diffraction bifocal optical element utilizing a circularly blazed diffraction grating to achieve its multifocal properties wherein the blazed grating allows for adjusting the split of light between two focal points by adjusting both the facet depth D_o and the profile of the blazed facet itself, and the blazed facet provides an alternating inclination divided in accordance with √n zone spacing.

The novel facet arrangements of the invention divide what in the prior art is considered a full-period (λ) spacing of the facets into alternating inclined half-period (λ/2) faceted zones that contain only one non-refractive cylindrical (or essentially cylindrical) surface for every two alternating half-period zones, and such two alternating half-period zones are interconnected by a smooth surfaced facet which effects a phase shift of the design wavelength light between the half-period zones. All of the non-refractive essentially cylindrical or cylindrical surfaces are less than λ/2 deep. The alternating zones of the invention provide control of the split of light between the focal points of the lens. By adjustment of the inclinations of the alternating zone, it is possible to vary the intensity of light to the focal points.

The invention embraces a diffraction bifocal optical element superimposed on, etched into and/or embedded within a surfaces layer of a lens possessing the ability to independently converge light to at least two (preferably two) primary focal points in which the element comprises alternating inclined half-period (λ/2) faceted zones that contain only one non-refractive cylindrical (or essen­tially cylindrical) surface for every two alternating half-period zones, and such two alternating half-period zones are interconnected by a smooth surfaced facet which effects a phase shift of the design wavelength light between the half-period zones. All of the non-refractive essentially cylindrical or cylindrical surfaces are less than λ/2 deep.

A remarkable aspect of the invention is the minimal difference in inclination required in the alternating facets to achieve the benefits of excellent intensity of light at the designed focal points and at the same time yield the improve­ments cited above, including glare and/or haloing reduction. Only a small difference in inclinations from a traditional parabolic shape is required in the half-period zones to generate a lens providing the advantages of the invention. Such small differences come about by reason of the smallness of the facets even over a full-period zone measurement. For example, one embodiment of the invention may employ in a contact lens ◇ where the phase plate is characterized as comprising 8 full-period zones and is located in the posterior surface of the lens, ◇ the lens conforms to the shape of the eye and provides a typical refrac­tion to the distant focal point, and ◇ the design wavelength is for yellow light, about 555 nanometers, the following dimensions: ■ the first zone at the optical axis has a radius of about 0.75 millimeters; ■ the last zone away from the optical axis has a width defined by the difference in the radius to the outer periphery of the zone and the radius to the inner periphery of the zone, of about 0.14 millimeters; and ■ the depth of each facet is about 0.003 millimeters.

This same structure, measured however, in terms of its 16 half-period zone spacings caused by a profile surfaces inflection occuring at a point at about √n dimensions: ■ the first zone at the optical axis has a radius of 0.053 millimeters; ■ the last zone away from the optical axis has a width defined by the difference in the radius to the outer periphery of the zone and the radius to the inner periphery of the zone, of about 0.067 millimeters.

On comparing the optical elements comprising facets that have a conventional parabolic shape over full-period zone spacing to optical elements comprising the half-period zone spacing and facet profiles of the invention, utilizing the depth of the step of 0.003 millimeter, the half-period zone spacing is found to have a slightly lower area under the curves reflecting the profile of the facets. That difference can be as little as about 1% area difference to about 10 % area difference. Typically the difference is about 2 to about 5% area difference. In the above illustration, the area difference is about 3%. As small as the area difference seems to be, its contribution to the performance of the lens is quite significant.

A lens having the prior art parabolic shaped echelettes, full-period spacing and with an echelette depth of 0.8 λ/2, provides the following light intensity distribution: <tables id="tabl0001" num="0001"><table frame="all"><tgroup cols="3" colsep="1" rowsep="0"><colspec colnum="1" colname="col1" colwidth="52.50mm" /><colspec colnum="2" colname="col2" colwidth="52.50mm" /><colspec colnum="3" colname="col3" colwidth="52.50mm" /><thead valign="top"><row><entry namest="col1" nameend="col1" align="left">-1</entry><entry namest="col2" nameend="col2" align="left">0</entry><entry namest="col3" nameend="col3" align="left">1</entry></row></thead><tbody valign="top"><row rowsep="1"><entry namest="col1" nameend="col1" align="char" char=".">.05</entry><entry namest="col2" nameend="col2" align="char" char=".">.57</entry><entry namest="col3" nameend="col3" align="char" char=".">.25</entry></row></tbody></tgroup></table></tables> That is to be compared with the Klein and Ho description of the λ/2 analog showing the following intensities: <tables id="tabl0002" num="0002"><table frame="all"><tgroup cols="2" colsep="1" rowsep="0"><colspec colnum="1" colname="col1" colwidth="78.75mm" /><colspec colnum="2" colname="col2" colwidth="78.75mm" /><thead valign="top"><row><entry namest="col1" nameend="col1" align="center">m =</entry><entry namest="col2" nameend="col2" align="center">3. nonalternating (b = .5)</entry></row></thead><tbody valign="top"><row><entry namest="col1" nameend="col1" align="right">-4</entry><entry namest="col2" nameend="col2" align="char" char=".">.0050</entry></row><row><entry namest="col1" nameend="col1" align="right">-3</entry><entry namest="col2" nameend="col2" align="char" char=".">.0083</entry></row><row><entry namest="col1" nameend="col1" align="right">-2</entry><entry namest="col2" nameend="col2" align="char" char=".">.0162</entry></row><row><entry namest="col1" nameend="col1" align="right">-1</entry><entry namest="col2" nameend="col2" align="char" char=".">.0450</entry></row><row><entry namest="col1" nameend="col1" align="right">0</entry><entry namest="col2" nameend="col2" align="char" char=".">.4053</entry></row><row><entry namest="col1" nameend="col1" align="right">1</entry><entry namest="col2" nameend="col2" align="char" char=".">.4053</entry></row><row><entry namest="col1" nameend="col1" align="right">2</entry><entry namest="col2" nameend="col2" align="char" char=".">.0450</entry></row><row><entry namest="col1" nameend="col1" align="right">3</entry><entry namest="col2" nameend="col2" align="char" char=".">.0162</entry></row><row rowsep="1"><entry namest="col1" nameend="col1" align="right">4</entry><entry namest="col2" nameend="col2" align="char" char=".">.0083</entry></row></tbody></tgroup></table></tables> A slight modification in the profile while maintaining the depth of 0.8 λ/2 yields a bifocal element encompassed by the invention that provides a light intensity distribution at 0^th and 1^st orders of .405.

Each facet of the alternating zones of the phase zone plate has a depth less than λ/2, where λ is the design wavelength of the phase zone plate. In those cases where one zonal facet is joined by a curved profile to another zonal facet, if only one of them is formed from a step riser representing a non-refractive surface, the two zonal facets will have a combined depth of less than λ/2. In this special case, and for convenience of calculations, the depth of the combina­tion is viewed from the concept of full-period zone spacing. However, such alternating inclined zonal facets are viewed as having a variable depth. The depth of the facets may range from about 0.01 to about 0.99 times (x) λ/2, preferably about 0.05 to about .95 x λ/2, most preferably about 0.1 to about 0.9 xλ/2.

Assuming <i>arguendo</i> it was logical to those in the art to want to reduce facet depth, until this invention, there was no reasonable way to form a diffractive bifocal with facet (echelette) depths shallower than 1/2 wavelength that would not adversely affect the energy split between the two emergent spherical waves.

This invention makes it possible to construct shallow facet (echelette) diffrac­tive bifocal lenses with the requisite equal, or substantially equal, energy split between the two spherical waves going to the zeroth and first orders.

This invention supports the novel concept that the energy split between the two emergent spherical waves is determined <ul id="ul0005" list-style="none"><li>1. by the facet (echelette) depths and</li><li>2. the actual facet (echelette) profile.</li></ul> It has been determined that by suitably contouring the facet (echelette) profiles an equal energy split is obtainable even when cutting a diffractive bifocal lens with shallow facet (echelette) depths.

With respect to Figure 1, there is described a diffractive bifocal lens <b>CL</b> with a curvature to effect convergent refraction and diffraction. In the figure, optical elements <b>E</b> (predicated on a presumed full-period spacing) transform an incident plane wave into a wave front predominately of two spherical waves. For example, incident light wave with planar phase fronts <b>P</b> passes through the anterior surface <b>AS</b> of lens <b>CL</b> and emerges from the posterior surface <b>PS</b> as a light wave of predominately the two spherical phase front <b>S</b>₁ and <b>S</b>₂ with intensities I₁ and I₂, respectively. The posterior surface <b>PS</b> contains diffrac­tive echelettes <b>E</b> and their corresponding non-optical edges <b>N</b>. The facet (echelette) spacing in a diffractive optical element is given by the standard formula r_n ≃√n ^· r₁ in which r_n is the radius of the n^th zone (utilizing full-period spacing). And η and η′ are the refractive indices of air and the lens <b>CL</b>, respectively. The location of the focal points of the two spherical wavefronts is determined by the radius of the first zone <b>r</b>₁ and the carrier power of lens <b>CL</b>. In particular, the n^th order focal point f_m is given by the equation f_m = (r₁)²/(2 ^·λ ^· m) with λ = wavelength; and m = 0, ±1, ±2, etc.

A desirable energy split has been suggested to occur when the two emergent spherical waves carry equal amounts of the total energy, that is, when I₁ = I₂. The current literature states that this is the case when the facet (echelette) depths D_o are set at 1/2 wavelength deep (see the Klein and Ho, <i>supra</i>).

Figure 2 depicts a standard parabolic profile used in the prior art (see Ziegler, <i>supra</i>). The depth <b>d</b> of the repetitive profile as a function of radial position <b>r</b> is shown in the following equation: d = D_o^· (1 - r²/b²) b = radius of the 1^st zone This profile is repeated in each zone but scaled down proportionally to the width of each such zone. The facet (echelette) depth for an equal energy split at the 0^th and 1^st orders is shown by the following equation: D_o = 0.500 ^· λ/(n-1) n = index of refraction and the intensity split is given by I₁ = I₂ = (2.0/π)² = 0.405.

Figure 3 shows a diffractive bifocal optical lens containing facets according to the design illustrated in Figure 4. The facet depths are .405/.500 = 80% of the depths required by prior art lenses.

Figure 4 illustrates a new cosine profile used in one embodiment of this invention. The repetitive profile is given by d = D_o^· {1/2 + 1/2 ^· cos (π^· r²b²)}

The facet depth, utilizing a full-period spacing between the non-­refractive edges of the steps but containing alternatingly inclined facets within half-period spacing, for an equal energy split is given by D_o = 0.405 ^· λ/(n-1) and the intensity split is given by I₁ = I₂ = J<maths id="math0001" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0001.tif" /></maths>(0.405 ^· π) = 0.403 where J_o is a bessel function.

Figure 3 comprises an optical lens <b>CL</b> possessing anterior surface AS and peripheral posterior surface <b>PS</b>. In this embodiment the posterior surface of the optic zone is comprised of the diffractive facets (echelettes) <b>E</b> and their corresponding non-optical edges <b>N</b>. The physical profile of the facets (echelet­tes) <b>E</b> is given by d = D_o^· {1/2 + 1/2 ^· cos (π ^· r²/b²)} where <b>d</b> is the thickness of the facet (echelette), <b>r</b> is the radial distance from the inner edge of the zone (and such profile is repeated in each zone but scaled down proportionally to the width of each such zone) within which the facet (echelette) is formed and the occurrence of such profile alternation, and <b>b</b> is the radius of the first zone. This particular profile is drawn in Figure 4.

Figure 5 is an overlay of the parabolic echelette design <b>a</b> characteristic of the prior art (see Figure 2), the cosine profile <b>b</b> of Figure 4 and another useable profile <b>c</b> for a bifocal lens. The purpose of the overlay is to illustrate the profile differences between the structures of the invention and the prior art illustrated by Figure 2. Note particularly the shift in profile of curve <b>b</b> at the √n spacing. That small difference allows the profile of curve <b>b</b> to be suitably employable as the facet profile for the lens element of the invention.

The physical profile of the facet <b>c</b> is given by y = 1 - {(r² - 1/√2)/(1 - 1/√2)} r&gt;1/√2

Profiles <b>a</b> and <b>c</b> at such reduced depth fail to give an equal intensity split of the light to the 0^th and 1^st orders whereas they do when D_o = 0.500 ^· λ/(n-1).

Figures 6 through 10 depict a variety of useful facet profiles that can be used according to the invention in the lens construction of Figure 2.

Figure 6 graphically depicts along an x-y axis the profile of Figure 4 in a repetitive sequence of alternating half-period inclined zones represented by the odd and the even zones. This particular embodiment is characterized by y = 0.405λ/(n - 1) ^· {1/2 + 1/2 cos (πr²/2r<maths id="math0002" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0002.tif" /></maths>} I_o = I₁ = 0.402 wherein λ is the designed wavelength and <i>n</i> is the index of refraction of the lens medium.

Figure 7 is another profile graphically depicted along an x-y axis in which the depth of the non-refractive edges of the step are further reduced to 0.31λ and the depth of the even half-period zones have a curved connection with the non-refractive edge. This embodiment of the invention is character­ized by y = 0.314λ/(n - 1) ^· 2.5{1/2 + 1/2 cos (πr²/2r<maths id="math0003" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0003.tif" /></maths>} - 0.314λ/(n - 1) ^· 1.5{1 - r²/2r<maths id="math0004" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0004.tif" /></maths>} I_o = I₁ = 0.390

Figure 8 shows a profile where the edge of the step is inclined, suggesting that it contributes to the optical quality of the phase zone plate. The profiles of the half-period alternating zones in this embodiment are different from the preceding designs, mainly because the non-refractive edge has been substantially removed. This embodiment is characterized by y = λ/(n - 1){r²/r<maths id="math0005" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0005.tif" /></maths> + cos(πr²/2r<maths id="math0006" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0006.tif" /></maths> - 1} I_o = I₁ = 0.314 It is to be noted in this embodiment that the depths of the facets for the odd zones were further reduced to 0.21λ but the even zones have a depth below the nadir of the odd zones by another 0.21λ.

Figure 9 shows a faceted profile where the inclination of the even zones have a bottom curvature which presents two opposite-facing curves before connecting with the non-refractive edge of the step. This embodiment of the invention is characterized by y = 0.394λ/(n - 1){0.287 + 0.731J_o{4.20^·r²/2r<maths id="math0007" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0007.tif" /></maths>)} I₀ = I₁ = 0.402 wherein J_o is a bessel function.

Figure 10 shows another facet profile that incorporates two phase zone plates and a pure refractive portion. In this embodiment, there is a decrease in depth from full-period zone to full-period zone, though it is not necessary for the decrease to exist throughout the optic zone. For example, the first half of the full-period zones of the optic zone may be only one depth, and the second half of the full-period zones may be progressively reduced in depth. In the preferred modes of such embodiments, each of the steps, whether of the same or different depth, is equally divided along a common plane of the optic zone. The pure refractive portion is preferably in the form of one or more channels which may be incorporated within the optic zone and/or circumscribing the optic zone. The particular embodiment of Figure 10 is characterized by y = αλ/(n - 1){1/2 + 1/2cosπ/2 ^· r²/r<maths id="math0008" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext></mrow><mrow><mtext>o</mtext></mrow></mfrac></mrow></math><img file="EP0351471A2_D0008.tif" /></maths>}/DL&gt; where α decreases from zone to zone.

The faceted profiles of Figures 11 and 12 introduce a space reduction in the full period zone at <b>q</b>₁ which allows the step to proceed from <b>q</b>₁ to <b>r</b>², etc. This space reduction in the alternating zone is not regarded to alter the √n spacing of the zones. Figure 11 is characterized by y_n =.40{1/2 + 1/2 cos[(π/q_n² - r_n²) (r² - r_n-1²)]} where r_n-1 &lt; r &lt; q_n y_n = .40{1/2 + 1/2 sin[π/r_n² - q_n² ^· (r² - (r_n² + q_n²)/2)]} where q_n &lt; r &lt; r_n-1 r_n≃√<o ostyle="single">2 n d λ</o> q_n = r_n-1 + (r_n - r_n-1/α) α = 1.086 Figure 12 is characterized y_n = .39{1/2 + 1/2 cos[π/q_n² - r_n² ^· (r² - r_n-1²)]} where r_n-1 &lt; r &lt; q_n y_n =.39{1 - (r - r_n/r_n - q_n)²} where q_n &lt; r &lt; r_n r_n≃√<o ostyle="single">2 n d λ</o> q_n = r_n-1 + (r_n - r_n-1/α) α = 1.086.

It should be appreciated that the invention is not limited to the exact details of construction shown and described herein for many obvious modifications will occur to persons skilled in the art. In particular, many different profiles may be determined which allow the reduction of facet (echelette) depths without changing the desirable equal energy split. However, the choice of facet profile is not dependent upon effecting an equal energy split. It is believed that the achievement of the energy splits, whether equal or not, is directly derived from the alternating inclinations of the half-period zones.