Abstract:
Mutifocal diffractive lenses are generally designed with concentric annular zones comprising blazed steps of equal area. Trifocal diffractive lenses differ in the intensity of light that they diffract into each of their three different powers. Usually, this light distribution has been adjusted by varying the step heights of the blazed steps within the annular zones. This invention discloses a trifocal diffractive lens wherein the equal area annular zones are further subdivided into two sub-zones wherein each sub-zone comprises a discrete blazed step. The sub-zones of this invention may be of unequal area. This allows the light distribution at its focal powers to be adjusted by varying not only the step heights of the blazed steps of the sub-zones, but also the relative areas of the sub-zones. The present invention allows for an increased flexibility in the design of multifocal diffractive lenses.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    Many people, particularly the aged, develop cataracts necessitating the removal of the natural crystalline lens from within their eye. Intraocular lenses (IOLs) are artificial (prosthetic) lenses that are used as a replacement for the natural lens of the human eye. The present invention relates generally to multifocal diffractive lenses, and more particularly to trifocal diffractive IOLs. Trifocal diffractive IOLs have three distinct powers that provide a patient, who has undergone cataract surgery, with far, intermediate, and near vision prescriptions. 
         [0003]    2. Description of the Prior Art 
         [0004]    A diffractive lens generally comprises a number of concentric annular zones of equal area with optical steps separating the adjacent annular zones. The width of the zones determines the separation between the diffractive powers (vision prescriptions) of the lens, the separation of the diffractive powers increasing with decreasing zone width. 
         [0000]    a. Diffraction Bifocals 
         [0005]    Diffractive lenses have been known and analyzed since the 1800s, but it wasn&#39;t until the 1960s that they were first used to correct human vision. The earliest such ophthalmic diffractive lens had a Fresnel Phase Plate design with “flat” zones, as disclosed in 1967 by Gunter Überschaar in his German Patent Publication 1,235,028. This Fresnel Phase Plate design used ½ wave deep flat steps which produced a bifocal lens that divided light equally between the +1 and −1 diffraction orders. 
         [0006]    We can better understand the Überschaar lens by referring to  FIG. 1   a  where we see a front view of a contact lens showing the boundaries r 1 , r 2 , r 3 , . . . of the flat annular zones  1  according to his invention.  FIG. 1   b  is a cross-section view showing the flat annular zones  1  comprising the anterior diffractive surface  2  of the contact lens  3  of  FIG. 1   a . The flat annular zones  1  are shown schematically in  FIG. 1   c  with the vertical axis representing step height S and the horizontal axis representing r 2 , where r is the radial distance from the center of the contact lens. Since all the annular zones in this diffractive lens have equal area, the zone boundaries r 1 , r 2 , r 3 , . . . are equally spaced in r 2 -space. 
         [0007]    In the 1980s Cohen (U.S. Pat. Nos. 4,210,391; 4,338,005; 4,340,283; 5,054,905; 5,056,908; 5,117,306; 5,120,120; 5,121,979; 5,121,980; 5,144,483) and Freeman (U.S. Pat. Nos. 4,637,697; 4,642,112;4,655,565; 4,641,934) disclosed the first ophthalmic diffractive lenses with blazed (angled) zones exhibiting a saw-toothed profile. These blazed designs used ½ wave deep substantially parabolic profiles which created bifocal lenses that divided light equally between the 0th and +1 diffraction orders. 
         [0008]      FIG. 2   a  is a cross-section of the blazed annular zones  4  comprising the anterior diffractive surface  5  of an IOL  6  according to the inventions of Cohen and Freeman. The blazed annular zones  4 , of this IOL, are shown schematically in  FIG. 2   b  with the vertical axis representing step height S and the horizontal axis representing r 2 , where r is the radial distance from the center of the contact lens. 
         [0009]    We also see in  FIG. 2   b  that each blazed annular zone  4  comprises a discrete step surface  4   a  and a blazed surface  4   b . In r 2 -space the blazed surfaces  4   b  take a linear form, and the zone boundaries r 1 , r 2 , r 3 , . . . are equally spaced. But, it should be recognized that, when graphed in r-space (as opposed to r 2 -space), not only will the zones be unequally spaced, but the profile of the blazed surfaces  4   b  will take on a quadratic form as illustrated in  FIG. 2   c.    
         [0010]    In 2003, Fiala (U.S. Pat. No. 6,536,899) disclosed a bifocal that divided each annular zone into two sub-zones. The sub-zones were designed as a way to eliminate the sharp steps of the standard blazed step bifocals. In his lens design, each annular zone comprised a main sub-zone of larger area and a phase sub-zone of smaller area and narrower width. In particular, he designed his phase sub-zones to cause the necessary phase shift needed to replace the optical steps of a diffractive lens. 
         [0011]    The annular zones of the Fiala invention, are shown schematically in  FIG. 3  with the vertical axis representing the step height S and the horizontal axis representing r 2 , where r is the radial distance from the center of the lens. The annular zones of this lens, bounded on the outside by the radii r 1 , r 2 , r 3 , . . . , are each divided into two sub-zones  7   a  and  7   b  which are generally of unequal area. While the sub-zones are of unequal area, the ratio of their areas remains unchanged from zone to zone. 
         [0000]    b. Diffraction Trifocals 
         [0012]    By the early 2000s, commercial diffractive IOLs were widely available as bifocals with blazed zone designs providing a split of light between the 0th and +1 diffraction orders. However, in 1994, Swanson (U.S. Pat. No. 5,344,447) had already disclosed a trifocal diffractive IOL based on a Fresnel Phase Plate design. This design uses ⅓ wave deep flat steps, thereby producing a trifocal lens that divides light equally between the +1, 0th, and −1 diffraction orders. A modification of this trifocal design was disclosed in 1998 by Kosoburd (U.S. Pat. No. 5,760,871). 
         [0013]    Then, in 2011, Schwiegerling (U.S. Pat. App. Pub. 2011/0292335) and Gatinel (Intn&#39;l. Pat. App. Pub. WO 2011/092169) proposed designs r a diffractive trifocal with blazed steps. These designs use equal area blazed annular zones with alternating step heights, thereby creating a trifocal lens that divides light between the 0th, +1, and +2 diffraction orders. 
         [0014]    The alternating annular zones  8   a  and  8   b  of these trifocal designs, are shown schematically in  FIG. 4 . We can see that all of the zones  8   a  have the step height Δa, while all of the alternate zones  8   b  have the step height Δb, where the step height Δb is not equal to the step height Δa. 
         [0000]    c. Apodization 
         [0015]    Meanwhile, it was seen to be advantageous to find designs that would provide a varying split of light between the different diffraction orders as the pupil of the eye opens and closes. In 1997 Simpson (U.S. Pat. No. 5,699,142) disclosed an “apodized” design wherein the light distribution between the 0th and +1 diffraction orders could be controlled by varying the step height (zone depth) of the individual zones. Since then, within the context of ophthalmic diffractive lenses, apodization has come to mean the gradual reduction of the step heights starting at the center of the lens and moving outward toward the periphery. Apodization has been widely adopted for multifocal diffractive IOLs and allows the light distribution between the  0 th and +1 diffraction orders to vary as the pupil of the eye opens and closes.  FIG. 5   a  illustrates the design profile of a typical apodized diffractive bifocal wherein the peaks of the blazed steps  9  follow a line of apodization  10 . 
         [0016]    In addition to the constant depth reduction across each zone progressing from the central zone outward, Simpson included a phase shift across each zone, again progressing from the central zone outward. This phase shift was introduced to allow the light from the various zones of different depths to all remain in phase.  FIG. 5   b  illustrates the design profile of a typical apodized and phase shifted diffractive bifocal wherein the peaks of the blazed steps  11  follow a line of apodization  12  and the blazed steps are also phase shifted to center on a phase shift line  13 . 
         [0017]    Schwiegerling and Gatinel also incorporated apodization schemes in their trifocal inventions.  FIG. 6   a  illustrates their trifocal design with apodization of the alternate blazed steps  14   a  and  14   b .  FIG. 6   b  illustrates their trifocal design with both apodization and phase shifting of the alternate blazed steps  15   a  and  15   b . Finally,  FIG. 6   c  illustrates a double apodization scheme for a diffractive trifocal lens as proposed by Schwiegerling wherein the peaks of the alternate blazed steps  16   a  and  16   b  each follow the different, non-parallel, lines of apodization  17  and  18  respectively. 
       BRIEF SUMMARY OF THE INVENTION 
       [0018]    Prior art multifocal diffractive lenses, employ multiple concentric annular zones of equal area. This invention relates to those multifocal diffractive lens designs wherein the annular zones comprise blazed steps and more particularly to such lenses that are designed to have three different focal powers. Trifocal lenses of this type differ in the intensity of light that they diffract into each of their three different powers. In general, this light distribution has been adjusted by varying the step heights of the blazed steps within the annular zones. 
         [0019]    It is an object of the present invention to provide a multifocal diffractive lens wherein each annular zone is divided into two sub-zones and wherein each sub-zone comprises a discrete blazed step. 
         [0020]    It is a further object of the present invention to provide a multifocal lens that allows the light distribution at its focal powers to be adjusted by varying not only the step heights of the blazed steps of the sub-zones, but also the relative areas of the sub-zones. This allows for an increased flexibility in the design of multifocal diffractive lenses. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0021]      FIG. 1   a  shows a front view of a contact lens of the Uberschaar design, showing the boundaries r 1 , r 2 , r 3 , . . . of the flat annular zones of the Überschaar invention. 
           [0022]      FIG. 1   b  is a cross-section view showing the flat annular zones  1  comprising the anterior diffractive surface  2  of the contact lens  3  of  FIG. 1   a.    
           [0023]      FIG. 1   c  is a schematic representation of the flat annular zones  1  of the contact lens  3  of  FIG. 1   b , where the vertical axis represents the step height S, the horizontal axis represents r 2 , and r is the radial distance from the center of the contact lens. 
           [0024]      FIG. 2   a  is a cross-section of the blazed annular zones  4  comprising the anterior diffractive surface  5  of an IOL  6  according to the inventions of Cohen and Freeman. 
           [0025]      FIG. 2   b  is a schematic representation of the blazed annular zones  4 , of the IOL of  FIG. 2   a , where the vertical axis represents the step height S, the horizontal axis represents r 2 , and r is the radial distance from the center of the contact lens. 
           [0026]      FIG. 2   c  shows the blazed surfaces  4   b , of the blazed zones of the IOL of  FIG. 2   a , taking on a quadratic form when graphed in r-space as opposed to r 2 -space. 
           [0027]      FIG. 3  is a schematic representation of a lens design according to the Fiala invention, showing the sub-zones  7   a  &amp;  7   b , where the vertical axis represents the step height S, the horizontal axis represents r 2 , and r is the radial distance from the center of the contact lens. 
           [0028]      FIG. 4  is a schematic representation illustrating the alternating annular zones  8   a  and  8   b  of the trifocal designs of Schwiegerling and Gatinel. 
           [0029]      FIG. 5   a  illustrates the design profile of a typical apodized diffractive bifocal wherein the peaks of the blazed steps  9  follow a line of apodization  10 . 
           [0030]      FIG. 5   b  illustrates the design profile of a typical apodized and phase shifted diffractive bifocal wherein the peaks of the blazed steps  11  follow a line of apodization  12  and the blazed steps are also phase shifted to center on a phase shift line  13 . 
           [0031]      FIG. 6   a  illustrates the Schwiegerling and Gatinel trifocal design with apodization of the alternate blazed steps  14   a  and  14   b.    
           [0032]      FIG. 6   b  illustrates the Schwiegerling and Gatinel trifocal design with both apodization and phase shifting of the alternate blazed steps  15   a  and  15   b.    
           [0033]      FIG. 6   c  illustrates a double apodization scheme for a diffractive trifocal lens as proposed by Schwiegerling wherein the peaks of the alternate blazed steps  16   a  and  16   b  follow the different nonparallel lines of apodization  17  and  18  respectively. 
           [0034]      FIG. 7   a  illustrates a flat step which introduces a constant phase shift to light passing through said step. 
           [0035]      FIG. 7   b  illustrates a pure blazed step which introduces a varying phase shift to light passing through said step. 
           [0036]      FIG. 7   c  illustrates a combination step which may be referred to as a blazed step with a phase shift. 
           [0037]      FIG. 8   a  illustrates the mth zone of a trifocal lens of this invention, wherein the vertical axis represents the step height S of the discrete blazed sub-zones  21  and  22 , and the horizontal axis represents r 2 , where r is the radial distance from the center of the contact lens. 
           [0038]      FIG. 8   b  illustrates the annular zone illustrated in  FIG. 8   a  graphed in T-ρ space where T=1−S is the inverse profile of said annular zone and ρ=π{r 2 /r 1   2 −(m−1)}. 
           [0039]      FIG. 9  illustrates zone by zone vector addition of the light amplitude diffracted into the various orders of diffraction. 
           [0040]      FIG. 10  illustrates a general 4 zone lens according to this invention. 
           [0041]      FIG. 11   a  illustrates a zone profile that produces a trifocal distribution of light. 
           [0042]      FIG. 11   b  illustrates the same zone profile of  FIG. 10   a  graphed in T-ρ space. 
           [0043]      FIG. 12  illustrates the profile of zones  4  through  9  of a 14 zone lens of this invention. 
           [0044]      FIG. 13  illustrates the light intensity distribution of the 14 zone lens of  FIG. 12 . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0045]    A lens, according to the present invention, comprises a number of equal area annular zones wherein at least some of the annular zones are subdivided into two sub-zones of equal or unequal areas each of said sub-zones comprising a discrete blazed step. 
         [0046]    For the purposes of this invention, a “discrete blazed step” may take the form of (1) a flat step (herein illustrated in  FIG. 7   a ) which introduces a constant phase shift to light passing through said step, (2) a pure blazed step (herein illustrated in  FIG. 7   b ) which introduces a varying phase shift to light passing through that step, or (3) a combination step (herein illustrated in  FIG. 7   c ) which may be referred to as a blazed step with a phase shift. 
         [0047]    By way of example, we consider a lens wherein all of the annular zones are of equal area, all of the annular zones are subdivided into two sub-zones of equal or unequal areas and each sub-zone comprises a discrete blazed step. In this case, the radial distance from the center of the lens to the outer boundary of the 1st annular zone may be given by r 1 , to the outer boundary of the mth annular zone by r m =mr 1   2 , and the area of each annular zone will then be equal to π(r m   2 −r m−1   2 )=πr 1   2 . 
         [0048]    The mth annular zone of this lens is illustrated in  FIG. 8   a  where we see its two sub-zones separated at the boundary r q   2 =p r 1   2 =(q+m−1) r 1   2  where q is a parameter ranging between 0 and 1. In this case, the area of the 1st sub-zone  21  is equal to q π r 1   2  while the area of the 2nd sub-zone  22  is equal to (1−q) π r 1   2 . In general, q may be different for each annular zone so that q=q(m), but the combined area of the two sub-zones of each annular zone will always equal π r 1   2  which is the area of the mth annular zone. 
         [0049]    For the purposes of analysis we now introduce a change of variables from Step Height S to T=1−S, and from radial distance r to ρ=π {r 2 /r 1   2 −(m−1)}. Graphing the profile of  FIG. 8   a  using the new variables T and ρ,  FIG. 8   b  shows an illustration of the mth annular zone in T-ρ space. It should be clear that the maximum and minimum heights of sub-zones  21  and  22  given by A, B, C and D as shown in  FIG. 8   a , are now represented by the new variables a=(1−A), b=(1−B), c=(1−C), and d=(1−D) as shown in  FIG. 8   b.    
         [0050]    A lens of this type will focus incident light into the various diffraction orders α, where α=0, ±1, ±2, . . . and the corresponding optical powers of this lens are P α =2 αλ/r 1   2  with λ being the design wavelength. To calculate the intensity of light at each of these diffraction orders, we start by finding the amplitude of light A1 and A2 focussed by the 1st and 2nd sub-zones of zone m as below: 
         [0000]        A 1=(1/π) ∫ 0   q π exp{2 πi [(α/π)ρ-( R /π)ρ− a]}dρ   (1)
 
         [0000]        A 2=(1/π) ∫ qπ   π exp{2 πi [(α/π)ρ−( R ′/π)ρ−( d−R ′)]} dρ   (2)
 
         [0000]    where α=diffraction order, 
         [0000]        R =( b−a )/ q,    (4)
 
         [0000]        R ′=( d−c )/(1− q )   (5)
 
         [0051]    Carrying out the integration gives us: 
         [0000]        A 1 =q  exp[ iπY ] sinc { q  (α− R )}  (6)
 
         [0000]        A 2=(1 −q )exp[ iπZ ] sinc {(1 −q )(α −R ′)}  (7)
 
         [0000]      where  Y=q  (α −R )−2  a    (8)
 
         [0000]      and  Z =(1 +q ) (α −R ′)−2 ( d−R ′)   (9)
       are the phase angles of A 1  and A 2  respectively       
 
         [0053]    Finally, we define Am (α), Im (α), and ωm (α) as follows:
       Am (α)≡the amplitude of light focussed by zone m at diffraction order α   Im (α)≡the Intensity of light focussed by zone m at diffraction order α   ωm (α)≡final phase angle of the light due to the first m zones       
 
         [0057]    We can calculate the intensity, and phase angle of the light focussed by zone m at each diffraction order α as: 
         [0000]        Im  (α)= Am   2  (α)= A 1 2   +A 2 2 +2  A 1  A 2 cos {π( Y−Z )}  (10)
 
         [0000]    and the phase angle ωm (α) of the light focussed by zone m at diffraction order α as 
         [0000]      ω m  (α)=tan −1 {( A 1 sin  Y+A 2 sin  Z )/( A 1 cos  Y+A 2 cos  Z ) }  (11)
 
         [0058]    But the total intensity of light at any diffractive order must be calculated by vector addition of the individual contributions to the light amplitude of each zone m. We start by defining 
         [0000]        Ãm  (α)≡total amplitude of light due to the first m zones
 
         [0000]        Îm  (α)≡total intensity due to the first m zones
 
         [0000]      Ω m  (α)≡final phase angle of the light due to the first m zones
 
         [0059]    Finally, zone by zone vector addition (geometrically illustrated in  FIG. 9 ) leads to the following recursive formulas: 
         [0000]        Îm (α)= Ãm   2 =[( m− 1)/ m ] 2   Îm− 1 2 +(1 /m ) 2    Im   2 +2 [( m− 1)/ m   2 ] Îm− 1  Im  cos(ω m− 1−Ω m )   (12)
 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0060]      FIG. 10 , which is appropriate for a front page view in this application, is illustrative of the present invention. In particular,  FIG. 10  illustrates a 4 zone diffraction lens that not only uses different step heights for some of the sub-zones (e.g. sub-zones  23  and  24  of zone  4 ), but also make use of “micro-modulation” wherein the areas of the different sub-zones differ from one annular zone to the next (e.g. between zone  1  and zone  2 ). In addition, we also see a phase shift incorporated into sub-zone  25  of zone  3 . 
         [0061]    As a more specific example, let us consider a single zone (shown in  FIG. 11   a ) where the zone profile has the parameters A=1.00, B=0.349, C=1.00, D=0.651, and q=0.652, so that the area of the first sub-zone  26  is 65% of the total zone area while the second sub-zone  27  is 35% of the total zone area. While  FIG. 11   a  graphed this single zone lens profile in S-r 2  space, the same lens profile is shown in  FIG. 11   b  graphed in T- r space. Now, making use of equation (10) and replacing A, B, C, and D with a=(1−A), b=(1−B), c=(1−C), and d=(1−D), we find that this zone will act as a trifocal by directing about 25% of the incident light into the 0th order, 28% of the incident light into the 1st order, and 25% of the incident light into the 2nd order. These results are shown in Table 1. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 zone 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 (m) 
                 a 
                 b 
                 c 
                 d 
                 q 
                 Im(0) 
                 Im(1) 
                 Im(2) 
               
               
                   
               
             
             
               
                 1 
                 0.0000 
                 0.6510 
                 0.0000 
                 0.3490 
                 .652 
                 25% 
                 28% 
                 25% 
               
               
                   
               
             
          
         
       
     
         [0062]    As a second example, let us consider a 14 zone lens where the zone profiles differ from zone to zone. The parameters for this lens are shown in Table 2 and the profile (for zones  5  through  9 ) is illustrated in  FIG. 12 . The first thing that we notice looking at Table 2, is that the widths of the sub-zones change from zone to zone. So, for example, we see that in zone  1 , the 1st and 2nd sub-zones are of equal area. But, in zone  3 , the 1st sub-zone only has an area equal to ⅔ that of the 2nd sub-zone. And in zone  5 , the 1st sub-zone only has an area equal to 3/7 of that of the 2nd sub-zone. Using formulas (12) and (13) we find that the intensities of light at orders 0th, +1, and +2, with a pupil aperture that blocks all but the first m zones are given by Îm(0), Îm(1), and Îm(2) as shown in table 2. These light intensities are also illustrated graphically in  FIG. 13 . 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 zone 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 (m) 
                 a 
                 b 
                 c 
                 d 
                 q 
                 Îm(0) 
                 Îm(1) 
                 Îm(2) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .50 
                 28% 
                 28% 
                 28%  
               
               
                 2 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .50 
                 28% 
                 28% 
                 28%  
               
               
                 3 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .40 
                 30% 
                 25% 
                 21%  
               
               
                 4 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .40 
                 31% 
                 24% 
                 19%  
               
               
                 5 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .30 
                 33% 
                 22% 
                 13%  
               
               
                 6 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .30 
                 34% 
                 21% 
                 10%  
               
               
                 7 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .20 
                 36% 
                 18% 
                 6% 
               
               
                 8 
                 0.3112 
                 1.0000 
                 0.3112 
                 0.6224 
                 .00 
                 40% 
                 13% 
                 5% 
               
               
                 9 
                 0.4967 
                 0.4967 
                 0.4967 
                 0.4967 
                 .50 
                 45% 
                 10% 
                 4% 
               
               
                 10 
                 0.4967 
                 0.4967 
                 0.4967 
                 0.4967 
                 .50 
                 50% 
                  8% 
                 3% 
               
               
                 11 
                 0.4967 
                 0.4967 
                 0.4967 
                 0.4967 
                 .50 
                 53% 
                  7% 
                 3% 
               
               
                 12 
                 0.4967 
                 0.4967 
                 0.4967 
                 0.4967 
                 .50 
                 57% 
                  6% 
                 2% 
               
               
                 13 
                 0.4967 
                 0.4967 
                 0.4967 
                 0.4967 
                 .50 
                 60% 
                  5% 
                 2% 
               
               
                 14 
                 0.4967 
                 0.4967 
                 0.4967 
                 0.4967 
                 .50 
                 62% 
                  4% 
                 2% 
               
               
                   
               
             
          
         
       
     
         [0063]    Table 2, illustrates two important features of this particular lens design. First, this lens acts as a trifocal lens when the pupil of the eye is small and acts as a single vision distance lens when the pupil is large. Second, the design of this lens rests upon the technique of “micro-modulation” wherein the relative area of the two sub-zones of each annular zones varies from zone to zone. 
         [0064]    Heretofore, in multifocal diffractive lenses, the sub-zones within individual annular zones, have not been separately and differently altered from one annular zone to the next. This sub-zone micro-modulation allows for a much greater flexibility in lens design. 
         [0065]    It is to be understood that there are many other useful designs that can be achieved by this method of “micro-modulation.”