US 2180887 A Abstract available in Claims available in Description (OCR text may contain errors) Nov. 21, 1 939. g I 2,180,887 OPHTHALMIC LENSES, SERIES OF SAID LENSES, AND METHOD OF M AKING THE SAME Filed March 31, 1937 2 Sheets-Sheet 1 I True Front Surface Powersflndex 1.5252) A. E G F 6 Convex Suyfys- I .Tfiries /I,[ 11: /III I! I m m: .m :1 x. 2 1.9o4'/ 2.170' 2-559 5-046 5-555 5. 505 4.552. 5.077 0.095 7. 010 e- ,1 I 0.25% +1.995 +1.746 +1.496 +1.z47 +1.1z2. +0990 +0075 +0745 +0025 +0499 0.50 5 9130 5.405 2.955 2.460 2.259 1.990 1.741 1.492 1.2/14 0.995 0.75 5.955 5.211 4.466 5.722 5.550 2.975 2-600 2255 1.501 1.409 1.00 7. 9 21 0.951 5.940 4.950 4.450 5. 960 5.405 2. 970 15.475 1. 900 1-2.5 5.876 8.642 7.407 6.1'13 5-55 4-958 4-521 5. 704- 3-055 2-4-69 1.50 11.825 10.545. 5.507 7.589 6.650 5.911 5.172 4.454 5.095 2.950 1.75 15.759 12.059 10.519 5.599 7.740 0.000 0.019 5.1 0 4.500 5.440 1.00 15.080 15.725 11.705 9.504 0.524 7.545 0.505 5.0192 4.902 5.922 2-25 1'1. G04- l5.405 13.203 11.002. 9.901 8.505 7.702 6.602. -501 4.401 2-50 19.512. 17.07.514.054 12.195 10.970 9.750 5.557 7.517 0.090 4.575 2.75 10.755 10.055 15.552. 12.044 10.700 9.505 5.029 0-091 5-555 500 1 17 475 14.505 15.107 '1 1.051 10.194 5.755 7.252. 5.525 3- 18-886 15.756 l4-.\65 lZ-591 II- 017 9.445 1-869 6-29 5:5 I 10.900 15.2.17 15.520 11.550 10.145 5.454 0.705 5.7.5 10.072 10.2.65 14.45 12.051 10.545: 9.050 7.229 4.00 g I I 9.2.51 17.508 15.555 15.401 11.559 9.015 7.692 4 25 I 15.545 1 507 14.269 12.250 104925-155 I 17.225 15.072 12-919 10700 5.012 -75 I I 151513 15.871 "15.00411-555 9.009 5.00 Y 0 19.048 10.607 14186 11.905 9.524 5-25 1 17.455 14.964 12-470 9.970 5 I 15.240 15.040 15.055 10.427 5.75 I 10.512 15.595 10 075 0.00 I 10.951 14.151 11.521 0.25 I I 17.047 14.706 11.755- 0.50 7 15.510 15.258 12.207 0.75 15.000 12.040 7.00 10.35711064- 7.25 I 10.900 15.520 7.50 1 7.442 15.955 7 17-981 14.385 5.00 15.519 14.515 5 25 I BT23? 8.50 I I 15.008 8-75 10.092 9.00 1 10.514 9.25 10.954 9.50 17.551 I 3 17.768 1 10.00% 15.152 INVENTOR 505/72 0 'T/LLYEE Patented Nov. 21, 1939 UNITED STATES SERIES OF SAID LENSES, AND METHOD OF MAKING THE SAME Edgar D. Tillyer, Southbridge, Mass.,- assignor to American Optical Company, Southbridge, Mass., a voluntary association of Massachusetts v Application March 31, 4 Claims. This invention relates to improvements in 'ophthalmic lenses and has particular reference to improved lenses,- series of lens blanks and method of making the same. 5 Oneof the'principal objects of the invention I is tofpr'ovide a series of semi-finished lens blanks graded ineach series in equal steps of shape magnification and method of making the same whereby the ocular surface of each lens blank may be altered 'to introduce the required prescriptive focal power without introducing odd fractions of the diopter so that the tools available in the usual prescription shop can be used for putting on these finished surfaces. Another object of the invention is to provide a series of lens blanks having factory made specially formed curved surfaces on one side thereof which with a given thickness will produce the shape magnification factor of the finished lens and which will enable the selection of a power surface to be added to the ocular or opposite surface of the lens which may be generated by the commercial curve generating tools now in common use by lens dispensers to obtain the. focal power desired in combination with said shape magnification. Another object is to provide an improved lens and method of making. the same of such a thickness that the shape magnification is an integer per cent and an integer fraction of a per cent greater than unity when the .ocular surface power is made in integer diopters-and integer fractions of a diopter for a focal power prescription in integer diopters and an integer fraction of a di- 35' opter combined with a front surface power which gives the required focal power. v Another object is to provide lens blanks giving desired shape magnification values to which the desired prescriptive focal power may be added 40 without changing said shape magnification values. Another object is to provide a method of dispensing ophthalmic lenses whereby a plurality of lens blanks having characteristics producing shape magnification values in graded percentages may be carried in stock by the dispensers and which may be selected in accordance with predetermined figures giving the resultant characteristics which the lens should have in order to obtain the shape magnification desired and the ocular surface power which is to be added to the prescriptive focal power to obtain the required optical surface power while maintaining the shape magnification value. Other objects and advantages of theinvention will become apparent from the following descrip- 1937, Serial No. 134,076 tion taken in connection with the accompanying drawings and it will be apparent that many changes may be made in the various details, arrangements and methods herein described without departing from the spirit of the invention as expressed in the accompanying claims. I, therefore,'do not wish to be limited to the exact details, arrangements and methods shown and. described, as the preferred forms only have been setforth by way of illustration. Referring to the drawings: Fig. I is the chart A embodied in the invention and listing the convex surfaces or front surfaces; and l Fig. II is a similar view of another chart B embodied in the invention, giving tabular values for zero effective power. Fig. III is a sectional view through one of the lens blanks of the series and illustrating the essential features ofthe invention. Heretofore, it has been usual in the forming of ophthalmic lenses embodying both a correction for shape magnification and for focal'power to compute and manufacture said lenses individual-. 1y. Such computations have been lengthy, difficult and costly and also hindered the dispensing of the lenses due to the time required in computing and forming such lenses with the result that the lenses'have been difficult to obtain. It, therefore, is one of the primary objects of this invention to overcome the above difliculties by providing a series of lens blanksgraded in step percentages of magnification which maybe supplied the dispenser and which may be finished in the manner usual in the art by his usual stock tools in obtaining the focal prescriptive power desired in combination with said shape magnification values. I Referring more particularly to the drawings, it will be noted that the chart A, shown in Fig. I, gives the true front or convex surface powers for lenses, formed of glass having an index of refraction of 1.5232. vIn this chart the first column of 4 I figures under the heading Mag. S'1 indicated at E, is given per cent magnifications in steps of /4 per cent. The front surface curvatures of each series numbered with headings I, II, III, etc., are. given in each corresponding column as indicated at F. The thickness to which each lens of a series is to be formed in combination with the front surface powers listed in each column is indicated at G alongside of the title Thickness in mm. Therefore,- if a lens having a 0.25 magnification is desired with the thickness 1.904 mm. a blank having a front surface power of 1.995 is seelected. If the finished thickness is to be 2.176 mm. a blank having a front surface power of 1.746 is selected, etc. If the magnification desired is 0.50% and the thickness is to be 1.904 a blank having a front surface power 3.980 is selected. If the thickness is to be 2.176 a blankhaving a front surface power of 3.483 is selected, etc. It will be seen from the above that by reference to chart A lens blanks having the desired characteristics for obtaining the magnification value of the prescription may be quickly and easily selected. It is to be noted, however, that these blanks are selected to their resultant aesthetical and optical features, that is, some of the lens blanks by which the desired per cent magnification will have betterwoptical properties as regards marginal, focal and astigmatic errors than other of said lens blanks and will also be better appearing. This, however, is well known in the art and due to the fact that several lens blanks having this different front surface powers and different thicknesses producing the same magnification values are provided in the chart, knowledge as to the resultant optical characteristics and appearance of lenses having different front surface and thickness will enable the dispenser to select the most practical lens blank for the lens desired. It will be noted that these front or convex surfaces are to be made at the factory and require the use of special tools. By special tools it is meant that the usual standard lens surfacing tools used by the dispenser cannot be employed in forming these front or convex surfaces as they do not possess the proper surface powers. Blanks having the surface powers listed in chart A and having thickness in excess to the thicknesses listed alongside of the title Thickness in mm. are, therefore, provided the dispenser and are adapted to be finished in the same manner as other commercial lens blanks used in the art. The chart B shown in Fig. II lists in the columns I, II, III, etc., the ocular surface powers which may be combined with the corresponding convex of front surface powers given in each respective column I, II, III, etc., of chart A to produce lenses having zero effective power. It will be noted that chart B has r'nagnification values listed under the title Mag. S'1" as shown at H similar to the corresponding magnification values listed at E in chart A and that alongside of each given per cent magnifications in each of the columns I, II, III, etc., as illustrated at J is given the ocular or concave surface which is to be combined with the front or convex surfaces listed at F in columns I, II, III, etc., of chart A. As stated above these ocular or concave surface powers when combined with the corresponding front or convex surface powers will produce a lens having zero effective power. To obtain the focal power desired with the shape magnification value of the respective blank selected the focal power is added algebraically to the ocular surface power. This will be set forth more in detail in the following discussion of the invention. Referring to chart B it will be noted that the finished thickness of the lenses of each series are given alongside of the title Thickness in mm. as illustrated at K. The thickness for each lens series given in the columns I, II, III, etc., correspond with the thicknesses given in the respective columns of chart A. It is to be noted that when the focal power to which the lens is to be formed is added algebraically to the ocular surface powers indicated in columns I, II, III, etc., the resultant required surface power which is to be formed on said ocular surface will follow directly within the range of the surface-powers of commercial tools carried in stock by lens dispensers so that a convenient method of forming such lenses has, therefore, been worked out particularly for lenses of the usual commercial type. Shape magnification lenses which require a different magnification in one meridian than in the other are obtained from the tables in the same'manner as magnification lenses with the same magnification in all meridians with the exception that any one column must be used twice to obtain the two curves of the toric surface corresponding with the two magnifications required. In the rare case of toric lenses in which the shape magnification axis does not coincide with the cylinder axis then the usual shop procedure for combining two oblique axis cylinders must be employed. The mathematical theory of size lenses has been given in Tillyer Patent No. 2,077,134, issued April 13, 1937. In this patent I have shown that the total magnification M can be separated into two factors, one involving the focal power and position of the lens system P and the other involving the shape magnification of the lens system S arrived at by the formula Also, I have shown that the ocular surface of the lens system does not produce any effect upon the shape magnification S. For convenience in this discussion we are going to consider only a single lens system, as shown in Fig. III, not a multiple lens system. From my patent referred to above we have where S' is the shape magnification, s is the reduced thickness, that is, the actual thickness of the lens divided by its refractive index and D1 is the surface power of the first surface of the lens, see Fig. III. Then, S'--1 is the amount of shape magnification greater than unity and may be expressed in per cent for convenience in tabulation as will be noted by the tables given in the drawings. Also, we have the equation for the effective power or vertex refraction from the shape magnification equation previously given, we have S'-1=--sD:. Frc.n this equation, if s is a. constant for a series of lenses, we see that S-1 varies linearly with D2, or expressing this linear relation as a variation we have 8(S'-1)=-S6D2. This shows that by choosing the thickness factor s with care, we can make even fractional values of D2 equivalent to fractional values of S'-l. As an example of this let us assume that we wish an integer fractional value of the variation of S'1 to be one-fourth of one per cent, that is, 0.0025, and for this value of the variation of S1 we wish 6Dz to be 1 diopter. Then we would have the equation 0.0025=s (-1) or s=0.0025. Therefore, if we are using a glass of a refractive index n=1.5232, the actual thickness t will be 0.0025 1.5232 which is equal to 0.003808. This is expressed in meters as all diopter values, etc., are on the basis of meters in practice. We will then call this 3.808 mm. the'actual thickness of this lens. Therefore, if each front surface power in a series is chosen to give zero focal power with the chosen ocular surface for that lens and we then make the ocular surfaces in equal steps of one diopter we will have the shape magnification of each lens of the series varying by 44%, and have no focal power, so that we can We can, however, have 5D: varying by integer fractions of the diopter, like A, etc., or ' any fractions which the optician usuallycarries in his tool stock, and obtain the necessary thickness to correspond with these even steps to give equal percentages of shape magnification. Likewise, if we wish to take instead of 4% steps in shape magnification, we can choose a or *6% or whatever we may wish and obtain equal diopter steps by proper y choosing the thickness. We have tabulated ten series of these lenses progressing by A% steps because this follows the customary method of prescribing such lenses. It is not necessary, however, to adhere to these step percentages as other sequences can be used. These two tables are as follows: Table A contains the front surface power which will be put on the semi-finished blanks at the factory. Table B contains the ocular surface power for the zero power lens. To this ocular surface power is to be added the required prescriptive focal power in order to obtain the ocular surface now to be ground on these lenses by the optician who finishes the blank. So far we have said nothing about magnification in one meridian. Obviously, if the magnification is the same in all meridians no one meridian need be considered separately. . Referring to the tables let us assume that a lens is found in Table A and is +7.389 diopters. The zero power lens would have 7.50 diopters for the ocular surface,- To this must be added our prescriptive focal power of 1 diopter in one meridian and +1.50 in the other meridian. Adding these respective values together we find that the required surface power as shown at L in Fig. III in one meridian of the ocular surface will be 6.50 diopters and in the other meridian 6.00 diopters. Of course, the axes of these curvatures must be placed at the required angle. Let us now select a lens which must have a magnification of 1.5% in one meridian and a magnification of 2% in the other meridian and a +1 prescriptive focal power. Obviously, we must take this lens from any one series because we cannot have two different thicknesses for the same lens. We can take any one of a number of these series in order to obtain a good lens. Series IV or series V could be used. Let us take series IV again. We have, as obtained before from Table A for the 1.5%, a front surface power of +7.389D and, for the 2% from Table A, series IV, a power of 9.804 diopters. This blank must obviously be a semi-finished toric blank having in one meridian the +7 .389D surface power and in the other meridian the +9.804D surface power. From Table B wefind the two ocular surface powers to correspond with the above surface powers to give zero focal power. These curves will be 7.50 diopters in the +7.389 meridian and -10.00 diopters in the +9.804D meridian. Now since we wish to have a +1 focal power on this lens we add to both of the above ocular surface powers +1 diopter power. Therefore, the optician must grind on this lens atoric ocular surface power of 6.50D in the same meridian that the +7.389D is in and a 9.00D toric in the same meridian that the +9.084D is in and finish this lens to the thickness that the series IV is to be finished to, that is, 3.046 mm. Now let us suppose that instead of requiring +1D spherical focal power we required +1D in the meridian that the 1.5% was required and a +1.50D in the meridian that the 2.0% was required. We would then add +1D to the -'7.50D and get 6.50D for the required ocular surface power in that meridian and to the l0.00D we would add +1.50D and obtain 8.50D for the required ocular surface power in that meridian. So far we have only considered cases in which the axis or meridian of magnification coincides with the axis of astigmatism or the cylindrical power. Let us assume the same +l.5% in one meridian and +20% in the other and let us assume that we have an axis or cylinder power not coinciding with the axis of magnification. We go through and obtain the zero power lens exactly as before. If we are using the same series IV, we have for the ocular surface of the zero power lens '7.50D in one meridian and l0.00D in ,the other meridian. If the axis of our prescription does not coincide with the axis of these two lenses we take this 7.50D in one meridian and l0.00D in the other me ridian and combine it with the prescription the same as we do to cross cylinder prescriptions in the usual ophthalmic methods and obtain the new ocular surface in that manner, or what is even easier we put this +7.50D with the l0.00D on a lens measuring instrument such as the Lensometer in the form of test lenses, and at the same time the required prescription on the Lensometer in the form of test lenses and measure the resultant power and axis and grind this on the blank to the thickness specified for series IV. In this one case the ocular surface curves required to be ground maynot come within the usual range of curvatures of standard ophthalmic tools. Of course, any two oblique axis cylinders without shape magnification when combined do not come always under the range of the usual ophthalmic tools. This is a special case the same as is in the usual combination of two oblique cylinders in regular ophthalmic practice. The procedure of supplying tools for lenses of this character therefore is the same as has been usual in the prior art and the same dif- -ficulties are encountered. Tables A and B have been written as is usual in commercial practice for the formation of torics. The way these tables for factory surface are used is as follows. Let us assume we wish to determine a semi-finished blank for a 1% shape magnification in one meridian and a 1.5% in series IV. The front surface power will be +4.950D by +7.389D in toric form. Now for a shape magnification of 1% in one meridian and 1.75% in the other we will havea toric with surface powers of +4.950D by +8.599 D. Of course, in finishing this lens the thickness 3.046 mm. for series IV must be followed. Likewise, for any other series. The thickness and surface powers are given to very close values. This accuracy is not necessary to this extreme. In Table A and Table B a varying range of spheres and toric combinations is given. Ob- viously in practice many of these series would be dropped and only the most used lens blanks would be finished in the semi-finished form. A number of additional series could be added, for instance, a series between I and II but it is believed to be, unnecessary. Likewise, between II and III, etc. It is also obvious that the lens could be designed for shape magnification other than the 4% steps although the 4% steps are the ones now employed for testing the shape magnification of the eyes. From the Table A and Table B, the method of forming such tables, and the examples given in their use, it will be seen that by the proper choice of the thickness it is possible to produce lenses having shape magnification of zero or integer per cent added to integer fractions of a per cent combined with an ocular surface power in integer diopters and integer fractions of a diopter when the prescription is in integer diopters and integer fractions of a diopter. The integer per cent of shape magnification is 1%, 2%, 3%, etc. The integer fractions of a per cent of shape magnification may be /2%, or /5%, 75%, 'or /3%, 73% or similar values having integers in the numerator and denominator of the fraction. We have shown in the Tables A and B, such thicknesses as correspond with the integer fractions /2% etc., but other tables may be formedby the methods described with the integer progression 73%, etc., or any similar values. The integer diopters of surface power, either plus or minus, are 0, 1, 2, 3, etc., the integer fractions of a diopter of surface power, either plus or minus, are A, /2, /3, The integer diopters, either plus or minus, of prescriptive focal power are 0, l, 2, 3, 4, etc. The integer fractional diopters of prescriptive focal power, either plus or minus, are A,, A, A,, 'Va- A change in the position of these lenses in front of the eyes and a change in magnification due to the change in position has been explained in Tillyer Patent No. 2,077,134, issued April 13, 1937, and has nothing to do with making the individual lenses to the required prescription at the distance at which they are to be placed from the eyes. This system is supposed to be applied to a finished prescription specifying the distance at which the lenses are to be placed before the eyes and the focal power and the shape magnification at that distance. However, let us take a simple example of changing the distance of the lens from the eye. Let us assume that we require a +1.75% shape magnification and a focal power of +1 diopter and also that we wish to move this lens 2 mm. further from the eye than the test lenses were used. Note, we assume that the prescription has been corrected for the shape magnification value of the test lenses as they were used so that the shape magnification given in the prescription is the true shape magnification in front of the eye. Now let us assume that we wish to move this +1 diopeter lens 2 mm. further from the eye. We have the diopter focal power multiplied by the increased distance in meters or numerically +1.00X0.0025=0.0025=0t25%. Thus we have an increase in the power magnification of A;% due to this change in distance from the eye. Therefore, we must take off from the prescribed shape magnification 1.75%, the extra power magnification caused by moving thislens further away and we will, therefore, design the lens for a 1.50% shape magnification in the same manner as previously given. Obviously, when we consider the two eyes, we will have shape magnification in front of both eyes and it is the ratio of the one magnification to the other that counts. We must, therefore, if we have given that the first eye has a shape magnification of 1% more than the second eye, design the first lens so that it will be of 1% in that eye more than the shape magnification in the other eye. We can add or subtract small percentages of shape magnification although we must multiply or divide S. Assume we have 1% in the first eye and wish the second eye to have 2% more, this gives the required 3% and is obtained as follows, S for the first eye is 1.01, S for the second eye is to be 1.02 times the first eye, that is 1.01 1.02 which is 1.0302 or to sufiicient accuracy 3%. For large values such as 10% the actual multiplication should be used. It will be noted by reference to Fig. III that the front surfaces D1 of the series of lens blanks which, in combination with the finished thickness t of said blanks, will produce the shape magnification desired are of special curvatures generated by special tools at the factory and that the said curvatures are such thatthey will permit the use of commercial tools now in common use by lens dispensers in forming the actual ocular surface L of the lens to obtain the focal power desired with said shape magnification. This enables the provision of series of lens blanks for producing shape magnification in step percentages which may be carried in stock in a manner similar to usual prior art ophthalmic lens blanks and to which the prescriptive curve may be added to the ocular surface of the blanks while maintaining the thickness t to obtain the focal power desired with said shape magnification. From the foregoing description it will be seen that a simple, efficient and economical arrangement and method has been set forth whereby series of lens blanks graded in step per cent magnifications may be provided to the dispensers and from which a blank may be selected and finished in the usual prior art manner to obtain the focal prescriptive correction and shape magnification value required. Having described my invention, I claim: 1. A series of lens blanks for lenses intended to correct refractive as well as shape magnification errors, the blanks of said series comprising pieces of lens medium of given indices of refraction having front optical surfaces D1 of curvatures calculated for given ocular surface power considerations D2 graded in equal steps of integer diopters or fractions of said diopters so that each of said surfaces D1 differfrom each other by amounts which, with a given predetermined constant finished thickness consideration if for said series, produce zero powerrlenses having equally graded percentages or fractions of percentages of shape magnification Sf according to the formula 1 I s 1 SD1 with the thickness t of said series obtained from the formula S1=8D2 by eliminating from the S equation D 1 SD wherein s is the thickness t'divided by the refractive index of the medium, each blank having a thickness in excess of said given predetermined thickness t to receive a final ocular surface which will introduce the focal power correction required, the curvature of said front surface D1 with said given index of refraction and predetermined thickness t being such that the final ocular surface to be formed on the blank will be of an integer diopter or fraction of a diopter, the curvature thereof being obtained by algebraically adding the prescriptive focal power desired to the given ocular surface power consideration D2 for said blank, the addition of said final ocular surfaces to said blanks, while maintaining said given thickness t, producing the refractive corrections required with substantially no change in the S values of the blanks. 2. The method of forming a series of lens blanks for lenses intended to correct refractive as well as shape magnification errors, comprising forming on pieces of lens medium of given indices of refraction front optical surfaces D1 of curvatures calculated for given ocular surface power considerations D2 graded in equal steps of integer diopters or fractions of said diopters so that each of said surfaces D1 differ from each other by amounts which with a given predetermined constant finished thickness consideration it for said series produce zero power lenses having equally graded percentages or fractions of percentages of shape magnification S according to the formula 1 r S 1-SD with the thickness t of said series obtained from the formula S'1=8 Dz by eliminating from the S, equation l 1SD wherein s is the thickness t divided by the refractive index of the medium, and providing each blank with a free surface on the side thereof opposite the front surface at a distance from said front surface in excess of said predetermined thickness t to receive the final ocular surface for introducing the focal power correction required, the curvature of said front surface D1, index of refraction of the lens medium and predetermined thickness t being so computed that the final ocular surface curvature to be formed on the blank will be of an integer diopter or fraction of a diopter obtained by algebraically adding the prescriptive focal power desired to the given ocular surface power consideration D2 for said blank, the addition of said final ocular surfaces to said blanks, while maintaining said given thickness t, producing the refractive corrections required with substantially no change in the S values of the blanks. 3. A series of lenses for correcting refractive as well as shape magnification errors, the lenses of said series comprising pieces of lens medium of given indices of refraction having front optical surfaces D1 of curvatures calculated for given ocular surface power considerations D2 graded in equal steps of integer diopters or fractions of said diopters so that each of said surfaces D1 differ from, each other by amounts which, with a given predetermined constant finished thickness consideration t for said series, produce zero power lenses having equally graded percentages or fractions of percentages of shape magnification S according to the formula with the thickness 12 of said series obtained from the formula S-1=sD2 by eliminating from the equation l 1sD wherein s is the thickness t divided by the refractive index of the medium, each lens having a given predetermined thickness t and an ocular surface which will introduce the focal power correction required, the curvature of said front surface D1 with said given index of refraction and predetermined thickness it being such that the ocular surface of the lens is of an integer diopter or fraction of a diopter, the curvature thereof being obtained by algebraically adding the prescriptive focal power desired to the given 'ocular surface power consideration D2 for the. considerations D2 graded in equal steps of integer diopters or fractions of said diopters so that each of said surfaces D1 differs from each other by amounts which with a given predetermined constant finished thickness consideration t for said series produce zero power lenses having equally graded percentages or fractions of percentages of shape magnification S according to the formula 1 8D1 with the thickness t of said series obtained from the formula S'-1=sD2 by eliminating from the 5' equation l 1 SD1 ceive the final ocularsurface for introducing the focal power correction required, the curvature of said front surface D1, index of refraction of the lens medium and predetermined thickness t being so computed that the final ocular surface curvatureto be formed on the blank will be of an integer diopter or fraction of a diopter obtained by algebraically adding the prescriptive focal power desired to the given ocular surface power consideration D2 for said blanks, and forming said final ocular surfaces on said blanks, of curvatures controlled according to the curvatures of said frontsurfaces D1 while maintaining said given thickness t so as to introduce the refractive correction required with substantially no change in the S values of the blanks. EDGAR D. TILLYER. Referenced by
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