Reproducibility of contact lens power measurements using the phase shifting schlieren method

Reproducibility of contact lens power measurements using the phase shifting schlieren method Luc Joannes, Tony Hough, Xavier Hutsebaut, Xavier Dubois, Renaud Ligot, Bruno Saoul, Philip Van Donink, Kris De Coninck Lambda-X s.a., Rue de l industrie 37, B-1400 Nivelles (Belgium) Phone : +32 67794080 Fax : +3267552791 e-mail : ljoannes@lambda-x.com 1. Abstract PURPOSE. To assess a new method of power measurement of soft and rigid contact lenses. The method is the phase shifting schlieren method, as embodied in the Nimo TR1504 instrument. MATERIALS and METHODS. Three Nimo TR1504 instruments were used to measure the power related dimensions of: a) a range of custom toric rigid lenses; b) a range of commercially available spherical hydrogel lenses; and c) a commercially available range of toric silicone hydrogel lenses. The measurements were carried out using a standard ISO ring test protocol where independent tests were carried out under conditions of reproducibility. The analysis of the measurements was carried out using ISO methods which enabled the reproducibility standard deviation, S R, of the method to be calculated. RESULTS. The results show that this new method has a reproducibility standard deviation S R of 0.048D for spherical soft (hydrogel) lenses. This means the back vertex power of spherical soft lenses having a power in the range ±20.0D can be determined to current ISO product tolerances with a single measurement. The method has SR of 0.059D for sphere power and 0.093D for cylinder power for toric soft lenses having powers in the range ±10.0D and cylinder powers in the range ±2.0D. A single measurement will determine sphere power to current ISO tolerance limits with 95% confidence while two measurements are required to determine the cylinder power to the same confidence level. Keywords : Deflectometry, Metrology, power, repeatability, reproducibility, wavefront, soft toric, aspheric soft contact lens. 2. Power measurement of soft contact lenses The measurement of the power-related dimensions of soft contact lenses has continued to be a challenge for manufacturing industry, research centers and clinical practice. There are internationally agreed standards for the determination of power for single vision lenses, both spherical and toric [1], but none for the measurement of bifocal, multifocal or varifocal lenses. There is also no standard method for the measurement of power characteristics of the increasing number of contact lenses which claim aberration control or wavefront-managed optics. In the past decade there has been a surge of new or modified products which promote power management characteristics which it is impossible for most manufacturers, researchers and practitioners to objectively validate. [2, 3, 4, 5, 6] Many soft lens manufacturers now either claim or suggest that there are vision or lifestyle benefits to be gained for wearers related to the use of lenses which have aspheric optics or which have optic zones that incorporate wavefront technology (or a similar phrase). Without the availability of a measurement method, it is unsurprising that clinical studies of the on-eye performance of such lenses do not provide any credible data on how such lenses might be used to modify wearer vision; the presumption of product similarity in such studies is naïve and emphasizes the inability of researchers to measure such lenses. [7]. Optical Measurement Systems for Industrial Inspection VI, edited by Peter H. Lehmann, Proc. of SPIE Vol. 7389, 73890Z 2009 SPIE CCC code: 0277-786X/09/$18 doi: 10.1117/12.827525 Proc. of SPIE Vol. 7389 73890Z-1

There is therefore a clear and increasing requirement within the contact lens manufacturing industry and research centers for affordable technology which can credibly determine the power and at least the primary aberration components, spherical aberration and coma, of soft contact lenses. ISO 18369 sets out three test methods; the focimeter, the Moiré method and the Hartmann method. All three are identified as being suitable to measure both spherical and toric lenses but only the power mapping devices, embodying the Moiré and the Hartmann methods, offer a realistic method for torics because according to 18369 the focimeter requires 19 independent readings to determine the sphere power to within ±0.25D and 17 to determine cylinder power to within ±0.25D. Any new measurement technology must be subject to careful and detailed appraisal before it can be accepted as part of a standard method. The accepted appraisal process is to carry out what is described as a ring test, in which a representative sample selection of the product to be measured is circulated to a number of sites and then measured repeatedly under well-controlled conditions, generally referred to as conditions of reproducibility. The results of these tests are then compared using an agreed protocol and various measures of the precision of the test method are calculated. Perhaps the most important parameter to emerge from a ring test is the reproducibility standard deviation of the method being assessed, denoted by S R, which may be used to calculate the number of independent readings required to determine the dimension we are interested in at the 95% confidence level. A study by Hough et al 1996 established the capability of the Moiré method as applied to toric lenses and describes the structures and underlying calculations related to ISO-style ring tests. [8] A similar international ring test was carried out for the Hartmann method to enable its incorporation within ISO 18369. The way in which ISO 18369 has been developed has effectively established a protocol for the introduction of new methods; first the capability of the method must be assessed for spherical and toric lenses, especially soft lenses when measured immersed in saline. Once this assessment has been accepted by the international technical community in the field of contact lens measurement it is then appropriate to extend the assessment of any new method to varifocal, multifocal, bifocal, aspheric optics and wavefront controlled contact lens products. The purpose of this study is to evaluate the capability of a new method, the phase shifting schlieren method, as applied to current commercial soft spherical and toric contact lenses. A range of custom made toric rigid lenses, manufactured using a variety of current lathing and polishing methods, was also measured because there is genuine industry interest in the measurement of such lenses for applications such as the correction of vision in keratoconus. 3. The schlieren method as embodied in the Nimo instrument The method being evaluated in this study is incorporated in the Nimo TR1504 manufactured by Lambda-X SA in Belgium. The instrument is based on a patented quantitative deflectometry technique described as phase-shifting schlieren [9, 10, 11]. The principle of schlieren imaging has been known for some time and is commonly used to visualise variations in density for gas flows; schlieren means streaks in German. [12] By combining this principle with a phase-shifting method, the Nimo instrument allows the measurement of light beam deviations which can be used to calculate the power characteristics of optical lenses, including both rigid contact lenses in air and soft contact lenses immersed in saline. A schematic layout of the Nimo instrument is shown in Figure 1. Referring to this, a cold cathode tube backlight source S emits green light at 546nm. An additional diffuser and a ±10nm bandwidth filter are incorporated in the source S to homogenise and limit the spectral width of the light beam. A liquid crystal display LCD is placed at the focal length of lens L1. Lenses L2 and L3 form an image on camera C through a telecentric arrangement. The lens to be measured will be placed in the object plane between lens systems L1 and L2. A fixed circular sinusoidal pattern is projected on the LCD. Contact lenses to be measured are placed in the object plane of the instrument, between lens systems L1 and L2, as shown schematically in figure 2, identified as TL. When there is no lens to measure, the camera is illuminated uniformly. Proc. of SPIE Vol. 7389 73890Z-2

Figure 1 : Schematic layout of the schlieren method instrument When a test lens TL is placed at the object plane of the instrument, it causes the light rays coming from the source to deviate or deflect. The light intensity reaching the camera pixels is also modulated by the LCD pattern. So-called schlieren fringes are generated by this; the higher the power of the test lens, the greater the deviation of the light beams and the higher the number of schlieren fringes. An example of this is shown in figure 3 which compares the schlieren fringes in the images obtained with lenses of high and low powers. SLCD Li ('\ L2 Figure 2 Schematic representation of light ray travel in the schlieren method when a positive power contact lens is placed in the instrument. Figure 3. The difference in schlieren fringes obtained with two different lens powers; the higher powered lens on the left has more schlieren fringes than the lower powered lens on the right. Proc. of SPIE Vol. 7389 73890Z-3

In addition to the power data, the inclusion of a high resolution camera allows lens surface features such as orientation marks or engraving to be observed, as shown in figures 4 and 5. Figure 4 : A single vision spherical soft contact lens observed in the schlieren Nimo instrument in a wet cell. Figure 5 : A soft toric contact lens as seen in the wet cell. The measurement operation consists of applying the phase-shifting principle [13] to obtain the mapping of the light beam deviation at as many points as available on the camera. The instrument resolution is therefore directly related to the number of pixels in the camera; this represents a significant increase in resolution by comparison to previous methods. Both x and y components of the light beam deviation are measured which taken together fully characterise the contact lens power because they are the derivative of the wavefront on each point on the lens. As with all power mapping devices, the instrument then uses customized software to calculate many different aspects of the power-related dimensions of the lens. The paraxial power, sphere, cylinder and axis, is calculated in a central 3mm zone. To do this, the calculated wavefront is fitted to a Zernike polynomial combination; the paraxial sphere power is deduced from the defocus coefficient while cylinder and axis are deduced from the astigmatism terms. In addition, power maps with a very high spatial resolution are calculated for each pixel within the optic zone of the contact lens. The instrument software also allows wavefront analysis via Zernike polynomial decomposition to be made at any aperture diameter of the lens being measured. Proc. of SPIE Vol. 7389 73890Z-4

4. Spatial resolution and the ability to detect step changes The deviation angle is measured at each pixel of the camera. The native pixel resolution of the camera in the Nimo instrument is 1396 x 1040 pixels, corresponding to a spacing of 69 pixel/mm or 1761pixel/inch. This is typically halved to 696 x 520 pixels by a process known as pixel binning. Pixel binning means unifying signal charges output from pixels in an image pickup device; in this case, adjacent groups of 2x2 pixels are combined using the control software to be calculated as a single pixel. Obviously the binning process, which is common in this technology, will reduce spatial resolution if it is employed. The Nimo instrument settings can be adjusted to control the binning. The power dimension measured is calculated from the average of the deviation angle on the confusion circle provided by the imaging optics. The ability to measure step profiles, such as in the case of a segment bifocal, is limited by the optical resolution of the imaging system composed by lenses L2, L3 and the aperture A shown schematically in figure 1. The Nimo instruments assessed in this study had a spatial resolution of 36 microns. To get a sense of the relative importance of this, it may be compared to a typical Shack-Hartmann device, such as the Visionix 2001 [14], which will have micro lenslets spaced at 0.25mm (250 microns). In an 8.0mm by 8.0mm square, the schlieren instrument will look at some 50,000 data points, compared to just over 1,000 for the Shack-Hartmann device. A summary of the Nimo instrument is given in table 1. The instrument is shown in figure 6. Field of view Power range Spatial resolution 15 x 15 mm² ±40D at a zone diameter of 5.0 mm ±30D at a zone diameter of 8.0 mm 36µm Table 1: Specification of the Nimo TR1504 instrument. Figure 6 : Nimo TR1504 5. Measurement of soft contact lenses Soft contact lenses are generally measured in a suitable wet cell while the lens dimensions are specified in air. The instrument software converts the effective power in saline to back vertex power in air. Proc. of SPIE Vol. 7389 73890Z-5

When measuring soft contact lenses it is essential to know the material refractive index n, the liquid refractive index n, the central thickness t and the contact lens back curvature r 0. From the effective power measured by the schlieren instrument in the wet state, the lens front curvature r a0 is calculated from: 2 ( n n' ) n. r0 + t.( n n' ) ra 0 = Equation 1 ϕ r n+ n n' n 0 ( ) Then, the back vertex power in air F' v is calculated from: n ( n 1) n 1 F ' v = Equation 2 nra0 ( n 1) t r0 The accuracy of the measurement is critically influenced by the values of refractive index for both the lens material and the solution in which the lens is immersed; small errors in these values can significantly influence the calculated values. 5.1. Dry measurement When rigid contact lenses are measured dry in the instrument, the same correction is applied to convert the effective into a back power in air. The liquid refractive index n is replaced by 1 in Equation 1. 6. Lenses measured 6.1. Toric rigid lenses Twelve toric rigid lenses were supplied by six independent laboratories randomly selected from the worldwide membership of the European Federation of the Contact Lens Industry (EFCLIN). The lenses were coded A to L by an administrator so that neither the project manager nor the measuring technician was aware of the labeled dimensions. They are made from a typical rigid lens material having a refractive index of 1.465 and a nominal Dk (permeability) of 60 traditional Fatt units. The labeled powers of the twelve lenses are given in Table 2. Lens Label Power (D) Code Sphere Cylinder A -3.25-1.50 B -3.50-2.00 C -3.00-1.50 D 3.50-1.75 E 3.50-2.00 F 3.00-1.50 G -3.25-1.75 H -3.50-2.00 I -3.00-1.50 J 3.25-1.75 K 3.50-2.00 L 3.00-1.50 Table 2 : Nominal powers of rigid toric contact lenses. Proc. of SPIE Vol. 7389 73890Z-6

6.2. Spherical soft lenses A range of Acuvue 2 lenses (etafilcon A) was measured in the lens packing solution to avoid any possible influence that saline characteristics, such as ph, may exert on lens dimensions. The following control parameters were used for the Acuvue 2 lenses: back optic zone radius 8.6mm; material refractive index 1.4008 and packing solution index 1.3345. Lens centre thicknesses were selected according to lens power based either on the manufacturer published data, which specifies a value of 0.084 for minus powers of -3.00 and above. For plus powers and low minus powers, sensible industry values were selected according to lens power. 6.3. Toric soft lenses A range of Acuvue Advance for Astigmatism (galyfilcon A) silicone hydrogel lenses was measured, again using the packing solution in which the lenses were delivered. The following control parameters were used for the Acuvue Advance toric lenses: back optic zone radius 8.60mm; material refractive index 1.4055 and packing solution index 1.3345. Lens centre thicknesses were selected according to lens power based either on the manufacturer published data, which specifies a value of 0.07 for minus powers of -3.00 and above or on sensible industry values for powers which were more positive than -3.00D. 6.4. Cuvette All soft lenses were measured in a quartz cuvette. This cuvette has an intrinsic power of less than 0.005D either when empty or when filled with saline. It is equipped with a v-shaped mechanical part, visible in the photograph (Figure 7) to get better positioning of the lens in the instrument. Figure 7 : The quartz cuvette with a soft lens For dry measurements, as used with rigid contact lenses, the lenses were placed in the same cuvette but without the saline solution. 6.5. Calibration Instrument absolute accuracy is defined by the maximum difference between the measured and the actual values. This can only be evaluated on reference lenses of known dimensions measured by a certified Proc. of SPIE Vol. 7389 73890Z-7

laboratory. Reference glass lenses for focimeters compliant with ISO 9342 [REFERENCE 15] were used to calibrate the instrument, having a power range from -25.00D to +25.00D, in steps of 5.00D. A set of 5 measurements was taken for each lens. The mean value of power compared to the actual lens power was used to provide a calibration curve for the instrument. 6.6. Reproducibility Reproducibility data for the method is obtained from a ring test in which different operators measure the same lenses on different instruments. The measurements are conducted so that the operators do not know the labeled lens dimensions. Ideally, for a reproducibility study the instruments should be at different locations but in this evaluation the instruments were located in the same building but with independent (different) operators. A statistical analysis as specified in ISO 5725 [16] was performed to obtain the reproducibility of the method. This procedure allows the determination of the reproducibility standard deviation SR which in turn enables the calculation of the number of readings required to measure to a specified tolerance limit. For contact lenses, it is required that the measurement tolerance (MT) of the test method shall be at least one-half of the product tolerance (PT). The measurement tolerance of the method for a single reading depends on the value of the reproducibility and is given by MT = 1.96SR, where 1.96 is the Student's t factor for 95% confidence. For multiple measurements MT is obtained by multiplying the standard error of the mean, SE, by the appropriate Student's t factor: MT 1.96SR = 1.96SE = Equation 3 N where N is the number of readings taken. This equation may be rearranged to calculate the number of readings required in cases where the product tolerance and SR are known: 1.96 S R N = Equation 4 MT For a given product tolerance, substitute MT = PT/2 and calculate the number of readings required to meet that tolerance. 7. Results The outcome of the calibration process is summarized in Table 3. Instrument Condition 1 2 3 Maximum Repeatability Absolute accuracy (D) 0.014 0.019 0.023 0.023 Standard deviation (D) 0.006 0.003 0.001 0.006 Reproducibility Absolute accuracy (D) 0.022 0.012 0.019 0.022 Standard deviation (D) 0.009 0.001 0.001 0.009 Table 3 : Absolute accuracy and instrument standard deviation on reference glass lenses. Proc. of SPIE Vol. 7389 73890Z-8

The absolute accuracy, as calculated according to ISO 5725, is better than ±0.023D over the range -25.00D to +25.00D. This is ten times better than the power tolerance on the contact lens. The standard deviation is less than 0.01D. Reproducibility standard deviation was found to be of the same order of magnitude as the repeatability. This confirms that the measurement capability of the instrument is independent of the placement of the lens and the cuvette in the instrument. 7.1. Reproducibility of the method for toric rigid lenses Each toric rigid lens was measured independently 10 times on each of three instruments under conditions of reproducibility. The results are shown in detail in Table 4. Referring to this, the column Measured power shows the average of all measurements on the same lens while the standard deviations given are the maximum the standard deviation of each set of measurements. Lens Code Label Power (D) Measured power (D) Sphere Cylinder Sphere Cylinder A -3.25-1.50-3.375 ± 0.024-1.474 ± 0.029 B -3.50-2.00-3.578 ± 0.026-1.854 ± 0.025 C -3.00-1.50-3.050 ± 0.013-1.141 ± 0.019 D 3.50-1.75 3.564 ± 0.010-1.779 ± 0.031 E 3.50-2.00 3.692 ± 0.011-1.818 ± 0.012 F 3.00-1.50 2.812 ± 0.007-1.382 ± 0.006 G -3.25-1.75-3.042 ± 0.017-1.755 ± 0.019 H -3.50-2.00-3.442 ± 0.009-2.007 ± 0.009 I -3.00-1.50-2.797 ± 0.009-1.559 ± 0.020 J 3.25-1.75 3.323 ± 0.015-1.635 ± 0.025 K 3.50-2.00 3.412 ± 0.011-2.079 ± 0.010 L 3.00-1.50 3.022 ± 0.009-1.680 ± 0.009 Table 4 : Summary of the measurements of toric rigid lenses using the schlieren method. Using the methods set out in ISO 5725, the overall reproducibility, S R, of the method was found to be 0.014D for sphere and 0.026D for cylinder. This test indicates that for toric rigid lenses one reading with this method is sufficient to meet the current product tolerance for both sphere and cylinder power. 7.2. Spherical soft lenses Based on the ring test using Acuvue 2 lenses the reproducibility standard deviation S R of the method for spherical soft lenses was found to be 0.048D. The number of readings required to be 95% confident of the test outcome for spherical lenses is given in Table 5. Parameter Tolerance SR Number of Back vertex power limit measurements 0 to ±10D Over ±10 to ±20D ±0.25D ±0.50D 0.048 0.048 1 1 Table 5. Number of readings required for spherical soft lenses Proc. of SPIE Vol. 7389 73890Z-9

7.3. Toric soft lenses The ring test result for the Acuvue Advance for Astigmatism toric soft lenses gives SR values of 0.059D for sphere power and 0.093D for cylinder power. We note that the lenses measured had no sphere power higher than -10.00 and no cylinder power higher than -2.00D. We therefore only calculate the number of measurements required for sphere powers up to ±10D and cylinder powers up to 2.00D (Table 6). Parameter Tolerance limit S R Number of measurements Sphere power 0 to ±10D ±0.25D 0.059 1 Cylinder power Up to 2.00D ±0.25D 0.093 2 Table 6. Number of readings required for toric soft lenses 8. Conclusion The principle application of the schlieren instrument, as embodied in the Nimo TR1504, will be to measure complex toric, multifocal, varifocal, bifocal and aspheric optics or wavefront controlled lenses, especially soft contact lenses. In order to establish the basic credibility of measurements, it is essential to validate any new method such as this for spherical and toric lenses, especially soft toric lenses when measured immersed in saline; this was the purpose of this study. The outcome has demonstrated that the schlieren method used here is more precise than any current ISO referenced method. Additionally, it is reasonably expected that this method, which has an inherently very much greater spatial resolution than previous methods will be suitable for the measurement of step change power profiles, such as in the case of segment bifocals and also will be applicable to the measurement of the growing number of aspheric optics soft lens products. It is reasonably expected that this technology can be used by manufacturers, universities and research centres to credibly determine the wavefront characteristics of soft lenses when measured immersed in saline. REFERENCES [1] International Standard 18369-3 Ophthalmic optics - Contact lenses Part 3 Measurement methods [2] Dave T. Aspheric contact lenses what s the deal? Optician 07.11.08 p22-25 [3] LOPEZ-GIL Norberto; CASTEJON-MOCHON José Francisco; BENITO Antonio; MARIN José Maria; LO-A-FOE George; MARIN Gildas ; FERMIGIER Bruno; RENARD Dominique; JOYEUX Denis; CHATEAU Nicolas; ARTAL Pablo; Aberration generation by contact lenses with aspheric and asymmetric surfaces. Journal of refractive surgery 2002, vol. 18, no5, pp. S603-S609 [4] HONG X; HIMEBAUGH N, THIBOS LN. On-Eye Evaluation of Optical Performance of Rigid and Soft Contact Lenses. Optometry & Vision Science (2001). 78(12):872-880. [5] http://www.bausch.com/en_us/downloads/ecp/visioncare/general/pv_product_comparison.pdf [6] DE BRABANDER J, CHATEAU N, BOUCHARD F, GUIDOLLET S. Contrast Sensitivity with Soft Contact Lenses Compensated for Spherical Aberration in High Ametropia. Optometry & Vision Science (1998). 75(1):37-43. [7] Lindskoog Pettersson A, Jarkö C, Alvin Å, Unsbo P, Brautaset R Spherical aberration in contact lens wear. Contact lens and anterior eye 31 (2008) 189-193 [8] Hough T, Livnat A, Keren E. Inter-laboratory reproducibility of power measurement of toric hydrogel lenses using the focimeter and the Moiré deflectometer.journal of The British Contact Lens Association Volume 19, Issue 4, 1996, Pages 117-127 [9] US Patent 7206079 - Apparatus and process for characterizing samples. Joannes Luc. [10] International patent application PCT WO 03/048837 Apparatus and process for characterizing samples. Joannes Luc. [11] Joannes L., Dubois F., Legros J.C., Phase-shifting schlieren : high-resolution quantitative schlieren that uses the phase-shifting technique principle. Appl Opt 2003;42:5046-53. Proc. of SPIE Vol. 7389 73890Z-10

[12]. Wheeler DR. A Simple Classroom Demonstration of Natural Convection. http://www.et.byu.edu/~wheeler/schlieren/schlieren.pdf [13] Creath K., Phase-measurement techniques, in Progress in Optics, E. Wolf Eds, Amsterdam: Elsevier, 1988:26,346-93. [14] The Visionix 2001 instrument is described here: http://www.visionix.com/site/prod/vc/vc.asp?s=all [15] ISO 9342-1:2005 Optics and optical instruments -- Test lenses for calibration of focimeters -- Part 1: Test lenses for focimeters used for measuring spectacle lenses [16] ISO 5725-2: 1994 Accuracy (trueness and precision) of measurement methods and results Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method. Proc. of SPIE Vol. 7389 73890Z-11