With 60 years of intense research and development, progressive addition lenses (PALs) have been increasingly accepted by presbyopes as the preferred spectacle lenses to compensate for the decline in accommodation with age.1–4 This acceptance can be attributed to the advantages of PALs over other forms of lenses as well as sound fitting and dispensing. The advantages of PALs are well-known, including corrected vision at all distances, no image jump caused by discontinuous power changes, and no lines on the lens to affect cosmesis.5,6
The optical characteristics of PALs are normally measured by a conventional lensometer in the clinic setting, which is an optical measurement method to conveniently and quickly give clinicians information about the distance power, near power, and thus the related add power. However, those powers only describe certain locations in a PAL (the distance power zone and near power zone) and are only a small part of the total characteristics of PALs.
From a visual performance perspective, two simple measurements of localized powers are not enough to characterize the properties of PALs and to predict clinical performance of a lens because of free eye movement behind the lens. Therefore, more comprehensive methods have been developed for measuring and evaluating the detailed optical properties of PALs over the past 60 years, including lensometry,7–16 ray tracing,17 photography,18–20 optical Fourier filtering,21,22 interferometry,23–31 and wavefront sensing.32–37 All these methods are based on direct optical measurements and have systematically revealed the key features of PALs, which consist of a vertical increase in spherical power from the upper to the lower portion of the lens and a lateral increase in unwanted astigmatism to either side of the progressive corridor.
In addition to direct optical measurement of PALs, an indirect non-optical method such as surface profilometry also can be used to measure the physical dimensions of the PAL surfaces.38–41 Mazuet38 used an accurate coordinate measuring machine (CMM) to measure both surfaces of each of two PALs. He stated that knowing the lens’s refractive index, spherical power, and astigmatism, maps can be computed. Recently, Raasch et al.39 also used the CMM to characterize and compare three PAL surfaces in terms of the Zernike polynomials. Although they only performed the surface height measurements on the progressive power surface, they mentioned that if both surfaces were freeform, then measurement of both surfaces, with careful registration of the measured regions on both surfaces, would be necessary to characterize the lens optics. Of course, the optical properties of the lens would be the combined effect of the two surfaces.
Most of the aforementioned studies measured the optical characteristics of PALs by a single measurement method, but comparison of different measurement methods is very important. Fowler and Sullivan14 first compared three different types of lensometer measurements on the same PAL (plano with a +2.00 D add), including a rotating mount, lateral movement of the lens, and surface reflection. The results show that the rotating mount method tends to measure more astigmatism than the other two methods by approximately 0.25 D. They also suggest that the discrepancies between the methods occur in the case of higher-power and thick positive PALs. Nakano et al.23 compared the moiré interferometer with a lensometer for measuring the power distribution of a PAL (plano with a +2.00 D add) along the progressive corridor. The refractive power measured by the moiré interferometer is close to that by the lensometer with a difference of <0.10 D. Spiers and Hull22 made another comparison of distance and near powers between the optical Fourier filtering with a chevron filter and an automatic lensometer of five designs of PAL (plano with a +2.00 D add). The results show good agreement between these two methods, with the difference in the near zone within 0.13 D.
It is clear that most of the reports assess PALs by a single measurement method. Few studies address the comparison of different measurement methods on the optical properties of PALs. Therefore, it is of great interest to see the comparison of the optical properties of PALs measured and evaluated by different measurement methods. In this study, Hartmann-Shack wavefront sensing, moiré interferometry, and surface profilometry were chosen for comparison. These three methods were selected for comparison for three major reasons. First, all have been developed recently and are featured in most of the recent articles on PALs, although no author has used more than one of these techniques. Second, all three methods use lateral displacement of the PALs (no rotation and no tilt), which makes the measuring results from these three methods more comparable. Finally, the choice of methods allows comparison between the optical properties of PALs by direct optical measurement (Hartmann-Shack wavefront sensing and moiré deflectometry) with those by direct physical dimension measurement (surface profilometry). Clinicians and researchers may ask whether the methods provide similar results for PALs. Comparison of optical measurement with physical surface shape measurement could thus provide important validation of the different methods.
A Hartmann-Shack wavefront sensor (HSWFS, WaveFront Sciences, Albuquerque, NM) on a custom-built optical bench was used to capture and measure wavefront aberrations of PALs. The PAL was illuminated by a tungsten white light source behind a 4 mm aperture, with source and aperture 5 meters from the PAL. This configuration approximates a distant point source, with the slight divergence (−0.2 D) of the wave front at the plane of the PAL being accounted for in the HSWFS calibration. The plane of the PAL and the plane of the lenslet array of the HSWFS were made conjugate by a pair of 75 mm focal length lenses separated by 150 mm. The array consists of lenslets with 8.19 mm focal length, in a 44 × 33 square array of 0.144 × 0.144 mm lenslets. Through a 4.5 mm aperture, 700+ lenslet spot images are captured, well in excess of that needed to compute the Zernike coefficients of the wave front through that lens location.
The PAL was translated horizontally and vertically to take measurements at different lens locations through a 4.5 mm pupil. HSWFS images were acquired over a grid of 70 measurement locations (7 horizontal × 10 vertical). The pupil center-to-center separation was 4.5 mm, producing a rectangular grid of measurements with an overall center-to-center spacing of 27 mm horizontal by 40.5 mm vertical (or 31.5 × 45 mm edge-to-edge). This region of the lens was chosen because it covers the most important optical areas of the PALs including the distance power zone, near power zone, the progression corridor area, and the central portion of the unwanted astigmatism peripheral area. The detailed information about this setup can be found elsewhere.42
A Rotlex Class Plus lens analyzer (Rotlex, Israel), operated as a moiré deflectometer using a point source rather than a collimated beam, was used to measure spherical and cylindrical powers of PALs, which were reported on a 0.5 mm grid. The measurement method has been reported elsewhere26 and was conducted at the Pacific University College of Optometry.
Surface height measurement was conducted using a precision Sheffield Cordax RS-30 Direct Computer-Controlled CMM. Both surfaces of the lens were measured to derive the full refractive properties of the lens. Each lens was measured on a grid of points (x, y) spaced approximately 0.49 mm apart, or about 4.15 measured points/mm2. A 61 mm diameter lens blank requires about 12,100 samples per lens to yield that measurement density. This is similar to that measured by the Rotlex Class Plus lens analyzer and is adequate for evaluating the optical properties of a PAL.39 These data were recorded as a text file and subsequently imported into MATLAB for analysis. The optical properties of PALs were calculated for each surface and for the combination of both surfaces. The analysis diameter of all PALs was limited to 60 mm except for the Hoya Lifestyle PAL, which was 40 mm owing to the asymmetric geometry of the blank. Each lens was oriented so the coma component of the lens was vertical. A detailed description of the measuring procedure and mathematical calculation has been explained elsewhere.39
Five PALs (Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph, and Zeiss Individual), listed in Table 1, were selected for comparison of optical properties measured by three different techniques. Lenses were chosen to include contemporary lenses using freeform technology. All lenses were specified as: right eye, plano distance power, +2.00 D add, and made from CR-39. The chosen lenses had the progressive surface shape either on the front, the back, or distributed across both surfaces. Finally, because the distance powers were plano, any potential effect on our measurements owing to prism would be minimal.
The optical properties of the PALs selected for comparison included spherical equivalent power (M), cylindrical power (J), and the Root Mean Square (RMS) of higher-order aberrations (HOAs). Results from the HSWFS measuring method were calculated and analyzed with custom MATLAB programs. Expansion coefficients of the Zernike polynomials up through the 10th order (66 terms) were calculated for a 4.5 mm analysis diameter, to simulate a subject’s natural pupil using a least-squares fitting method. CMM height data of front and back surfaces were used to derive the Zernike coefficients up through the 10th order, defining the surface shape for the full 60 mm diameter lens. A matrix method43 was used to derive Zernike coefficients for a 4.5 mm pupil at each lens position(s). The method uses matrices to transform between Zernike and Taylor coefficients. Expression as a Taylor series facilitates the translation and size rescaling of subapertures of the surface. The spherical equivalent and cylindrical powers were calculated from the relevant Zernike coefficients based on the following equations:
where r is the radius of the pupil (2.25 mm).
Results from the Rotlex measuring method consist only of sphere and cylinder, so aberrations cannot readily be derived from the commercially available moiré deflectometry software.
The contour plots of M and J for a 4.5 mm pupil diameter within the 60 mm lens diameter were compared between the Rotlex and CMM methods. For the HSWFS method, only the contour plots of the area of 27 mm by 40.5 mm (Hoya Lifestyle PAL = 27 × 36 mm) are presented. In addition to the contour plot, the numerical differences including the M, J, and RMS of HOAs inside the selected area were also compared among the three different methods.
Spherical and Cylindrical Power
Fig. 1 and Fig. 2 show comparisons of the three measurement methods (Rotlex, HSWFS, and CMM) among these five PALs. The area of the lens measured by the HSWFS method is indicated by the rectangle on the plots for the Rotlex and CMM methods.
The results show that the M and J contour plots measured by the HSWFS, Rotlex, and CMM methods all look quite similar in the central area, from the distance power zone through the progressive corridor to the near power zone.
The differences in spherical equivalent (ΔM) and cylindrical power (ΔJ) between the Rotlex and the HSWFS methods and between the CMM and the Rotlex methods in all five PALs are shown in Fig. 3 and Fig. 4, respectively. There is little difference across the measurement area except near the edge of the lens, where the CMM method can differ from the Rotlex method by >0.50 D in all PALs.
Fig. 5 shows a comparison of the CMM and the HSWFS methods of the root mean square (RMS) of HOAs in five PALs, with a 4.5 mm pupil. Again, the area measured by the HSWFS is indicated by the rectangle on the plots for the CMM method.
The results show that the HOAs measured by the CMM are similar to those with the HSWFS within the rectangular area for all five PALs. It is apparent that the RMS of HOAs is higher in the progressive corridor area and the surrounding near power zone area in all five PALs. However, there are subtle differences in the distribution of HOAs between the CMM and the HSWFS. The RMS of HOAs measured by the CMM is lower than that measured by the HSWFS by about 0.02 to 0.04 μm in the progressive corridor area and the surrounding near power zone area. In contrast, the RMS measured by the CMM in the near power zone area is higher by about 0.02 to 0.04 μm than that measured by the HSWFS method, especially in the Physio and Zeiss PALs. In addition to the confined area, the CMM method also indicates that higher HOAs occur at the edge of the lens in all five PALs. The differences in the RMS (ΔRMS) of higher-order aberrations between the CMM and the HSWFS methods in all five PALs are shown in Fig. 6.
Comparison between the Rotlex and the HSWFS Methods
According to the results of spherical and cylindrical contour plots shown in Fig. 3, it is clear that there is no meaningful difference in power measurements between the Rotlex method and the HSWFS method for the five PALs. The observable maximum differences in spherical and cylindrical power in all five PALs are clustered at the central and peripheral bottom areas, respectively, which are the areas below the near power zone (y < −15 mm).
The HSWFS method measures more positive spherical power than the Rotlex method by about 0.50 D. There are two possible reasons for this discrepancy. The first might be the difference in the conjugate position between the PAL and the wavefront sensor owing to the lateral displacement during measurements, causing differences in lens surface location owing to different curvatures. The conjugate point at the bottom area (near zone) of the PAL is off by about 2.6 mm at y = −18 mm and 4.2 mm at y = −22.5 mm, respectively, for five PALs owing to the surface curvature of the superimposed add power of +2.00 D compared with the center area of the PAL, which is the designed conjugate point. Compared with the same position at the top area (distance zone) of the PAL, the off conjugate distance is only 2.0 mm at y = +18 mm. The results show that the larger differences in M always occur at the farthest positions away from the center of the lens, which is consistent with this possibility. Therefore, the greater the off-conjugate distance, the greater the differences in spherical power. However, ray tracing indicates that the magnitude of this error is no more than 0.03 D for a 2.00 D lens, although it would increase for higher lens powers.
The second possible reason for the discrepancy might be due to a prismatic effect in the lower part of the lens owing to the +2.00 D add. However, any small prismatic effect of the lens would displace all lenslet spots equally, manifesting as a tilt, but not in terms of sphere or cylinder or any other higher-order terms. Higher lens powers might act as thick prisms, and the displacement of spots would vary and might be interpreted by the aberrometer as cylinder.
In addition to the power comparison, there is another difference between the HSWFS method and the Rotlex method. That is the HSWFS method is more sensitive than the Rotlex method in detecting surface defects on a PAL. The surfacing process produced a small indentation on the lower right area of the Shamir PAL as shown in Figs. 1, 2, and 5. When the detecting light is passing through a surface defect of a PAL, the wavefront image formed by the wavefront sensor is affected by the surface defect and shows higher aberrations, not observed in the Rotlex method.
Comparison between the CMM and the Rotlex Methods
Comparing the CMM method with the Rotlex method for the M and J contour plots, it is apparent that there is no systematic difference in spherical and cylindrical power between the CMM and the Rotlex methods for the five PALs shown in Fig. 4. The observable maximum differences in spherical and cylindrical power in all five PALs are approximately 0.50 D and occur at the edge area of the lens in all five PALs. This discrepancy can be attributed to three factors. First, the calculation of power from CMM data uses an assumed index of refraction of 1.5. The measured PALs were CR-39 with an actual index of refraction of 1.498; sphere powers could be affected by this small error (0.4%), but only at much higher lens powers than used in the present study. Second, these CMM calculations were based on the combination of front and back surfaces without consideration of lens thickness. If lens thickness is considered, the M power would be increased by about 0.05 D with an assumed 2 mm lens thickness—insufficient to account for the observed discrepancy of up to 0.50 D. One more possibility might be due to the prismatic effect. As mentioned earlier, not much prismatic effect was observed. Although the discrepancy exists, the portion at the edge area of the lens would be truncated during the lens-edging process, so would not have a role in vision correction. In general, the CMM method is comparable with the Rotlex method in the power measurement and evaluation.
Comparison between the CMM and the HSWFS Methods
In addition to the power comparison, the HOAs were compared between the CMM method and the HSWFS method shown in Fig. 5 and 6. Differences of about 0.02 to 0.04 μm are observed in some PALs, especially in the progressive corridor area, with the area surrounding the near power zone showing lower HOAs and the near power zone area showing higher HOAs when measured by the CMM method. It demonstrates that the parameters used in the CMM method such as the measurement density (12,100 points), the refractive index (n = 1.5), and the combined two-surface approach are acceptable. Moreover, it also shows that the CMM method has the ability to detect the surface defects as the HSWFS method did in the Shamir PAL, even though it is not as obvious. In conclusion, both methods are quite comparable in terms of the HOAs. Of course, the magnitude of the HOAs is small in comparison with astigmatism observed in the peripheral portions of all the PALs.34
General Comparison of Three Methods
Other factors such as the measurement speed, equipment cost, and availability of these three instruments are also important. In general, measurement time is <2 min for all measurements for the Rotlex, about 40 min for 70 measurements using the HSWFS method, and about 16 h for 12,100 measurements using the CMM method to yield similar measurement density to the Rotlex (one data point per 0.5 mm). We have since established that PAL surfaces can be characterized satisfactorily with 3000 measurements. The HSWFS is the cheapest method at <$10,000 for the custom-built, manual experimental set up. The Rotlex is a commercially available instrument costing around $30,000, and the CMM method is the most expensive method costing >$100,000.41 The three methods are obviously not as commonplace as lensometry, in part because of equipment cost. However, the lensometer only provides power information at specific locations and no HOA data. Of course, techniques can be easily established to acquire multiple measures across the lens surface similar to that used in other techniques.14,15 Nonetheless, if considering research and development of PALs, one of the three measurement methods described here is necessary for a better understanding of the distribution of spherical power, unwanted astigmatism, and HOAs. Our results show that the three methods are quite comparable.
One limitation of the present study is the fact that lenses were translated and not rotated. The latter would more accurately represent the power as worn by the patient. When a patient’s eye rotates behind a lens, the vertex distance varies and there is oblique incidence of light on the lens. These factors combine to affect the wavefront incident on the eye, thereby influencing, among other things, oblique astigmatism and mean oblique error. The benefits of using translation rather than rotation include ease of execution, quick measurement, low cost, and their widespread use in the optical industry for testing. Fowler and Sullivan14 compared three different types of lensometer measurements on the same PAL (plano with a +2.00 D add), including a rotating mount, lateral movement of the lens, and surface reflection. Their results show that the rotating mount method tends to measure more astigmatism than the other two methods by approximately 0.25 D. Given that meniscus lenses are designed to minimize prism and off-axis astigmatism associated with peripheral viewing, this finding might be construed as counterintuitive and suggests that using translation could underestimate astigmatism. They also suggest that the discrepancies between the methods occur in the case of higher-power and thick positive PALs. Fowler further developed an automated approach for lateral translation measurements of PALs.15 He concluded that the accuracy of measurement is considered to be sufficient for the purpose intended, that of making comparisons between designs. Only lenses with plano distance power were measured in this study, which would have mitigated any discrepancies between translational and rotational measures. Nonetheless, we are cautious about extrapolating our findings to thicker higher power lenses.
The three measurement methods, HSWFS, Rotlex, and CMM, are comparable for measuring spherical and cylindrical power across PALs. The non-optical method, CMM, can be used to evaluate the optical properties of a PAL by measuring front and back surface height measurements, although its estimates of HOAs are lower than those from the HFWFS.
Mark A. Bullimore
356 Ridgeview Lane
Boulder, Colorado 80302
Received November 20, 2011; accepted July 10, 2012.
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Keywords:© 2012 American Academy of Optometry
progressive addition lenses; Hartmann-Shack aberrometry; moiré interferometry; surface profilometry; coordinate measuring machine; wavefront aberrations