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Optical Fourier filtering for whole lens assessment of progressive power lenses
Ophthal. Physiol. Opt. Vol. 20, No. 4, pp. 281–289 䉷 2000 The College of Optometrists. Published by Elsevier Science Ltd All rights reserved. Printed in Great Britain 0275-5408/00/$20.00 + 0.00 www.elsevier.com/locate/ophopt
PII: S0275-5408(99)00105-2
Optical Fourier filtering for whole lens assessment of progressive power lenses T. Spiers and C. C. Hull Applied Vision Research Centre, Department of Optometry & Visual Science, City University, 311–321 Goswell Road, London EC1V 7DD, UK Summary Four binary filter designs for use in an optical Fourier filtering set-up were evaluated when taking quantitative measurements and when qualitatively mapping the power variation of progressive power lenses (PPLs). The binary filters tested were concentric ring, linear grating, grid and “chevron” designs. The chevron filter was considered best for quantitative measurements since it permitted a vernier acuity task to be used for measuring the fringe spacing, significantly reducing errors, and it also gave information on the polarity of the lens power. The linear grating filter was considered best for qualitatively evaluating the power variation. Optical Fourier filtering and a Nidek automatic focimeter were then used to measure the powers in the distance and near portions of five PPLs of differing design. Mean measurement error was 0.04 D with a maximum value of 0.13 D. Good qualitative agreement was found between the iso-cylinder plots provided by the manufacturer and the Fourier filter fringe patterns for the PPLs indicating that optical Fourier filtering provides the ability to map the power distribution across the entire lens aperture without the need for multiple point measurements. Arguments are presented that demonstrate that it should be possible to derive both iso-sphere and iso-cylinder plots from the binary filter patterns. 䉷 2000 The College of Optometrists. Published by Elsevier Science Ltd. All rights reserved.
Single vision lenses, bifocals and trifocals are easy to verify using standard focimetry since they have clearly defined regions of uniform power (ignoring aberrations and image shifts). Progressive power lenses (PPLs), by their very nature, have power that varies across the aperture. This seems to imply that mapping the spherical power across the surface of the lens will be sufficient to characterise its optical properties. However, the aspheric nature of a PPL leads to significant astigmatism, distortion and other aberrations particularly in the transition zones. Many authors have therefore used multiple point focimetry, which allows mean sphere, cylinder and cylinder axis to be obtained for a grid of points across the PPL aperture (Simonet et al., 1986; Sheedy et al., 1987; Atchison, 1987; Diepes and Tameling, 1988; Fowler and Sullivan, 1988, 1989, 1990; Atchison and Kris, 1993). All of these techniques are time consuming and Fowler and Sullivan’s attempt to automate the scanning of a PPL across the stop of an electronic focimeter needed 80 min to complete an assessment of 798 points, although the time taken nowadays is likely to be of the order of several minutes with modern computers and data logging equipment (Fowler and
Introduction Progressive power lenses (varifocals) first became commercially available to help presbyopes in the 1960s with the development by Maitenaz of the Varilux I (Maitenaz, 1966). However lenses with a progressive power variation date back to the early part of this century according to Bennett (1973). There is now a large number of different designs on the market and it is difficult to make comparisons between them. This is partly because the optical assessment of these non-rotationally symmetric strong aspheric lenses is not easy and is not part of standard test procedures. In fact, a survey carried out by us at the start of this work demonstrated that none of the six major progressive power lens suppliers in the UK currently have the facility to measure/ verify these lenses (survey carried out November 1996). Received: 26 March 1999 Revised form: 4 November 1999 Accepted: 15 November 1999 Correspondence and reprint requests to: C. C. Hull, Tel.: ⫹ 44-171-4778339.
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Figure 1. Arrangement of components in an optical Fourier filtering set up. The test lens has a “focal length” ftl at point B. The Fourier Transform lens, of focal length f2, images the lens under test on to the observation screen. Superimposed on this image is a distorted pattern of the binary filter fringes. For point B on the test lens, the fringe at point P in the Fourier plane is imaged at a height yos on the observation screen.
Sullivan, 1990). A review of the ability of modern measurement systems to measure the “wearer” power of progressive power lenses has been provided by Bertrand (1998). Alternative techniques have also been described including interferometry and Moire´ methods (Mohr, 1989; Nakano et al., 1990; Rosenblum et al., 1992; Keren et al., 1996; Illueca et al., 1998), beam deflection (Castellini et al., 1994) and optical Fourier filtering (Liu, 1994). All of these methods have the advantage of entire lens testing with the exception of the modified Hartman test (Castellini et al., 1994), which is a beam deflection method similar to that used in the Humphrey lens analyser. The methods reported have varied in their implementation. A Moire´ system developed by Rosenblum, O’Leary and Blaker (Rosenblum et al., 1992) used image capture and digital image subtraction to generate Moire´ fringe patterns. However, it is possible to generate the Moire´ fringe patterns directly as has been shown by several other authors (Kafiri et al., 1988; Keren et al., 1988, 1992; Kreske et al., 1988; Nakano et al., 1990). More traditional optical test methods such as Newton’s rings between a test plate and a lens surface (Illueca et al., 1998) or Mach–Zehnder interferometry (Mohr, 1989) have also been applied. The former method has the disadvantage of producing a very narrow fringe spacing, particularly for the non-rotationally symmetric strongly aspheric PPLs we are interested in here, whereas the latter requires compensating lenses and a reference lens and is therefore more suited to production testing. Essilor have recently developed a variation of the Ronchi test to measure the surface profile of PPLs indirectly (Bertrand, 1998), although no data from actual measurements has been presented to the authors’ best knowledge. Optical Fourier filtering has received little attention in the literature but is inherently simple and avoids most of the pitfalls of the other techniques. The aim of this paper is to examine the design of binary filters for entire lens testing of PPLs using optical Fourier filtering and to present some initial results on measurement accuracy and the ability
to assess the entire lens power distribution with this technique. Theory Figure 1 shows the arrangement of the components in an optical Fourier filtering set up. The lens under test is placed at a distance ⫺2f2 from the Fourier transform lens where f2 is the second focal length of the Fourier transform lens. A binary filter is placed in the Fourier (back focal) plane of the transform lens and an observation screen is placed at a distance 2f2 from the transform lens. This system provides an image of the lens on the observation screen with a magnification of ⫺1 and superimposes on it the distorted pattern of the binary filter. We shall first explain the theory behind the Fourier filter pattern on the observation screen for a single vision lens and then see how the theory is readily extended to all lenses. The ray shown in Figure 1 is incident on the test lens at a height ytl above the optical axis and is therefore deviated through an angle u where
tan θ =
ytl : ftl′
1
If the binary filter has a spatial period of I then let the ray after passing through the transform lens strike the filter at point P, which is at a height nI in the Fourier plane where n is a decimal value. From elementary geometrical optics all rays incident on the transform lens at angle u will be imaged to point P and hence an alternative expression for tan u is given by
tan θ =
nI : –f2′
2
Equating the right-hand sides of Equations (1) and (2) and recasting in terms of the powers of the test lens, Ftl and
Optical Fourier filtering for whole lens assessment of progressive power lenses: T. Spiers and C. C. Hull
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Figure 2. Arrangement of components along the optical bench in the Fourier filtering set up described in this paper. S is a He–Ne laser (l 632.8 nm), SF a spatial filter to clean and expand the beam, CL an aberration-controlled doublet to collimate the beam, OL is the ophthalmic lens under test, TL the transform lens (another aberrationcontrolled doublet), FF the binary Fourier filter and OS a ground glass observation screen. The separation of the components is as shown in Figure 1.
transform lens, F2, we find that the power of the test lens is given by Ftl
⫺F2 nI : ytl
3
where ytl is the only value that can not be directly measured. However, since the test lens is imaged on to the observation screen with a magnification of ⫺1, the position on the observation screen yos ⫺ytl hence Ftl
F2 nI : yos
4
Rearranging and differentiating Equation (4) yields dyos F I 2 Ftl dn
5
and setting dn 1 gives the relationship between the fringe spacing in the image (dyos) and the power of the test lens as Ftl
F2 I : dyos
6
Equation (6) demonstrates that the fringe interval at the observation screen can be used to find the local power of the test lens. For both positive and negative lens powers the fringe spacing is inversely related to the test lens power. This highlights a minor limitation in the method; for a symmetrical filter, the measured fringe spacing will be the same for both a ⫹2 D lens power and a ⫺2 D lens power. However, this can easily be overcome using a filter with some asymmetry or orientation specific features incorporated into its design. We shall return to this in the Methods section when optimum filter designs are considered. Experimental method Figure 2 shows the experimental arrangement for the Fourier filtering system used to produce the results presented in this paper. Light from a He–Ne laser (l 632.8 nm) was first passed through a spatial filter to remove any spatial impurities caused by diffraction effects
and to provide a rapidly diverging point source for the collimating lens (CL). The collimating lens was an aberration controlled doublet of back vertex power 3.21 D and diameter 58 mm. The optical performance of this lens closely approximates the Abbe Sine Condition when working at infinite conjugate as is the case here. The collimating lens was first verified on a Nidek LM870 automatic focimeter that had been checked against reference lenses, which had in turn been calibrated by the National Physical Laboratory. To aid accurate alignment of components along the optical axis the lens had its centre marked. The degree of collimation was tested by placing a 1 mm diameter pinhole just after the collimating lens. The collimating lens was then moved longitudinally relative to the spatial filter until the size of the image of the pinhole at a distance of 1.5 m from the collimating lens was equal to the original pinhole size. The alignment of the optical components along the optical bench was carried out as follows. First, the observation screen (a ground glass plate) was added and the image of the collimating lens centre marked on the screen. The transform lens, again an aberration controlled doublet of back vertex power 7.19 D, was placed on the optical bench and its alignment adjusted to make its centre mark aligned with the mark on the collimating lens. This was sufficient to define the optical axis of the system. The relative longitudinal position of the optical components were then adjusted using a distance bar, which had been measured with a travelling microscope (resolution 0.01 mm), and the vernier scales on the optical bench mounts (resolution 0.1 mm) to agree with the component separations shown in Figure 1. All filters were produced by first designing them using a computer graphics package and then printing them on to A4 paper before reducing them using a Polaroid slide maker onto 35 mm slide transparencies. With this technique a reduction factor of about 8.75 was achieved and good filter quality was maintained. Concentric ring, linear, grid and “chevron” designs were developed during the course of this work for the reasons given in the Results section below. Figure 3 illustrates the form of these binary filters.
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Ophthal. Physiol. Opt. 2000 20: No 4 Previously the filter spacing had been measured using a travelling microscope and was found to within ^0.004 mm (^1 standard error). Five readings of the filter fringe spacing were recorded for each trial lens and a calibration graph of dyos/I against 1/Ftl plotted. The gradient of this graph gives the equivalent power of the transform lens F2, which is needed to calculate the unknown lens power. Five different designs of PPL were obtained from Sola (UK) Ltd (XL, XL Gold, Graduate, Graduate Gold and Percepta). All lenses had a plano distance zone and a ⫹2 D near zone. These lenses were evaluated for their power in the distance and near zones using the Fourier filtering system with a chevron filter and were also qualitatively evaluated for aberrations in the transition zones.
Figure 3. The four binary Fourier filter designs tested: (a) concentric ring, (b) linear, (c) grid and (d) “chevron” designs.
Results Fourier filter designs
The Fourier filtering measurement system, with a chevron filter, was first calibrated against known test lenses. These were 20 trial case lenses with powers in the range ^12 D which had been measured on a Nidek LM870 automatic focimeter. The Nidek focimeter had previously been checked against our standard lenses, which in turn had been calibrated by the National Physical Laboratory. The error between the Nidek reading and the standard lenses was within 1% for powers in the range ^12 D and reproducibility in the measurements was ^0.016 D (95% confidence limits). The Nidek readings were therefore taken as accurate for the trial lenses used for calibration. For each trial lens the chevron spacing was measured using an electronic micrometer which had its RS 232 output connected to a PC.
The four filter designs (Figure 3) were tested to assess, initially, their qualitative ability to display the power distribution of a lens. Figure 4(a) and (b) demonstrates the patterns obtained through a single vision spherical lens and a toric lens, respectively, using a filter consisting of concentric rings. Figure 4(a) was generated using a ⫺10 D spectacle lens. Although the rings are concentric, peripheral aberrations are evident from the narrowing of the ring spacing away from the optical axis. This was probably due to an aspheric design or spherical aberration. Figure 4(b) shows a toric lens, specification ⫺1.50/⫺0.50 × 180⬚, which produces different fringe spacings along the two principal meridians and hence produces elliptical fringes. Figure 4 solely demonstrates the ability of Fourier filtering
Figure 4. Fourier filter fringe patterns using a concentric ring filter with (a) a single vision spherical lens and (b) a single vision toric lens. The elliptical distortion of the rings is clearly visible for the astigmatic lens.
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Figure 5. A bifocal lens tested with a grid filter. The difference in grid spacing between the distance and near portions of the lens clearly demonstrates the difference in power. This lens is astigmatic and (a) demonstrates the distortion of the grid squares into parallelograms due to the astigmatism. Rotation of the lens to orientate the grid lines along the principal meridians reduces the parallelograms to rectangles whose side lengths are proportional to the powers in the principal meridians. The angular position of the lens indicates the astigmatic axes.
to display the power variation across the entire lens aperture. It has no other advantage for measuring the power of single vision or bi-focal/tri-focal lenses. A grid filter was also evaluated and Figure 5 demonstrates its use in assessing a toric bi-focal lens. Figure 5(a) is the grid pattern with the lens aligned vertically. The difference in power between the distance and add portion of the lens is clearly seen from the difference in the grid spacings. However, the grid has been skewed by the presence of astigmatism. Rotation of the lens can elim-
inate this effect and make the grid rectangular [Figure 5(b)]. The angle of rotation of the lens determines one of the principal meridians and measurement of the fringe spacing of the grid along the long and short dimensions of the rectangle can determine the power along each principal meridian (see Quantitative measurements of this Results section). Both grid and linear filters were initially used for the qualitative evaluation of a PPL that had a plano distance zone and a ⫹2 D near zone. Figure 6(a) and (b) shows
Figure 6. The Fourier filter fringe pattern from a PPL measured with (a) a grid filter and (b) a linear filter. The authors consider that the linear filter gives a clearer impression of the aberrations in the transition zone. However, the grid filter is more amenable to quantitative analysis (see text for details).
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Figure 7. Comparison between manufacturer’s supplied iso-cylinder plots and the fringe patterns generated using optical Fourier filtering with a linear binary filter. The iso-cylinder plots are nominal for a lens design and are not specific to the lens tested. All five PPLs were kindly provided by Sola (UK) Ltd with plano distance zones and ⫹2 D near zones. The designs tested were (a) XL, (b) XL Gold, (c) Graduate, (d) Graduate Gold and (e) Percepta. There is good qualitative agreement between the Fourier filter fringe patterns and the iso-cylinder plots.
Optical Fourier filtering for whole lens assessment of progressive power lenses: T. Spiers and C. C. Hull the fringe patterns obtained from this PPL using (a) a grid filter and (b) a linear filter. The distortions of the linear filter pattern appear to give a clearer qualitative impression of the power distribution of the lens. For the linear filter, no fringes are apparent in the distance portion of the lens, which has no power. The fringes appear as vertical lines within the near zone whereas in the transition zone there is considerable distortion of the fringes. Linear filters do not permit resolution of the sphere and cylinder component together with its axis whereas a grid filter does. Arguments as to how this can be achieved are given in the Discussion. The linear filter was finally used to assess qualitatively the five sample lenses provided by Sola (UK) Ltd for this study. Figure 7 presents these results alongside the isocylinder plots provided by Sola where Sola’s plots have been obtained using a modified Humphrey Lens analyser from a method described by Atchison and Kris (1993). Although the Fourier filter patterns do not represent iso-cylinder information, any distortion of the fringes from their vertical orientation in the binary filter is caused by astigmatism (spherical power would not alter the orientation of the fringes, just their spacing). More specifically, the amount of distortion of the lines is due to not only the magnitude of the cylinder component but also its axis. It is therefore reasonable to assume that increasing amounts of astigmatism will cause an increase in the distortion of the fringes in the binary filter pattern since the cylinder axis, although not constant, must change continuously across the lens surface. This latter point is demonstrated by the iso-cylinder plots presented by previous authors (see, for example, Simonet et al., 1986; Sheedy et al., 1987; Atchison, 1987), which all show that, within the transition zones, the cylinder axis does not change significantly. It is therefore reasonable to compare the iso-cylinder plots supplied by the manufacturer and the fringe patterns produced by Fourier filtering. In Figure 7 there is a good qualitative agreement between the Fourier filter images and the iso-cylinder plots provided by the manufacturer. Fourier filtering clearly demonstrates the difference between a “hard” design such as the Graduate [Figure 7(c)], where the distance and near zones are relatively large with consequently large amounts of aberration in the transition zones, and “soft” designs such as the XL Gold [Figure 7(b)], which has noticeably smaller near and distance zones and hence the aberrations in the transition zone are more gradual. Quantitative measurements Linear and grid filters are both capable of displaying the power variation across the entire aperture of a lens although the grid filter is the only one that can resolve the spherical and cylindrical components. However, these two filter designs have two disadvantages. Firstly it is difficult to
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Figure 8. Calibration graph demonstrating the linear relationship between the ratio of the measured fringe spacing on the observation screen to the actual fringe spacing in the filter and the focal length of the test lens. This relationship is predicted by Equation (6) and is used to determine empirically the calibration constants needed to calculate unknown lens power.
determine the prism power of the lens being measured. Secondly, linear and grid filters do not convey any information about the sign of the power since they contain no orientation specific features. Liu (1994) has suggested using the orientation of just two reference marks on the target. However, this does not allow for any changes in the sign of the power across the lens aperture. A new filter was designed using a repeated chevron pattern [Figure 3(d)] that had the following advantages. Firstly, the measurement distance for this design was between the apices of the chevrons making the positioning of the graticule line a vernier alignment task. Secondly, the sign of the power was given by the orientation of the chevrons and distortions of the lines of chevrons indicated aberrated regions of the lens. This filter design was therefore used to take quantitative measurements on the lenses. The calibration graph (Figure 8) demonstrates the expected linear relationship between 1=F and dyos/I. After performing a weighted least squares line fit on the data, the power of the transform lens, F2, which is given by the gradient of the graph, was found to be 6.569 D (95% confidence limits 6.544–6.593 D). The goodness of fit to the theory outlined above is further demonstrated by an adjusted R 2 value of 1.0 and the fact that the intercept of the graph is not significantly different from zero (t-test; P 0.1015). This value for the power of the transform lens was used in all subsequent calculations of test lens power as was the y-axis intercept which was found to be c 0.0124. Thus Equation (6) for the test lens power becomes: Ftl
F2 : dyos =I ⫺ c
7
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Table 1. Power in Dioptres of the distance and near zones of five designs of PPL provided by Sola (UK) Ltd measured using a Nidek LM 870 automatic focimeter and optical Fourier filtering with a chevron filter (see text). All PPLs are nominally plano/⫹2.00 D and the errors quoted are ^1 SD (n 5) Fourier filtering Lens name
Near (D)
XL XL Gold Graduate Graduate Gold Percepta
1.91 ^ 0.01 2.06 ^ 0.01 2.16 ^ 0.01 1.94 ^ 0.05 2.14 ^ 0.06
Nidek focimeter
Distance Near (D) (D) 0.00 0.00 0.00 0.00 0.00
1.89 2.05 2.06 1.89 2.01
Distance (D) ⫺0.01 0.03 ⫺0.01 0.02 0.01
Table 1 summarises the results of measuring the distance and near zones of the five Sola PPLs using both Fourier filtering and the Nidek focimeter. No fringes were visible in the distance zone using Fourier filtering and so the power was recorded as zero. This demonstrates a possible weakness of Fourier filtering, which we shall return to in the discussion. Agreement between the values for the near zone are all within 0.12 D with the exception of one case where the difference was 0.13 D. However, the standard deviations when measuring the near zone are so small that all Fourier filtering readings were statistically different from the Nidek values. Possible reasons for this are discussed below.
Discussion It has been demonstrated that Fourier filtering offers a clear advantage in mapping the power variation over the entire lens diameter without the need for scanning or making multiple measurements. However, the quantitative measurements presented were difficult to make manually, suggesting that some form of automation, most probably using digital image analysis of the fringe patterns, is needed. Design of the Fourier filters is therefore of great importance and this study has demonstrated that good qualitative agreement with iso-cylinder plots is possible for entire lens aperture testing and that spherical power measurements with a high degree of accuracy can be achieved with appropriate filters. In the Results section, it was noted that linear filter patterns do not provide sufficient information to resolve the axis and cylinder component of the lens under test whereas a grid filter does. The grid filter permits an analysis, analogous to the four ray method used in the Humphrey Lens Analyser, to be performed by utilising the four corners of a square on the grid. It is then possible to resolve sphere, cylinder and cylinder axis for a localised area on the PPL. Iso-sphere and iso-cylinder plots can then be recovered from the Fourier filter fringes by using a digital camera and image processing system to analyse the filter patterns produced. Analysis of fringe patterns is routinely carried out in the optics industry for lens metrology.
Another advantage of optical Fourier filtering is that any features marked on the lens surface are also imaged on the screen superimposed on the Fourier filter fringes. This is clearly evident in Figures 6 and 7 where the fitting cross, distance design reference point and near design reference point are clearly visible superposed on the fringe patterns. However, widely differing lens powers require the use of different Fourier filters because of the inverse relationship between lens power and Fourier filter fringe spacing [Equation (6)]. This problem was particularly evident with low power lenses where a filter with high spatial frequency was needed to allow small changes in power to be measured. The only practical solution would be to have a filter wheel in the optical Fourier filtering system that allows different filters to be selected. A less obvious, but potentially more serious disadvantage related to this is the dichotomous filter requirements when measuring high power lenses with small power variations across their aperture: high power lenses require Fourier filters with coarse spatial detail due to the minification of the final image whereas small changes in power require filters of high spatial frequency. This latter effect has been demonstrated by our inability to measure low powers in the distance portions of PPLs even with the finest filters that have been fabricated in this study. Only a fully quantitative system, which can analyse the filter patterns and derive isosphere and iso-cylinder power variation, will determine if this is a serious drawback. It may then be possible to adapt the system to measure power variation with respect to the best sphere as follows. A coarse filter can be used to determine the absolute power and then the source vergence changed to compensate the absolute power, a technique known as optical biasing. A fine filter can then be used to look at small power variations across the aperture. However, with the strongly aspheric nature of the PPLs and current evidence from iso-cylinder plots, this may not be necessary. Several authors have argued that it is necessary to map the lens power with respect to the vertex sphere (Simonet et al., 1986; Atchison, 1987; Bourdoncle et al., 1992; Atchison and Kris, 1993), although others have shown that the difference between measurements made with respect to the centre of rotation of the eye and with the lens static is small (Fowler and Sullivan, 1989). At present the optical Fourier filtering system described here does not meet this requirement since the source is collimated for all points on the lens surface and no attempt is made to compensate for the rotation of the eye behind the lens. It is not immediately apparent to the current authors how a Fourier filtering system can be modified in this respect. Acknowledgements The authors would like to thank Mr Alick Taylor of Sola (UK) Ltd for providing the lenses used in this study, Mr B. Staples of Sola International Holdings Ltd for providing
Optical Fourier filtering for whole lens assessment of progressive power lenses: T. Spiers and C. C. Hull technical information and Mr S.G.A. Smele of Mitutoyo (UK) Ltd for providing the RS 232 compatible digital readout vernier gauge. We would also like to thank Michael Burke for photographing the Fourier filter patterns that have been scanned for the figures in this paper. References Atchison, D. A. (1987). Optical performance of progressive power lenses. Clin. Exp. Optom. 70, 149–155. Atchisn, D. A. and Kris, M. (1993). Off-axis measurements of a plano distance power progressive addition lens. Ophthalm. Physiol. Opt. 13, 322–326. Bennett, A. G. (1973). Variable and progressive power lenses: 4. Manuf. Opt. Int. 26, 137–144. Bertrand, P. (1998). Wearer power measurement of progressive addition lenses. In: Vision Science and Its Applications, vol. 1, OSA Technical Digest Series, Optical Society of America, Washington, DC, pp. 180–183. Bourdoncle, B., Chauveau, J. P. and Mercier, J. L. (1992). Traps in displaying optical performance of a progressive-addition lens. Appl. Opt. 31, 3586–3593. Castellini, C., Francini, F. and Tiribilli, B. (1994). Hartmann test modification for measuring ophthalmic progressive lenses. Appl. Opt. 33, 4120–4124. Diepes, H. and Tameling, A. (1988). Comparative investigations of progressive lenses. Am. J. Optom. Physiol. Opt. 65, 571–579. Fowler, C. W. and Sullivan, C. M. (1988). Varifocal spectacle lens surface power measurement. Ophthalm. Physiol. Opt. 8, 231–233. Fowler, C. W. and Sullivan, C. M. (1989). A comparison of 3 methods for the measurement of progressive addition lenses. Ophthalm. Physiol. Opt. 9, 81–85. Fowler, C. W. and Sullivan, C. M. (1990). Automatic measurement of varifocal spectacle lenses. Ophthalm. Physiol. Opt. 10, 86–89. Illueca, C., Vazquez, C., Hernandez, C. and Viqueira, V. (1998).
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The use of Newton’s rings for characterising ophthalmic lenses. Ophthalm. Physiol. Opt. 18, 360–371. Kafiri, O., Keren, E., Kreske, K. M. and Zac, Y. (1988). Moire´ deflectometry with a focused beam: Radius of curvature, microscopy and thickness analysis. Appl. Opt. 27, 1383–1385. Keren, E., Berman, R., Hochner, M. 1996. An optical method for mapping the power and cylinder of multifocal progressive lenses. Private communication. Keren, E., Kreske, K. M. and Kafiri, O. (1988). Universal method of determining the focal length of optical systems by Moire´ deflectometry. Appl. Opt. 27, 1383–1385. Keren, E., Zac, Y., Nabeth, F., Kreske, K. M. and Livnat, A. (1992). Quantitative criteria for determining the quality of ophthalmic lenses. Current developments in optical design and optical engineering II. In: Proc. SPIE, 1752, (eds Robert E. Fischer and Warren J. Smith), 264–273. Kreske, K. M., Keren, E. and Kafiri, O. (1988). Moire´ deflectometry — Applications to lens analysis. 6th Mtg in Israel on Optical Engineering. In: Proc. SPIE, 1038, (eds Rami Finkler and Joseph Sjamir), 92–99. Liu, L. R. (1994). Contour mapping of spectacle lenses. Optom. Vis. Sci. 71, 265–272. Maitenaz, B. (1966). Four steps that led to varilux. Am. J. Optom. Arch. Am. Acad. Optom. 43, 441–450. Mohr, W. (1989). Interferometry and progressive lenses. Optometrie 1989 (2), 31–35. Nakano, Y., Ohmura, R. and Murata, K. (1990). Refractive power mapping of progressive power lenses using Talbot interferometry and digital image-processing. Opt. Laser Technol. 22, 195–198. Rosenblum, W. M., O’Leary, D. K. and Blaker, W. J. (1992). Computerised Moire´ analysis of progressive addition lenses. Optom. Vis. Sci. 69, 936–940. Sheedy, J. E., Buri, M., Bailey, I. L., Azus, J. and Borish, I. M. (1987). Optics of progressive addition lenses. Am. J. Opt. Physiol. Opt. 64, 90–99. Simonet, P., Papineau, Y. and Lapointe, R. (1986). Peripheral power variations in progressive addition lenses. Am. J. Optom. Physiol. Opt. 63, 873–880.
PII: S0275-5408(99)00105-2
Optical Fourier filtering for whole lens assessment of progressive power lenses T. Spiers and C. C. Hull Applied Vision Research Centre, Department of Optometry & Visual Science, City University, 311–321 Goswell Road, London EC1V 7DD, UK Summary Four binary filter designs for use in an optical Fourier filtering set-up were evaluated when taking quantitative measurements and when qualitatively mapping the power variation of progressive power lenses (PPLs). The binary filters tested were concentric ring, linear grating, grid and “chevron” designs. The chevron filter was considered best for quantitative measurements since it permitted a vernier acuity task to be used for measuring the fringe spacing, significantly reducing errors, and it also gave information on the polarity of the lens power. The linear grating filter was considered best for qualitatively evaluating the power variation. Optical Fourier filtering and a Nidek automatic focimeter were then used to measure the powers in the distance and near portions of five PPLs of differing design. Mean measurement error was 0.04 D with a maximum value of 0.13 D. Good qualitative agreement was found between the iso-cylinder plots provided by the manufacturer and the Fourier filter fringe patterns for the PPLs indicating that optical Fourier filtering provides the ability to map the power distribution across the entire lens aperture without the need for multiple point measurements. Arguments are presented that demonstrate that it should be possible to derive both iso-sphere and iso-cylinder plots from the binary filter patterns. 䉷 2000 The College of Optometrists. Published by Elsevier Science Ltd. All rights reserved.
Single vision lenses, bifocals and trifocals are easy to verify using standard focimetry since they have clearly defined regions of uniform power (ignoring aberrations and image shifts). Progressive power lenses (PPLs), by their very nature, have power that varies across the aperture. This seems to imply that mapping the spherical power across the surface of the lens will be sufficient to characterise its optical properties. However, the aspheric nature of a PPL leads to significant astigmatism, distortion and other aberrations particularly in the transition zones. Many authors have therefore used multiple point focimetry, which allows mean sphere, cylinder and cylinder axis to be obtained for a grid of points across the PPL aperture (Simonet et al., 1986; Sheedy et al., 1987; Atchison, 1987; Diepes and Tameling, 1988; Fowler and Sullivan, 1988, 1989, 1990; Atchison and Kris, 1993). All of these techniques are time consuming and Fowler and Sullivan’s attempt to automate the scanning of a PPL across the stop of an electronic focimeter needed 80 min to complete an assessment of 798 points, although the time taken nowadays is likely to be of the order of several minutes with modern computers and data logging equipment (Fowler and
Introduction Progressive power lenses (varifocals) first became commercially available to help presbyopes in the 1960s with the development by Maitenaz of the Varilux I (Maitenaz, 1966). However lenses with a progressive power variation date back to the early part of this century according to Bennett (1973). There is now a large number of different designs on the market and it is difficult to make comparisons between them. This is partly because the optical assessment of these non-rotationally symmetric strong aspheric lenses is not easy and is not part of standard test procedures. In fact, a survey carried out by us at the start of this work demonstrated that none of the six major progressive power lens suppliers in the UK currently have the facility to measure/ verify these lenses (survey carried out November 1996). Received: 26 March 1999 Revised form: 4 November 1999 Accepted: 15 November 1999 Correspondence and reprint requests to: C. C. Hull, Tel.: ⫹ 44-171-4778339.
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Figure 1. Arrangement of components in an optical Fourier filtering set up. The test lens has a “focal length” ftl at point B. The Fourier Transform lens, of focal length f2, images the lens under test on to the observation screen. Superimposed on this image is a distorted pattern of the binary filter fringes. For point B on the test lens, the fringe at point P in the Fourier plane is imaged at a height yos on the observation screen.
Sullivan, 1990). A review of the ability of modern measurement systems to measure the “wearer” power of progressive power lenses has been provided by Bertrand (1998). Alternative techniques have also been described including interferometry and Moire´ methods (Mohr, 1989; Nakano et al., 1990; Rosenblum et al., 1992; Keren et al., 1996; Illueca et al., 1998), beam deflection (Castellini et al., 1994) and optical Fourier filtering (Liu, 1994). All of these methods have the advantage of entire lens testing with the exception of the modified Hartman test (Castellini et al., 1994), which is a beam deflection method similar to that used in the Humphrey lens analyser. The methods reported have varied in their implementation. A Moire´ system developed by Rosenblum, O’Leary and Blaker (Rosenblum et al., 1992) used image capture and digital image subtraction to generate Moire´ fringe patterns. However, it is possible to generate the Moire´ fringe patterns directly as has been shown by several other authors (Kafiri et al., 1988; Keren et al., 1988, 1992; Kreske et al., 1988; Nakano et al., 1990). More traditional optical test methods such as Newton’s rings between a test plate and a lens surface (Illueca et al., 1998) or Mach–Zehnder interferometry (Mohr, 1989) have also been applied. The former method has the disadvantage of producing a very narrow fringe spacing, particularly for the non-rotationally symmetric strongly aspheric PPLs we are interested in here, whereas the latter requires compensating lenses and a reference lens and is therefore more suited to production testing. Essilor have recently developed a variation of the Ronchi test to measure the surface profile of PPLs indirectly (Bertrand, 1998), although no data from actual measurements has been presented to the authors’ best knowledge. Optical Fourier filtering has received little attention in the literature but is inherently simple and avoids most of the pitfalls of the other techniques. The aim of this paper is to examine the design of binary filters for entire lens testing of PPLs using optical Fourier filtering and to present some initial results on measurement accuracy and the ability
to assess the entire lens power distribution with this technique. Theory Figure 1 shows the arrangement of the components in an optical Fourier filtering set up. The lens under test is placed at a distance ⫺2f2 from the Fourier transform lens where f2 is the second focal length of the Fourier transform lens. A binary filter is placed in the Fourier (back focal) plane of the transform lens and an observation screen is placed at a distance 2f2 from the transform lens. This system provides an image of the lens on the observation screen with a magnification of ⫺1 and superimposes on it the distorted pattern of the binary filter. We shall first explain the theory behind the Fourier filter pattern on the observation screen for a single vision lens and then see how the theory is readily extended to all lenses. The ray shown in Figure 1 is incident on the test lens at a height ytl above the optical axis and is therefore deviated through an angle u where
tan θ =
ytl : ftl′
1
If the binary filter has a spatial period of I then let the ray after passing through the transform lens strike the filter at point P, which is at a height nI in the Fourier plane where n is a decimal value. From elementary geometrical optics all rays incident on the transform lens at angle u will be imaged to point P and hence an alternative expression for tan u is given by
tan θ =
nI : –f2′
2
Equating the right-hand sides of Equations (1) and (2) and recasting in terms of the powers of the test lens, Ftl and
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Figure 2. Arrangement of components along the optical bench in the Fourier filtering set up described in this paper. S is a He–Ne laser (l 632.8 nm), SF a spatial filter to clean and expand the beam, CL an aberration-controlled doublet to collimate the beam, OL is the ophthalmic lens under test, TL the transform lens (another aberrationcontrolled doublet), FF the binary Fourier filter and OS a ground glass observation screen. The separation of the components is as shown in Figure 1.
transform lens, F2, we find that the power of the test lens is given by Ftl
⫺F2 nI : ytl
3
where ytl is the only value that can not be directly measured. However, since the test lens is imaged on to the observation screen with a magnification of ⫺1, the position on the observation screen yos ⫺ytl hence Ftl
F2 nI : yos
4
Rearranging and differentiating Equation (4) yields dyos F I 2 Ftl dn
5
and setting dn 1 gives the relationship between the fringe spacing in the image (dyos) and the power of the test lens as Ftl
F2 I : dyos
6
Equation (6) demonstrates that the fringe interval at the observation screen can be used to find the local power of the test lens. For both positive and negative lens powers the fringe spacing is inversely related to the test lens power. This highlights a minor limitation in the method; for a symmetrical filter, the measured fringe spacing will be the same for both a ⫹2 D lens power and a ⫺2 D lens power. However, this can easily be overcome using a filter with some asymmetry or orientation specific features incorporated into its design. We shall return to this in the Methods section when optimum filter designs are considered. Experimental method Figure 2 shows the experimental arrangement for the Fourier filtering system used to produce the results presented in this paper. Light from a He–Ne laser (l 632.8 nm) was first passed through a spatial filter to remove any spatial impurities caused by diffraction effects
and to provide a rapidly diverging point source for the collimating lens (CL). The collimating lens was an aberration controlled doublet of back vertex power 3.21 D and diameter 58 mm. The optical performance of this lens closely approximates the Abbe Sine Condition when working at infinite conjugate as is the case here. The collimating lens was first verified on a Nidek LM870 automatic focimeter that had been checked against reference lenses, which had in turn been calibrated by the National Physical Laboratory. To aid accurate alignment of components along the optical axis the lens had its centre marked. The degree of collimation was tested by placing a 1 mm diameter pinhole just after the collimating lens. The collimating lens was then moved longitudinally relative to the spatial filter until the size of the image of the pinhole at a distance of 1.5 m from the collimating lens was equal to the original pinhole size. The alignment of the optical components along the optical bench was carried out as follows. First, the observation screen (a ground glass plate) was added and the image of the collimating lens centre marked on the screen. The transform lens, again an aberration controlled doublet of back vertex power 7.19 D, was placed on the optical bench and its alignment adjusted to make its centre mark aligned with the mark on the collimating lens. This was sufficient to define the optical axis of the system. The relative longitudinal position of the optical components were then adjusted using a distance bar, which had been measured with a travelling microscope (resolution 0.01 mm), and the vernier scales on the optical bench mounts (resolution 0.1 mm) to agree with the component separations shown in Figure 1. All filters were produced by first designing them using a computer graphics package and then printing them on to A4 paper before reducing them using a Polaroid slide maker onto 35 mm slide transparencies. With this technique a reduction factor of about 8.75 was achieved and good filter quality was maintained. Concentric ring, linear, grid and “chevron” designs were developed during the course of this work for the reasons given in the Results section below. Figure 3 illustrates the form of these binary filters.
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Ophthal. Physiol. Opt. 2000 20: No 4 Previously the filter spacing had been measured using a travelling microscope and was found to within ^0.004 mm (^1 standard error). Five readings of the filter fringe spacing were recorded for each trial lens and a calibration graph of dyos/I against 1/Ftl plotted. The gradient of this graph gives the equivalent power of the transform lens F2, which is needed to calculate the unknown lens power. Five different designs of PPL were obtained from Sola (UK) Ltd (XL, XL Gold, Graduate, Graduate Gold and Percepta). All lenses had a plano distance zone and a ⫹2 D near zone. These lenses were evaluated for their power in the distance and near zones using the Fourier filtering system with a chevron filter and were also qualitatively evaluated for aberrations in the transition zones.
Figure 3. The four binary Fourier filter designs tested: (a) concentric ring, (b) linear, (c) grid and (d) “chevron” designs.
Results Fourier filter designs
The Fourier filtering measurement system, with a chevron filter, was first calibrated against known test lenses. These were 20 trial case lenses with powers in the range ^12 D which had been measured on a Nidek LM870 automatic focimeter. The Nidek focimeter had previously been checked against our standard lenses, which in turn had been calibrated by the National Physical Laboratory. The error between the Nidek reading and the standard lenses was within 1% for powers in the range ^12 D and reproducibility in the measurements was ^0.016 D (95% confidence limits). The Nidek readings were therefore taken as accurate for the trial lenses used for calibration. For each trial lens the chevron spacing was measured using an electronic micrometer which had its RS 232 output connected to a PC.
The four filter designs (Figure 3) were tested to assess, initially, their qualitative ability to display the power distribution of a lens. Figure 4(a) and (b) demonstrates the patterns obtained through a single vision spherical lens and a toric lens, respectively, using a filter consisting of concentric rings. Figure 4(a) was generated using a ⫺10 D spectacle lens. Although the rings are concentric, peripheral aberrations are evident from the narrowing of the ring spacing away from the optical axis. This was probably due to an aspheric design or spherical aberration. Figure 4(b) shows a toric lens, specification ⫺1.50/⫺0.50 × 180⬚, which produces different fringe spacings along the two principal meridians and hence produces elliptical fringes. Figure 4 solely demonstrates the ability of Fourier filtering
Figure 4. Fourier filter fringe patterns using a concentric ring filter with (a) a single vision spherical lens and (b) a single vision toric lens. The elliptical distortion of the rings is clearly visible for the astigmatic lens.
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Figure 5. A bifocal lens tested with a grid filter. The difference in grid spacing between the distance and near portions of the lens clearly demonstrates the difference in power. This lens is astigmatic and (a) demonstrates the distortion of the grid squares into parallelograms due to the astigmatism. Rotation of the lens to orientate the grid lines along the principal meridians reduces the parallelograms to rectangles whose side lengths are proportional to the powers in the principal meridians. The angular position of the lens indicates the astigmatic axes.
to display the power variation across the entire lens aperture. It has no other advantage for measuring the power of single vision or bi-focal/tri-focal lenses. A grid filter was also evaluated and Figure 5 demonstrates its use in assessing a toric bi-focal lens. Figure 5(a) is the grid pattern with the lens aligned vertically. The difference in power between the distance and add portion of the lens is clearly seen from the difference in the grid spacings. However, the grid has been skewed by the presence of astigmatism. Rotation of the lens can elim-
inate this effect and make the grid rectangular [Figure 5(b)]. The angle of rotation of the lens determines one of the principal meridians and measurement of the fringe spacing of the grid along the long and short dimensions of the rectangle can determine the power along each principal meridian (see Quantitative measurements of this Results section). Both grid and linear filters were initially used for the qualitative evaluation of a PPL that had a plano distance zone and a ⫹2 D near zone. Figure 6(a) and (b) shows
Figure 6. The Fourier filter fringe pattern from a PPL measured with (a) a grid filter and (b) a linear filter. The authors consider that the linear filter gives a clearer impression of the aberrations in the transition zone. However, the grid filter is more amenable to quantitative analysis (see text for details).
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Figure 7. Comparison between manufacturer’s supplied iso-cylinder plots and the fringe patterns generated using optical Fourier filtering with a linear binary filter. The iso-cylinder plots are nominal for a lens design and are not specific to the lens tested. All five PPLs were kindly provided by Sola (UK) Ltd with plano distance zones and ⫹2 D near zones. The designs tested were (a) XL, (b) XL Gold, (c) Graduate, (d) Graduate Gold and (e) Percepta. There is good qualitative agreement between the Fourier filter fringe patterns and the iso-cylinder plots.
Optical Fourier filtering for whole lens assessment of progressive power lenses: T. Spiers and C. C. Hull the fringe patterns obtained from this PPL using (a) a grid filter and (b) a linear filter. The distortions of the linear filter pattern appear to give a clearer qualitative impression of the power distribution of the lens. For the linear filter, no fringes are apparent in the distance portion of the lens, which has no power. The fringes appear as vertical lines within the near zone whereas in the transition zone there is considerable distortion of the fringes. Linear filters do not permit resolution of the sphere and cylinder component together with its axis whereas a grid filter does. Arguments as to how this can be achieved are given in the Discussion. The linear filter was finally used to assess qualitatively the five sample lenses provided by Sola (UK) Ltd for this study. Figure 7 presents these results alongside the isocylinder plots provided by Sola where Sola’s plots have been obtained using a modified Humphrey Lens analyser from a method described by Atchison and Kris (1993). Although the Fourier filter patterns do not represent iso-cylinder information, any distortion of the fringes from their vertical orientation in the binary filter is caused by astigmatism (spherical power would not alter the orientation of the fringes, just their spacing). More specifically, the amount of distortion of the lines is due to not only the magnitude of the cylinder component but also its axis. It is therefore reasonable to assume that increasing amounts of astigmatism will cause an increase in the distortion of the fringes in the binary filter pattern since the cylinder axis, although not constant, must change continuously across the lens surface. This latter point is demonstrated by the iso-cylinder plots presented by previous authors (see, for example, Simonet et al., 1986; Sheedy et al., 1987; Atchison, 1987), which all show that, within the transition zones, the cylinder axis does not change significantly. It is therefore reasonable to compare the iso-cylinder plots supplied by the manufacturer and the fringe patterns produced by Fourier filtering. In Figure 7 there is a good qualitative agreement between the Fourier filter images and the iso-cylinder plots provided by the manufacturer. Fourier filtering clearly demonstrates the difference between a “hard” design such as the Graduate [Figure 7(c)], where the distance and near zones are relatively large with consequently large amounts of aberration in the transition zones, and “soft” designs such as the XL Gold [Figure 7(b)], which has noticeably smaller near and distance zones and hence the aberrations in the transition zone are more gradual. Quantitative measurements Linear and grid filters are both capable of displaying the power variation across the entire aperture of a lens although the grid filter is the only one that can resolve the spherical and cylindrical components. However, these two filter designs have two disadvantages. Firstly it is difficult to
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Figure 8. Calibration graph demonstrating the linear relationship between the ratio of the measured fringe spacing on the observation screen to the actual fringe spacing in the filter and the focal length of the test lens. This relationship is predicted by Equation (6) and is used to determine empirically the calibration constants needed to calculate unknown lens power.
determine the prism power of the lens being measured. Secondly, linear and grid filters do not convey any information about the sign of the power since they contain no orientation specific features. Liu (1994) has suggested using the orientation of just two reference marks on the target. However, this does not allow for any changes in the sign of the power across the lens aperture. A new filter was designed using a repeated chevron pattern [Figure 3(d)] that had the following advantages. Firstly, the measurement distance for this design was between the apices of the chevrons making the positioning of the graticule line a vernier alignment task. Secondly, the sign of the power was given by the orientation of the chevrons and distortions of the lines of chevrons indicated aberrated regions of the lens. This filter design was therefore used to take quantitative measurements on the lenses. The calibration graph (Figure 8) demonstrates the expected linear relationship between 1=F and dyos/I. After performing a weighted least squares line fit on the data, the power of the transform lens, F2, which is given by the gradient of the graph, was found to be 6.569 D (95% confidence limits 6.544–6.593 D). The goodness of fit to the theory outlined above is further demonstrated by an adjusted R 2 value of 1.0 and the fact that the intercept of the graph is not significantly different from zero (t-test; P 0.1015). This value for the power of the transform lens was used in all subsequent calculations of test lens power as was the y-axis intercept which was found to be c 0.0124. Thus Equation (6) for the test lens power becomes: Ftl
F2 : dyos =I ⫺ c
7
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Table 1. Power in Dioptres of the distance and near zones of five designs of PPL provided by Sola (UK) Ltd measured using a Nidek LM 870 automatic focimeter and optical Fourier filtering with a chevron filter (see text). All PPLs are nominally plano/⫹2.00 D and the errors quoted are ^1 SD (n 5) Fourier filtering Lens name
Near (D)
XL XL Gold Graduate Graduate Gold Percepta
1.91 ^ 0.01 2.06 ^ 0.01 2.16 ^ 0.01 1.94 ^ 0.05 2.14 ^ 0.06
Nidek focimeter
Distance Near (D) (D) 0.00 0.00 0.00 0.00 0.00
1.89 2.05 2.06 1.89 2.01
Distance (D) ⫺0.01 0.03 ⫺0.01 0.02 0.01
Table 1 summarises the results of measuring the distance and near zones of the five Sola PPLs using both Fourier filtering and the Nidek focimeter. No fringes were visible in the distance zone using Fourier filtering and so the power was recorded as zero. This demonstrates a possible weakness of Fourier filtering, which we shall return to in the discussion. Agreement between the values for the near zone are all within 0.12 D with the exception of one case where the difference was 0.13 D. However, the standard deviations when measuring the near zone are so small that all Fourier filtering readings were statistically different from the Nidek values. Possible reasons for this are discussed below.
Discussion It has been demonstrated that Fourier filtering offers a clear advantage in mapping the power variation over the entire lens diameter without the need for scanning or making multiple measurements. However, the quantitative measurements presented were difficult to make manually, suggesting that some form of automation, most probably using digital image analysis of the fringe patterns, is needed. Design of the Fourier filters is therefore of great importance and this study has demonstrated that good qualitative agreement with iso-cylinder plots is possible for entire lens aperture testing and that spherical power measurements with a high degree of accuracy can be achieved with appropriate filters. In the Results section, it was noted that linear filter patterns do not provide sufficient information to resolve the axis and cylinder component of the lens under test whereas a grid filter does. The grid filter permits an analysis, analogous to the four ray method used in the Humphrey Lens Analyser, to be performed by utilising the four corners of a square on the grid. It is then possible to resolve sphere, cylinder and cylinder axis for a localised area on the PPL. Iso-sphere and iso-cylinder plots can then be recovered from the Fourier filter fringes by using a digital camera and image processing system to analyse the filter patterns produced. Analysis of fringe patterns is routinely carried out in the optics industry for lens metrology.
Another advantage of optical Fourier filtering is that any features marked on the lens surface are also imaged on the screen superimposed on the Fourier filter fringes. This is clearly evident in Figures 6 and 7 where the fitting cross, distance design reference point and near design reference point are clearly visible superposed on the fringe patterns. However, widely differing lens powers require the use of different Fourier filters because of the inverse relationship between lens power and Fourier filter fringe spacing [Equation (6)]. This problem was particularly evident with low power lenses where a filter with high spatial frequency was needed to allow small changes in power to be measured. The only practical solution would be to have a filter wheel in the optical Fourier filtering system that allows different filters to be selected. A less obvious, but potentially more serious disadvantage related to this is the dichotomous filter requirements when measuring high power lenses with small power variations across their aperture: high power lenses require Fourier filters with coarse spatial detail due to the minification of the final image whereas small changes in power require filters of high spatial frequency. This latter effect has been demonstrated by our inability to measure low powers in the distance portions of PPLs even with the finest filters that have been fabricated in this study. Only a fully quantitative system, which can analyse the filter patterns and derive isosphere and iso-cylinder power variation, will determine if this is a serious drawback. It may then be possible to adapt the system to measure power variation with respect to the best sphere as follows. A coarse filter can be used to determine the absolute power and then the source vergence changed to compensate the absolute power, a technique known as optical biasing. A fine filter can then be used to look at small power variations across the aperture. However, with the strongly aspheric nature of the PPLs and current evidence from iso-cylinder plots, this may not be necessary. Several authors have argued that it is necessary to map the lens power with respect to the vertex sphere (Simonet et al., 1986; Atchison, 1987; Bourdoncle et al., 1992; Atchison and Kris, 1993), although others have shown that the difference between measurements made with respect to the centre of rotation of the eye and with the lens static is small (Fowler and Sullivan, 1989). At present the optical Fourier filtering system described here does not meet this requirement since the source is collimated for all points on the lens surface and no attempt is made to compensate for the rotation of the eye behind the lens. It is not immediately apparent to the current authors how a Fourier filtering system can be modified in this respect. Acknowledgements The authors would like to thank Mr Alick Taylor of Sola (UK) Ltd for providing the lenses used in this study, Mr B. Staples of Sola International Holdings Ltd for providing
Optical Fourier filtering for whole lens assessment of progressive power lenses: T. Spiers and C. C. Hull technical information and Mr S.G.A. Smele of Mitutoyo (UK) Ltd for providing the RS 232 compatible digital readout vernier gauge. We would also like to thank Michael Burke for photographing the Fourier filter patterns that have been scanned for the figures in this paper. References Atchison, D. A. (1987). Optical performance of progressive power lenses. Clin. Exp. Optom. 70, 149–155. Atchisn, D. A. and Kris, M. (1993). Off-axis measurements of a plano distance power progressive addition lens. Ophthalm. Physiol. Opt. 13, 322–326. Bennett, A. G. (1973). Variable and progressive power lenses: 4. Manuf. Opt. Int. 26, 137–144. Bertrand, P. (1998). Wearer power measurement of progressive addition lenses. In: Vision Science and Its Applications, vol. 1, OSA Technical Digest Series, Optical Society of America, Washington, DC, pp. 180–183. Bourdoncle, B., Chauveau, J. P. and Mercier, J. L. (1992). Traps in displaying optical performance of a progressive-addition lens. Appl. Opt. 31, 3586–3593. Castellini, C., Francini, F. and Tiribilli, B. (1994). Hartmann test modification for measuring ophthalmic progressive lenses. Appl. Opt. 33, 4120–4124. Diepes, H. and Tameling, A. (1988). Comparative investigations of progressive lenses. Am. J. Optom. Physiol. Opt. 65, 571–579. Fowler, C. W. and Sullivan, C. M. (1988). Varifocal spectacle lens surface power measurement. Ophthalm. Physiol. Opt. 8, 231–233. Fowler, C. W. and Sullivan, C. M. (1989). A comparison of 3 methods for the measurement of progressive addition lenses. Ophthalm. Physiol. Opt. 9, 81–85. Fowler, C. W. and Sullivan, C. M. (1990). Automatic measurement of varifocal spectacle lenses. Ophthalm. Physiol. Opt. 10, 86–89. Illueca, C., Vazquez, C., Hernandez, C. and Viqueira, V. (1998).
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The use of Newton’s rings for characterising ophthalmic lenses. Ophthalm. Physiol. Opt. 18, 360–371. Kafiri, O., Keren, E., Kreske, K. M. and Zac, Y. (1988). Moire´ deflectometry with a focused beam: Radius of curvature, microscopy and thickness analysis. Appl. Opt. 27, 1383–1385. Keren, E., Berman, R., Hochner, M. 1996. An optical method for mapping the power and cylinder of multifocal progressive lenses. Private communication. Keren, E., Kreske, K. M. and Kafiri, O. (1988). Universal method of determining the focal length of optical systems by Moire´ deflectometry. Appl. Opt. 27, 1383–1385. Keren, E., Zac, Y., Nabeth, F., Kreske, K. M. and Livnat, A. (1992). Quantitative criteria for determining the quality of ophthalmic lenses. Current developments in optical design and optical engineering II. In: Proc. SPIE, 1752, (eds Robert E. Fischer and Warren J. Smith), 264–273. Kreske, K. M., Keren, E. and Kafiri, O. (1988). Moire´ deflectometry — Applications to lens analysis. 6th Mtg in Israel on Optical Engineering. In: Proc. SPIE, 1038, (eds Rami Finkler and Joseph Sjamir), 92–99. Liu, L. R. (1994). Contour mapping of spectacle lenses. Optom. Vis. Sci. 71, 265–272. Maitenaz, B. (1966). Four steps that led to varilux. Am. J. Optom. Arch. Am. Acad. Optom. 43, 441–450. Mohr, W. (1989). Interferometry and progressive lenses. Optometrie 1989 (2), 31–35. Nakano, Y., Ohmura, R. and Murata, K. (1990). Refractive power mapping of progressive power lenses using Talbot interferometry and digital image-processing. Opt. Laser Technol. 22, 195–198. Rosenblum, W. M., O’Leary, D. K. and Blaker, W. J. (1992). Computerised Moire´ analysis of progressive addition lenses. Optom. Vis. Sci. 69, 936–940. Sheedy, J. E., Buri, M., Bailey, I. L., Azus, J. and Borish, I. M. (1987). Optics of progressive addition lenses. Am. J. Opt. Physiol. Opt. 64, 90–99. Simonet, P., Papineau, Y. and Lapointe, R. (1986). Peripheral power variations in progressive addition lenses. Am. J. Optom. Physiol. Opt. 63, 873–880.