GeoTOP project: geometric measurements

This report is concerned with measurements of micro- and macro-geometry parameters of plastic lenses and moulding metal inserts, with the aim of establishing correlation between sizes, form and texture parameters measured at INRiM, and optical properties measured at Luxottica. This study was performed within the framework of the industrial project between INRiM and Luxottica named GeoTOP (Geometry To Optical Performance). The plastic lenses are produced by injection moulding with two mating metallic inserts mounted on two mould halves. The investigation had to trade-off between diversity of moulding inserts to excite the effect of their micro- and macro-geometries on the optical performance, and the availability of such inserts. It required diverting the inserts and the moulding machine from ordinary production and had to be limited. A set of 4 different insert pairs was investigated, each producing 3 lenses for a total of 12 lenses overall. The macro-geometry was measured with a CMM (Coordinate Measuring Machine) and the micro-geometry with a profilometer at INRIM. The optical performance was measured with conventional equipment and procedures at Luxottica. This report focuses on the geometric measurements and their correlation to the optical performance. The geometric measurements were challenged by the spherical shape of the inserts and lenses: a concave or convex cap for the insert pairs and two nearly concentric concave-convex caps for the lenses. The caps exhibited a small central angle (±25°), which posed severe ill-conditioning in the determination of the geometrical parameters and particularly of the sphere radii. The geometrical measurements (inserts and lenses, with the CMM and the profilometers) had to be referred to a common coordinate system (CSY), to couple the measured points on inserts and lenses. Spheres are rotation invariant about their centres (spherical invariance class, ISO 17450-1 [5]), that is, 3 angular degrees of freedom (DoF) cannot be established from spheres and other geometrical features had to be considered for constraining the CSY in full. Two DoF were constrained (spatial orientation) with the plane of the cap edge; one (planar orientation) with either two diametrically opposed protrusions from the lens edge – nicknamed “nose” and “foot” – or their correspondent cuts in the moulds holding the inserts. There were five sets of geometrical measurements: (1-2) two mould halves each holding a set of either concave od convex inserts (done with the CMM); (3) 12 lenses (CMM); (4) 12 lenses (profilometer); and (5) 8 inserts (profilometer). The sets could not be carried out but with different coordinate systems, which had to be reconciled. The two mould halves (1-2) were through the mating sets of four segments laid out as a cross, aligning in the closure. The lenses (3) were fixtured to a holder specially designed and manufactured at INRIM incorporating a set of five contacting pins that effectively served as datums for alignment. To reconcile this CSY with 1-2, the positions of the pins were determined by simulation during the measurement of one of the mould half, and mathematical rototranslations from the pins’ to the insert’s coordinate systems were evaluated, stored and then used to reconcile the CSY of the lenses. In general, profilometric measurements are relative to a reference plane and then insensitive to its three DoF (one translational and two angular, the spatial alignment), which cancel out when associating the reference plane. The planar orientations and the centre positions (4) were established with reference to points probed on the edge of the lenses and of the nose and foot. The inserts showed key cuts on their sides, mating corresponding keys in the mould. In the measurement with the profilometer, the key cuts were aligned to a profilometer axis through a special holder designed for the purpose, which made fiducials available in view of the profilometer (5). The measurement of the mould halves and the lenses were made with a CMM (Leitz PMM-C 12107). The mould halves were measured one after the other with replacement on the CMM table. The workpiece CSYs were taken in a way to simulate a common one when the halves are closed. Each lens was measured with the CMM when fixtured to the specially designed holder, in a vertical position, that is, with a horizontal optical axis. This allowed to probe both faces of the lens without re-fixturing, enabling measurement of the entire lens in a native single CSY. 3 A special holder was designed and manufactured at INRiM by 3D printing to measure either the concave or convex face of the lenses with the profilometer, which accommodated the lenses in their convex/concave positions. Profilometry measurements were performed with a 20 objective in coherent scanning interferometry (CSI) mode. The measurands examined were morphological parameters, such as Power Spectral Density (PSD), and roughness and texture parameters, according to ISO 21920 [8] and ISO 25178 [6], respectively. The optical properties measured at Luxottica were the lateral resolution, the optical power and the astigmatism, by means of a resolution test chart target, and the prismatic power by means of a viewfinder target. The measurements were all performed successfully. The techniques used at INRiM for data analysis ranged from classical mathematical classification methods to modern statistical machine learning models. Data was clustered and quantitative correlations between optical and geometric parameters were found by using supervised learning regressions. The following conclusions could be drawn from the analysis: 1. A method has been developed and is now available for measuring macro- and micro-geometry of lenses and moulds and to correlate the results. A repetition of the exercise on a larger experimental scale is now possible with a consolidated procedure. 2. The macro-geometry showed far more influence than micro-geometry on the optical parameters. This may have been due to the limited range of micro-geometry parameter values available: all surfaces were glossy with parameter values much smaller than the light wavelength (40-50 nm vs 390-760 nm). The glossy surface finishing may not be needed for the lenses’ performance and the current tight requirement could be relaxed with little or no performance loss1. Furthermore, most measured lenses were uncoated, whereas the standard products are coated. The coating likely affects the lens surface texture, to the point that the native one may be not so relevant. 3. The macro-geometry measurement is inevitably impaired by the calotte form of lenses and inserts. The limited angular portion of spherical surface (±22.3° about the pole resulting in 0.47 sr or 3.7 % of the whole sphere) ill-conditions the derivation of the geometrical parameters of the spheres. The uncertainty of the centre position off the optical axis (x,y) is 11 times larger than it would were a full hemisphere available for probing with the same probing density (number of points per unit area). Similarly, the uncertainties are 49 and 82 times larger for the centre position along the optical axis (z) and the radius, respectively [13]. Fortunately, the accuracy of the used CMM is high enough not to impair this study in spite of the 1 to 2 orders of magnitude loss due to ill conditioning. 4. The found correlation of the macro geometry with the optical performance was unexpected. The resolution showed correlation with nearly all macro-geometry parameters (centres’ positions and radii of the convex and concave surfaces). The optical power showed substantially different correlations between convex and concave parameters, whereas the prediction was for a combination of the two. The astigmatism showed mild correlation to the convex radius, whereas expectation was for form or lateral parameters such as centres’ horizontal positions. The prismatism correlated to the convex radius but not with the concave one, whereas the expectation was for correlation with horizontal parameters; in particular, the eccentricity (nominally null distance of the centres in the horizontal plane) showed no correlation at all. Two possible explanation of this deviation from the expected behaviour are possible: either the available samples (4 insert pairs) were too few and not diverse enough to draw conclusions, or technological factors other than the macro- and micro-geometry have influence. 5. The form deviation maps of all inserts followed similar patterns, different for concave and convex inserts. The convex showed different magnitudes (1.6 μm to 5.1 μm) but very similar shapes, two being oriented 45° apart from the others. The inserts had been manufactured by different suppliers, which made manufacturing difficult to blame. More likely, the fixturing of the inserts to the mould may have deformed them: this would explain the variable amount (depending on how tight the clamping was 1 The finishing may be due to technological reasons of to the moulding process, which are not considered in this report. 4 screwed) and the constant orientation (aligned to the mould). Another possible explanation is the wear due to repeated injections, which always occurs in the same direction and affects the convex inserts more than the concave because the plastic inlets are in the convex mould half. 6. The measurement of lenses was made difficult by the limited stiffness of the lenses combined with the practical need of fixturing them at their edges only. The probing contacting forces (up to 0.5 N) and the clamping forces bent the lenses. The former was minimised by reducing the contacting force to a minimum and compensating the deformation by extrapolation to zero-force. The latter was minimised by design of the holder: the elastic elements pushing the lens onto the supporting pins were oriented and positioned so that the force lines were aligned to the calculated lens/pin contact points, so inducing harmless local compression rather than global bending. Non-contacting probing (e.g. optical) is recommended in a possible repetition of the exercise. This would eliminate the contacting force and allow a lighter and gentler fixturing released from the need of opposing the contacting forces. 7. The geometries of corresponding inserts and lenses aligned generally well, as expected. An exception was found for the concave inserts and the convex surface of the lenses: the radii differed 1 mm and so did the vertical separation of the concave and convex centres, so that the vertical positions of the poles exhibited negligible differences instead (effect of the correlation between vertical position of centres and radii). This anomaly was investigated in depth to exclude mistakes in the part programme and in the derivation of results, with no evidence found. This may suggest an independent technological issue instead, such as different injection behaviours in the two mould halves. 8. The sets of three lenses moulded with the same insert pair showed highly similar values of all macro- and micro-geometrical and optical parameters, proving very good reproducibility of the process.