Due to the fast development in the domain of communication and an ongoing trend of digitization and digitalization, manufacturing enterprises are facing important challenges in today's market environments: a continuing tendency towards reduction of product development times and shortened product lifecycles. In addition, there is an increasing demand of customization, being at the same time in a global competition with competitors all over the world. This trend, which is inducing the development from macro to micro markets, results in diminished lot sizes due to augmenting product varieties (high-volume to low-volume production) [1]. To cope with this augmenting variety as well as to be able to identify possible optimization potentials in the existing production system, it is important to have a precise knowledge of the product range and characteristics manufactured and/or assembled in this system. In this context, the main challenge in modelling and analysis is now not only to cope with single products, a limited product range or existing product families, but also to be able to analyze and to compare products to define new product families. It can be observed that classical existing product families are regrouped in function of clients or features. However, assembly oriented product families are hardly to find.
On the product family level, products differ mainly in two main characteristics: (i) the number of components and (ii) the type of components (e.g. mechanical, electrical, electronical).
Classical methodologies considering mainly single products or solitary, already existing product families analyze the product structure on a physical level (components level) which causes difficulties regarding an efficient definition and comparison of different product families. Addressing this
Freeform optical surfaces are a rapidly emerging design form, which allows new design freedom and opportunities to develop optical systems with better performance in a given volume or a significant volume reduction for a given optical function [1]. Starting in the 1980s, an evolution began from load controlled full aperture optics fabrication to increasing use of small tool processes using ultra-precision machines and displacement control (such as diamond turning and milling machines) or combinations of position and dwell time control (such as magnetorheological finishing and computercontrolled polishing). These processes enabled cost-effective fabrication of on-and off-axis aspheric optical surfaces. Further advances in these processes and in design enable use of optical surfaces with no axis of invariance on or off the part [2,3].
Manufacturing of state-of-the-art optics does not conform to the conceptual structures of mainstream production. Concurrent engineering, taught to mechanical engineers often in sophomore year in the USA (see for example [4]), is a foreign topic academically in most optics and physics faculties, although one that is practiced in some vertically integrated optics manufacturing organizations. A significant fraction of state-of-the-art optics are developed using sequential processes; "completed" optical designs are passed off to "opto-mechanical engineers" who may negotiate with the optical designers before turningoften --to small, specialized fabricators. The transition from systems of spherical and plano optics, dominantly produced by classical polishing processes, to aspheric and freeform optics is a driving force for change.
From the perspective of manufacturing, arrays of aspheric micro-optics and off-axis aspherics share many of the characteristics of freeform fabrication. The latter, however, pose additional metrology challenges, the topic of this paper.
Elements of optical systems comprising spherical and plano (flat) surfaces have an "optical axis: typically defined by the outside diameter of the part acting as a datum after "centering" (see for example [5]). Aspheric optics have an axis (on or off the part) defined by the prescription and typically realizable in measurement of the surface.
Freeform optical surfaces are a rapidly emerging design form, which allows new design freedom and opportunities to develop optical systems with better performance in a given volume or a significant volume reduction for a given optical function [1]. Starting in the 1980s, an evolution began from load controlled full aperture optics fabrication to increasing use of small tool processes using ultra-precision machines and displacement control (such as diamond turning and milling machines) or combinations of position and dwell time control (such as magnetorheological finishing and computercontrolled polishing). These processes enabled cost-effective fabrication of on-and off-axis aspheric optical surfaces. Further advances in these processes and in design enable use of optical surfaces with no axis of invariance on or off the part [2,3].
Manufacturing of state-of-the-art optics does not conform to the conceptual structures of mainstream production. Concurrent engineering, taught to mechanical engineers often in sophomore year in the USA (see for example [4]), is a foreign topic academically in most optics and physics faculties, although one that is practiced in some vertically integrated optics manufacturing organizations. A significant fraction of state-of-the-art optics are developed using sequential processes; "completed" optical designs are passed off to "opto-mechanical engineers" who may negotiate with the optical designers before turningoften --to small, specialized fabricators. The transition from systems of spherical and plano optics, dominantly produced by classical polishing processes, to aspheric and freeform optics is a driving force for change.
From the perspective of manufacturing, arrays of aspheric micro-optics and off-axis aspherics share many of the characteristics of freeform fabrication. The latter, however, pose additional metrology challenges, the topic of this paper.
Elements of optical systems comprising spherical and plano (flat) surfaces have an "optical axis: typically defined by the outside diameter of the part acting as a datum after "centering" (see for example [5]). Aspheric optics have an axis (on or off the part) defined by the prescription and typically realizable in measurement of the surface.
The ISO standard on preparation of drawings (ie specification) of optical elements and systems has separate parts for aspheric surfaces [6] and general (including freeform) surfaces [7]. It should be noted that the standard applies to optical elements as well as assemblies and systems. Hence, the designer's intent (if any) regarding assembly is not necessarily captured in an element drawing.
Since a freeform does not have an "optical axis", a "reference axis" is defined [7] as a "theoretical axis given by the optical designer which does not depend on the symmetries of the surface and usually represents the center of the optical path for the main function". The standard continues "… the position and orientation of the reference axis is defined by measurable references at and/or on the general surface…". Hence, according to the standard, acceptance of an element's surface shape is limited in part by the uncertainty in the realization of the coordinate system using fiducials and other references and the tolerances in positioning the surface with respect to the reference axis. Positional compensators (adjustments) allow optimization of the system wavefront error for both element placement and fabrication errors. These adjustments enable relaxation of tolerances on the optical surface at the price of increased system complexity.
One key difference between on-axis aspheric systems and freeforms is the limited ability with freeforms to use rotation of the optical elements about their reference axes to minimize rotationally varying system wavefront error arising from manufacturing errors in individual element surfaces. A related limitation arises in some optical methods of measuring surfaces. For tight tolerance rotationally invariant surfaces, rotations are used to separate errors in the part from errors in the test set-up in an analogous manner to roundness testing. This is not possible for freeforms.
Clearly concurrent engineeringspecifically concurrent optical design, design for manufacture, design for metrology, and design for assemblyis required for appropriate allocation of tolerances.
In the early 1990s some work was done to enable "snap together" aspheric optical systems, i.e. systems in which no adjustments are provided [8]. This approach was limited to IR systems, primarily by the tolerances associated with machining of locating features and the capabilities of the machine tools available. The absence of adjustments tightens the tolerances on surface form and location.
More recent advances in machine design, including 4-and 5-axis ultraprecision systems where coordinate axis turning and micromilling can be implemented in a single set-up, has resulted in revived interest in "snap together" systems (see [9,10] for example). Recent publications describe snap together freeform systems [11], multiple optical surfaces on a single substrate [12] and monolithic systems [13]. One attraction of two separate surfaces on a single substrate is that the relative position location accuracy is determined by the (small) error motions of the precision machine. However, thermal effects scale with the substrate size, not the element size.
Coordinate systems should be realizable both in manufacturing steps as well as metrologya key task in design for metrology. Further, design for metrology should be part of concurrent engineering that allocates tolerances based on system requirements and manufacturing and metrology capabilities.
One vision of concurrent engineering in advanced optics development would provide summary data to optical designers on the manufacturing capabilities integrated with optical design tools. For example, "soft" constraints in the optimization code might flag elements with apertures larger than can be fabricated or measured using equipment available in-house or tolerances tighter than the maximum permissible error on an available coordinate measuring machine.
A less ambitious approach, being developed within the Center for Freeform Optics (CeFO), is to develop a data hierarchy in which the capabilities of different metrology tools appropriate for measurement of form, mid-spatial frequencies (waviness) and surface finish of freeform optical surfaces. In addition to optics designers, the same data may be useful to fabricators. Target data characteristics include:
"Coherent": the same data representations (from standards where possible) are used for different types of instrument; "Stratified": layers of information, with active links.
The highest level data shows measurement technologies and capabilities to help down selection of approaches relevant to the most general description of the part to be tested. The lowest level gives detailed discussion of individual commercially available instruments and instruments in development, which could be used to measure the part under test; and "Curated": The source of the data used, at every level, will be reported. The user of the information can weigh manufacturer reported performance against data from other sources. For some of the generic instruments, examples are installed at CeFO sites.
Performance test data and experience on those instruments are reported and the source of the data cited. In some cases, newer models have been developed, and appropriate data from the manufacturer are given (and sources cited). This tool specific information on the capabilities of different instruments is akin to the Quality Information Framework (QIF) [14] although not planned to be integrated into enterprise management systems. The current implementation uses a text document (.docx or .pdf) with navigation links, viewed as a precursor to implementation in HTML.
Currently, there are 3 levels of information. Level 1 shows broad instrument capabilities by category (scanning white light interferometers (SWLI), contact profilometers, Fizeau interferometers, and coordinate measuring machines.
Basic capabilities (and more detailed information at lower levels) are shown on a "Freeform Optics Metrology Capability Diagram" (FOMCD). This is based on the approach pioneered by Stedman [e.g. 15, 16] using amplitudewavelength space (i.e. considering the optical surface prescription and topography in the Fourier domain). Notably, this representation is global; in some instruments better performance may be achieved over smaller apertures. Here we use "aperture" (projected maximum dimension of the optic under test) and "sag" (departure from the reference) which are more familiar to optical designers and optical fabricators and hence more appropriate for this use.
Note also that the FOMCD assumes smooth, continuous surfaces, especially for optical measurement methods. The FOMCD should be used with caution (if at all) when considering surfaces which give stronger diffraction effects [18].
Figure 1 shows a generic capability diagram; in the tool we are developing, there is an accompanying table with numeric values for the limits, the source of the information and/or how it was calculated. Note that the limits plotted appear as "hard limits". In practice, these limits are more nuanced. For example, min (the minimum sag or vertical resolution) in Figure 1 for a SWLI system is, in practice, noise limited. Trading-off resolvable amplitude with increased measurement time pushes down the minimum vertical resolution. At the same time,the minimum spatial wavelength "measurable" is a function of spatial wavelength. At the highest spatial frequencies, the instrument transfer function shows that the ratio of "true" to measured amplitude decreases as the spatial frequency approaches the Nyquist limit [17].
The original Stedman approach implies that instruments are limited at 1 cycle per aperture. This is clearly not true, for example when measuring optical surfaces with large base radii or designed astigmatism, which are measurable but noise limited.
In previous work [19], we attempted to capture these and other nuances, as well as retaining the original Stedman format. It is possible to plot a metrology capability diagram for a SWLI system, for example, showing multiple objectives (each discontinuity in the slope limit line represents a change of objective), the trade-off between measurement time and the noise floor, etc (Figure 2). Similarly, it is possible to show the effect of trace length and area measured in a sequential instrument such as a 3D profilometer. Industry feedback, however, suggested that the increased fidelity impeded understanding. Hence, we have focussed on the simplified diagram at the highest level of the information hierarchy, giving increased detail in subsequent levels, and using simple industry terminology. Figure 1 shows limits for a full aperture figure measuring interferometer. These limits are, in fact, specific to a particular measurement configuration. Fizeau interferometers are commercially available with a variety of "accessories" (transmission flats and transmission spheres) that allow for measurement of a range of departures from specified spherical base radii. Leaving aside the limitations imposed by "nulls", commercial interferometers have limitations on radii that can be measured around the in-cavity focus [20] as well as limitation posed by the depth of focus in the field . We are working to develop an "angular capability diagram" which captures these limits in a manner analogous to the Stedman based capability diagram.
Once the user of the tool has selected a "generic technology", Level 2 provides a "Use case" and a "Discussion". The use case is specific to measurement of optical surfaces. For a Scanning White Light Interferometer (also known by a number of other names including Coherence Scanning Interferometer), the stated use case is "Area measurement of finish and mid-spatial frequencies (MSF) with stitching as required. Form metrology over limited aperture sizes (slope dependent) using stitching.". This use case deliberately ignores the many other applications of this type of instrument.
The discussion provides a brief description of the physical operating principle of the instrument (with references) and
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