During the last ten years, deflectometric profilometers have become indispensable tools for the precision form measurement of optical surfaces. They have proven to be especially suitable for characterizing beam-shaping optical surfaces for x-ray beamline applications at synchrotrons and free electron lasers. Deflectometric profilometers use surface slope (angle) to assess topography and utilize commercial autocollimators for the contactless slope measurement. To this purpose, the autocollimator beam is deflected by a movable optical square (or pentaprism) towards the surface where a co-moving aperture limits and defines the beam footprint. In this paper, we focus on the precise and reproducible alignment of the aperture relative to the autocollimator’s optical axis. Its alignment needs to be maintained while it is scanned across the surface under test. The reproducibility of the autocollimator’s measuring conditions during calibration and during its use in the profilometer is of crucial importance to providing precise and traceable angle metrology. In the first part of the paper, we present the aperture alignment procedure developed at the Advanced Light Source, Lawrence Berkeley National Laboratory, USA, for the use of their deflectometric profilometers. In the second part, we investigate the topic further by providing extensive ray tracing simulations and calibrations of a commercial autocollimator performed at the Physikalisch-Technische Bundesanstalt, Germany, for evaluating the effects of the positioning of the aperture on the autocollimator’s angle response. The investigations which we performed are crucial for reaching fundamental metrological limits in deflectometric profilometry.
The precision form measurement of optical surfaces has been greatly advanced by the development of deflectometric profilometers which use surface slope (angle) to assess topography. They are capable of measuring surfaces which, due to size, as well as topography range and gradient, pose a challenge to classical interferometry. Because of these advantages, deflectometry has turned out to be especially suitable for characterizing beam-shaping optical surfaces for x-ray beamline applications, e.g., at the modern synchrotrons and Free Electron Lasers (FELs).1–8 Due to their large size (up to 1.5 m length), aspherical, rotationally asymmetric shape, and extremely stringent demands on their form accuracy (<1 nm peak-to-valley in form, <50 nrad root-mean-squared in slope9–11), they pose equally stringent demands on the quality, alignment, and characterization of the components of deflectometric devices used for their measurement.
Fig. 1 presents the basic setup of a deflectometric profilometer, using the Developmental Long Trace Profiler (DLTP)5,12 available at the Advanced Light Source (ALS) X-Ray Optics Laboratory (XROL)13,14 as an example. (Note that the current DLTP arrangement depicted here is a reversed version of the setup described in Ref. 5.) To assess the local slope (tilt angle) of the surface under test (SUT), the beam of an angle-measuring device is deflected by a movable optical square (pentaprism) towards the SUT, where an aperture limits the beam footprint. Both the optical square and the aperture are moved together to scan the beam along a trace on the SUT. Commercial electronic autocollimators (ACs)15 are capable of providing precise and traceable angle metrology for this purpose. For a comprehensive overview of the usage of autocollimators in deflectometric profilometers and the specific challenges associated with this application see Ref. 16.
After being reflected by the SUT, the returning beam generally follows different geometric paths through the optical components of the profilometer (autocollimator, optical square, and aperture stop) and thus is affected by their aberrations and alignment errors, leading to systematic errors in the autocollimator’s angle measurements. For approaching fundamental metrological limits in the deflectometric form measurement, it is essential to reduce the optical aberrations of the profilometer’s components and to align them precisely, both relative to each other and internally.
These issues are aggravated by the strong dependence of the systematic errors on the optical path length of the autocollimator’s light beam that can change by 1-2 m when scanning along the SUT.17,18 A number of approaches have been proposed to tackle this problem. One example is the method based on the Universal Test Mirror (UTM)19 which is directed at revealing the systematic error in deflectometric measurements through a specific experimental arrangement. New calibration devices, such as the Spatial Angle Autocollimator Calibrator (SACC),20 were developed to accurately calibrate autocollimators over the extended range of application parameters. Modified deflectometric scanning schemes6 have been suggested which avoid path-dependent angle measurement errors. With all of these methods, the proper alignment of all components of deflectometric profilometers remains of prime importance in order to reduce systematic errors and to use the calibration data for correcting them properly. The need for high lateral resolution in deflectometric profilometry is driving autocollimator apertures towards even smaller diameters which further increases the demands placed on the alignment of the optical components and on the calibration of the autocollimator.
In a number of publications,12,21,22 we extensively treated the alignment of the optical square, including mirror-based pentaprisms. In the cited papers, we provided strategies necessary for the in situ alignment of the optical square, including its optical faces, the angle measuring axes of the autocollimator, and the SUT, relative to each other. The developed methods have advanced the state-of-the-art to a level at which the error influence of the optical square on form measurement becomes negligible.
In this paper, we focus on one more important issue which has so far been neglected in the literature: the precise and reproducible alignment of the aperture relative to the autocollimator’s optical axis. The importance of this task has been recognized by its inclusion in the European Metrology Research Programme (EMRP) SIB 58 Angle Metrology.23 One topic is the development of a device and a standardized procedure for the positioning of small (1.5-2.5 mm) apertures relative to the autocollimator’s optical axis with reproducibility <0.1 mm. In Section II, we present the aperture alignment procedure developed at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory, USA, for use with their DLTP.5,12 In Section III, we present results of ray tracing simulations of a commercial autocollimator at the Physikalisch-Technische Bundesanstalt (PTB) for evaluating the effects of the positioning of the aperture on the autocollimator’s angle response. In Section IV, we corroborate the procedures and ray tracing results from Secs. I–III by means of autocollimator calibrations performed at the PTB.
II. APERTURE ALIGNMENT WITH THE ALS DLTP
In this section, we describe an experimental method for the precise and reproducible alignment of the beam limiting aperture with respect to the optical axis of the autocollimator in the ALS DLTP.5,12 The ALS DLTP is a classical deflectometer based on a movable pentaprism and an electronic AC Elcomat-3000/8 in an arrangement schematically shown in Fig. 1. The strength of the method is that it relies on the propagation of the autocollimator’s measuring beam itself which also serves as a natural straightness standard in deflectometric profilometers. As this is a natural choice, there are some similarities to approaches developed at other places.24
To extend the slope variation measurements into the short spatial wavelength region, a beam limiting aperture (iris diaphragm) of 2.5 mm diameter is used. This is the recommended smallest size of the aperture through which the autocollimator is able to perform reliable angular measurements. The aperture is mounted on an X-Y translation stage (Thorlabs model LM1XY) and attached to the aperture mount of the mirror based pentaprism assembly (Fig. 2). The X-Y stage is used to align the aperture with respect to the AC optical axis.
The optical head of the DLTP (including the pentaprism and the aperture) is placed on an air-bearing movable carriage. Note that in the current version of the DLTP, there are two replaceable optical heads, one for measurements with face up (it is shown in Fig. 2) and other with side facing SUTs.
The aperture alignment procedure consists of a few steps.
First, the AC optical axis is aligned to be collinear with the axis of translation of the carriage. For this, the AC beam is apertured with a pinhole mounted in the center of the autocollimator output light beam. Practically, a plastic cap with an approximately 1 mm hole in the center is attached to the autocollimator lens tube (Fig. 2). The position of the apertured AC beam is monitored with a CCD camera (IPX-4M15-L) placed on the carriage in front of the pentaprism assembly. The cross section of the apertured beam has characteristic cross-like shape shown in Fig. 3 as imaged with the camera placed at a distance of approximately 470 mm from the autocollimator. The high resolution and large field of view of the camera with 2048 × 2048 pixels of 7.4 μm × 7.4 μm size allow visual positioning of the center of the cross-like beam with sub 0.1-mm accuracy. The collinearity of the AC optical axis and the carriage translation axis is adjusted by tilting the autocollimator with a dedicated kinematic stage to minimize the variation of the aperture beam position when translating the carriage over the entire translation range of about 1 m.
When the collinearity is adjusted, the CCD camera is removed from the carriage and mounted on the optical table in the position of the SUT in Fig. 1. This arrangement, depicted in Fig. 2, is suitable for recording the AC apertured beam after it passes through the DLTP pentaprism and the beam limiting aperture (iris diaphragm) at a certain fixed position of the carriage. This allows achievement of the alignment goal on this step, that is, to center the iris diaphragm with respect to the apertured beam.
Starting with the iris diaphragm removed, an image of the cross-shaped beam is recorded in order to accurately determine its center. To simplify the positioning of the beam center, we use specially developed LabView™-based software for the camera control and image acquisition and analysis. However, sub 0.2-mm accuracy of the positioning is easily achievable with manual centering of a marker shown with the green square in Fig. 4. If higher accuracy is desired, a more sophisticated procedure can be implemented, e.g., calculating the centroid of the beam intensity distribution.
Next, the iris diaphragm is mounted back on the X-Y translation stage which is part of the DLTP optical head and located right after the pentaprism (see also Fig. 1). With the stage, manual positioning of the aperture in the plane perpendicular to the autocollimator beam is provided. Fig. 5 shows the images of the intensity distribution of the autocollimator light beam in Fig. 4 but limited by the aperture orifice. The optimal positioning consists of matching the orifice center to the center of the cross-like beam depicted in the images with the green square marker. Note that the images may also be used for the precise setting of the aperture size when an adjustable aperture (e.g., iris diaphragm) is used.
So far we have assumed that the profiler’s pentaprism is optimally aligned with respect to the AC optical axis. In the case of the DLTP, where the pentaprism is made of two mirrors, a special alignment procedure has been developed and described in detail in Refs. 12 and 21. The procedure for optimal alignment of the pentaprism relies on the appropriate alignment of the profiler’s beam limiting aperture. Therefore, alignment of the aperture, described above in this section, generally requires sequential realignment of the pentaprism. For the global optimization of the DLTP optical head, we perform a few iterative optimizations of the aperture position with subsequent realignment of the pentaprism (at the position of the aperture determined in the previous iteration).
Finally, usually after 1-2 iterations, when the mutual alignment of the all DLTP components is fixed, we check that the alignment stays optimal for the entire translation range of the DLTP carriage. The check is performed at the extreme carriage positions, the closest and the furthest possible ones, separated by approximately 1 m. With the camera placed at each of these extreme positions on the optical table and with the iris diaphragm totally open, we find the position of the center of the AC apertured cross-like beam (the first step of the beam limiting aperture alignment procedure, described above). After that, with the iris diaphragm set to the desired 2.5-mm diameter, we check the coincidence of its orifice center with the center of the AC beam.
III. AUTOCOLLIMATOR RAY TRACING
Deflectometric profilometry requires the use of an aperture which restricts the footprint of the autocollimator’s measuring beam on the SUT, see Fig. 1. As mentioned above, if the position of the aperture relative to the autocollimator’s optical axis is changed, both the outgoing and the returning beams (i.e., the illumination and imaging beams, respectively) follow different paths through the autocollimator’s optics. In the presence of aberrations of its optical components and errors in their alignment (including that of the CCD detector), angle measuring deviations are an unavoidable outcome. They are sensitive to the aperture’s location perpendicular to the optical axis of the autocollimator and along it, i.e., the distances to the autocollimator’s objective and to the SUT.16,17
As mentioned above, in the case of deflectometric profilometers, to access different points on the SUT, the aperture is moved along the autocollimator’s optical axis together with the pentaprism. If straightness errors of the linear stage used for moving them are present or if the stage and the autocollimator’s optical axis are not parallel, parasitic changes in the aperture’s position perpendicular to the optical axis are unavoidable.
A. Model for ray tracing
The effect of lateral shifts of the aperture on the autocollimator’s angle measurement can be illustrated with ray-tracing simulations. To this purpose, a general model of an Elcomat-3000/8,15 which is commonly used for high-precision deflectometric applications, has been created with the optic simulation software ZEMAX. It considers the major optical components of this autocollimator type (but not all of them), which features two different beam paths for its horizontal and vertical measurement axes with separate illumination units, reticles, and CCD lines, but a common objective. The beam paths and the respective illumination units and CCD lines are divided by beam splitters.
The exact optical schematic of the autocollimator is proprietary information of the AC vendor that is not available for disclosure in this publication. Instead, for the simulation in this section, we use a generalized AC schematic that does not reproduce all significant details of its optical schematic. As a result, one should expect the simulations to only provide an estimated scale of the problem. Nevertheless, we believe that the simulation results give substantial information when considered as an indication of the influence of aperture alignment on deflectometric profilometry.
Because of the expected approximation due to the generalization mentioned above, the model has been additionally simplified to speed up the simulations (see Fig. 6): The two beam paths have been simulated by a single beam path. Therefore, only one point light source (simulating the illuminations and the reticles) and one plane detector (simulating the CCD lines), located at the same position in the model, were implemented. To retain the original optical path length, two plane-parallel plates simulate the beam splitters.
The aperture diameter was set to B = 2.5 mm as this is a typical value chosen in autocollimator-based deflectometry. The spacing between the aperture and the SUT was fixed at 5 mm. In the simulations, the SUT was rotated in such a way that only one of the autocollimator’s measuring axes was engaged, i.e., the axis which is parallel to the plane of the beam deflection. For the presented simulations, the aperture was decentered from the autocollimator’s optical axis in the direction parallel to this plane. The lateral position of the aperture, X, is defined as the distance between the autocollimator’s optical axis and the aperture’s centre. Note that varying the lateral position of the aperture in the perpendicular direction has no effect on the presented results.
For all investigations, one reference simulation (lateral position of the aperture: X = 0 mm, i.e., the aperture is centered on the optical axis of the autocollimator) and several measurement simulations (X = 0.5 mm, X = 1 mm, X = 1.5 mm, and X = 2 mm) have been performed. The mirror angles were varied from −1350 arc sec to 1350 arc sec in steps of 54 arc sec. The differences between the measured angles of the measurement simulations and the reference simulation were calculated.
The influence of the lateral aperture position on the angle measurement of the autocollimator has been investigated at distances between the SUT and the autocollimator of D = 25 mm, 300 mm, 600 mm, 900 mm, 1200 mm, and 1500 mm. The distances were equal for the reference simulations and the respective measurement simulations with the laterally shifted aperture.
B. Simulation results
Figs. 7-10 show the angle measuring deviations caused by lateral shifts of the aperture. The figures present a selection of the simulation results. In Figs. 7 and 8, the lateral aperture position X was varied, and in Figs. 9 and 10, the distance D was varied.
The standard deviations of the angle differences (in arc sec) within the simulated measurement range of −1350 arc sec to 1350 arc sec for the respective lateral aperture positions X and distances D are given in Table I.
|X/mm .||25 .||300 .||600 .||900 .||1200 .||1500 .|
|X/mm .||25 .||300 .||600 .||900 .||1200 .||1500 .|
For constant angles of the mirror, the measured angles differ when the aperture is shifted laterally in the direction of the beam deflection even for a SUT angle of α = 0. Fig. 11 shows a magnified section of Fig. 7 to highlight this effect. It necessitates a precise adjustment of the optical axis of the autocollimator with respect to the linear stage (i.e., the movement direction of the aperture).
The light source and the detector have been placed at the position of the objective’s focal plane which was determined by ZEMAX with an optimization algorithm. The optimization was performed with a centered full aperture (B = 32 mm) in accordance with the manufacturers adjustment procedure. However, the focal plane is different for an aperture with B = 2.5 mm. When the aperture is shifted laterally, this causes a displacement of the position of the incident rays on the detector and, therefore, an angle response of the autocollimator for α = 0. For an aperture shift of X in meters, the angle deviation of the autocollimator, Δα, is given by the relation
The performed simulations show the sensitivity of the angle measurement of the simulated autocollimator with respect to variable lateral shifts of the aperture at different distances. An analysis of the simulations for a distance D = 1500 mm, an aperture size B = 2.5 mm, and an angle range of ±1350 arc sec, see Fig. 8, indicates that for an aperture centered within X = ±0.08 mm, the errors in the autocollimator’s angle measurement remain below 50 nrad peak-to-valley.
Notice that the results of the ray-tracing simulations and the derived equations are valid for the simulated autocollimator only.
IV. AUTOCOLLIMATOR CALIBRATION DATA
Angle measurement with autocollimators is sensitive to the measuring conditions.11,16,17,25 The factors influencing the angle response of an autocollimator can be sub-divided into two broad categories: internal vs. external.
Internal factors are specific to the each autocollimator’s internal design and, therefore, are generally beyond user control. They include aberrations of the optical components (objective, reticle illumination, beam splitter cubes, etc.), including figure errors and inhomogeneities, their alignment (including that of the CCD detector), the non-orthogonality of the measuring axes, internal specular reflections and stray light, geometrical imperfections of the reticles, inter-pixel variations of the CCD (geometry, quantum efficiency, dark current, and more), and intra-pixel quantum efficiency patterns (across single CCD pixels, due to their internal structure).
External factors are given by the measuring conditions under which the device is used in the setup and, therefore, to a certain extent, are subject to control by the user. These include the reflectivity and curvature of the SUT, the path length of the autocollimator beam probing it, the diameter and shape of the aperture stop, and the position of the aperture stop along the autocollimator’s optical axis and perpendicular to it.
Traceable autocollimator calibration is central to making full use of their potential by correcting their angle measurement errors and, therefore, is essential for approaching fundamental metrological limits in deflectometric form measurement. At the PTB, autocollimator calibration is realized by its direct comparison to the primary angle standard, the Heidenhain WMT 220 angle comparator, manufactured by Dr. Johannes Heidenhain GmbH, Traunreut, Germany.26 With the aid of various self- and cross-calibration techniques, the standard measurement uncertainty27 of the WMT 220 could be reduced to u = 0.001 arc sec (5 nrad).28,29 With highly stable autocollimators, calibrations with standard uncertainties down to u = 0.003 arc sec (15 nrad)11,16,17,25 have been achieved. The uncertainty budget for the autocollimator calibration includes components which depend on the type of autocollimator and the calibration parameters. They usually dominate the final uncertainty budget and may result in budgets larger than the one stated above. In contrast, the uncertainty contribution of the primary angle standard WMT 220 is of subordinate importance. Even better autocollimator calibration results have been achieved by the application of a novel error-separating shearing approach.30
By use of the primary angle standard WMT 220 of PTB, we obtained calibration data of an autocollimator type Elcomat 3000, Möller-Wedel Optical.15 The standard calibration setup follows the scheme laid out in Fig. 6 with a coated SUT placed at a distance of 300 mm with respect to the front end of the autocollimator’s objective (note that due to constraints in the available calibration time, we had to restrict ourselves to one distance). The SUT was coated with aluminum (resulting in a high reflectivity). A circular aperture 2.5 mm in diameter was placed close (at a distance of 3 mm) to the optical surface of the SUT. The aperture was shifted laterally in the direction of the primary measuring plane, i.e., in the plane of the beam deflection. Displacements of the aperture with respect to the autocollimator’s optical axis of 0.75 mm to 5 mm were realized.
Fig. 12 shows the differences between the angle responses of the autocollimator for the selected off-centre locations of the aperture and for a centered aperture. For the selected calibration range of ±1000 arc sec, differences of several tenths of an arc sec are visible. (Note that autocollimators are not designed for use with small apertures and therefore show angle deviations which are much larger than the ones expected when they are used within the parameter range for which their design has been optimized.) These results stress the importance of a reproducible alignment of the aperture during calibration and subsequent use of the autocollimator. A comparison of the results of the ray tracing simulations (Sec. III) and of the experimental data shows no strong similarities, neither with respect to the course of the differences nor their magnitude. It is our conclusion that the shifting of the aperture makes visible effects which are dominated by the influence of minor manufacturing differences of each individual autocollimator rather than by the influence of its general design. These may include limits in the alignment of the autocollimator’s optical components, small-scale inhomogeneities, and flatness deviations of the components, as well as inhomogeneities in the pixel response and geometrical layout of the CCD detector, etc. These results furthermore stress the importance of a reproducible aperture alignment.
In deflectometric profilometers, the precise and reproducible alignment of the beam-limiting aperture relative to the autocollimator’s optical axis and its maintenance, while it is scanned across the surface under test is important for reaching fundamental metrological limits. These requirements aim at creating reproducible measuring conditions for the autocollimator during calibration and during its use in the profilometer to ensure optimal traceability of the angle metrology to national standards. Ultimately, calibration data are only applicable to correcting the autocollimator’s angle readings if differences between the measuring conditions remain within tightly specified limits.
In this paper, we demonstrated recent progress in this field. The aperture alignment procedure developed at the ALS provides an approach that allows reproducing—in different experimental arrangements and in different metrology labs—exactly the same alignment of the particular autocollimator and aperture. The described procedure has a potential to be accepted as a standard alignment procedure for autocollimator-based deflectometric profilometers. Its strength is that it relies on the propagation of the autocollimator’s measuring beam which serves as a natural straightness standard in deflectometric profilometers.
The ray tracing simulations and calibrations of a commercial autocollimator performed at the PTB demonstrated that additional effort needs to be put into understanding all effects of the displacement of the aperture relative to the autocollimator’s optical axis on its angle response. Especially, the discrepancy between simulations and calibrations demonstrates that the idealized ray tracing model needs to be augmented by incorporating, e.g., misalignments and imperfections of the autocollimator’s optical components. As a result of the ray tracing simulations, we recommend a reproducibility of the aperture alignment within ±0.1 mm.
The authors are very grateful to Wayne McKinney and Gary Centers for useful discussions.
Part of this research was undertaken within the EMRP JRP SIB58 Angle Metrology. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.
The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Material Science Division, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory.
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