We present a 2D Slope measuring System based on a Stitching Shack Hartmann Optical Head (SSH-OH) aiming to perform high accuracy optical metrology for X-ray mirrors. This system was developed to perform high-accuracy automated metrology for extremely high quality optical components needed for synchrotrons or Free Electrons Lasers (FEL), EUV lithography and x-ray astronomy with slope error accuracy better than 50 nrad rms.
© 2014 Optical Society of America
Today, manufacturing techniques allow for figuring arbitrary optical surfaces. The form of these elements can be corrected at the nanometer level by computer controlled polishing or deterministic polishing processes (like ion beam figuring or Elastic Emission Machining for example) but the accuracy of absolute form metrology limits the possibilities of the manufacture of modern optical elements. This makes new metrology developments necessary. The actual state-of-the-art optical instruments available in optical metrology laboratory do not have adequate sensitivity for highly curved mirror and do not cover a wide range of spatial frequencies to provide the manufacturer with useful information necessary to feedback the polishing process to improve the quality of the optical component. Metrology plays a critical role in modern figuring because computer-controlled figuring is performed using the measured surface profiles. Thus, the key point for fabricating elliptically curved surfaces is the improvement of the metrology, as the measurement accuracy determines the final figure accuracy of the fabricated mirror.
Over the last decade, X-ray mirrors have evolved rapidly accelerated by the intense use of extremely brilliant 3rd generation synchrotron and Free Electrons Laser (FEL) radiation sources. These X-ray mirrors, planes or off axis ellipses with lengths of up to 1 m, must preserve the incoming wavefront are characterized by residual slope errors in the range of 50 nrad rms and values of 0.3 nm rms or less for micro-roughness [1–5].
The NSLSII synchrotron radiation facility has developed its optical metrology services in order to ensure the quality of optical elements installed at its beamlines. This involves characterizing the figure error of gratings and mirrors, which at the current levels of accuracy is strongly determined not only by the polishing error but also by other factors such as the gravitational sag, the stress caused by the clamping, or the cooling scheme. One of the main instruments of the Optics and Metrology laboratory of the NSLS II facility is the Stitching Shack Hartmann Optical Head (SSH-OH), a new 2D Slope measuring System develop to perform high accuracy optical metrology for X-ray mirrors. This paper is organized as follows. In Section 2, we present the general description of the technique and the principle used, in Section 3 we describe its applicability to problems related to X-ray optics metrology and show some metrology results and discussion. Finally, conclusions and perspectives are drawn is Section 4.
2. Description and principle of the SSHOH optical head
2.1 Generalities and principle of Shack–Hartmann Wavefront Sensors (SHWS)
The basic measurement principle of a Hartmann test from the early 1900s  is quite simple: in this test, a mask with holes was placed in front of the lens to be tested. Light passing through the holes was examined at two planes, typically before and after the focal plane. By examining the shift in position of the rays compared to that of an ideal lens, the aberrations, wavefront map, and other parameters could be determined. In the late 1960s, Roland Shack proposed first shifting the measurement plane to the pupil plane and then using of a grid of lenslets to sample larger areas, while still providing measurements over a localized area . A (Shack-) Hartmann sensor divides up the incoming beam into sub-beams, dividing up the wavefront into separate beamlets, each focused by pinholes (microlens) onto a sub array of CCD camera pixels. These sensors are based, not on interferometry, but on geometric properties of light that allow robust determination of the wavefront slope. Depending upon where the focal spot from each facet strikes its sub array of pixels, it is then possible to determine the local wavefront inclination (or tilt). Subsequent analysis of all beamlets together leads to determination of the overall wavefront form. The positions of the individual spot centroids are then measured and compared with reference positions. This enables the local slopes of the wavefront (i.e., its derivative) to be measured at a large number of points within the beam. Critical aspects of sensor design include having sufficient resolution over the whole wavefront for the application in mind and simultaneously providing enough CCD pixels per beamlet to accurately determine the spot “center of mass” and the local inclination of the wavefront. Once these resolution issues have been decided, the overall range of measurable wavefront distortion is then a question of balancing sensor geometry against diffraction issues. Any predetermined wavefront later modified by reflection or transmission can then be analyzed and the information used to determine the surface shape or the transmissive optical quality, respectively, of the optical component responsible for the wavefront change. More details on SHWS can be found in the following literature [8, 9].
2.2 Description of the Stitching Shack Hartmann Optical Head (SSH-OH)
The characterization of optical surfaces in generally done with interferometers. They can perform precise measurements for a large range of radii of curvature but they need reference surfaces or holograms to produce ultra-stable and high-quality reference wavefronts so they are limited in dynamic range. For the characterization of high-quality x-ray mirrors, the long trace profiler (LTP) [10–16] or the NOM [17–19], used in most of the synchrotron radiation facilities, has become the state-of-the-art off-line metrology tool. However, these instruments present some drawbacks: 1D measurement (slope along one single direction and only on a profile), some 2D tests have been reported but with very long measuring time [20, 21], limited dynamic range and relatively slow measurement time.
The NSLSII SSH-OH provides a measurement of the slope profile of the surface under test by scanning a High accuracy Shack Hartman wavefront sensor (SHWS) along the mirror surface. At each point of the mirror, the SHWS measures the 2D local deflection of the beam: both mirror shape derivatives (X and Y) are measured simultaneously. These slopes are measured on each microlens hence the 2D derivatives maps are obtained. The mirror topography is then obtained by integration. The first idea to use a SHWS to characterize x-ray mirror was proposed by Imagine Optic  and SOLEIL synchrotron [23, 24].
The innovative metrology technology proposed here consists of three main improved key components:
- • The first one is a Shack Hartmann wavefront sensor as optical head with very high precision (more than lambda/1500), sensibility, repeatability and large dynamics range.
- • The second component is a high precision positioning system for scanning/positioning large and heavy surfaces. The SHWS optical head is mounted on the translation stage to perform bidimensional mappings by stitching together successive sub-aperture acquisitions.
- • The third component is a robust metrology software for accurate reconstruction of large surfaces, correction of residual imperfections of the motion platform, as well as analyzing and treating the collected data.
The innovative approach of this project is to combine those described three main elements in order to construct a stand-alone non-contact optical large surface metrology system with the following properties: (see Table 1)
The minimum mirror radius of 1.2 m is determined by considering the slope measurement accuracy of the Shack-Hartmann wavefront sensor. In order to keep the high accuracy, the focal spots on the CCD camera must not be too close otherwise the slope calculation is not accurate. The smallest distance between adjacent spots that still gives the precision more than lambda/1500 was used to estimate the dynamic range of SSH-OH. A radius of curvature less than 1.2m will create a very strong converging beam onto the Shack-Hartmann. The curvature will be large enough at the scale of a single microlens to create a defocus image on the CCD. The spots on the CCD will then not be a (Sinc2) as expected but defocused. On such spot shapes, the centroid calculation will not be accurate anymore.
In general, space and X/EUV optics have dimensions much larger than the dimensions of the entrance pupil of the profilometric head used to perform the measurement. Obtaining a complete surface mapping requires translation stages to shift the surface under test or the profilometric head. For the characterization of long mirrors and/or improvement of the spatial resolution, a stitching process has to be applied. Well known using interferometer [25–27], it consists in the overlapping of adjacent surface measurements by translation of the optical head or of the mirror under test. Redundancy of the information is used to subtract all systematic errors including measurement errors induced by the imperfections of the translation stage. In our case, the slope measurements in the overlap regions are used in a linear squares fitting routine to determine the relative tilts between frames of data. These relative tilts are then used to correct the data and to construct a stitched gradient map for the mirror under test (MUT). Once the map of the surface gradient is reconstructed, the surface itself is reconstructed using a wavefront reconstructor algorithm such as that described by Southwell .
In our system, the wavefront sensor was designed based on the need for high spatial resolution, but also high accuracy. A summary of the optical head parameters is given in Table 1. The source is a 405 nm diode laser, pigtail coupled to a single mode fiber. This light is collimated and then injected into the optical path through a beam splitter cube. A relay beam expander is used so that the lenslet array is in conjugation to the test optic (Fig. 1). The dimension of the optical head is L = 545 mm x W = 280 mm x h = 122 mm. Its weight is about 7 kg.
The basic principle of the SSH-OH is roughly the same as for a conventional Long Trace Profile (LTP) or a NOM. However, the analysis pupil size of the sensor is 18 × 13.2 mm2, with a spatial resolution of 1.2 mm (size of the microlenses) and at each point the local slopes are measured in both directions X and Y. These slopes maps are the two derivatives of the mirror surface height. We have then redundancy that can be used to reduce the measurement noise and systematic errors. Moreover, the 2D integration is less noisy than 1D integration as several paths can be considered to calculate the mirror height by integration of the slope maps.
The measuring area of the NSLSII/SSH-OH covers 1,500 mm in length and 300 mm laterally thanks to a 5.5 T granite two axis gantry design by Q-SYS . The accuracy of guidance of the scanning carriage system is about ± 1 μm for a range of motion of 1.5 m. The optics platform can carry a 200 kg load and the optical head motion system is able to accommodate several different optical head with a total load of more than 30 kg (Fig. 2).
From Fig. 1 (top), the deflecting mirror (bottom part of the picture) allows the SSH-OH to work both for Horizontal and Vertical geometry in order to test the x-ray mirror in the beamline working condition. The change from Horizontal to Vertical testing mirror geometry can be done in less than 1 minute.
In order to provide stable measurement conditions, the whole system is contained in a thermally isolated enclosure. The temperature in the enclosure is not actively stabilized, and it relies simply on the huge heat capacity of the granite bench and the very small power dissipation inside it. The enclosure itself is installed in the class 10,000 clean room of the Optics Laboratory of NSLSII, which is stabilized in temperature within 0.1 °C by the air conditioning system . Figure 3 shows a record of the temperature inside the enclosure over more than 12 hours.
3. Application of the SSH-OH to x-ray mirror metrology
To demonstrate the capabilities of the SSH-OH, we characterized x-ray mirrors with flat, spherical and elliptical shape.
Figure 4 represents the 2D slope map of a spherical mirror (R ~140 m, L = 250 mm). After best fit removed (radius of 140 m) and comparing the 10 scans measured during the test, a repeatability of 50 nrad rms have been achieved. Figure 4 (top) represents the 2D slope map obtain with the SSH-OH. If we extract a 1D profile from this 2D map for example following A and B lines in Fig. 4, it is clear that the 1 D result will be different (Fig. 4, bottom). This illustrates the importance to have a 2D map of the mirror under test instead of a single line.
Figure 5 represents the measurements done on an elliptical mirror with an inspected aperture length of 100 mm. The local radii of curvature is varying from R = 250 m down to R = 150 m. To have an idea on the systematic error of the instrument, four measurements were taken at different angle between the optical head and the mirror surface from 0 to 1 mrad in horizontal geometry. The rms variation of these four different measurements is around 20 nrad proving the very high repeatability of our instrument. With the best polynomial fit removed, this ellipse is at 54 nrad rms slope error (JTEC Fabrication ).
The SSH-OH is also used to measure very large optical component. Figure 6 shows a 1.4 m silicon bendable mirror developed by WinlightX/ France for the NSLS II XPD beamline.
Figure 7 (top) is a 2D slope map obtain for a radis of curvature of R = 16 kms. A single line (average of the 2D map in one direction) with the best radius removed is shown in Fig. 7 (bottom part). The scanning time to get the 2D map (forward + backward measurements) is less than 2 hours for a length of 1200 mm (the number of measured points in this 2D map is 11 x 1200 points).
Figure 8 shows several measurements made on this mirror for different radius of curvature from flat (0 steps: curve green) to R~9.2 km (135000 steps: black curve).
Using these measurements, we can determine the calibration curve (curvature versus actuator motion) of this bendable mirror (Fig. 9).
In Fig. 10, the measurement of a 100 mm long silicon flat mirror was done in forward direction (from edge A to edge B) and after 180° rotation and re alignment in reverse direction (from edge B to A). From the results in Fig. 10 (top), the agreement of both measurements is excellent. In Fig. 10 (bottom), the difference between AB and BA measurements is in the range of 34 nrad rms which is close to the noise level of our instrument. This slope error translates after integration to 0.3 nm rms height difference between both scans. This result can be taken as indication for the achieved measurement accuracy in terms of slope and height measurement.
The NSLSII SSH-OH, the last generation deflectometric instrument, is operational and fully characterized at the Laboratory of Optics and Metrology of NSLS II. The SSH-OH makes possible precise noncontact bidimensional measurement of the surface slope and it is proven to be capable of reaching accuracies limited to a few tens of nanoradians. At a conventional working wavelength (λ = 405 nm), high accuracy (below 50 nrad), high repeatability (below 50 nrad), high dynamic, high-spatial resolution and insensitivity to vibrations are among the main advantages of this new instrument. Radii of curvature down to 1.2 m can be measured with 0.1% accuracy, and large optics can be measured with sub-microradian performances thanks to the stitching approach.
In this paper, we have shown the successful applications of the SSH-OH to rapidly and robustly measure the profile of an X-ray reflective optics. This new, simple, non-contact measurement system offers the characteristics desired for a high-end, single-piece, freeform optics metrology tool. Future calibrations and development of the control and data-processing software will certainly further improve the potential performances of this instrument.
The authors would like to thanks WinlightX/France, JTEC corporation/Japan, Q-SYS/Netherlands and all colleagues from Imagine Optic/France and NSLSII for useful discussions and contributions to this project. This work was supported by the US Department of Energy, Office of Science, Office of Basic Energy sciences, under contract No. DE-AC-02-98CH10886.
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