**4.1 Pencil beam scanning method for nano-accuracy surface figure measurements**

Progress in nano-accuracy metrology is dependent upon new scientific demands, advanced technology developments, and innovation in metrology methods and metrology instruments.

Though traditional null phase-shift interferometers can reach excellent repeatability with high accuracy, the required reference surface is still an obstacle, which restricts its metrology accuracy. Making a null lens is time-consuming work and is very expensive, especially for one used to test large-aperture optical surfaces. Though the three flats absolute calibration method can reach an accuracy /100 or better theoretically (Schulz et al., 2008), it is very difficult to achieve for large surfaces. In addition, the reference surfaces have to be routinely

Fig. 7. Vertical Scan LTP (VSLTP) at Marshall Space Flight Center set up for measuring x-ray

In 25 years of development, there have been a number of other applications of the LTP: insitu heat load test, measurement at machine shop, calibration of the profiler, thermal shift treatment, 2D detector development and so on. Some will be described in the following

Precise metrology is the basis for enabling fabrication of precision optics. The rule-of-thumb requires that the metrology accuracy should be at least 3-fold (< 50 nrad) better than the specification of the optics. The great challenge for metrology and manufacturing is that nanometer and nano-radian accuracy is needed for spherical or aspheric mirrors with large

**4.1 Pencil beam scanning method for nano-accuracy surface figure measurements**  Progress in nano-accuracy metrology is dependent upon new scientific demands, advanced technology developments, and innovation in metrology methods and metrology

Though traditional null phase-shift interferometers can reach excellent repeatability with high accuracy, the required reference surface is still an obstacle, which restricts its metrology accuracy. Making a null lens is time-consuming work and is very expensive, especially for one used to test large-aperture optical surfaces. Though the three flats absolute calibration method can reach an accuracy /100 or better theoretically (Schulz et al., 2008), it is very difficult to achieve for large surfaces. In addition, the reference surfaces have to be routinely

**4. Current development and trends in nano-accuracy surface figure** 

telescope mirrors and mandrels in the vertical orientation

sections.

**metrology** 

instruments.

surface slope angles.

but inconveniently calibrated. As described above, the stitching methods accumulate small systematic interferometer errors that limit their high accuracy. Hence, the accuracy of measurements of a full-size surface with sub-aperture stitching method needs to be calibrated precisely

Pencil beam scanning methods have become a promising metrology method to make nanoaccuracy surface profilers, because of their many advantages: non-contact test, absolute measurement without need of using a large reference, high accuracy, possibility of measuring large dimension optics and aspheric optics with moderate cost, and no need for working distance adjustment due to the use of a collimated beam. These advantages keep this method as one of most important solution for the optical metrology in the future even though it has a disadvantage of being only a one-dimension measurement with lower test speeds. The sub-aperture interferometer stitching method is beginning to be used with LTP and SR-optics measurements (Assoufid et al., 2004; Polack et al., 2010) with linear scanning. It will extend to large optics the ability to perform 2-D and mid-spatial frequency testing. However, improvements are needed in LTP stitching accuracy, along with research on precise calibration methods.

#### **4.2 Various nano-accuracy profilers with scanning pencil beam method have been developed**

The Nano-Optic-Measuring Machine (NOM, Fig. 8) (Lammert et al., 2006; Siewert et al., 2004) is the most accurate instrument so far for evaluating SR and other large optics. The NOM incorporates a special commercial autocollimator and an LTP optical head with a scanning penta-prism system to measure long-radius optics. It applies a small aperture of about 2 mm near the mirror under test in order to increase the spatial frequency range. The demonstrated uncertainty of the NOM in the measurements was low: for a plane mirror it was 0.05 μrad rms, and, for curved mirror, it was 0.2 μrad rms. Both instruments operate in a scanning penta-prism mode without the need to use a reference beam to correct for slide pitch error. A similar and improved Diamond-NOM has also been developed (Alcock et al., 2010).].

Fig. 8. The NOM, Courtesy of F. Siewert, T. Noll, T. Schlegel, T. Zeschke, H. Lammert, The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY, AIP CONFERENCE PROCEEDINGS Vol.705, 847-850 (2004)

A new Traceable Multiple Sensor (TMS) system was developed by the Physikalisch-Technische Bundesanstalt (PTB) for measurement with nanometer accuracy (Fig. 9) (Schulz et al., 2010; Wiegmann et al., 2010; PTB Working Group 8.42, 2011). It encompasses coupled multiple distance-sensors that are scanned along the surface under test. By using a small sensor head, a high lateral resolution is achieved. In addition to the multiple distance sensors, the TMS utilizes an autocollimator measuring the tilt of the sensor's head, thereby eliminating systematic errors in the distance sensors. The TMS can reach nanometer or better accuracy with high lateral resolution. Both the NOM and TMS are suitable for plano and near-plano mirror measurements with nano-radian accuracy. During a scan on a plane mirror, the reflected beams are always parallel and remain steady except for very tiny angle variations produced by the slope error on the surface. In this fixed beam direction condition when testing plane mirrors, if the temperature is very stable and the scan system has very small pitch, yaw and roll errors, the beam will not have any error that impacts the test accuracy except for the noise. So it is possible to achieve nano-accuracy on plane surfaces regardless of what instrument is used.

Fig. 9. Traceable multiple sensor (TMS) system, Courtesy of Schulz, G. Ehret, M. Stavridis, C. Elster, Concept, design and capability analysis of the new Deflectometric Flatness Reference at PTB, Nuclear Instruments and Methods in Physics Research A 616 (2010) 134–139

## **4.3 Difficulties to approach nano-accuracy metrology for large slope surfaces**

Testing of strongly curved surfaces presents significant difficulties to pencil beam scanning profilers, as it does to most optical measuring techniques. In this case, measurement nanoaccuracy is hard to reach in large part due to the impact of insufficient optical system quality of the profiler.

Let us analyze the beam position variation in the optical system during the measurements. We use as an example a spherical mirror under test (MUT) scanned by the scanning optical head of the LTP II (Qian, S. N. & Qian, K., 2010; Qian, 2011). The sample beam (solid line, Fig. 10 a)) measures the slope of a MUT, and the reference beam (dashed line) measures the air bearing pitch error. In order to avoid the overlapping of sample and reference beams on the CCD, the LTP II reference beam is tilted to move the spot to one end of the detector. During the scan both sample and reference beams have lateral motions (BLM) over the optical components inside the optical head, shown as solid and dashed shadow areas, which will pick up large local phase shift errors that show up as surface slope error. These errors are produced by surface figuring error, inhomogeneity of

A new Traceable Multiple Sensor (TMS) system was developed by the Physikalisch-Technische Bundesanstalt (PTB) for measurement with nanometer accuracy (Fig. 9) (Schulz et al., 2010; Wiegmann et al., 2010; PTB Working Group 8.42, 2011). It encompasses coupled multiple distance-sensors that are scanned along the surface under test. By using a small sensor head, a high lateral resolution is achieved. In addition to the multiple distance sensors, the TMS utilizes an autocollimator measuring the tilt of the sensor's head, thereby eliminating systematic errors in the distance sensors. The TMS can reach nanometer or better accuracy with high lateral resolution. Both the NOM and TMS are suitable for plano and near-plano mirror measurements with nano-radian accuracy. During a scan on a plane mirror, the reflected beams are always parallel and remain steady except for very tiny angle variations produced by the slope error on the surface. In this fixed beam direction condition when testing plane mirrors, if the temperature is very stable and the scan system has very small pitch, yaw and roll errors, the beam will not have any error that impacts the test accuracy except for the noise. So it is possible to achieve nano-accuracy on plane surfaces

Fig. 9. Traceable multiple sensor (TMS) system, Courtesy of Schulz, G. Ehret, M. Stavridis, C. Elster, Concept, design and capability analysis of the new Deflectometric Flatness Reference at

Testing of strongly curved surfaces presents significant difficulties to pencil beam scanning profilers, as it does to most optical measuring techniques. In this case, measurement nanoaccuracy is hard to reach in large part due to the impact of insufficient optical system

Let us analyze the beam position variation in the optical system during the measurements. We use as an example a spherical mirror under test (MUT) scanned by the scanning optical head of the LTP II (Qian, S. N. & Qian, K., 2010; Qian, 2011). The sample beam (solid line, Fig. 10 a)) measures the slope of a MUT, and the reference beam (dashed line) measures the air bearing pitch error. In order to avoid the overlapping of sample and reference beams on the CCD, the LTP II reference beam is tilted to move the spot to one end of the detector. During the scan both sample and reference beams have lateral motions (BLM) over the optical components inside the optical head, shown as solid and dashed shadow areas, which will pick up large local phase shift errors that show up as surface slope error. These errors are produced by surface figuring error, inhomogeneity of

PTB, Nuclear Instruments and Methods in Physics Research A 616 (2010) 134–139

**4.3 Difficulties to approach nano-accuracy metrology for large slope surfaces** 

regardless of what instrument is used.

quality of the profiler.

optical components, system aberration and system alignment errors. However, sample beam lateral motion is an unavoidable condition in testing the slope of curved mirrors, but we can effectively reduce the sample BLM magnitude by adopting a novel system scheme.

In contrast the penta-prism scan mode (by use of the LTP optical head or autocollimator) has much larger BLM than scanning optical head (Fig.10 b), so it is not recommended for measuring larger slope optics.

Fig. 10. a) Sample and reference beams' lateral motion in scan optical head mode; b) Beams' lateral motion on a scan in the penta-prism mode

How large is the slope error produced by the BLM? The following measurement compares a tilted reference and a non-tilted reference. Two scans were done only with the reference arm of the LTP III over a 900 mm length scan in sequence. The first scan is with a reference beam angle of 1.5 mrad, which results in a 3 mm lateral motion across the PBS (Fig. 11 a); the second scan is with a non-tilted reference beam (Fig. 11 b). The difference (Fig. 11 c)) between both scans is ±5 µrad (P-V) which is a serious slope error for a nano-radian surface profiler. If the tilt angle increases due to strongly curved mirror, the systematic error of the profiler will be more severe. Also, if the reference beam spot is displaced away from system center even in the case of using a second linear CCD or 2D CCD, it will still produce considerable BLM in vertical direction in 2-3 mrad angle level. This method should also not be suitable for the nano-accuracy system. Results of several tests indicate that the magnitude of the slope error caused by BLM could be larger than 1 rad rms. If the BLM is larger due to the larger test angle, the error will increase quickly. The problem is that the real error is so larger even though we use available highest quality optics, it is still not enough to reach 0.1 rad accuracy for strongly curved surface test. The following simulation analysis illustrates this effect.

Fig. 11. LTP III slope error produced by tilted reference: a) reference beam spot is tilted in 1.5 mrad; b) non-tilted reference beam at CCD center; and c) slope error caused by tilted reference.

#### **4.4 Error simulation analysis of surface figure errors and inhomogeneity of profiler optics based on wave-front distortion**

A sinusoidal wave-front is used to simulate the surface figure error and slope error. A sinusoidal wave-front error of ±1nm (P-V) in 20 mm (Fig. 13 a) will produce ± 0.314 rad slope error (Fig. 12).

Fig. 12. Angle error produced by sine wave-front error of ±1 nm

#### **4.4.1 Slope error produced by surface figure error**

If a refractive surface figure error is a ±1 nm sine wave (/317), it will produce a sinusoidal wave-front error of ±0.5nm and a slope error of 0.157rad for a material with an index of 1.5 (Fig. 13 b), which is a value large enough to destroy the nano-accuracy. If there are multiple surfaces in the optical system, the error will be larger than 0. 1 rad.

If a reflective surface figure error has a sinusoidal error of ±1 nm, it will produce a reflective sinusoidal wave-front error of ±2nm and a slope error of 0.628 rad (Fig. 13 c), which is a much larger impact than a refractive surface.

The best surface figure quality typically available in customer optics is about /100 with very high cost. This means that even if we use the highest quality available optics it will probably not be easy to reach 0.1 rad accuracy.

**LTP III slope error produ ced by tilted reference**

Fig. 11. LTP III slope error produced by tilted reference: a) reference beam spot is tilted in 1.5 mrad; b) non-tilted reference beam at CCD center; and c) slope error caused by tilted reference.


b )

distance (m m )

c )

**4.4 Error simulation analysis of surface figure errors and inhomogeneity of profiler** 

A sinusoidal wave-front is used to simulate the surface figure error and slope error. A sinusoidal wave-front error of ±1nm (P-V) in 20 mm (Fig. 13 a) will produce ± 0.314 rad

**Angle error produced by sine wavefront error of +/- 1 nm**

If a refractive surface figure error is a ±1 nm sine wave (/317), it will produce a sinusoidal wave-front error of ±0.5nm and a slope error of 0.157rad for a material with an index of 1.5 (Fig. 13 b), which is a value large enough to destroy the nano-accuracy. If there are multiple

0 5 10 15 20

Distance (mm)

If a reflective surface figure error has a sinusoidal error of ±1 nm, it will produce a reflective sinusoidal wave-front error of ±2nm and a slope error of 0.628 rad (Fig. 13 c), which is a

The best surface figure quality typically available in customer optics is about /100 with very high cost. This means that even if we use the highest quality available optics it will

**optics based on wave-front distortion** 

a )

slope (urad)

Fig. 12. Angle error produced by sine wave-front error of ±1 nm


surfaces in the optical system, the error will be larger than 0. 1 rad.

**4.4.1 Slope error produced by surface figure error** 

slope (urad)

much larger impact than a refractive surface.

probably not be easy to reach 0.1 rad accuracy.

slope error (Fig. 12).

Fig. 13. a) 1nm distorted wave-front and its slope error; b) 1nm refractive surface error and its distorted wave-front; c) 1 nm reflective surface error and its distorted wave-front
