**5.2 Calibration by use of commercial angle testing devices**

Instrument calibration with nano-accuracy can be done by use of commercial angle measuring instruments such as the theodolite, goniometer and other angle measurement

linear encoders (Heidenhain CertoCP 60 K) enable a controlled tilting of the VAC. The linear encoder provides a constant uncertainty of ±50nm over a range of 60mm. The measuring resolution of the Certo is ±5 nm; this corresponds to a tilting resolution of about 10 nrad. The achievable angular resolution of the VAC is about 0.015 rad, limited by the performance of

Recent developments in precise interferometric distance sensors has improved measurement accuracy to the one nanometer level, which significantly increases the reliability for trigonometric function calibration. The displacement interferometer can be used for small angle metrology. Fig. 19 is the example that uses a ZYGO system (ZYGO, 2003). The difference of two distance sensor readings divided by the distance between two points is the tilt angle. Its advantages are non-contact and nanometer accuracy. The National Research Council Canada uses this principle in their angle calibration systems (Pekelsky &

the linear stepper motor. The error budget of the VAC is estimated to 50nrad rms.

Courtesy of ZYGO, http://www.zygo.com/?/met/markets/stageposition/zmi/

The fiber-based Fabry-Perot interferometer (FFPI) is a typical multiple-beam interferometer that can be used as a non-contact distance sensor. The space separating the reflecting surface is called the cavity length. The reflected light in the FFPI is wavelength modulated in exact accordance with the cavity length (Pullteap, 2010). The attocube's ultra-high precision displacement FPSsensor has a repeatability of 1 nm at 20 mm cavity length, making it is suitable for small angle calibration with sine bar or tangent bar due to the advantages of high accuracy and non contact measurement characteristic (Attocube, 2010). Assuming its accuracy is 3 nm and it is used with a 250 mm sine bar, the error will be 0.012 rad. In addition, its very compact size is very attractive. However, larger test angles will impact the

Instrument calibration with nano-accuracy can be done by use of commercial angle measuring instruments such as the theodolite, goniometer and other angle measurement

Munro, 2005).

Fig. 19. Displacement Measuring Interferometers,

**5.2 Calibration by use of commercial angle testing devices** 

test accuracy significantly.

devices. However, they provide nanometer resolution or nanometer repeatability but rarely are nano-accuracy. They can not be used for nano-accuracy calibration over large angular ranges. There are only a few angle calibration devices that have been developed that can reach high accuracy with a large angular test range, which is expected by surface profiler.

The first calibration of the LTP angle error was made at ELETTRA in Italy in 1995 by use of a precision theodolite, Leica Wild T3000, with a sensitivity of 0.1" (Qian et al., 2000). A small mirror M is fixed on the theodolite telescope in order to reflect the beam back to the LTP (Fig. 20). In this way we can know the mirror rotation angle precisely. The LTP records a stability scan as a function of time while the theodolite is rotated step by step with a separation of 0.1° or 0.05°. A step-like slope file can be obtained. The differences between the LTP angle values and theodolite reading angles determine the calibration angle error. By changing the LTP scale factor coefficient, *e*, the LTP angles can be adjusted. This is an absolute angle calibration. This test should be done after the precise adjustment of focal plane position has been done. 0.1 arc second (0.5 rad) was suitable for 1 rad accuracy calibration at that time but it is not sufficient for recent nano-accuracy calibration requirements unless a higher accuracy theodolite is available.

Fig. 20. Setup of precise LTP angular calibration: WILD T3000 is used as an accurate angle generator. While The LTP is making stability scan and data acquisition continuously, the theodolite angle is changed step by step

The PTB angle comparator is the most accurate standard angular measuring device today with a test range of 360 degrees (Probst et al., 1998). It is well suited for pencil beam profiler calibration, especially for the larger slope profiler test. The angle-measuring system of the comparator consists of a ring-shaped index disc of glass with a radial reflected-light phase grating with 217 = 131 072 graduation periods on a circle approx. 400 mm in diameter. Eight scanning heads uniformly distributed over the circumference of the graduation are used for scanning this graduation. 218 = 262 144 signal periods are formed in each scanning head, which corresponds to an angular period of approximately 5". Digital interpolation of the signal period with the factor 2¹² = 4096 finally furnishes 2³º = 1 073 741 824 measurement steps per 360°, which corresponds to an angle-measuring step of approx. 0.0012" per scanning head. The angle value measured is finally obtained by averaging over all scanning heads. At present, this angle comparator allows an uncertainty of measurement of 0.005" (k = 2) to be reached.

Angular calibrations of profilers can be made at national standards bureaus. However, for researchers involved in precision angular R&D projects, it is necessary to check the nanoradian accuracy of a profiler frequently, and for calibration at remote sites, a low cost precision angle calibration device is desired.

In the case of sine bar and tangent bar systems for large angle measurements, the contact surface in using mechanical length gauge or reflection mirror surface in interferometric distance sensor is tilted. This will degrade the measurement accuracy considerably.
