**3.1 Scanning profilers**

Except for the PMI and SSI, various specialized optical metrology techniques have been developed over the years to measure this class of optics, based upon scanning profilers: the Random Devices slope scanner (DeCew et al., 1986), the Zeiss M400 CMM in Germany (Becker et al., 1987), various instruments at the National Physical Laboratory in the UK (Ennos et al., 1982; Stedman et al., 1979), and the fringe scanner developed by Hughes Aircraft for the measurement of the AXAF (Chandra) x-ray telescope optics (Sarnik & Glenn, 1987) are examples of scanning profilers. These instruments employ various kinds of metrology methods, contact stylus and non-contact optical, developed to suit the particular metrology problem at hand. The Stedman-Stanley profiler (Stedman et al., 1979) and the Heynacher profilers (Heynacher & Reinhardt, 1979) were stylus instruments that made contact with the surface under test. These instruments made it possible to assess the height of steep aspheric surfaces at the nanometer level in two dimensions. Nevertheless, they are contact measurements, and during the final testing of optics with delicate coatings applied, there is always the possibility of leaving a very slight mark on the reflecting surface. Non-contact profiling methods have superceded contact stylus methods in the production of most grazing incidence optics today. Profiling instruments based upon the pencil-beam interferometer (PBI) are now widely employed in the manufacture and testing of SR and x-ray telescope optics (von Bieren, 1983a; 1983b; Takacs et al., 1988; Takacs et al., 1989). The PBI has been shown to be quite versatile and ideally suited for the testing of large cylindrical aspheres with nano-accuracy.

### **3.2 Pencil beam scanning surface profiler development in past 25 years**

Soon after the NSLS x-ray ring was commissioned in the early 1980's, it was realized that the quality of the focused beam was being compromised by the less-than-perfect figure of the mirrors. The normal-incidence surface figure measurement techniques available to manufacturers at the time were inadequate for characterizing the slope errors in the grazing incidence optics, slope errors that produced blurring of the focus by several times the expected source-size-limited spot size. Conventional interferometry was practically useless in attempting to extract useful surface error information from extremely foreshortened apertures seen at grazing incidence angles on the paraboloids, toroids and ellipsoids in beam line instruments, making it difficult for manufacturers to produce good quality optics. Null lenses did not (and still do not) exist to allow the use of Fizeau interferometers to easily measure simple cylinders for use at 3 mrad grazing incidence angles. With these limitations in mind, we sought to develop a versatile measuring instrument that did not require the use of null lenses and that could handle a wide variety of grazing incidence optics: long, flat mirrors; long-radius spheres; cylinders; toroids; ellipsoids and elliptical cylinders; and bent optics with radii of curvature in the range of kilometers down to tens of meters.

#### **3.2.1 Original pencil beam profiler**

Fortunately, around this time period in the early 1980's, the pencil beam interferometer was developed by von Bieren at Rocketdyne (von Bieren, 1983a; 1983b). His system was designed to measure the profile of conical axicon mirrors with a long radius in the tangential direction and an extremely small sagittal radius that vanished at the tip of the axicon. A schematic diagram of his optical system is shown in Fig. 2. We recognized that this slope-measuring profilometer would be ideally-suited for solving our grazing incidence mirror metrology problem.

Fig. 2. Schematic of original pencil beam interferometer from von Bieren (vonBieren, 1982). The minimum separation distance between probe beams, M, is set by the size of the cube beam-splitter and mirror. The beam is scanned by moving the penta prism. A dual lens system projects the interference spot onto the detector.

#### **3.2.2 The Long Trace Profiler LTP I and LTP II**

82 Modern Metrology Concerns

during the final testing of optics with delicate coatings applied, there is always the possibility of leaving a very slight mark on the reflecting surface. Non-contact profiling methods have superceded contact stylus methods in the production of most grazing incidence optics today. Profiling instruments based upon the pencil-beam interferometer (PBI) are now widely employed in the manufacture and testing of SR and x-ray telescope optics (von Bieren, 1983a; 1983b; Takacs et al., 1988; Takacs et al., 1989). The PBI has been shown to be quite versatile and

Soon after the NSLS x-ray ring was commissioned in the early 1980's, it was realized that the quality of the focused beam was being compromised by the less-than-perfect figure of the mirrors. The normal-incidence surface figure measurement techniques available to manufacturers at the time were inadequate for characterizing the slope errors in the grazing incidence optics, slope errors that produced blurring of the focus by several times the expected source-size-limited spot size. Conventional interferometry was practically useless in attempting to extract useful surface error information from extremely foreshortened apertures seen at grazing incidence angles on the paraboloids, toroids and ellipsoids in beam line instruments, making it difficult for manufacturers to produce good quality optics. Null lenses did not (and still do not) exist to allow the use of Fizeau interferometers to easily measure simple cylinders for use at 3 mrad grazing incidence angles. With these limitations in mind, we sought to develop a versatile measuring instrument that did not require the use of null lenses and that could handle a wide variety of grazing incidence optics: long, flat mirrors; long-radius spheres; cylinders; toroids; ellipsoids and elliptical cylinders; and bent

ideally suited for the testing of large cylindrical aspheres with nano-accuracy.

**3.2 Pencil beam scanning surface profiler development in past 25 years** 

optics with radii of curvature in the range of kilometers down to tens of meters.

Fortunately, around this time period in the early 1980's, the pencil beam interferometer was developed by von Bieren at Rocketdyne (von Bieren, 1983a; 1983b). His system was designed to measure the profile of conical axicon mirrors with a long radius in the tangential direction and an extremely small sagittal radius that vanished at the tip of the axicon. A schematic diagram of his optical system is shown in Fig. 2. We recognized that this slope-measuring profilometer would be ideally-suited for solving our grazing incidence

Fig. 2. Schematic of original pencil beam interferometer from von Bieren (vonBieren, 1982). The minimum separation distance between probe beams, M, is set by the size of the cube beam-splitter and mirror. The beam is scanned by moving the penta prism. A dual lens

system projects the interference spot onto the detector.

**3.2.1 Original pencil beam profiler** 

mirror metrology problem.

The Long Trace Profiler (LTP), based on the principle of the pencil-beam interferometer, was developed by Takacs and Qian and collaborators for the metrology of second-generation synchrotron radiation optics (Takacs et al., 1987; Takacs & Qian, 1989). Its operating principle is similar to that underlying an autocollimator, but with a laser pencil beam employed to scan the mirror being tested. The pencil beam is usually the direct output from a collimated laser diode or fiber-coupled laser. A schematic of the LTP optical system is shown in Fig. 3. The first beam-splitter produces a colinear pair of beams separated by a variable distance set by the adjustable prism. The separation distance can be adjusted from full overlap, M=0, to any desired value, while maintaining zero optical path difference (ZOPD) between the beams. The ZOPD system design is a vital improvement for a successful PBI profiler, because it eliminates the interference fringe movement due to the laser frequency shift (Qian & Takacs, 2004). This increases measurement accuracy significantly even when using an unstabilized laser. In contrast, the original von Bieren design had a very large OPD between the two beams. The ZOPD system allows the beams to be adjusted with a separation distance equal to the nominal 1mm beam diameter for maximum spatial frequency range information. The beam pair passes through the polarizing beam-splitter, PBS, and is split into a reference beam (REF) that is directed horizontally to a stationary mirror and a test beam that is directed down to the test surface. The return beams are focused onto a linear array detector by a Fourier transform lens, where each beam pair produces an interference pattern adjusted to have a minimum in the center. The position of the minimum on the detector, y, is proportional to the local slope of the surface between the two components of the beam pair:

$$y = \mathbf{F} \* \tan 2x \tag{1}$$

where α is the local surface slope and F is the focal length of the lens. By scanning the beam across the mirror surface, the slope profile is measured, from which the height can be derived by integration. In the case of synchrotron optics for 2nd and 3rd generation machines, the slope error profile is a more useful measure of the surface quality for the end user, but the height profile is necessary for the manufacturer to use in correcting the surface.

Fig. 3. Schematic of the LTP-II optical system. The PBS generates a reference beam from a plane mirror fixed to the optical bench surface. Pitch error in the movement of the optical head on the air bearing is corrected by adding the signals from the test and reference arms.

Some recent versions of the LTP use a single probe beam instead of the dual beam, eliminating the need for the initial beam splitting optics. The probe beam is focused to a single spot with no internal interference structure. The peak or centriod of the intensity distribution on the sensor determines the angle of the surface seen by the beam footprint. In this respect, the LTP operates very much like an autocollimator. Various algorithms are used to extract the centroid location of the spot with high precision.

Over the years, many improvements have been made to the original LTP-I design by many collaborators involved in synchrotron and x-ray telescope optics metrology. The original LTP system utilized an external electronic autocollimator to measure the pitch angle error of the optical head as it moved along the air bearing. The autocollimator was replaced by the internally-generated reference beam, shown in Fig. 3, by Irick, et al. (Irick et al., 1992) This allowed for simple correction of the measured profile for mechanical pitch errors by adding the two signals together. The relative intensity between the test and reference beams could now be adjusted easily by the use of polarizers and wave plates added to the optical system (not shown). The commercial version of the instrument, the LTP-II, produced by Continental Optical Corp. for several years, incorporated the internal reference beam and used a dualarray linear photodiode sensor as the detector. The dual array detector allowed the reference beam to be aligned nearly along the optical axis of the system instead of at an extreme angle, which places the spot at the end of the sensor. Having the reference beam centered in the lens aperture minimizes the introduction of phase shifts by glass inhomogeneities that translate into beam spot location variations with lateral movement of the beam across the aperture during a long scan. Bresloff added a Dove prism into the reference beam to change the phase of the laser pointing direction drift to be the same as the mechanical pitch angle error, allowing for correction of both error signals simultaneously by addition of the two signals (Takacs & Bresloff, 1986; Takacs et al., 1999).

Fig. 4. The LTP II optics board layout showing the 10 mrad surface slope acceptance angle optics in place. A 4-mirror arrangement folded the beams from the 1.25 m focal length lens with 7 reflections onto the detector mounted in back of the plane of the figure. The Dove prism mounted on the optics board in the REF arm inverted the phase of the pitch error signal to allow for simultaneous correction of pitch and laser drift

A sketch of the LTP-II optical head is shown in Fig. 4. This optical head used a Fourier transform lens with a focal length of 1.25 meters, which necessitated a folding mirror system to keep the size of the system within reason. The system was designed to measure surfaces with a total angular range of 10 milliradians. While this may seem like a small acceptance angle, it was sufficient to handle 99% of the long-radius optics used in NSLS beam lines. The LTP excels at measuring large flat and long-radius surfaces up to 1 meter in length. Other versions of the LTP-II can handle mirrors up to 1.5 meters long.

Improvements to the LTP-II and its successors, the LTP-IV and -V, manufactured by Ocean Optics, eventually enabled reliable surface slope error measurements down to the 0.5 µrad RMS level. However, recent advancements in synchrotron machine technology have resulted in the need for mirrors with slope errors in the 100 nrad range in order to allow for nanometer focal spot sizes. This quest for nano-accuracy in metrology has led to the development of specially-engineered machines that must be used in thermally-stable special environments in order to achieve this level of accuracy. The NOM machine developed at BESSY II in Germany by Lammert and collaborators (Lammert et al., 2006; Siewert et al., 2004) is the prime example of this next-generation profiler, which we will discuss in the next section.
