**1. Introduction**

76 Modern Metrology Concerns

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**7. References** 

1998

Precision optical surface figure measurement is the most important aspect for optical systems development of telescopes, microscopes, cameras and imaging or focusing systems. Any optical surface slope error or surface figure error departure from the theoretical surface will produce beam deviations according to Snell's law (law of refraction) for transmission optics or to the law of reflection for mirrors. Beam deviations can be easily calculated by use of ray tracing methods. The deviated beam will blur the image quality, enlarge the focus point, degrade the accuracy of the wave-front, and harm the performance of the optical system. To avoid such errors, surface figure must be manufactured and measured precisely.

"If you can not measure it, you can not improve it." This famous quote, attributed to Sir William Thomson, Lord Kelvin, describes exactly the dilemma faced by manufacturers of precision optical surfaces. It is especially true in the fabrication of mirrors used at extreme grazing incidence angles to focus x-rays in telescope and synchrotron applications. Mirrors used in synchrotron beam lines in the 1970s and '80s suffered from excessive surface roughness, generating excessive amounts of scattered light which reduced focal spot intensity and produced spectral contamination in VUV monochromators. The diamond stylus profilometers available at the time were ill-suited for measurements of surface roughness on full-size optical components. The development of the non-contact interferometric phase-measuring microscope early in the 1980's made surface roughness measurements in the Angstrom range on full-sized mirrors possible, and improvements in surface finishing techniques were quick to follow (Bhushan et al., 1985; Koliopoulos et al., 1980; Wyant et al., 1984)

The traditional measurements of plane and spheres applied test plate as a reference to test the surface with interferometric method in early years, which can reach /10 or better accuracy. However, this is contact test, and they are difficult to achieve with low-coherence sources prior to the development of the HeNe laser. See the excellent discussion of various historic interferometers in Malacara's book *Optical Shop Testing* (Malacara, D., 1992)*.* Later the development of different kind interferometers and the application of interference laser promise the non contact measurements. Computerized interferometer with the CCD sensor application and rapid fringe analysis enhanced the measurement technology accuracy quickly. Computer generated holograph (CGH) method (Pruss, 2008) can replace the troublesome preparation of test plates. In recent decades the development of the phase measuring interferometer (PMI) becomes an excellent metrology method to promote the interferometer accuracy and repeatability significantly, which has become a standard procedure for the interferometers. The basic concept of the PMI is that one can calculate the precise phase by acquiring several phase shifted frames of interferograms, each phase is shifted by a certain amount. Measurement method accuracy of the PMI could be >1/1000 fringe comparing to previous fringe analysis accuracy of only 1/10 fringe. The advantages of the PMI are the high accuracy can be obtained with low contrast fringes and is independent of intensity variations across pupil. Measurement of /20 surfaces is no longer a black art practiced by master opticians but is possible by ordinary shop technicians using modern phase measuring interferometers. These PMI instruments are widely used in the workshop and the research laboratory because of their ability to make non-contact measurements over large areas with high precision.

The PMI has successfully resolved two major tasks for precise metrology of routine or research surfaces: a) measuring surface roughness with height resolution of less than 1 Angstrom; b) measuring larger 2D surface profiles with /1000 repeatability and improving the test accuracy. In a conventional phase-shifting laser interferometer, multiple frames of data are acquired in sequence, so there is enough time for vibration and turbulence to degrade the measurement results. Recently developed technology acquires all phase data simultaneously. This will be very useful for in situ precision testing in the workshop (Zecchino, M., 2008; ESDI, 2011)

However, in the case of using PMI, a reference mirror is always required as the measurement standard, which dominates the final possible measurement accuracy.

The metrology problem is more acute in the fabrication of aspheric optics. In recent decades, high technology developments of computer numerical control (CNC), diamond turning, magnetorheological finishing (MRF), ion polishing, and elastic emission machining (EEM) have removed many of the difficulties involved in the manufacture of aspherics and high accuracy conventional optics. These manufacturing techniques have enabled the fabrication of nano-radian and nanometer accuracy components required in various applications.

Several recently-developed metrology techniques extend the measurement capabilities of conventional interferometers. Liu, et al., developed a sub-aperture technique for measuring on-axis aspheres by combining annular regions measured with a Twyman-Green interferometer (Liu et al., 1988). This technique works by adjusting the distance to the test surface to match the wavefront curvature to the surface radius at each zonal region. Subaperture stitching interferometry (SSI), developed by QED, enables the testing of larger aperture optics with standard Fizeau reference optics, without the need for dedicated large null optics, by automatically combining multiple overlapping sub-aperture measurements to form a full-aperture measurement (Fleig et al., 2003; Murphy et al., 200; 2003). The QED system simultaneously produces an error map of both the larger test surface and the smaller reference surface, correcting for rigid body alignment in each sub-aperture and for reference surface errors. Measurement error repeatability has been demonstrated to be 2 nm rms. Relative angle determinable stitching interferometry (RADSI) was also developed by the Osaka University group to measure steeply curved X-ray mirrors with nanometer accuracy

quickly. Computer generated holograph (CGH) method (Pruss, 2008) can replace the troublesome preparation of test plates. In recent decades the development of the phase measuring interferometer (PMI) becomes an excellent metrology method to promote the interferometer accuracy and repeatability significantly, which has become a standard procedure for the interferometers. The basic concept of the PMI is that one can calculate the precise phase by acquiring several phase shifted frames of interferograms, each phase is shifted by a certain amount. Measurement method accuracy of the PMI could be >1/1000 fringe comparing to previous fringe analysis accuracy of only 1/10 fringe. The advantages of the PMI are the high accuracy can be obtained with low contrast fringes and is independent of intensity variations across pupil. Measurement of /20 surfaces is no longer a black art practiced by master opticians but is possible by ordinary shop technicians using modern phase measuring interferometers. These PMI instruments are widely used in the workshop and the research laboratory because of their ability to make non-contact

The PMI has successfully resolved two major tasks for precise metrology of routine or research surfaces: a) measuring surface roughness with height resolution of less than 1 Angstrom; b) measuring larger 2D surface profiles with /1000 repeatability and improving the test accuracy. In a conventional phase-shifting laser interferometer, multiple frames of data are acquired in sequence, so there is enough time for vibration and turbulence to degrade the measurement results. Recently developed technology acquires all phase data simultaneously. This will be very useful for in situ precision testing in the workshop

However, in the case of using PMI, a reference mirror is always required as the

The metrology problem is more acute in the fabrication of aspheric optics. In recent decades, high technology developments of computer numerical control (CNC), diamond turning, magnetorheological finishing (MRF), ion polishing, and elastic emission machining (EEM) have removed many of the difficulties involved in the manufacture of aspherics and high accuracy conventional optics. These manufacturing techniques have enabled the fabrication of nano-radian and nanometer accuracy components required in various applications.

Several recently-developed metrology techniques extend the measurement capabilities of conventional interferometers. Liu, et al., developed a sub-aperture technique for measuring on-axis aspheres by combining annular regions measured with a Twyman-Green interferometer (Liu et al., 1988). This technique works by adjusting the distance to the test surface to match the wavefront curvature to the surface radius at each zonal region. Subaperture stitching interferometry (SSI), developed by QED, enables the testing of larger aperture optics with standard Fizeau reference optics, without the need for dedicated large null optics, by automatically combining multiple overlapping sub-aperture measurements to form a full-aperture measurement (Fleig et al., 2003; Murphy et al., 200; 2003). The QED system simultaneously produces an error map of both the larger test surface and the smaller reference surface, correcting for rigid body alignment in each sub-aperture and for reference surface errors. Measurement error repeatability has been demonstrated to be 2 nm rms. Relative angle determinable stitching interferometry (RADSI) was also developed by the Osaka University group to measure steeply curved X-ray mirrors with nanometer accuracy

measurement standard, which dominates the final possible measurement accuracy.

measurements over large areas with high precision.

(Zecchino, M., 2008; ESDI, 2011)

(Mimura et al., 2005; Yamauchi et al., 2003; Yumoto et al., 2010). In this method, the relative angles between overlapping sub-apertures are determined simultaneously with one interferometer while acquiring the sub-aperture profiles with another. Because stitching analysis eliminates certain systematic errors inherent in large aperture systems, the SSI enhances the accuracy of measurements. However, stitching methods can accumulate small
