1. Introduction

Rapid processing and testing of a few hundred - if not thousand - 1–2m class hexagonal mirrors of next generation large telescopes such as CELT [1], EURO50[2] and OWL [3] have attracted much attention from the optics fabrication community worldwide. In particular, the technical requirement for testing is illustrated by the primary mirror segments of EURO50, which must handle a sag of ~10 mm, an absolute height accuracy of ~40 nm, a maximum slope of <1 degree, a lateral range of up to 2 m and a horizontal accuracy of ~1 µm [4]. Accomplishing this may require four principle challenges: - i) a straightness datum, ii) measurement of height with respect to the datum, iii) measurement of lateral displacement, and iv) measurement speed. Yang et al [5] has recently addressed the first, straightness datum, and presented a new laser datum system for nanometric form assessment for large optical surfaces up to 1m in diameter.

Moving onto the second, measurement of height with respect to the datum, a contact stylus or non-contact optical probe forms an essential part of the system. Most optical probe systems utilize a non-contact laser beam to measure the surface slope or curvature. The height information is then obtained by the integration of the slope or curvature [6,7,8]. Whilst its probe exerts no contact force onto the sample surface, the measuring capability in some cases is confined to near-flat polished surface due to the limited size of light-collecting optics and the scattering of the light from the ground surface.

The contact stylus probes typically use either an electro-mechanical encoder, or more precisely, a length-interferometer. The latter can reach the measurement resolution at the Å scale, but at the expense of limited ranges in height measurement. Examples include the Veeco Dektak 8000 surface profiler with 1Å resolution in vertical measurement, but with the vertical range of only 100 µm. Tencor Alpha Step 500 offers 10Å resolution, but only 2 mm in vertical range [9]. The well-known commercial stylus profilometer, the Form Talysurf, has a vertical measurement range limited to 10 mm [10]. The Swing Arm profilomter [11] of Steward Observatory is, however, capable of measuring the form of large aspheric mirrors, using a stylus with a short vertical measurement range. During the measurement run, the stylus rides on the spheroidal motion of the swing arm. This allows for the stylus to measure only the departure from the best-fit sphere (typically less than a few millimeters). However, constrained by the uncertainty of arm-length, tilt-error of the rotation axis, and errors in defining the mirror vertex, this instrument has been used mainly for rapid form measurement during rough grinding and initial polishing.

The commercial Coordinate Measuring Machines (CMM) typically uses the touch trigger probe (TTP) stylus with a long measurement range in a point-by-point measurement process. However, due to uncertainty in pre-travel, CMMs suffer from a low repeatability at the micron scale [12]. This, coupled with the high contact force of up to a few grams, shows that CMMs are not suitable for the rapid nanometric form measurement during optical figuring.

Aforementioned stylus techniques tend to be too limited in slope capability [6,7,8], height range [9,10,11] and measurement accuracy [12], if applied to the primary mirror segments. Having realized these shortcomings, we present the technical details of a new hybrid plunger and pivot stylus capable of achieving nanometric form accuracy over the height range of >10 mm. We described the stylus subsystem working in conjunction with the laser datum system [5], followed by the geometric error analysis and the stylus performance.

2. Plunger and pivot hybrid stylus

Contact stylus systems can be grouped into pivot (cantilever) or plunger systems [13, 14]. Figure 1 shows our hybrid, giving the plunger’s long range with the precision of a pivot system. The probe tip is a commercial spherical ruby of 1mm ±0.5 µm in roundness, supplied by Taylor Hobson Pneumo. There are many measurement approaches that can be used, and Dobosz [15] for example, used a grating based transducer. In our case, the probe-tip is carried by a short vertical shaft of zero expansion material, the top of which carries a retro-reflector. The shaft is mounted at one end of a horizontal lever, with a counterweight at the other, and the lever is pivoted about its centre on a horizontal polyester-fiber torsion-wire. The entire assembly is mounted in a 30mm travel vertical precision slide, driven by a DC Motormike™. In operation, the assembly is driven towards the part under test, and the stylus eventually contacts the surface. As the vertical travel continues, the lever starts to rotate, because the stylus-end is constrained to be stationery by the part. Finally, a paddle attached to the counterweight-end of the lever cuts the beam of an optical switch, sending a signal to disable the motor drive. By adjusting the applied torque to the torsion wire, a contact force of 0.7 mN has been achieved.

The retro-reflector is part of the measurement arm of a polarizing interferometer. This is furnished with photodiodes which generate sine and cosine signals. The interferometer’s reference arm is derived directly from the laser beam which defines the datum of straightness. Therefore there is a tight metrology-loop between probe-tip and datum. During the entire vertical sequence, fringe-signals are followed by a DSP-based data acquisition system. In the standard data acquisition technique, the fringes are numerically interpolated when the data have settled to give the distance of the retro-reflector from the datum. The profilometer is therefore designed to operate as a ‘pick and poke’ device, making a series of discrete measurement of the surface rather than a continuous scan. This approach is driven by the need for fast measurement operation with a horizontal sampling interval smaller than half the size of the smallest sub-diameter polishing tool. For processing a 1 m part with a polishing tool as small as 5 cm, only about 40 or so measurement points across the diameter would be sufficient to feed the global form back to the polishing run.

 

Fig. 1. Plunger-Pivot hybrid stylus system.

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3. Geometric stylus model and error sources

‘Pre-travel’ is the primary error source with the standard data acquisition technique. The errors arise from the uncertainties in i) the probe’s continued travel after surface-contact until the optical switch has triggered, and ii) the motor over-run after the optical switch has triggered. Figure 2 shows a geometric model of the stylus system. The height error z_o is defined as the post-movement of the retro-reflector after the probe tip hits the surface and, using l₁ cosϕ=x_o, l₁ sinϕ=h₁-z_i and sample surface tilt angle of 0 degree, can be expressed as

where $x_o=\sqrt{l_1^2-{\left(h_1-z_i\right)}^2}$ and z_i represents the pre-travel length. The friction between the probe and the surface is negligible as the loading is limited to about 0.7 mN. With such small a load, the stylus deflection becomes insignificant. Meanwhile, the induced lateral displacement e_x of the tip is expressed as

It should be noted from both equations that the precise determination of ‘pre-travel’ z_i plays a key role in height error estimation. Using z_i ≅ 50 µm and e ≅-0.1 mm (distance between the center of retro-reflector and probe), the equations yield z_o=-0.182 µm and e_x=19.1 µm. This amount of height error is experimentally verified later in section 4. When the surface has the finite slope angle θ, the additional height error of e_xtanθ is added to the primary error z_o. The HDV measurement technique described in Section 4 demonstrates the successful removal of the combined uncertainty of z_o, e_x and e_xtanθ at the level smaller than the height sampling resolution.

 

Fig. 2. Geometric stylus model and height error. The solid line shows the stylus in contact with the surface. The dotted line depicts the probe tip location after the stylus pre-travel motion has been completely stopped on the surface.

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4. Measurement techniques

Figure 3 shows typical DSP height signals when the probe tip touches the part’s surface at four stylus speeds (viz. 30, 120, 170 and 260 µm/sec). The data sample rate was one data point per every 1.4 msec, providing the height sampling resolution of 40 nm between two successive readings at the probe speed of 30 µm/sec. As indicated in Fig.3, the measured signals exhibit four distinctive phases: - i) stylus moving down vertically where the DSP height reading changes rapidly (Phase A), ii) stylus (contacting the surface) starts showing the variation of height difference between successive measurement points (Phase B), iii) the height difference variation, caused by the pre-travel, is reduced, indicating the stylus ‘pre-travel’ motion is slowing down. It should be noted that, as the system has e ≅-0.1 mm, all four DSP height signals continue dropping (Phase C) and iv) until the stylus motion is halted completely, the pre-travel is finished, and the probe tip settled on the surface of the part (Phase D).

The standard data-acquisition technique with point-by-point probing (such as used in CMMs) uses the Phase D data for height determination. As indicated in Table 1, however, the height determined with the Phase D data has the uncertainty of Z_o=-0.178 µm caused by the pre-travel (at stylus speed of 30 µm/sec). Whilst that is in good agreement with the error model prediction of Z_o=-0.182 µm, it should be noted that the uncertainty in pre-travel varies under the complex interplay among the variables defining the probe system, the sample surface and the measurement operation. Table 1 shows clearly that the stylus speed, one of the operation variables, affects the uncertainty in pre-travel.

The removal of this uncertainty was achieved with the new ‘Height Difference Variation (HDV)’ technique using the Phase B data, as it is indicative of first contact with the surface of the part. Implementation of the HDV technique is described by the following formulation:

where δR is the DSP height resolution and |H_i+1-H_i| the absolute value of height difference between successive measurements. The variation in height difference from five successive data points (i.e. 6 in total) is monitored. The first data would be stored as the correct height, if all five variations meet the condition defined in Eq. (3).

 

Fig. 3. DSP height signal at four stylus speeds i.e. 30 µm/sec (▪), 120 µm/sec (●), 170 µm/sec (▲), and 260 µm/sec (▼). The arrows indicate the Phase B.

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Table 1. Measurement summary

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5. Repeatability and form measurement

Table 2 summarizes the repeatability measurement at two slope angles, demonstrating that the HDV technique using the Phase B data produces higher repeatability than the standard technique using the Phase D data.

Table 2. Repeatability (i.e. measurement standard deviation) from 20 measurements at slope angle 0 and 8.1 degree.

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A trial form measurement, using the calibration ball of R=21.9983 mm (serial number 282 from Rank Tayler Hobson Ltd.) and the HDV measurement technique, was made over 10 mm scan length along the center line, representing the sag of 575 µm. The measurement yielded R=21.99926 mm and 22.00054 mm with the HDV and standard techniques respectively. This implies the maximum form difference of only 26 nm (HDV technique) and 60 nm (standard technique) at the radius of 5 mm. The HDV technique, when measuring a sphere of 157 mm in diameter, resulted in the rms height difference of about 84 nm with respect to the measurement data with a WYKO 6000 phase shifting interferometer.

The above measurement accuracies were obtained from the small work pieces representing the vertical range of 0.575 mm and the lateral travel range of 157mm. We now scale up the parts in linear dimension by a factor of 17.4 (vertical range) and of 12.7 (lateral range) to produce the vertical range of 10 mm and the lateral range of 2 m for the segmented mirrors mentioned earlier. These scaling factors, whilst being the first order linear extrapolation, would convert 26 nm to about 452 nm in form difference over 10 mm in sag (i.e. vertical height range) and increase the rms height difference from 84 nm to about 1.07 µm over 2 m in size (i.e., lateral travel range). This performance prediction demonstrates that, whilst it is not the multilateration concept as suggested by National Physical Laboratory [2], the hybrid probe system together with the laser datum system [5], as built, could be applicable for the global form metrology in earlier stages of fabrication, for the primary segments and the deformable secondary for extremely large telescopes such as ERUO50.

6. Concluding remarks

A new hybrid plunger and pivot stylus, working in conjunction with the laser datum system [5], was developed for efficient point-by-point form-measurement. The height error caused by the stylus pivot motion was modeled and experimentally verified. With the inherent ability to remove the uncertainty in pre-travel, the HDV technique resulted in a superior repeatability of better than 10 nm, and a small form departure of 26 nm from the calibration sphere. It is recognized that the stylus performance over the full height range of >10mm is yet to be measured. Nevertheless, the trial laboratory tests indicate that the stylus system, if mounted on a long-traverse slide-way, with a laser datum of straightness, may offer an efficient solution for the rapid metrology of large segmented mirrors for the proposed extremely large telescopes.