Aleksandr Gorbashev

Figure 2.8 - Carriage Pitch and Yaw Behavior
Abbé Offset) between the object being measured and the accuracy determining element. In this case the Abbé error is present due to the Abbé offset and the angular motion of the carriage.
Considering a sixty meter tape bench it can be understood that its assembly cannot be performed without possible deflections on a micrometer scale. Such deflections or small waves are responsible for tilting of the carriage in the pitch or yaw direction as it is rolled. Calibration uncertainty due to Abbé errors are generated from an angular displacement under Yaw and Pitch conditions.
As shown in Figure 2.8 above:
*Yaw – Rotation of carriage about the vertical axis.

* Pitch – Rotation of carriage about the horizontal axis.
From previously gathered data it was found that pitch behavior of the carriage is responsible for the largest source of uncertainty (≈ 250 µm) in comparison to the yaw related behavior. Any pitch motion of the microscope carriage will cause an Abbé length measurement error.
Figure 2.9 provides the description of the source of Abbé Error due to carriage pitch. The top diagram shows the carriage in parallel with the bench top, which is the desired position for proper calibration as no angular related error is present. In the top diagram, the microscope is focused directly on the desired graduation. Yet, due to the geometry of the carriage and the

i
Figure 2.9 – Abbé Error due to Abbé Offset

mperfections of the

bench top, the carriage is able to tilt or “pitch” in a clockwise direction

of angle Ө as seen at the bottom of Figure 2.9. If the tilt angle is not corrected (as done manually in the current design by microscrew adjustment) a displacement error is present as the actual reading is displaced from the desired measurement. The displacement error seen in Figure 2.9 is what is responsible for calibration uncertainty.
3.2 Operator Error
Operator error due to manual pitch adjustment is another large source of measurement uncertainty. In the current design the pitch of the carriage is adjusted and maintained approximately constant using a bubble level (for pitch detection) and microscrew. As the pitch is corrected manually by monitoring the bubble level, the accuracy of pitch adjustment can be done by eye with minimal error of 5 arc - seconds.
Operator error also occurs during the centering of the microscope reticule on the measurement graduation. After the reticule is aligned and centered on the graduation, the operator must eliminate the carriage pitch by manually adjusting it back to zero pitch. After this, the graduation alignment must be checked to make sure that it is still centered. In multiple instances, the last step is forgotten as the carriage may have shifted after pitch adjustment. Therefore, an error due to operator negligence is also present. Because such adjustments cannot be done perfectly, operator error contributes greatly to the measurement uncertainty.
4.0 Problem Analysis
Before attempting to find a possible solution, it was necessary to evaluate the problem parameters. The first step was to evaluate the pitch deflection of bench along its full length to define the scale of pitch. The evaluation of the bench pitch was performed by using the Wyle Fowler Digital Levelmeter shown on the carriage

in Figure 3.0. This Levelmeter was c

Figure 3.0 – Wyler Fowler Digital Level
hosen

for this experiment as it

allowed me to obtain a digital read out and direction of the pitch within a milliradian scale.
The pitch evaluation was performed by taking pitch measurements in 100 and 400 millimeter increments to check for consistency. The results from this evaluation can be seen in on Page 20. The data plotted in the Microsoft Excel spread sheet allowed me to see how much the bench fluctuates in pitch along its length. It can be noted that in some cases an amplitude of up to 7 Arc-Minutes is attained. With Ө = 7 Arc-Minutes (≈0.117 degrees), an error of approximately 101 micrometers¹⁴ may be present.

One of the most important factors of performing this experiment was to gain an understanding of the bench behavior with respect to pitch. The scale of the pitch can define the type of design and technological sensitivity necessary to create pitch measurement. In this case, it is necessary to be able to measure pitch within an arc-minute scale with up 7 arc minute maximum.

5.0 Possible Solution
After considering an electromechanical self leveling system as a possible solution for pitch correction, I have come to a conclusion that it is not the best approach. This approach would be difficult to assemble as multiple technological p
Figure 3.1 – Error Diagram
roblems could potentially arise. Particularly,

incorporating this system would involve a major carriage design overhaul to provide a structure that would work for this leveling system.

After brainstorming possible solutions, I have come up with a pitch correction approach that may have great potential. From a simple calculation, measurement error (Figure 3.1) can be calculated by knowing the magnitude of the carriage pitch. Therefore, the final measurement may be corrected by subtracting the error out. This approach would eliminate the necessity to manually adjust pitch, thus eliminating operator error while correcting for the Abbé error. The approach would incorporate a digital inclinometer¹⁵ on board of the carriage to detect the magnitude of carriage pitch. The pitch value can also be easily sent wirelessly to the Renishaw software by the use of a wireless modem transmitter and receiver. By knowing the value of the pitch (Ө), the software could be adjusted to create a calculation of error [Error = Abbé Offset*Tan(Ө)] seen in Figure 3.1. By knowing the error involved in the measurement, the measurement could be corrected within software to eliminate the Abbé error and the operator error.

This approach would be the simplest and most affective way to decrease measurement uncertainty by correcting for Abbé and operator errors. It would provide the benefit of not having to change the current carriage design, higher precision in pitch measurement (no bubble scale) and no manual operation.

5.1 Experimental Comparison
5.1.1 Introduction
Before I could begin the search for possible inclinometers and wireless modems compatible for this task, it was necessary to evaluate whether the proposed approach would work and would it work better then the current approach to calibration. To create a comparison between the two methods of calibration I performed an experiment consisting of two calibration simulations. One simulation involved the current method of calibration, or manual pitch adjustment with the bubble level. Second simulation involved the use of the Wyler Fowler Digital Levelmeter¹⁶ or inclinometer (conveniently owned by the LSCMG) to record pitch without manual adjustment for resulting measurement correction. This experiment would allow me understand whether the use of digital inclinometer and the process of displacement correction by software (through pitch) is better then the use of the bubble level and manual pitch adjustment by the operator.
To check for consistency of data, the comparison experiment was performed three times by using manual pitch adjustment and then twice by using pitch measurement. Using statistical analysis of the gathered data, the best approach would be defined by a comparison of standard deviations of error from both data sets to understand which method of calibration is more efficient. Both data sets can be seen in Appendix A.
5.1.2 Experimental Setup Description
Wyler Fowler Digital Levelmeter 2000
The Wyler Fowler Digital Levelmeter is a digital instrument that is used to measure angles of pitch or tilt. This particular version, Levelmeter 2000, can measure angles of pitch within ±1.9 milliradian range¹⁷.
This instrument incorporates a tilt sensor, a signal transmitter and a receiver. In Figure 3.2, the combination of the tilt sensor and signal transmitter can be seen on the carriage. As the tilt sensor defines the pitch, the signal is then sent wirelessly to the receiver (Figure 3.2 – Top Left Corner) which displays the reading of the pitch in milliradians. The receiver was also connected to the Renishaw software to directly output a pitch reading with respect to a calibration displacement value from Renishas software.



Figure 3.2 – Level Setup

5.1.3 Simulation 1: Manual Leveling Procedure

(3 Trials Total)
Purpose:
- To simulate tape calibration process by an operator with the use of the bubble level and manual pitch correction.

- To gain the standard deviation of error that is involved in such process.

Procedure:
- Using a ruler or a tape on a tape bench, define a zero mark.
- Level the carriage at a zero mark by adjusting the micro-screw to attain the zero mark reading (zero pitch) on the bubble level. Zero the Renishaw laser. Through the use of the Renishaw tape calibration software, record the displacement and the pitch values respectively.
- Reset the position and the pitch of the carriage by adjusting the displacement off the zero mark and pitching the carriage off the zero pitch. Now re-adjust the carriage to the zero mark for both, the pitch and the displacement using the bubble level and the microscope. Again, through the use of the Renishaw tape calibration software, record the displacement and the pitch values respectively.
- Repeat for any number of trials.

5.1.4 Simulation 2: Pitch Correction with Wyler Fowler Level Procedure

(2 Trials Total)
Purpose:
- To simulate a newly proposed tape calibration process through the use of the Wyler Fowler digital level and technique of displacement correction through pitch.

- To gain the standard deviation of error that is involved in such process.
Procedure:
- Using a ruler or a tape on a tape bench, define a zero mark.
- Level the carriage at a zero mark by adjusting the micro-screw to attain the zero mark reading (zero pitch) for a digital read-out on the Level Meter. Zero the Renishaw laser. Through the use of the Renishaw tape calibration software, record the displacement and the pitch values respectively (as a zero measurement).
- Pitch the carriage manually through the use of the micro-screw to a desired increment in the desired + or - direction, the microscope cross hairs will have moved from zero mark. Align the carriage with the zero mark and then record the displacement and the pitch values respectively.
- Repeat at pitch increments until the minimum and maximum values of the Level Meter are reached (≈±1.9 mRad).
- The following Pitch increments for data collection were used:

Upscale (mRad)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1.9

Downscale (mRad)
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
-1.8
-1.9

6.0 Conclusion

This section will provide the experimental result and discussion along with concluding decisions and future plans for lowering uncertainty in calibration.

6.1 Experimental Results
After performing the experimental comparison between the two methods, it became evident that displacement correction through pitch detection has some benefits. Experimental data shows that both methods are rather equivalent in calibration accuracy. By taking a look at the plotted standard deviation of error in Figure 3.3, it can be seen that the e
Figure 3.3 – Standard Deviation of Error Plot
rror deviations between both techniques overlap. The trend line between the two methods also suggests close consistency in pitch correction for both. Considering these results it can be seen that the measurement uncertainty in both methods is nearly equivalent.
6.2 Concluding Discussion
Although the experimental results suggest that uncertainty in calibration is equivalent, the displacement correction method has multiple benefits over the current calibration process.
One benefit is that the manual adjustment by the operator is no longer necessary. The absence of manual pitch adjustment eliminates sources of error that may lie within this technique. The possibility of error due to shifting of carriage before or after the graduation alignment and imprecision of alignment based on a bubble level scale is eliminated. This method avoids room for human error due to manual bubble level style pitch control. In addition, this technique makes the process of calibration more automated. With the new technique, it is only necessary to locate the gradation through the microscope and then record the measurement value. There are no steps to graduation alignment, then pitch adjustment, then checking for realignment. By a more automated process, the required time for calibration is lowered, thus creating a shorter return time to the customer and lower use of the laboratory utilities.
A second benefit may be found by a suggested further research. Considering the experimental comparison of both methods it can be understood that uncertainty through displacement correction may be improved drastically through the use of more accurate and precise equipment. As this was a preliminary experiment in search of a possible solution, the Wyler Fowler Digital Levelmeter had the necessary specifications for the experimental comparison, but it was not an optimized piece of equipment. For this reason, uncertainty equivalency between both methods suggests that displacement correction technique can be used. In fact, it can be further optimized to lower the measurement uncertainty in calibration.

6.3 Future Steps
Currently, the LSCMG is taking this approach to improve their calibration method. For the future, the group plans to take this approach of calibration as they will try to optimize this method by incorporating a more precise digital system for pitch measurement.
Before leaving my position at NIST, I spent time researching a possible system that would accomplish this task. After speaking with the representative of the Applied Geomechanics Inc., an order had been placed for a customized level system designed for the microscope carriage and laboratory use.

The new level system will incorporate the Applied Geomechanics IRIS Tilt Controller (Figure 3.4) with two precision ceramic sensors for pitch detection, wireless modems for wireless signal transfer and other necessary equipment for functioning. Due to the time constraints, I was not able to work with the new inclinometer system. But

L
Figure 3.4 – IRIS Tilt Controller
SCMG will follow this approach to lower the measurement uncertainty through a more precise pitch measurement. In the future, to reach the 10 micrometer uncertainty goal, the group plans to combine the new approach to pitch correction with a new microscope carriage design of minimal Abbé Offset.
Appendix A
Data: Pitch Correction with Wyler Fowler Level – Trial 1

Abbe Offset	106.8 mm
Time	Renishaw (mm)	Time	Pitch (mRad)	Error (mm)
2:43:34	-0.00032	14:43:36	0.001	-0.0004268
2:45:47	-0.03035	14:45:50	-0.206	-0.0083492
2:47:19	-0.0432	14:47:22	-0.41	0.000588
2:48:17	-0.06867	14:48:19	-0.623	-0.0021336
2:49:23	-0.07935	14:49:26	-0.822	0.0084396
2:50:01	-0.10179	14:50:04	-1.036	0.0088548
2:50:53	-0.12403	14:50:56	-1.233	0.0076544
2:51:46	-0.14156	14:51:48	-1.444	0.0126592
2:52:54	-0.16432	14:52:58	-1.616	0.0082688
2:53:46	-0.18817	14:53:49	-1.822	0.0064196
2:54:39	-0.19889	14:54:44	-1.917	0.0058456
2:55:29	-0.18892	14:55:32	-1.828	0.0063104
2:57:00	-0.1624	14:57:04	-1.621	0.0107228
2:57:40	-0.15024	14:57:43	-1.439	0.0034452
2:58:30	-0.12703	14:58:32	-1.227	0.0040136
2:59:36	-0.1048	14:59:39	-1.038	0.0060584
3:01:23	-0.07677	15:01:26	-0.833	0.0121944
3:02:06	-0.06029	15:02:08	-0.604	0.0042172
3:02:37	-0.04283	15:02:40	-0.44	0.004162
3:03:37	-0.01243	15:03:40	-0.207	0.0096776
3:04:30	0.00876	15:04:34	0.002	0.0085464
3:05:28	0.02911	15:05:33	0.232	0.0043324
3:06:20	0.05073	15:06:22	0.424	0.0054468
3:07:12	0.06939	15:07:14	0.633	0.0017856
3:07:52	0.09698	15:07:56	0.845	0.006734
3:08:35	0.12209	15:08:38	1.055	0.009416
3:09:07	0.13603	15:09:10	1.217	0.0060544
3:09:38	0.15076	15:09:41	1.41	0.000172
3:10:24	0.18316	15:10:26	1.618	0.0103576
3:11:02	0.20108	15:11:05	1.816	0.0071312
3:11:42	0.20618	15:11:44	1.933	-0.0002644
3:12:58	0.20283	15:13:01	1.817	0.0087744
3:13:29	0.18184	15:13:32	1.628	0.0079696
3:14:01	0.16384	15:14:04	1.428	0.0113296
3:14:24	0.13393	15:14:27	1.198	0.0059836
3:16:34	0.11681	15:16:37	1.033	0.0064856
3:17:10	0.09577	15:17:12	0.816	0.0086212
3:18:20	0.07812	15:18:22	0.633	0.0105156
3:19:14	0.05856	15:19:16	0.433	0.0123156
3:20:01	0.03166	15:20:04	0.228	0.0073096
3:20:32	0.00467	15:20:35	-0.003	0.0049904