Abstract - NPL Publications
88
NPL Report CBTLM 3 January 2000 NMS Programme for Length 1997 -1999 MPU 8/44.2 David R Flack Dimensional Metrology Section Centre for Basic, Thermal and Length Metrology National Physical Laboratory Queens Road Teddington Middlesex United Kingdom TWIIOLW Abstract The aim of the Small Angle Generator project was to develop and commission a small angle measurement facility to provide a traceable measurement service of angles over a range of 60 seconds of arc with an uncertainty of :!:: 0.01 second of arc. The Small Angle Generator was designed, built and installed at NPL by Renishaw PIc. This document is the Final Traceability Report that forms part of WP4 of the Small Angle Generator Project. It describes work at NPL to verify the encoder system against calibrated angle standards. It covers the use of the standards to calibrate the encoder and the calibration of the standards "themselves. The use of the standards with a calibrated system is also described and the report also summarises the main achievements of the project. This document demonstrates that the target specification has been met. 1
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Transcript of Abstract - NPL Publications
NPL Report CBTLM 3
January 2000
NMS Programme for Length 1997 -1999MPU 8/44.2
David R FlackDimensional Metrology Section
Centre for Basic, Thermal and Length MetrologyNational Physical Laboratory
Queens RoadT eddingtonMiddlesex
United KingdomTWIIOLW
Abstract
The aim of the Small Angle Generator project was to develop and commission a small angle
measurement facility to provide a traceable measurement service of angles over a range of 60
seconds of arc with an uncertainty of :!:: 0.01 second of arc. The Small Angle Generator was
designed, built and installed at NPL by Renishaw PIc. This document is the Final Traceability
Report that forms part of WP4 of the Small Angle Generator Project. It describes work at NPL to
verify the encoder system against calibrated angle standards. It covers the use of the standards to
calibrate the encoder and the calibration of the standards "themselves. The use of the standards
with a calibrated system is also described and the report also summarises the main achievements
of the project. This document demonstrates that the target specification has been met.
1
NPL Report CBTLM 3
@ Crown Copyright 2000Reproduced by permission of the Controller of HMSO
ISSN 1469-4921
National Physical LaboratoryQueens Road, Teddington, Middlesex, United Kingdom, TWll OLW
No extracts from this report may be reproduced without the prior written consent of the Managing
Director, National Physical Laboratory; if consent is given the source must be acknowledged and
may not be used out of context.
Approved on behalf of the Managing Directorby Dr David Robinson, Head of Centre for Basic, Thermal and Length Metrology
2
NPL Report CBTLM 3
CONTENTS
1. INTRODUCTION
.1
THE SMALL ANGLE GENERATOR PROJECT.
.2 THE SMALL ANGLE GENERATOR
6
7
2.
METHODS CONSmERED
3. SIGN CONVENTIONS 10
4. PROCEDURE FOR DETERMINING TRACEABILITY 11
13
13
15
17
17
18
18
18
20
22
4.1 OUTLINE OF METHOD 4.2 EXAMPLE CALIBRATION AT 12 DEGREES 4.2.1 Measurements at -12 degrees 4.2.2 Measurements at + 12 degrees 4.3 EXAMPLE CALIBRATION OF THE STANDARD (12°) 4.4 DETERMINING THE ENCODER ERRORS AT 12° 4.5 UNCERTAINTY IN CALffiRATION OF ANGLE STANDARD ,
4.5.1 Type A 4.5.2 Type B 4.5.3 Combined and expanded uncertainty 4.5.4 Summary of angle standard uncertainties
5.
RESULTS 23
6. UNCERTAINTY OF ENCODER CALffiRA TION 25
25
25
25
26
26,
26
27
6.1 TYPE A 6.2 TYPE B 6.2.1 Autocol/imator calibration 6.2.2 Pyramidal error 6.2.3 Centrality of beam 6.2.4 Wavefront 6.2.5 Uncertainty in the calibration of the angle gauge.
6.3 COMBINED STANDARD UNCERTAINTY ,
6.4 SUMMARY
27
28
7. UNCERTAINTY OF ANGLES GENERATED BY THE SMALL ANGLE GENERATOR 29
29
30
30
31
31
32
7.1 TYPE A UNCERTAINTIES 7.2 TYPE B UNCERTAINTIES 7.2.1 Calibration of the interferometer against the encoder. 7.2.2 Encoder repeatability. 7.2.3 Drift. 7.2.4 Setting up of interferometer signals
3
NPL Report CBTLM 3
.33
.33
._~4
35
36
.36
.37
7.2.5 Resolution 7.2.6 Resolution of DSP 7.2.7 Scale factor 7.2.8 Resolution of autocollimator 7.2.9 Combined standard uncertainty
7.2.10 Best Measurement Capability..
7.3 SUMMARY
8. CHECKS USING A CALIBRATED SYSTEM 38
38
38
39
40
40
41
41
42
43
8.1 MEASUREMENTS AT 30 MINUTE POSITION 8.1.1 Measurements at -30 minutes 8.1.2 Measurements at +30 minutes """"""""""""""""""""""""""" 8.1.3 Calibration of 30 minute angle gauge combination 8.1.4 Evaluation at 30 minute positions , 8.2 MEASUREMENTS AT 1 DEGREE POSITION 8.2.1 Measurements at -1 degree 8.2.2 Measurements at + 1 degree 8.2.3 Calibration of 1 degree angle standard 8.2.4 Evaluation at 1 degree positions
9. CALIBRATION AGAINST AN AUTOCOLLIMA TOR 44
9.1 METHOD
9.2 RESULTS
.44
.44
10. CONCLUSION
11. SUMMARY OF THE MAIN PROJECT ACHIEVEMENTS 49
12. REFERENCES
13. DATA FILES
FIGURE LEGENDS
8Figure 1 The Small Angle Generator ..,
Figure 2 Central 60 seconds comparison with NPL interferometer ,
TABLES
..12
.13
Table 1 Combinations of angle gauges used in the tests.
Table 212 degree encoder calibration (negative)
4
NPL Report CBTLM 3
14
15
Table 3 Summary of data at -12 degrees Table 4 12 degree encoder calibration (positive side) Table 5 Summary of data at + 12 degrees
16
,
17Table 6 Calibration of 12 degree angle standard Table 7 Summary at all encoder positions, (all values in seconds)
23
Table 8 System calibration at -30 minute position 38
Table 9 System calibration at +30 minute position
,
39
Table 10 calibration of 30 minute angle gauge ,
Table 11 System calibration at -1 degree position
43
Table 12 System calibration at + 1 degree position Table 13 Calibration of 1 degree angle gauge combination.
Table 14 Autocollimator calibration: Run 1 .44
...45
...45
Table 15 Autocollimator calibration: Run 2
Table 16 Summary of runs 1 and 2
5
NPL Report CBTLM 3
1. INTRODUCTION
1.1 THE SMALL ANGLE GENERATOR PROJECT
In the latter part of 1996 a consortium comprising Renishaw PIc and NPL began work on a Project
to develop a Small Angle Generator. The Small Angle Generator was to be designed and built by
Renishaw PIc. It was installed at NPL in June 1999. NPL's role in the project was to prove the
system and demonstrate traceability
The Small Angle Generator project was split into four work packages. Work package one involved
a feasibility study. Work package two involved developing the first prototype system. Report
DS/9901A/OO9/01A covered work package three, the evaluation of the prototype system.
Report DS/9901A/OO9/01A is Restricted Commercial but its conclusions can be summarised as
follows:
.The ability to successfully interface the Small Angle Generator software with an external
instrument was demonstrated.
The automatic calibration of an autocollimator was successfully demonstrated. Results showed
that the combined error of the autocollimator and the small angle generator was less than 0.03
second of arc.
The Small Angle Generator was compared with the NPL angular interferometer over a range of
::!: 140 seconds of arc. Over a six hour test the drift in the zero position reading was typically less
than 0.2 second of arc. When grouping the data, the differences from the mean value were
generally less than 0.05 second of arc. With a cubic used to correct the NPL interferometer
fringe counts to seconds of arc the differences were centred on zero with a spread of ::!: 0.06
second of arc. If the mean value at each position is calculated and a cubic used to correct the
NPL interferometer fringe counts to seconds of arc the differences between the two instruments
are less than 0.03 second of arc. Over the sets of data taken on three days the mean differences
between the NPL interferometer and the Small Angle Generator were less than 0.01 second of
arc over the central :t 30 seconds of arc.
This report covers work package four and in particular the establishment of traceability.
6
NPL Report CBTLM 3
1.2 THE SMALL ANGLE GENERATOR
The Small Angle generator is shown in Figure 1. The main measurement system of the Small
Angle Generator is an angular interferometer. The design of the interferometer system is such that
a one second of arc rotation results in one full Lissajous count of the sine and cosine signals. The
type of interferometer used is based on the principle that as a glass block rotates the optical path
length of a beam passing through it changes. In the Small Angle Generator two glass blocks are
used to improve the linearity of the system and to make the system more-or-less equally sensitive
at both ends of its angular range.
The angular interferometer is precise but not accurate. As pointed out above the interferometer is
non-linear and also its calibration is dependent on the ambient temperature, pressure and
humidity.
To make the Small Angle Generator accurate its interferometer system is regularly calibrated
against its own internal encoder system. The accuracy of the encoder system is specified as
:t 1 second of arc. The interferometer is calibrated over a range of 300 to achieve a scale factor
accuracy of 0.001 second of arc in 30 seconds of arc. Software routines were provided by Renishaw
to perform this calibration
If one can demonstrate that the encoder is traceable one can easily show that the whole system is
traceable
7
NPL Report CBTLM 3
Figure 1 The Small Angle Generator
8
NPL Report CBTLM 3
2. METHODS CONSIDERED
Work reported on in Report DS/9901A/009/01A showed that the mean differences between an
NPL designed angular interferometer and the calibrated interferometer in the Small Angle
Generator were less than 0.01 second of arc. However at the time that this exercise was performed
traceability of the Small Angle Generator encoder had not been demonstrated. Both the NPL
interferometer and the Small Angle Generator's interferometer had scale factors derived from the
Small Angle Generator's built in encoder. Therefore although both interferometers agreed to better
than 0.01 second of arc it had not been demonstrated that the Small Angle Generator was
traceable. Establishing that the Small Angle Generator was traceable therefore basically involved
calibrating the in-built encoder.
Three basic methods were considered for making the system traceable. They were
(1) calibration of the encoder against a Moore Precision Index or AA Gage Ultradex@,
(2) calibration of the encoder against a polygon,
(3) calibration of the encoder using several optical wedges and
(4) calibration of the encoder against angle gauge combinations.
At the start of the project method (1) was considered the best route to obtain traceability. However
it transpired that the Moore Precision Index was too heavy for the servo control system. A lighter
Ultradex table was a possible alternative. However since no Ultradex tables are available at NPL
this option was not considered further although the best route to traceability in the long run may
be via an Ultradex table.
Method (2) was quickly rejected because the smallest angle between faces obtainable is 5 degrees
which would allow only five calibration points (-10, -5, 0, 5,10 degrees).
Method (3) was also considered. However this method was rejected as suitable optical wedges
could not be procured in time.
In the end method (4) was used. Method (4) involved wringing pairs of angle gauges to a glass
block. The glass block was wrung in such a way that the weight of the combination was taken by
the bottom angle gauge. Each combination was measured on the Small Angle Generator using a
9
NPL Report CBTLM 3
4. PROCEDURE FOR DETERMINING TRACEABILITY
4.1 OUTLINE OF METHOD
The combinations of angle gauges given in Table 1 were used to calibrate the encoder of the Small
Angle Generator. A list of equipment used follows:
(1) Hilger and Watts 100 second of arc range photo-electric autocollimator type TA9057 (inventory
number ST806) Calibration certificate 08B071/99012/NPLlO/1 dated 4 March 1999.
(2) Moore Precision Index 8-1440-28 Calibration certificate C2/66 dated 19 December 1997
(3) Combination Angle Gauges (British patent 5307/40) made by Coventry gauge and Tool Co.
Limited Set No. 171. Calibrated for these tests in wrung combinations.
(4) Hilger and Watts Microptic Autocollimator No. 98462 NPL inventory number MO(1)1873.
Calibration certificate LD08/000001/NPLl1/44 dated 8 February 2000
To create an angle standard, a pair of combination angle gauges was wrung to a glass block. The
glass block was wrung in such a way that the weight of the combination was taken by the bottom
angle gauge. Each combination was measured on the Small Angle Generator using photo-electric
autocollimator MO(1)1873 to view the faces.
The wrung combination was placed nominally at the centre of the Small Angle Generator work
table. Rotations were generated, using the encoder calibration routine in the software, equal to the
nominal angle of the wrung combination and the change in autocollimator reading noted over
several rotations.
The angle combination was then checked against a Moore Precision Index and photoelectric
autocollimator ST806.
Ideally autocollimator ST806 would have been used both on the Small Angle Generator and with
the Moore Precision Index used to calibrate the combinations but this was not practicable. The
only other autocollimator that gave a suitable image and had a photo-electric detector was
MO(1)1873. This autocollimator's resolution (0.1 second) is not as good as the resolution of ST806
(0.01 second) but was adequate for this task.
11
NPL Report CBTLM 3
Table 1 Combinations of angle gauges used in the tests
Section 4.2 gives an example calibration at the 120 positions.
12
NPL Report CBTLM 3
4.2 EXAMPLE CALIBRA nON AT 12 DEGREES
The procedure used is described below using the 120 degree case as an example. The data was
collected using the software's encoder calibration routine.
First the Small Angle Generator table was rotated to 0.00 seconds and the autocollimator reading
noted. The table was then rotated to -43200 seconds (-12°), i.e. an absolute move of -43200. This
was repeated a further two times and finally a zero reading recorded. The angle standard was then
repositioned on the worktable to allow the calibration of the +12° interval. Examples from the 12°
calibration are given below at 4.2.1 and 4.2.2.
4.2.1 Measurements at -12 degrees
Filename n12a.edr
Table 2 12 degree encoder calibration (negative)
Rotation
entered
Actual Autocollimator Difference
(Seconds)
Autocollimator
Position reading
5'06.9"
(Seconds)
0 -0.19 306.9
-43200 -43199.8 5'09.1 " 309.1 2.2
0 -0.22 5'06.95" 306.95
-43200 -43199.8 5'09.05" 309.05 2.1
0 -0.22 5'07.0" 307.0
-43200 -43199.9
5'09.2"
309.2 2.2
0 -0.22 5'07.0" 307.0
Mean 2.17
The data content of the file is shown below7
-8.80
-43090.43
-8.80
-43090.43
-8.81
-43090.44
-8.81
-151410
-741293288
-151460
-741293251
-151649
-741293484
-151554
-2552.45
-71590969.87
-267/.17
-11590967.04
-2680.69-71590985.04
-2676.63
-137.49
-71516103.64
-83.96
-71576128.87
-84.73
-71576134.66
-82.92
-0.19853 0.00029 306.9000
-43199.83876 0.00038 309.1000
-0.22001 0.00029 306.9500
-43199.84552 0.00037 309.0500
-0.22131 0.00034 307.0000
-43199.85270 0.00029 309.2000
-0.21954 0.00034 307.0000
13
NPL Report CBTLM 3
If we look at the two important columns (column 5 the encoder average and column 7 the
autocollimator reading) we have
Table 3 Summary of data at -12 degrees
Encoder Difference--
A utocollimator
Reading
(seconds)
Difference
Average
(seconds) (seconds) (seconds)
-0.19853 306.9
-43199.83876 43199.64023 309.1 2.2
-0.22001. 306.95
-43199.84552 43199.62551 309.05 2.1
-0.22131 307.0
-43199.85270 43199.63139 309.2 2.2
-0.21954 307.0-
-43199.63238 MeanMean 2.17
Std. Dev 0.0074 Std Dev 0.058
The mean angle generated is: -43199.63 seconds and the mean difference in autocollimator
readings is 2.17 seconds. However the encoder did not rotate through 43200 seconds falling short
by 0.37 seconds. To reach 43200 seconds we would have had to rotate a further -0.37 second. This
would have increased the autocollimator reading by 0.37 second resulting in a bigger difference.
The error in the angle gauge combination measured by the Small Angle Generator is therefore 2.17
+ 0.37 = 2.54 seconds.
14
NPL Report CBTLM 3
4.2.2 Measurements at +12 degrees
Filename ~ 12.edr
Table 412 degree encoder calibration (positive side)
-8.84
43073.72
-8.82
43073.71
-8.81
43073.72
-8.80
-152007
741005827-151658
741005708-151482
741005848-151378
-2601.54
71582732.39
-2483.05
71582721.33
-2451.1371582726.96
-2447.05
-1
715804
-1
715804
-1
715804
-1,
-0.21704 0.00032 296.1000
43199.89512 0.00027 293.6000
-0.19251 0.00027 296.0500
43199.88979 0.00030 293.6000
-0.18091 0.00042 296.0000
43199.89360 0.00046 293.6000
-0.17998 0.00035 296.0500
1
1
1
1
1
1,
15
49.63.86.57.80.64.81.
74
91
9230
39
28
42
NPL Report CBTLM 3
If we look at the two important columns we have
Table 5 Summary of data at +12 degrees
Encoder---
Difference DifferenceAutocollimator
Reading
(seconds)
Average
(seconds} (seconds) (seconds)
-0.21704 296.1
43199.89512 43200.11216 293.6 -2.5
-0.19251 296.05
43199.88979 43200.0823 293.6 -2.45
-0.18091 296.0--
43199.89360 43200.07451 293.6 -2.4
-0.17998 296.05
43200.089657Mean Mean 2.45
Std. Dev. Std.Dev 0.050.0199
The mean angle generated is: 43200.09 seconds and the mean difference in autocollimator readings
is -2.45 seconds. However the encoder rotated through more than 43200 seconds by 0.09 second.
To reach 43200 seconds we would have had to rotate -0.09 second. This would have increased the
second autocollimator reading by 0.09 seconds resulting in a smaller difference. The error in the
angle gauge combination measured by the Small Angle Generator is therefore 2.45 -0.09 = 2.34
seconds.
The two files relating to the example above are given in full in section 11
16
NPL Report CBTLM 3
4.3 EXAMPLE CALIBRA nON OF THE STANDARD (12°)
The standard was then placed on a Moore Precisiol) Index (8-1440-28) and calibrated against the
appropriate index on the table. The faces were viewed using autocollimator 51806. The angle was
measured eight times in total and a mean value calculated. The results are summarised for the 120
case in Table 6.
Table 6 Calibration of 12 degree angle standard
Number Difference
(second~)
00 120
1 29.20 26.75 -2.45
2 29.25 26.76 -2.49
3 29.21 26.76 -2.45
4 29.28 26.76 -2.52
5 29.25 26.76 -2.49
6 29.24 26.75 -2.49
7 29.26 26.77 -2.49
8 29.25 26.76 -2.49
Mean -2.48
4.4 DETERMINING THE ENCODER ERRORS AT 120
For the two examples given in section 4.2 we have
-12 degrees
The calibrated angle of the angle gauge is -2.48 seconds of arc. The error in the Small Angle
Generator is therefore 2.54 -2.48 = 0.06 second of arc. The table has therefore rotated too far and so
the error is -0.06 second of arc.
17
NPL Report CBTLM 3
+ 12 degrees
The calibrated angle of the angle gauge is -2.48 seconds of arc. The error in the Small Angle
Generator is therefore 2.34 -2.48 = -0.14 second of arc. The table has therefore rotated too far and
so the error is -0.14 second of arc.
4.5 UNCERTAINTY IN CALIBRATION OF ANGLE STANDARD
The calibration of the angle gauge combination provides the reference value for the calibration of
the Small Angle Generator. However, there is an uncertainty associated with these reference
values.
4.5.1 Type A
A spread sheet summarising the measured angles of each angle gauge combination is given below
12-2.45
-2.49
-2.45
-2.52
-2.49
-2.49
-2.49
-2.49
-2.48
0.0230.008
6-0.75
-0.80
-0.81
-0.83
-0.79
-0.83
-0.81
-0.81
-0.800.026
0.009
4+1.69+1.72+1.71+1.70+1.74+1.75+1.75+1.68
+1.720.0270.010
2-1.19
-1.15
-1.18
-1.16
-1.13
-1.14
-1.17
-1.18
-1.16
0.0210.008
3-4.07
-4.06
-4.09
-4.08
-4.06
-4.07
-4.04
-4.01
-4.06
0.025
0.009
9-4.15
-4.08
-4.10
-4.10
-4.11
-4.09
-4.10
-4.13
-4.11
0.023
0.008
-5.72
-5.74
-5.69
-5.74
-5.72
-5.68
-5.71
-5.73
-5.72
0.022
0.008
2345678
meanstandard deviationexperimental
As can be seen the maximum experimental standard deviation is 0.01 second of arc (AI).
4.5.2 Type B
(1) Autocollimator calibration
The autocollimator used had an error of up to 0.36 second of arc over its 100 second range and a
error of up to 0.08 second of arc over half a revolution of the micrometer drum (5 seconds of arc).
The uncertainty associated with this calibration was :t 0.02 second of arc (k = 2). However over any
10 second interval of the progressive calibration the error in the autocollimator is less than 0.10
second of arc. No attempt was made to correct for these errors. This introduces an uncertainty of
18
NPL Report CBTLM 3
0.10 second of arc. It will be assumed that this error has a rectangular a priori probability
distribution. Its contribution is therefore:
0.10"-+.J3
0.02"2
=0.07" (Bl)
This value is known with a high degree of confidence and the number of degrees of freedom to
associate with it is infinite.
(2) Pyramidal error
The autocollimator was set up so as to minimise pyramidal errors. It was estimated that the
residual pyramidal error was approximately 0.05 second of arc for a displacement normal to the
measurement axis of 200 seconds of arc. Since it is difficult to judge the exact vertical movement of
the cross wire we will assume this uncertainty to be 0.10 second of arc and to have a rectangular a
priori probability distribution. Its contribution is therefore:
0.10"-::r;- = 0.06" (B2)
It is judged that this value of u(xJ is reliable to about 20% therefore the number of degrees of
freedom to assign is v;=(0.20)- 2/2 = 12.5
Note:
1-2
(3) Centrality of beam
The estimated uncertainty due to the autocollimator axis not coinciding with the centre of the
gauge face is 0.10 second of arc. It will be assumed that this error has a rectangular a priori
probability distribution. Its contribution is therefore:
19
NPL Report CBTLM 3
0.10"~ .J3- = 0.06"
It is judged that this value of u( xJ is reliable to about 20% therefore the number of degrees of
freedom to assign is v;=(O.20)- 2/2 = 12.5
(4) Moore Precision Index
In the measurement of the standard it has been assumed that there is no error in the intervals of
the Moore Precision Index. Past calibrations of this table at thirty degree intervals have revealed
errors of up to 0.15 second of arc. These errors have been ignored for this exercise. It will be
assumed that this error has a rectangular a priori probability distribution. Its contribution is
therefore:
0.15".J3 = 0.09'1
This value is known with a high degree of confidence and the number of degrees of freedom to
associate with it is infinite.
(5) Wavefront
Since each angle gauge is subtended by different parts of the autocollimator the wavefront errors
in the autocollimator optics will add an additional source of uncertainty. It is estimated that this
contribution is of the order of 0.1 second of arc. It will be assumed that this error has a rectangular
a priori probability distribution. Its contribution is therefore:
0.10"~ = 0.06"
It is judged that this value of u( xJ is reliable to about 20% therefore the number of degrees of
freedom to assign is v;=(O.20)- 2/2 = 12.5
4.5.3 Combined and expanded uncertainty
The combined standard uncertainty of the calibration of the standard angle gauge combination is
0.012 +0.072 +0.062 +0.062 +0.092 +0.062 = 0.155"
20
NPL Report CBTLM 3
The expanded uncertainty of the calibration (k = 2) is therefore 0.31 second of arc. The total number
of degrees of freedom is calculated using the Welch-Satterthwaite formula
4
This equals
0.1554i.e. 185
effective degrees of freedom justifying the use of k = 2 (if Veff is >30 then kp is less than 2.09 and
can be approximated by k = 2). Values of k used in this document have been taken from the table in
Appendix B of UKAS document M3003 Uncertainty and Confidence in Measurement. The values
that appear in this table actually relate to a level of confidence of 95.45%.
21
NPL Report CBTLM 3
4.5.4 Summary of angle standard uncertainties
ValueComponent Divisor u v. or VeffIProbability
distribution sec
sec
Al 0.01 normal 1.0 0.01 7
B1 (a) 0.10 ..J3rectangular 0.07 00
Bl (b) 0.02 normal 2.0 0.01 00
B2 0.10 rectangular ~3 0.06 12.5
B3 0.10 rectangular -../3 0.06 12.5
B4 0.15 rectangular -.13 0.09 00
B5 0.10 -43rectangular 0.06 12.5
normal 0.155 185ti"
u normal (k = 2) 0.310 185
22
NPL Report CBTLM 3
5. RESULTS
The following table is a summary of the measurements at each position. As can be seen from the
table the encoder errors are no greater than 0.9 second of arc. Strictly the column labelled encoder
error contains some error due to the uncertainty in determining the error in the angle standard.
Table 7 Summary at aU encoder positions, (all values in seconds)
Nominal Actual Measured
error of
Corrected
error of
Calibrated error Encoder
Rotation Rotation of angle error
angle gauge angle gauge gauge
-2.48-43200 -43199.63 -2.17 -2.54 -0.06
43200 43200.09 -2.45 -2.34 -2.48 0.14
-21600 -21599.79 -0.48 -0.69 -0.80 0.11
21600 21600.19 -0.82 -0.63 -0.80 0.17
-14400 -14400.73 +0.40 1.13 1.72 -0.59
14400 14400.05 +1.23 1.28 1.72 -0.44
-7200 -7200.02 -1.72 -1.36 -1.16 -0.2
7200 7200.22 -1.38 -1.50 -1.16 -0.34
-10800 -10800.19 -4.85 -4.66 -4.06 -0.6
10800 10800.60 -5.18 -4.58 -4.06 -0.52
-3600 -3599.82 -6.35 -6.53 -5.72 -0.81
3600 3600.20 -6.82 -6.62 -5.72 -0.9
-32400 -32400.02 -4.68 -4.66 -4.11 -0.55
32400 32400.19 -4.40 -4.21 -4.11 -0.1
Encoder errors
-"-60 )00
23
NFL Report CBTLM 3
Note on 1. 9 and 3 degree standards
The 3, 9 and 1 degree standards are actually nominally 20 59' 54", 80 59' 54" and 00 59' 54".
However when generating the nominal rotations and when calibrating them they are treated as 3,
9 and 1 degree standards, hence the errors of approximately 6 seconds in column 5 of Table 7.
Note on signs of encoder error.
If the indicated rotation is 43200.1 and the actual rotation 43200 the encoder is said to have an error
of 0.1 second of arc. If the indicated rotation is -43200.1 and the actual rotation -43200 the encoder
is said to have an error of -0.1 second of arc.
Table 7 shows that the largest error occurs at the 1 degree position (the smallest rotation). An error
of 0.9 second of arc in 1 degree is equivalent to an error of 0.015 second of arc in a 60 second of arc
rotation. However, larger angular rotations show a proportionally smaller error. Since a calibration
of the system is made at 120 positions over a rotation of :t54000 seconds of arc (:t 15°) in 900
seconds of arc (15') steps the error over any 60 seconds of arc will be less than 0.01 second of arc.
24
NPL Report CBTLM 3
6. UNCERTAINTY OF ENCODER CALIBRATION
This section derives the total uncertainty associated with the calibration of the encoder within the
Small Angle Generator. The various contributions are listed below.
6.1 TYPE A
The maximum standard deviation of the measurements on the angle standard was 0.28 second of
arc. Three measurements were made and this contribution equates to
0.28.J3 = 0.17"
6.2 TYPE B
6.2.1 Autocollimator calibration
The autocollimator used had an error of up to 0.40 seconds of arc over its 10 minute range and a
error of up to 0.15 second of arc over a revolution of the micrometer drum (30 seconds of arc).
However the autocollimator was only used between 4 and 6 minutes of arc and the largest
difference measured was 6 seconds of arc. Over this two minute interval of the progressive
calibration the error in the autocollimator is less than 0.10 second of arc. No attempt was made to
correct for these errors. This introduces an uncertainty of 0.25 second of arc. It will be assumed that
this error has a rectangular a priori probability distribution. Its contribution is therefore:
0.25"~ = 0.15"
In addition the uncertainty in this calibration is 0.13 second of arc (k=2.5). Six degrees of freedom
have been associated with this uncertainty. This contribution is therefore 0.06 second of arc (B2).
25
NPL Report CBTLM 3
6.2.2 Pyramidal error
The autocollimator was set up so as to minimise pyramidal errors. It was estimated that the
residual pyramidal error was approximately 0.05 second of arc for a displacement normal to the
measurement axis of 200 seconds of arc. Since it is difficult to judge the exact vertical movement of
the cross wire we will assume this uncertainty to be 0.10 second of arc and to have a rectangular a
priori probability distribution. Its contribution is therefore:
0.10"~ = 0.06"
It is judged that this value of u(xJ is reliable to about 20% therefore the number of degrees of
freedom to assign is vi=(0.20)- 2/2 = 12.5
6.2.3 Centrality of beam
The estimated uncertainty due to the autocollimator axis not coinciding with the centre of the
gauge face is 0.10 second of arc. It will be assumed that this error has a rectangular a priori
probability distribution. Its contribution is therefore:
0.10".J3 = 0.06"
It is judged that this value of u( xJ is reliable to about 20% therefore the number of degrees of
freedom to assign is vi=(0.20)- 2/2 = 12.5
6.2.4 Wavefront
Since each angle gauge is sub tended by different parts of the autocollimator the wavefront errors
in the autocollimator optics will add an additional source of uncertainty. It is estimated that this
contribution is of the order of 0.1 second of arc. It will be assumed that this error has a rectangular
a priori probability distribution. Its contribution is therefore:
0.10"~ = 0.06"
It is judged that this value of u(xJ is reliable to about 20% therefore the number of degrees of
fr~~dom to assign is vi~(O.20)- 2/2 ~ 12.5
26
NPL Report CBTLM 3
6.2.5 Uncertainty in the calibration of the angle gauge
The derivation of this term is given in section 4.5. This contribution is equal to 0.155 seconds of arc
(B6)
6.3 COMBINED STANDARD UNCERTAINTY
The combined standard uncertainty of the calibration of the encoder calibration is
.J0.172 + 0.152 + 0.062 + 0.062 + 0.062 + 0.062 + 0.1552 = 0.300"
The expanded uncertainty of the calibration, k = 2.14, (see below) is therefore 0.641 seconds of arc.
The total number of degrees of freedom is calculated using the Welch-Satterthwaite formula
Veff =
The correct value of k to use is k = 2.14 (Taken from Appendix B of M3003).
27
NPL Report CBTLM 3
6.4 SUMMARY
Value ProbabilityComponent Divisor U.t
v or V'1f1
distribution sec
sec.
Al 0.17 normal 1.0 0.17 2
.J3Bl Q25 rectangular 0.15 00
B2 0.13 normal 2.5 0.06 6
-..13B3 0.10 rectangular 0.06 12.5
B4 0.10 -.13rectangular 0.06 12.5
0.10 -.i3B5 rectangular 0.06 12.5
B6 0.31 normal 2 0.155 00
normal 0.300 19.2u
u normal (k = 2.14) 0.642 19.2
28
NPL Report CBTLM 3
7. UNCERTAINTY OF ANGLES GENERATED BY THE SMALL ANGLE GENERATOR
The uncertainty achievable when using the Small Angle Generator will be considered in two cases.
The first case is the uncertainty that can be achieved when calibrating a typical high accuracy
autocollimator. This uncertainty will have terms that relate to the autocollimator being tested. The
second case is the Best Measurement Capability where only those terms relating to the Small
Angle Generator will be considered
7.1 TYPE A UNCERTAINTIES
This uncertainty is associated with the modulation of the interferometer optical path length. The
main sources for this uncertainty are air turbulence, mechanical vibration and the response time of
the servo-control loop. Shielding the optical path lengths has reduced the effect of air turbulence
on the interferometer system. Air turbulence will also affect the autocollimator under test.
Mechanical vibration will alter the optical path length of the interferometer by vibrating the optical
components and disturbing the position of the air bearing. Anti vibration mounting the system
reduces this effect. In addition the frequency response of the servo-control loop has been set as
high as possible so as not to cause mechanical resonance problems.
The measurement cycle is at least fifty times longer than the servo control loop response time to
reduce the effect of small control loop oscillations on the measurement, and this also helps to
reduce the effect that mechanical vibration has on the readings.
The net result of these effects on the readings is averaged out and will contribute to the type A
term. It will affect the reproducibility of both the difference in Small Angle Generator readings and
the difference in autocollimator readings.
The reproducibility of making several determinations of the error at each position is determined
experimentally, e.g. for three measurements at -5 seconds of arc:
-4.998 seconds of arc (mean of ten determinations)
-4.998 seconds of arc (mean of ten determinations)
-4.957 seconds of arc (mean of ten determinations)
29
NPL Report CBTLM 3
the standard deviation crn-! = 0.0237 second of arc. Since three determinations of the mean error are
made the contribution is 0.0137 second of arc (AI). The number of degrees of freedom to associate
with this contribution is 29.
7.2 TYPE B UNCERTAINTIES
7.2.1 Calibration of the interferometer against the encoder.
The interferometer system is calibrated against the encoder at intervals of 900 seconds of arc over a
range of:t 54000 seconds of arc.
The uncertainty in the angular encoder's calibration is :t 0.300 second of arc (19.2 degrees of
freedom). That is to say we have an uncertainty of 0.3 seconds of arc in :t12°. The angular errors of
the encoder are of the order of 1 second of arc (measured over :t12°) and are ignored. This gives
If we assume we could have a total error of 0.9 second of arc in 43200 seconds of arc the total
contribution (assuming the system is linear) is:
0.9x 60 = 0.0012 seconds of arc (Bl)
It is judged that this value of u(x) is reliable to about 20% therefore the number of degrees of
freedom to assign is Vj=(0.20j2/2 = 12.5
This term is probably pessimistic as it does not take into account the fact that the interferometer is
calibrated against the encoder at several positions and therefore averaging occurs. This term will
be derived more rigorously when producing the measurement procedure relating to the
measurement service.
30
NFL Report CBTLM 3
7.2.2 Encoder repeatability.
The repeatability of the encoder was measured in situ against the laser interferometer system. This
experimental term is a combination of electrical, optical and mechanical noise. Renishaw obtained
a repeatability of 0.1 second of arc with the system anti vibration mounted. This figure along with
thel encoder accuracy determines the angular range needed to calibrate the laser interferometerI
system to achieve an accuracy of 0.01 second of arc over the central 60 seconds. If a repeatability of
0.1 second of arc can be achieved against the encoder then, in theory and ignoring other errors
with a 240 calibration band an accuracy of 0.01 second of arc over 20 can be obtained. The encoder
repeatability is less than the errors in the encoder and will be ignored. Its effect in any case is
negligible over 60 seconds of arc.
7.2.3 Drift.
The interferometer is of a balanced design so the drift results from how well arms of the
interferometer were matched during manufacture. If the interferometer could be held thermally
stable there would be no drift. Glass, steel, and granite control the differential physical path
lengths. The linear coefficients of expansion of these materials are about +7, +11 and +4 ppm K-1
respectively. The optical path lengths are in glass and air. The thermal coefficients of refractive
index for these materials are +1.2 and -0.9 ppm K-1 respectively. A differential optical path length
change of 0.63 microns corresponds to about 1 arc second. Thus a 1 mm physical path length
difference in glass, steel and granite would produce a drift in readings for +1 Kelvin change in
temperature of +11, +17 and +6 milli-arc-seconds respectively. The contribution to the drift from
the thermal refractive effect is for 1 mm of glass and air are 1.9 and -1.4 milli-arc-seconds
respectively. Although these two figure have opposite sign in practice the effect will add, because
an increase in glass displaces an air path.
The Small Angle Generator is designed so that the physical path lengths in glass are matched to
within 1 mm. The same precision cannot be claimed for the path lengths controlled by the steel
and granite.
Drift also results from instability between the detector and beam. The detector is centrally
mounted in the horizontal plane on a circuit board. Here a movement of 0.040 mm corresponds to
31
NPL Report CBTLM 3
a drift in readings of 1 second of arc. Renishaw did not evaluate the positional stability of the
detector in the horizontal plane.
The only way to measure this drift is to alter the Small Angle Generator's temperature and
measure its drift. This test has not been performed in a controlled manner. Stability of better than
0.01 second of arc over an hour were achieved at Renishaw, in a poorly temperature controlled
room. At NPL the Small Angle Generator was compared against an existing NPL interferometer.
The combined drift of the two systems oyer eight hours was less than 0.15 second of arc i.e.
approximately 0.02 second per hour. Some of this drift will have been in the NPL interferometer
system. A typical autocollimator calibration takes about three hours. However the normal practice
of returning to zero between measurements removes this term. It also hides the drift in the
instrument to be calibrated.
Setting up of interferometer signals
The Small Angle Generator uncertainties depend partly on how well the interferometer signals
have been set up. Ideally if the Lissajous figure is a perfectly centred circle there will be no error. If
the figure is any other shape or is not perfectly centred there will be errors in sub-division. The
manual states in appendix 3 that the Lissajous should be set up to have a DC offset of no greater
than 1% of the diameter and that the circularity should be no greater than 1% of the diameter.
DC Offset
A DC Offset of 1 % results in a maximum error around the Lissajous of 0.8 degrees
1 0.01 + sin{}It is calculated by comparing e with tan-
0.01 + case
0.8The equivalent error in angle measured is 360 x 1.05 = 0.0023 seconds of arc
Circularit~
A circularity of 1 % results in a maximum error around the Lissajous of 0.3 degrees
1 1.Olsin8It is calculated by comparing e with tan-
cos()
32
NPL Report CBTLM 3
0.3The equivalent error in angle measured is 360 x 1.05 = 0.0009 seconds of arc
Assuming the interferometer has been set up correctly the actual error could lie anywhere between
these bounds. We will assume a rectangular a priori probability distribution, although arguments
could be made for a V-shaped distribution.
Total contribution from interferometer set up is 0.0015 seconds of arc and is calculated from:
.J0.00232 + 0.00092
.J3 (B2)
It is judged that this value of u(x) is reliable to about 20% therefore the number of degrees of
freedom to assign is Vj=(0.20)-2/2 = 12.5
7.2.5 Resolution
12 bit analogue to digital converters are used to digitise the sine and cosine signals from the
interferometer. The instrument resolution is therefore 1/8192 of a fringe. This component of
uncertainty is estimated to be distributed with a symmetric, rectangular a priori probability
distribution
0.00012
-~-u= = 0.0001 second of arc (rounding to 4dp and rounding up)
(B3)
The value is known with a high degree of confidence so the number of degrees of freedom to
associate with it is infinite.
7.2.6 Resolution of DSP
The DSP has a 16 bit resolution i.e. 1/65536 of a fringe. This component of uncertainty is estimated
to be distributed with a symmetric, rectangular a priori probability distribution
0.15 x 10-4
J12= 4.4 X 10.6 secondsu= (B5)
33
NPL Report CBTLM 3
The value is known with a high degree of confidence so the number of degrees of freedom to
associate with it is infinite.
Scale factor
The following affect the scale factor of the instrument.
-the frequency stability of the laser (better than 0.5 ppm)
-the physical thickness of the sensing glass blocks
-the refractive index of the sensing glass blocks
-the refractive index of air
The stability of the fringe detection optics will alter the DC value and the fringe contrast
and not the scale factor.
The thermal stability of the scale factor is 9.9 ppm K-1 This value was derived by Renishaw using
knowledge of the interferometer design. Renishaw Mathematica file SAGThermalb.nb refers.
The room the Small Angle Generator is housed in currently is temperature controlled to
20 ::!: 0.25 °C. The total error introduced by this term is therefore 3 ppm.
The scale factor is also dependent upon atmospheric pressure, directly and indirectly. The
refractive index of air is proportional to atmospheric pressure. At room temperature and pressure
this dependence is approximately 0.031 ppm Pa"l. The graph below shows the air pressure over a
typical seven days in the Teddington area. A typical change over a day is 10 hPa. (1000 fa) i.e. 31
ppm.
34
NPL Report CBTLM3
Rtnospheric pressure in Teddington for the past 7 days
If)Q...c"(\II-:)(II(II(\I
~I-
Change in air pressure also affects the refractive index of the glass via the stress coefficient. The
effect is small; a 10% change in atmospheric pressure would alter the scale factor by 0.03 ppm.
This is negligible compared to the direct term.
The main two terms are the direct pressure and temperature terms. Summing these gives a total
scale factor term of 32 ppm i.e. 0.002 seconds of arc in 60 seconds of arc. It is estimated that this
term is known with a high degree of confidence (infinite degrees of freedom). Therefore its
contribution to the uncertainty is
0.002r:: = 0.0012 seconds of arc
,,3 (B4)
7.2.8 Resolution of autocollimator
The contribution from the autocollimator will depend on the item under test. For a 0.005 second of
arc resolution autocollimator this contribution will be
0.005~ = 0.0014 second of arc
",12(B5)
35
NPL Report CBTLM 3
The value is known with a high degree of confidence so the number of degrees of freedom to
associate with it is infinite.
7.2.9 Combined standard uncertainty
Taking an example where the angle measured is 60 seconds of arc
Uc = .J0.01372 + 0.00122 + 0.00152 + 0.00012 + 0.00122 + 0.00142 = 0.014
The expanded uncertainty U at k = 2 is therefore 0.028 seconds of arc which would be quoted as
0.03 seconds of arc.
7.2.10 Best Measurement Capability
The best measurement capability is the uncertainty that results when all terms relating to the
instrument under test tend to zero i.e. it is the uncertainty associated with the generation of the
angles.
Uc = ~0.00122 + 0.00152 + 0.00012 + 0.00122 = 0.0023 second of arc
The expanded uncertainty U at k = 2 is therefore 0.0042 seconds of arc which would be quoted as
0.005 second of arc.
3(;
NPL Report CBTLM 3
7.3 SUMMARY
ValueComponent Probabilitydistribution
Divisor v or V.if1Ui
sec
sec
Al 0.0137 l'lorrnal 1.0 0.0137 29
B1 0.0012 normal 1.0 0.0012 12.5
B2 0.0025 rectangular -;3 0.0015 12.5
B3 0.00012 "12rectangular 0.0001 00
B4 0.0020 .J3rectangular 0.0012 00
B5 0.0050 rectangular "12 0.0014 00
normalUc 0.0140 32
u normal (k = 2) 0.0280 32
The total number of degrees of freedom is calculated tlSing the Welch-Satterthwaite formula
This equals
i.e. 32
effective degrees of freedom justifying the use of k = 2/ as k9o' = 2.08 (if vtJ)° is >30 then kp is less than
2.09 and can be approximated by k = 2)
37
NPL Report CBTLM 3
8. CHECKS USING A CALIBRATED SYSTEM
The system was also checked using angle gauges at two positions after a calibration had been
performed on the Small Angle Generator. The checks were made at the 30 minute and 1 degree
positions. The procedure was similar to that described in Section 4 except that the autocollimator
calibration routine was used instead of the encoder calibration routine.
8.1 MEASUREMENTS AT 30 MINUTE POSITION
8.1.1 Measurements at -30 minutes
Filename n30min.dat
Table 8 System calibration at -30 minute position
Rotation
entered
Autocollimator Autocollimator
(seconds)reading
6'32.3"
Difference
(seconds)
0
Actual
position
0.00 392.3
-1800 -1800.00 6'33.75" 393.75 +1.45
0 -0.00 6'32.25" 392.25
-1800 -1800.00 6'33.7" 393.7 +1.45
0 0.00 6'32.2" 392.2
-1800 -1800.00
6'33.7"
393.7 +1.50
0 0.00 6'32.4" 392.4
Mean +1.47
The data content of the file is shown below:
7
0.0000
-1800.0000
0.0000
-1800.0000
0.0000
-1800.0000
0.0000
-49677
-30470020
-49680
-30470020
-49681
-30470020
-49681
0.0000
-1800.0000
-0.0002
-1800.0000
-0.0002
-1800.0000
-0.0002
0.00080
0.00039
0.00028
0.00034
0.00026
0.00020
0.00039
0.009
-1800.052
0.011
-1800.057
0.009
-1800.059
0.011
392.3000 1393.7500 1392.2500 1393.7000 1392.2000 1393.7000 1392.4000 1
38
NPL Report CBTLM 3
8.1.2 Measurements at +30 minutes
Filename 1230min.dat
Table 9 System calibration at +30 minute position
Rotation Actual Autocollimator DifferenceAutocollimator
entered position
0.00reading
5'38.7"
(seconds) (seconds)
0 338.7
1800 1800.00
5'37.2"
337.2 -1.50
0 0.00 5'38.75" 338.75
1800 1800.00 5'37.3" 337.3 -1.45
0 0.00 5'38.7" 338.7
1800 1800.00 5'37.25" 337.25 -1.45
0 0.00 5'38.75" 338.75
Mean -1.47
The data content of the file is shown below:
7
0.0000
1800.0000
0.0000
1800.0000
0.0000
1800.0000
0.0000
-496
303707
-496
303707
-496
303707
-496
0.0000
1799.9997-0.0003
1799.9996-0.0002
1799.9997-0.0001
0.000760.000250.000260.000340.000180.000290.00040
O.1799.
O.
1799.O.
1799.O.
338.7000 1
337.2000 1
338.7500 1
337.3000 1
338.7000 1
337.2500 1
338.7500 1
39
7719
8317
801979
.000.919
,012
921
013
920
017
NPL Report CBTLM 3
8.1.3 Calibration of 30 minute angle gauge combination
Table 10 calibration of 30 minute angle gauge
Number 30' Difference
(seconds)
00
1 20.35 19.13 -1.22
2 20..32 19.14 -1.18
3 20.30 19.12 -1.18
4 20.30 19.13 -1.17
5 20.30 19.15 -1.15
20.30 19.156 -1.15
7 20.30 19.14 -1.16
8 20.32 19.15 -1.17
Mean -1.17
8.1.4 Evaluation at 30 minute positions
The angle generated was 1800.00 seconds of arc and the error in the angle gauge combination
measured as 1.47 seconds of arc for both positive and negative rotations. The error in the angle
gauge combination as measured on the Moore Precision Index table was 1.17 seconds of arc. The
'error' in the Small Angle Generator is 0.30 second of arc. However some of this error can be
attributed to the uncertainty in measuring the angle using the Moore Precision Index table.
However, assuming all the error was in the Small Angle generator (worst case) leads to an error of
0.3 second of arc in 1800 seconds of arc. This is equivalent to 0.01 second of arc in 60 seconds.
40
NPL Report CBTLM 3
8.2 MEASUREMENTS AT 1 DEGREE POSITION
8.2.1 Measurements at -1 degree
Filename nldeg.dat
Table 11 System calibration at -1 degree position
Rotation Actual Difference
(Seconds)
Autocollimator
entered Position reading
4' 44.2"
Autocollimator
(Seconds)
0 0.00 284.2
-3600 --'3600.00 4'50.7" 290.7 +6.5
0 -0.00 4'44.15" 284.15
-3600 -3600.00
4'50.7"
290.7 +6.55
0 0.00 4'44.1 " 284.1
-3600 -3600.00 4'50.65" 290.65 +6.55
0 0.00 4'44.1" 284.1
Mean +6.53
The data content of the file is shown below:
7
0.0000
-3600.0000
0.0000
-3600.0000
0.0000
-3600.0000
0.0000
-49677
-60895142
-49680
-60895141
-49681
-60895142
-49680
0.0000
-3599.9999
-0.0002
-3599.9999
-0.0003
-3599.9999
-0.0002
0.000800.000350.000330.000250.000200.000330.00027
0.033
-3600.005
0.044
-3600.010
0.035
-3600.011
0.041
284.2000 1
290.7000 1
284.1500 1
290.7000 1
284.1000 1
290.6500 1
284.1000 1
41
NPL Report CBTLM 3
8.2.2 Measurements at + 1 degree
Filename ~ldeg.dat1 degree calibration
Table 12 System calibration at +1 degree position
Rotation Actual Autocollimator Autocollimator
(Seconds)entered Position reading
5'28.4"
Difference
(Seconds)
0 0.00 328.4
3600 3600.00 5'22.1 " 322.1 -6.3
0 0.00 5'28.5" 328.5
3600 3600.00 5'22.0" 322.0 -6.5
0-
0.00 5'28.5" 328.5
3600 3600.00 5'22.0" 322.0 -6.5
0 0.00 5'28.4" 328.4
Mean -6.43
The data content of the file is shown below:
328
0
328
322
328
0
328
o.3600.
O.3600.
o.3600.
O.
-49
60796
-49
6079E
-45
6079E
-49
O.
3599
-0
3599
-0
3599
-0
0.00073
-0. 000i10
0.000~2
O.OOOr?0.00034
0.00042
0.00024
O.3600.
o.3600.
O.3600.
o.
42
.4000 1
.0000 1
.5000 1
.0000 1
.5000 1
.0000 1
.4000 1
0000
0000
0000
0000
0000
0000
0000
1676
iO18
1681;013
1682
;012
1680
0000
9997
0002
9994
0003
9993
0002
051042
045
035
043
036
043
NPL Report CBTLM 3
8.2.3 Calibration of 1 degree angle standard
The results of the calibration of the 10 standard are given in Table 13 below,
Table 13 Calibration of 1 degree angle gauge combination
Number-~
Difference00 10
1 19.35 13.26-
-6.09
2-
19.32 13.2] -6.11
3 19.31 13.24 -6.07
19.35 13.26 -6.094
5 19.34 13.25 -6.09
6 19.34 13.23 -6.11
7-
19.34 13.24 -6.10
19.368 13.24 -6.12
Mean -6.10
8.2.4 Evaluation at 1 degree positions
The angle generated was 3600.00 seconds of arc and the error in the angle gauge combination
measured as -6.5 seconds of arc for the negative rotation and -6.4 seconds of arc for the positive
rotation. The error in the angle gauge combination as measured on the Moore index table was -6.10
seconds of arc. The 'error' in the Small Angle Generator is 0.40 seconds of arc. However some of
this error can be attributed to the uncertainty in measuring the angle using the Moore table.
However, assuming all the error was in the Small Angle Generator (worst case) leads to an error of
0.4 seconds of arc in 3600 seconds of arc. This is equivalent to 0.007 seconds of arc in 60 seconds.
43
NPL Report CBTLM 3
9. CALIBRATION AGAINST AN AUTOCOLLIMATOR
9.1 METHOD
Autocollimator MO(1)1873 was calibrated by the Small Angle Generator in its calibrated state.
Whilst this is a fairly low resolution autocollimator (0.1 second of arc) it does have a range 10 times
that specified for the accuracy of the Small Angle Generator. For the Small Angle Generator to be
accurate to 0.01 second in 60 seconds we would expect an accuracy of 0.1 second of arc in 600
seconds.
9.2 RESULTS
Table 14 Autocollimator calibration: Run 1
Angle
Generated
Difference
from zero
Error-
AutocollimatoI Autocollimator
Reading readingsecondsseconds seconds seconds
0.00 0' 04.1" 4.1 0.0 0.0
-60.00 I' 04.2" 64.2 60.10 0.1
-120.00 2/ 04.05" 124.05 119.95 -0.05
0.0-180.00 3' 04.1" 184.1 180.00
-240.00 4' 04.15" 244.15
304.15
240.05
300.05
359.95
0.05
-300.00 5' 04.15" 0.05
-360.00 6' 04.05"
7' 04.05"
364.05 -0.05
-420.00 424.05 419.95
480.00
-0.05
0.0-480.00 8' 04.10" 484.10
-540.00 9' 04.2" 544.2 540.10 0.1.
-600.00 10' 04.4" 604.4 600.30 0.3
44
NPL Report CBTLM 3
Table 15 Autocollimator calibration: Run 2
Difference
from zero
ErrorAutocollirnatorAutocollimatorAngle
Generated Reading readingsecondsseconds seconds seconds
0.00-
0' 04.0' 4.0 0.0 0.0
-60.00 l' 04.05" 64.05 60.05 0.05
-120.00 2' 04.05" 124.05 120.05 0.05
-180.00 3' 04.0" 184.0
244.0
180.00 0.0
-240.00 4' 04.0" 240.00 0.0
-300.00 5' 04.0" 304.0 300.00 0.0
-360.00 6' 04.15" 364.15 360.15 0.15
-420.00 7' 04.15" 424.15 420.15 0.15
-480.00 8' 04.1" 484.10 480.10
540.20
0.1
0.2-540.00 9' 04.2" 544.20
-600.00 10' 04.3" 604.30 600.30 0.3
Combining the above two tables we get table 16. Column 5 of table 16 is the error in the
autocollimator as determined by the Small Angle Generator. Column 6 contains data from the
most recent calibration of this autocollimator.
Table 16 Summary of runs 1 and 2
Run 1 Run 2
--
Mean Calibrated CalibratedAutocollimatorAngleGenerated error error error
seconds seconds seconds seconds seconds
1/2000
secondsSeconds
1983
0.00 0.00 0.00~
0.0 0.00 0 0
-60.00 60.10 60.05 60.08 + 0.08 +0.25 +0.12
-120.00 119.95 +0.15120.05
180.00
120.0 0.00
0.00
+0.30
+0.25-180.00 180.00 180.0 +0.10
-240.00 240.05 240.00 240.03 +0.02 +0.40 +0.20
-300.00 300.05
359.95
300.00
360.15
300.02
360.05
+0.02
+0.05
+0.35
+0.30
+0.16
+0.10-360.00
-420.00 419.95 420.15 420.05 +0.05 +0.30 +0.06
-480.00 480.00 480.10 480.05 +0.05 +0.25
+0.30
+ 0.08
+ 0.16-540.00 540.10 540.20
600.30
540.15 + 0.15
+ 0.30-600.00 600.3 +0.40 + 0.34600.30
45
NPL Report CBTLM 3
At the six hundred second position the calibration of the autocollimator agrees with a previous
calibration using the existing NPL Small Angle Generator (a sine-bar based device) to better than
0.1 arc second. This again is equivalent to 0.01 second of arc in 60 seconds of arc.
It should be borne in mind that the autocollimator's resolution is at best 0.05 second of arc and the
calibration of the autocollimator by traditional means will also have an uncertainty approaching
0.15 second of arc (k = 2).
10. CONCLUSION
The encoder of the Small Angle Generator was calibrated against known angles. The results
indicate that the errors in the encoder system from which the interferometer gains its calibration
are no greater than 0.9 second of arc. It was shown that the effect of these errors on the
performance of the Small Angle Generator is less than 0.01 second of arc for rotations of :t 60
seconds of arc. The uncertainty in the encoder calibration was also calculated.
The uncertainty in the angles generated by the Small angle Generator and the total uncertainty
when calibrating a typical high accuracy autocollimator were also presented.
Further tests were carried out using the Small Angle Generator in its calibrated mode. The Small
Angle Generator was calibrated against its internal encoder. The calibrated system was then used
to measure two angle standards. The results indicate that the errors in the system are
commensurate with errors of less than 0.01 second of arc in 60 seconds of arc.
A further calibration of a 10 minute range autocollimator with a 0.1 second of arc resolution over
its full range confirmed the above
These results combined with those in document DS/9901A/009/01A (see figure 2) where it was
shown that the Small Angle Generator agreed to better than 0.01 seconds of arc with the NPL
angular interferometer (both instruments being calibrated against the Small Angle generator's
internal encoder) show that the instruments scaling is traceable and that the fringe sub-division is
functioning within specification.
At the time that the work described in DSj9901AjOO9jOlA was performed traceability of the
Small Angle Generator encoder had not been demonstrated. Both the NPL interferometer and the
46
NPL Report CBTLM 3
Small Angle Generators interferometers had their scale factors determined from the Small Angle
Generator's built in encoder. Therefore although both interferometers agreed, it had not been
demonstrated that the Small Angle Generator was traceable. By showing that the encoder is
traceable at the 1 second of arc level we have demonstrated that both interferometers are traceable.
Although the NPL interferometer had a range of only about :t 3600 seconds it was compared
against, and gained its calibration from, the interferometer in the Small Angle Generator that was
calibrated over a much wider range. By making the encoder traceable, both interferometer's scale
factors were then determined traceably.
The results of the comparisons with the NPL interferometer over the sub 1.0 second of arc range
that were performed to highlight any non-linearity could also then be considered to be traceable.
Third order fit
0.01
-0.01
-30 -20 -10 0SAG
10 20 30
Figure 2 Central 60 seconds comparison with NPL interferometer
The tests described in this document show that the Small Angle Generator is capable of traceably
generating rotations over a 60 seconds of arc of arc range centred on zero to 0.01 second of arc. The
47
NPL Report CBTLM 3
method chosen to demonstrate traceability is not ide~l and could be improved by procuring an,
Ultradex table. An Ultradex table could be calibrated n)ore easily and would enable the encoder to~
be checked at every 1 degree over its range. Since ~e use of an Ultradex would not involve
wringing of angle gauges its calibration would not need to be checked every time it was used. In
addition the encoder intervals could be checked in quick succession rather than over several days
as is the case with the technique described in this document.
48
NPL Report CBTLM 3
11. SUMMARY OF THE MAIN PROJECT ACHIEVEMENTS
The main project achievements are:
A Small Angle Generator capable of producing rotation accurate to 0.01 second of arc over a range
of :f: 60 seconds of arc has been designed and built by Renishaw. Software has been developed by
Renishaw to calibrate the system and to rotate the table to user-defined positions. Routines to
allow automatic instrument calibration via a dll call have also been developed. Renishaw have
produced all the appropriate design documentation and a user manual. The Small Angle
Generator has been installed and set up at NPL by Renishaw.
NPL have developed a routine to automatically collect data from a Moller Wedel high accuracy
autocollimator and have integrated that routine with the Small Angle Generator Software. The
automatic calibration of an autocollimator has been demonstrated. NPL have compared the
rotations generated by the Small Angle Generator against an existing angular interferometer at
NPL. Results agreed over :t 30 seconds of arc to better than 0.01 second of arc. At this stage since
both the Small Angle Generator and the NPL interferometer had their scale factors derived from
the Small Angle Generator's in-built encoder, traceability had not been demonstrated
Further work was then carried out to demonstrate traceability. This work is described in this
document. This work showed that the Small Angle Generator is capable of generating angles
traceably over :t 30 seconds of arc to better than 0.01 second of arc. Uncertainties have been
derived from first principles that confirm this
The Small Angle Generator is now ready to be used in measurement services at NPL. Initially NPL
calibration certificates will be issued. When the instrument moves to the new building in May
2000, UKAS permission for this system to replace the existing UKAS accredited method will be
sought.
Some of the work carried out at NPL during assessment of the Small Angle Generator will feed
into the project in the new programme to reduce turn-around times of angle measurements by
10%. In particular the software routines developed for reading the Moller Wedel autocollimator
from Microsoft Windows 95 will be used to automate some angle measuring tasks. Now that the
Small Angle Generator is traceable it will be used to calibrate the Moller Wedel Elcomat high
accuracy autocollimator allowing its use for measurement service work.
49
NPL Report CBTLM 3
The project has had problems during its duration but the final result is that the UK now has a
facility for the calibration of high accuracy autocollimators manufactured by Taylor Hobson,
Newport, Moller Wedel, Micro-Radian and others. iThe service has several advantages over
existing methods at NPL in that it has a smaller uncertainty and allows for autocollimators to be
calibrated at any customer-specified intervals and not j*st those specified by NPL.
50
NPL Report CBTLM 3
12. REFERENCES
Report DS/9901A/OO9/01A Final System Performance Hardware report
Small Angle Generator User manual DS/9901/0006/01B
Ultradex -manufactured by A.G. Davis/ AA Gage, Sterling Heights, MI 48313, USA
(www.agdavis.com)
Knoyle, C.H. NPL Combination Angle Gauges Methods of Production and Size Generation
Machinery, August 31,1950
British Patent 569/002 (1945)
BIPM, IEC, IFCC, ISO, IUP AC, IUP AP, OIML Guide to the Expression of Uncertainty in Measurement.
International Organisation for Standardisation, Geneva, Switzerland. ISBN 92-67-10188-9, First
Edition 1993
M3003, The Expression of Uncertainty and Confidence in Measurement, United Kingdom Accreditation
Service, Edition 1 December 1997
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NPL Report CBTLM 3
Tests on a calibrated system
Filename n30min.dat
0.0000.1800.0000
0.0000
1800.0000
0.0000.1800.0000
0.0000
-49677
-30470020
-49680
-30470020
-49681
.30470020
-49681
0.0000.1800.0000
-0.0002
-1800..0000
-0.0002
.1800.0000
-0.0002
0.00080
0.00039
0.00028
0.00034
0.00026
0.00Q200.00039
o.1800.
O..1800.
O.1800.
O.
392.393.392.393.392.393..392.
Reading Data
ValidCode(count)
,, Table Actual Actual Hold Encoder
, Position Position Position Error Average
, (arc secs) (count) (arc secs) (arc secs) (arc secs)
,,'Each data point reading is the average of two sets of 8000 readings, each set being taken
'over a 1.0 second period. One set of readings is taken prior to user data entry, the second
'set after data entry.
'The hold error is the average of the second set of interferometer readings minus the average
'the first set of interferometer readings.
,'Instrument Name Autocollimator and Angle Gauges
'Manufacturer Hilger and Watts/Coventry Gauge'Instrument Type / Model Number Photoelectric Autocollimator
'Instrument Serial/Identification Number MO(1)1873 and Set 171
,'Calibration Certificate Number ,
,'Client Name ,
'Client Address ,'Contact Name 'Contact Telephone Number ,
,'Time of Table Calibration 10 : 46
'Date of Table Calibration 19 / 1 / 2000
'Start Time of Instrument Calibration Cycle 11 : 31
'Start Date of Instrument Calibration 19/1 / 2000
'Finish Time of Instrument Calibration Cycle 11 : 44
'Finish Date of Instrument Calibration Cycle 19 / 1 / 2000
,'Number of Collimator readings taken while table within calibration time frame 7
,'Number of Collimator readings taken while table out of calibration time frame 0
,'Polynomial generator routine used Renishaw 9th order Chebyshev generator Vl.O'Angle to count correction routine used Renishaw 9th order Chebyshev Vl.O
'Count to angle correction routine used Renishaw 9th order Chebyshev Vl.O
,'Encoder polynomial used :-
'Offset error term 0.000000
'Correction scale factor 1..!000000
'Quadratic error term 0.000000.1'Cub"c error term 0.0010000
'Quartic error term 0.000000,'operator Name
'Additional Information
,David Flack
3 minute top -apex right
27 minute bottom apex left
%Readings Per Calibration Point
%Manual or Automatic Test
%Automatic Access Routine Used
%Target Position File Used
1
Manual
'Table Calibration not Requested
,,'Program name Small Angle Generator Software
80
009
052
011057
009
,059
011
3000
7500
2500
7000
2000
1000
4000
NPL Report CBTLM 3
Version 1..001
Small Angle Generator Table
001
%Program version nwnber%
%Hardware details
%Hardware serial nwnber
%End of File
81
NPL Report CBTLM 3
Filename p30min.dat7
-49677
30370719-49683
30370717-49680
30370719
-49679
0.00r760.00p250.00026
0.00~340.00~180.00q290.00040
338.7000
337.2000
338.7500
337.3000338.7000
337.2500
338.7500
0.000
1799.919
0.012
1799.921
0.013
1799.920
0.017
L800.0000
0.0000
800.0000
0.0000
~800.00000.0000
1799.9997
-0.0003
1799.9996
-0.0002
1799.9997
-0.0001,, Table Actual Actual Hold Encoder Reading
, Position position Position Error Average 1
, (arc secs) (count) (arc secs) (arc secs) (arc secs) (count)
,,'Each data point reading is the average of two sets of 8000 readings. each set being taken
'over a 1.0 second period. One set of readings is taken prior to user data entry. the second
'set after data entry.
'The hold error is the average of the second set of interferometer readings minus the average of
'the first set of interferometer readings.
Data
Valid
Code
%Instrument Name Autocollimator and Angle Gauges
%Manufacturer Hilger and Watts/Coventry Gauge
%Instrument Type / Model Number Photoelectric Autocollimator
%Instrument Serial/Identification Number MO(1)1873 and Set 171
%
%Calibration Certificate Number %
%
%Client Name %
%Client Address %
%Contact Name %Contact Telephone Number %
%
%Time of Table Calibration 10 : 46
%Date of Table Calibration 19 / 1 /200P
%Start Time of Instrument Calibration Cycle 11 : 47
%Start Date of Instrument Calibration 19 / 1 / 2000
%Finish Time of Instrument Calibration Cycle 12 : 06
%Finish Date of Instrument Calibration Cycle 19 / 1 / 2000
%
%Number of Collimator readings taken while table within calibration time frame 7
%
%Number of Collimator readings taken while table out of calibration time frame 0
%
%Polynomial generator routine used Renishaw 9th order Chebyshev generator Vl%Angle to count correction routine used Renishaw 9th order Chebyshev Vl.O
%Count to angle correction routine used Renishaw 9th order Chebyshev Vl.O
0.000000
1.000000
O.OQOOOO0.000000
0.000001
David Flack
3 minute top -apex right
27 minute bottom -apex left
ManuaJ
Small Angle Generator Software
Version 1.001
%Encoder polynomial used:-
%Offset error term
%Correction scale factor
%Quadratic error term
%Cubic error term
%Quartic error term
%
%Operator Name
%Additional Information
%
%
%Readings Per Calibration Point
%Manual or Automatic Test
%Automatic Access Routine Used
%Target Position File Used%
%Table Calibration not Requested
%
%
%program name
%program version number
%
%Hardware details
%Hardware serial number
%End of File
Small Angle Generator Table
001
82
NPL Report CBTLM 3
Filename nldeg.dat
0.0000-3600.0000
0.0000'3600.0000
0.0000.3600.0000
0.0000
-49677-60895142
-49680
.60895141
-49681-60895142
-49680
0.0000-3599.9999
-0.0002
-3599.9999
-0.0003
-3599.9999
-0-0002
0.00080
0.00035
0.00033
0.00025
0.00020
0.00033
0.00027
0.033
-3600.005
0.044-3600..010
0.035
-3600.011
0.041
284.2000
2~0.7000
284.1500
2~0.7000
284.1000
290.6500
284.1000
1
1
1
1
~ Table Actual Actual Hold Encoder Reading
~ Position Position Position Error Average 1
~ (arc secs) (count) (arc secs! (arc secs! (arc secs) (count)
~~
~Each data point reading is the average of two sets of 8000 readings. each set being taken
~over a 1.0 second period. one set of readings is taken prior to user data entry. the second
~set after data entry.
~The hold error is the average of the second set of interferometer readings minus the average of
~the first set of interferometer readings.
~~Instrument Name
~Manufacturer
~Instrument Type / Model Number
~Instrument Serial/Identification Number
~
'Calibration Certificate Number ~
~~Client Name ~
~Client Address ~
~Contact Name ~Contact Telephone Number ~
~~Time of Table Calibration 10 : 46
~Date of Table Calibration 19 ( 1/2000
~Start Time of Instrument Calibration Cycle 13 : 41
~Start Date of Instrument Calibration 19 / 1 / 2000
~Finish Time of Instrument Calibration Cycle 13 : 56
'Finish Date of Instrument Calibration Cycle 19/1 / 2000
~
~Number of Collimator readings taken while table within calibration time frame 7
~
~Number of Collimator readings taken while table out of calibration time frame 0
~
'Polynomial generator routine used Renishaw 9th order Chebyshev generator Vl.O~Angle to count correction routine used Renishaw 9th order Chebyshev Vl.O
~Count to angle correction routine used Renishaw 9th order Chebyshev Vl.O
,~Encoder polynomial used :-
'Offset error term 0.000000
~Correction scale factor 1.000000
~Quadratic error term 0.000000~Cubic error term 0.000000
~Quartic error term 0.000000
~
~Operator Name
~Additional Information
~
~~Readings Per Calibration Point 1
~Manual or Automatic Test Manual
~Automatic Access Routine Used ~Target Position File Used ~
~Table Calibration not Requested
~
~
~Program name
~Program version number
,~Hardware details
~Hardware serial number
~End of File
Data
ValidCode
Autocollimator and Angle Gauges
Hilger and Watts/Coventry Gauge
Photoelectric AutocollimatorMO(1)lB73 and Set 171
David
Flack0.1
minute top -apex right1 degree bottom -
Small Angle Generator Software
Version 1.001
Small
Angle Generator Table
001
83
NPL Report CBTLM 3
Filename pldeg.dat
0.0000
3600.0000
0.0000
3600.0000
0.00003600.0000
0.0000
-49676
60796018
-49681
60796013
-49682
60796012
-49680
0.00p73
-O.OOplO
0.00\1220.000170.00034
0.00042
0.00024
0
3599
-0
3599
-0
3599
-0
O.3600.
o.3600.
O.3600.
O.
328.COOO
0.0000
328.5000
322.0000328.5000
0.0000
328.COOO,, Table Actual Actual Hold Encoder Reading
, Position Position Position Error Average 1
, (arc secs) (count) (arc secsl (arc secs) (arc secs) (count)
,,'Each data point reading is the average of two sets of 8000 readings, each set being taken
'over a 1.0 second period. one set of readings is taken prior to user data entry, the second
'set after data entry.
'The hold error is the average of the second set of interferometer readings minus the average of
'the first set of interferometer readings.
,'Instrument Name
'Manufacturer
'Instrument Type I Model Number
'Instrument Serial I Identification Number_~ ,cc~.,,",
,'Calibration Certificate Number ,,'Client Name ,'Client Address ,
'Contact Name 'Contact Telephone Number ,
,'Time of Table Calibration 10 : 46
'Date of Table Calibration 19 I 1 I 2000
'Start Time of Instrument Calibration Cycle 14 : 40
'Start Date of Instrument Calibration 19 I 1 12000
'Finish Time of Instrument Calibration Cycle 14 : Sl
'Finish Date of Instrument Calibration Cycle 19 I 1 I 2000
,'Number of Collimator readings taken while table withih calibration time frame 7
,
Data
ValidCode
Autocollimator and Angle Gauges
Hilger and Watts/Coventry Gauge
Photoelectric Autocollimator
MO(1!1873 and Set 171
of Collimator readings taken while table out of calibration time frame
,'Polynomial generator routine used Renishaw 9th order Chebyshev generator Vl
'Angle to count correction routine used Renishaw 9th order Chebyshev Vl.O
'Count to angle correction routine used Renishaw 9th order ChebYshev Vl.O
,'Encoder polynomial used :-
'Offaet error term 0.000000
'Correction scale factor 1..000000
'Quadratic error term o.odoooo
'Cubic error term O.oqoooo
'Quartic error term 0.000000
,'Operator Name David Flack
'Additional Information 0.1 minute top -apex right
, 1 degree bottom -apex left
,'Readings Per Calibration Point 1
'Manual or Automatic Test Manual
'Automatic Access Routine Used 'Target Position File Used ,
'Table Calibration not Requested
,,'Program name
'Program version number
,'Hardware details
'Hardware serial number
'End of File
Small Angle Generator Software
Version 1.001
Small Angle Generator Table001
84
.0000
.9997
.0002
.9994
.0003
.9993
.0002
051042
045
035
043
036
043
NPL Report CBTLM 3
Filename peac.datAutocollirnator test
0.0000
60.0000
-60.0000
-120.0000
-180.0000
.240.0000
.300.0000
-360.0000
.420.0000
-480.0000
-540.0000
-600.0000
0.0000
-60.0000
-120.0000
.180.0000
.240.0000
.360.0000
.300.0000
-360.0000
-420.0000
-480.0000
-540.0000
-600.0000
-53698
960282
-1067686
-2081670
-3095655
-4109639
-5123628
-6137614
-7151601
-8165591
-9179582.10193574
-53700
-1067687
-2081671
-3095655
-4109639
-6137614
-5123626
-6137613
-7151602
-8165589
-9179582-10193574
0.0001
59.9999
-60.0001
-120.0001
-180.0001
-240.0000
.300.0001
.360.0000
420.0000
-480.0000
-540.0001
-600.0001
-0.0001
-60.0001.120.0001
.180.0001
-240.0000
.360.0000
.300.0000
-360.0000
-420.0000
-479.9999
.540.0000
.600.0000
0.00073
0.00037
0.00033
0.00029
0.00008
0.00032
0.00022
0.00039
0.00035
0.00029
0.00035
0.00030
0.00040
0.00033
0.00027
0..00045
0.00034
0.00024
0.00029
0.00027
0.00053
0.00030
0.00024
0.00032
-0.011
59.960
-59.993
-119.965
-179.942
-239.947
-299.971
-360.032
-420.026
-480.012
-539.999
-599.987
-0.028
-59.999
-119.977
-179.957
-239.962
-360.047
-299.997
-360.042
-420.039
-480.004
-540.005
-600.021
4.1000
0.0000
64.2000
124.0500
184.1000
244.1500
304.1500
364.0500
424.0500
484.1000
544.2000
604.4000
4.0000
64.0500
124.0500
184.0000
244.0000
0.0000
304.0000
364.1500
424.1500
484.1000
544.2000
604.3000
%
% Table Actual Actual Hold Encoder Reading
% Position Position Position Error Average 1
% (arc secs) (count) (arc secs) (arc secs) (arc secsl (count)
%
%
%Each data point reading is the average of two sets of 8000 readings, each set being taken
%over a 1.0 second period. one set of readings is taken prior to user data entry. the second
%set after data entry.%The hold error is the average of the second set of interferometer readings minus the average of
%the first set of interferometer readings.
%
%Instrument Name
%Manufacturer%Instrument Type I t " ~-- %Instrument Serial I MO(1)1873
%
%Calibration Certificate Number %
%
%Client Name %
%Client Address %
%Contact L
%Contact Telephone Number %
%
%Time of Table Calibration 10 : 47
%Date of Table Calibration 20 I 1 I 2000
%Start Time of Instrument Calibration Cycle 11 : 33
%Start Date of Instrument Calibration 20 I 1 I 2000
%Finish Time of Instrument Calibration Cycle 12 : 10
%Finish Date of Instrument Calibration Cycle 20 I 1 I 2000
Data
ValidCode
Microptic Autocollimator
Hilger and Watts
Photoelectric Autocollimator.~. ..~.~~.Identification NumbeI
'Number of Collimator readings taken while table within calibration time frame 2
,'Number of Collimator readings taken while table out of calibration time frame 0
,'Polynomial generator routine used Renishaw 9th order Chebyshev generator Vl.O
'Angle to count correction routine used Renishaw 9th order Chebyshev Vl.O'Count to angle correction routine used Renishaw 9th order Chebyshev Vl.O
,'Encoder polynomial used:-
'Offset error term 0.000000
'Correction scale factor 1.000000
'Quadratic error term 0.000000
'Cubic error term 0.000000
'Quartic error term 0.000000
David Flack
None'Operator Name
'Additional Information
85
NPL Report CBTLM 3
Manua
Small Angle Generator Softwar
Version 1.001
%Readings Per Calibration Point
%Manual or Automatic Test
%Automatic Access Routine Used
%Target Position File Used
%
%Table Calibration Requested
%
%
%Program name
%Program version number
%
%Hardware details
%Hardware serial number
%End of File
Small Angle Generator Table
001
86
NPL Report CBTLM 3
The small angle generator configuration file for these tests
Small Angle Generator configuration file
Parameters for the encoder correction polynomial
0
1
0
0
0
Offset
Correction scale factor
Quadratic error termCubic error term
Quantic error term
define automatic collimator read routines
mw_dllItest.tpd
name of first auto DLL routine
name of first auto routine test point file
dr f_dl 1
drf.tpd
name of second auto DLL routine
name of second auto routine test point file
fringe_dll
Iftestcl.tpd
name of third auto DLL routine
name of third auto routine test point file
Calibration Test
sweep_l.tpd
name of fourth auto DLL routine
name of fourth auto routine test point file
position Hold Test
hold_OOO.tpd
name of fith auto DLL routine
name of fith auto routine test point file
position Hold Test
hold_P1O.tpd
name of sixth auto DLL routine
name of sixth auto routine test point file
Position Hold Test
hold_N3.tpd
name of seventh auto DLL routine
name of seventh auto routine test point file
position Hold Test
hold_P3.tpd
name of eighth auto DLL routine
name of eighth auto routine test point file
define automatic encoder read routines
Encoder Test 1
enc_l.tpd
name of first auto DLL routine
name of first auto routine test point file
enc_timeenc_time.tpd
name of second auto DLL routine
name of second auto routine test point file
enc_date-prog
enc_date.tpd
name of third auto DLL routine
name of third auto routine test point file
P.7
NPL Report CBTLM 3
enc_random_num
enc_random.tpd
name of fourth auto DLL routine
name of fourth auto routine test point file
name of fith auto DLL routine
name of fith auto routine test point file
name of sixth auto DLL routine
name of sixth auto routine test point file
name of seventh auto DLL routine
name of seventh auto routine test point file
name of eighth auto DLL routine
name of eighth auto routine test point file
define valid table calibration period
0
1
hours
minutes
minutes left before approaching end of calib message flashed
define range of calibration sweep and step size
54000
900
+/- calibration sweep range in arc secs
step size in arc secs
define number of decimal places to which collimator readings displayed
3 collimator reading will be displayed to 3 dec places
define table optical offset value
0 offset value in arc secs
88
