Calibration of Displacement Laser Interferometer Systems for Industrial Metrology
Abstract
:1. Introduction
2. Laser Frequency Calibration: λv
2.1. Calibration Against an Iodine Stabilized Laser
2.2. Calibration Against Another Stabilized Laser
2.3. Omitting Calibration by Considering the Laser as a Primary Standard
2.4. Indirect Calibration by Comparing to a Reference System
3. Counting System: The Comparison Test Bench: N
4. Short Range Interpolation and Nonlinearity Errors: δ
5. Software Checks on Environmental Conditions: na,Tm
Birch and Downs: | na = 1.000271376 | |
Ciddor | na = 1.000271373 | |
Bönsch | na = 1.000271374 |
5.1. Indirect Software Check
5.2. Direct Software Check
5.3. Indirect and Direct Check of Material Temperature Compensation
5.4. Complete System Check
6. Environmental and Material Temperature Sensor Calibration: Ta, Tm, p, H
6.1. Material Temperature Calibration: Tm
6.2. Air Temperature Calibration Ta
6.3. Air Pressure Calibration: p
6.4. Air Humidity Calibration: H
7. Calibration of Laser Interferometer Optics
7.1. Calibration of Linear Optics
7.2. Calibration of Angular Optics
7.3. Calibration of Straightness Optics
7.4. Calibration of Squareness Optics
8. Reporting and Discussion
9. Conclusions
Supplementary Materials
Funding
Conflicts of Interest
References
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Year | Mean Frequency | Standard Uncertainty | Relative Standard Uncertainty | Iodine Cell Temperature | Modulation Frequency | Reference |
---|---|---|---|---|---|---|
ff in MHz | u/kHz | urel | T(I)/°C | Mod/MHz | ||
1983 | 473,612,353.692 | 161 | 3.4 × 10−10 | 15.0 ± 1.0 | 6.0 ± 1.0 | [3] |
1992 | 473,612,353.597 | 12 | 2.5 × 10−11 | 15.0 ± 0.2 | 6.0 ± 0.3 | [10] |
2001 | 473,612,353.604 | 10 50 | 2.1 × 10−11 1.0 × 10−10 | 15.0 ± 0.2 15.0 ± 1.0 | 6.0 ± 0.3 6.0 ± 1.0 | [8] |
Influencing Factor | Deviation | Deviation in Indication of Length l Uncertainty Based on k = 2 | |
---|---|---|---|
Wavelength λ nominal vacuum wavelength λnom = 632.991370 nm | +(7 ± 6) × 10−9 × λnom | −(7 ± 6) × 10−9 × l | |
or | Frequency f nominal frequency fnom = 473.612236 MHz | −(7 ± 6) × 10−9 × f | −(7 ± 6) × 10−9 × l |
or | Wavelength λ nominal vacuum wavelength λnom = 632.991370 nm | (0 ± 2.4) × 10−8 × λnom | (0 ± 2.4) × 10−8 × l |
Laser Type | Nominal Wavelength in nm | Nominal Frequency fnom in MHz | Nominal Beat Frequency with Iodine d-dip fd = 473,612,379.821 ∆f = fnom − fd in MHz |
---|---|---|---|
HP5526 (before 1980) | 632.991480 | 473,612,154 | −226 |
HP5526 (after 1980) | 632.991400 | 473,612,213 | −167 |
HP5528 (before 1990) | 632.991393 | 473,612,219 | −161 |
HP5528 (after 1990) | 632.991370 | 473,612,236 | −144 |
HP5529 | 632.991354 | 473,612,248 | −132 |
Renishaw ML10 | 632.990580 | 473,612,827 | 447 |
Renishaw RLU | 632.990000 | 473,613,261 | 881 |
Heidenhain ILM1101 | 632.991257 | 473,612,320 | −60 |
SIOS | 632.991400 | 473,612,213 | −167 |
ZYGO | 632.991193 | 473,612,368 | −12 |
Influencing Factor | Deviation | Deviation in Indication of Length l | |
---|---|---|---|
Calculation of na | −(8 ± 2) × 10−8 | +(8 ± 2) × 10−8 × l | |
or | Compensation factor ca | +(8 ± 2) × 10−8 | +(8 ± 2) × 10−8 × l |
or | VOL factor (HP/Agilent) | +(8 ± 2) × 10−5 | +(8 ± 2) × 10−8 × l |
Tested Laser Interferometer/mm | Reference Laser Interferometer/mm | Drift/mm | |
---|---|---|---|
Laser readings without compensation | 6988.25646 | 6988.25626 | 0 |
Tested laser with compensation Reference without compensation | 6986.36065 | 6988.25578 | −0.00048 |
Influencing Factor | Deviation | Deviation in Indication of Length l |
---|---|---|
Material temperature Tm | +(0.07 ± 0.02) °C | +(0.07 ± 0.02) × αm × l |
Influencing Factor | Deviation | Deviation in Indication of Length l |
---|---|---|
Air temperature Ta | −(0.10 ± 0.10) °C | −(1.0 ± 1.0) × 10 −7 × l |
Influencing Factor | Deviation | Deviation in Indication of Length l |
---|---|---|
Air pressure p | −(1.2 ± 0.3) hPa | +(3.2 ± 0.8) × 10−7 × l |
Influencing Factor | Deviation | Deviation in Indication of Length l |
---|---|---|
Air humidity H | +(20 ± 10) %Rh | +(1.7 ± 0.8) × 10−7 × l |
Measured Angle | Angle When Zeroing φ0 | |||
---|---|---|---|---|
6′ | 30′ | 1° | 2° | |
maximum deviation | ||||
6′ | <0.01″ | 0.02″ | 0.06″ | 0.2″ |
1° | 0.06″ | 0.4″ | 1.1″ | 3.2″ |
2° | 0.2″ | 1.4″ | 3.2″ | 8.8″ |
5° | 1.4″ | 7.5″ | 17″ | 39″ |
10° | 5.6″ | 29″ | 1′ | 1′48″ |
15° | 12.8″ | 1′06″ | 2′16″ | 4′05″ |
Influencing Factor | Deviation and Standard Uncertainty | Deviation in Length Indication l and Standard Uncertainty | |
---|---|---|---|
1 | Vacuum wavelength | +(0.07 ± 0.06) × 10−7 × λ | −(0.07 ± 0.06) × 10−7 × l |
2 | Counting system | <(0.01 µm + 2 × 10−8 × l) | (0.00 ± 0.01) µm ± 0.2 ×10−7 × l |
3 | Air pressure | +(0.4 ± 0.1) hPa | − (1.0 ± 0.3) ×10−7 × l |
4 | Air temperature | −(0.06 ± 0.10) °C | −(0.6 ± 1.0) ×10−7 × l |
5 | Air humidity | +(20 ± 10) %Rh | +(1.7 ± 0.8) ×10−7 × l |
6 | Calculation of air refractive index na | −(0.8 ± 0.3) × 10−7 × na | +(0.8 ± 0.3) × 10−7 × l |
Total deviation in length measurement without material-temperature correction | (0.00 ± 0.01) µm − (0.8 ± 1.4) × 10−7 × l | ||
7 | Material temperature sensor | −(0.02 ± 0.01) °C | −(0.02 ± 0.01) × α × l |
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Haitjema, H. Calibration of Displacement Laser Interferometer Systems for Industrial Metrology. Sensors 2019, 19, 4100. https://doi.org/10.3390/s19194100
Haitjema H. Calibration of Displacement Laser Interferometer Systems for Industrial Metrology. Sensors. 2019; 19(19):4100. https://doi.org/10.3390/s19194100
Chicago/Turabian StyleHaitjema, Han. 2019. "Calibration of Displacement Laser Interferometer Systems for Industrial Metrology" Sensors 19, no. 19: 4100. https://doi.org/10.3390/s19194100