Abstract

A modern fringe-pattern-analyzing interferometer with a resolution of 1 × 10-9 and without exclusion of systematic uncertainties owing to optic effects of less than 1 nm was used to test a new method of interferometric length measurement based on a combination of the reproducible wringing and slave-block techniques. Measurements without excessive wringing film error are demonstrated for blocks with nominal lengths of 2–6 mm and with high surface flatness. The uncertainty achieved for these blocks is less than 1 nm. Deformations of steel gauge blocks and reference platens, caused by wringing forces, are investigated, and the necessary conditions for reproducible wringing are outlined. A subnanometer uncertainty level in phase-change-correction measurements has been achieved for gauge blocks as long as 100 mm. Limitations on the accuracy standard method of interferometric length measurements and shortcomings of the present definition of the length of the material artifact are emphasized.

© 2000 Optical Society of America

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References

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  1. N. a., “Documents concerning the new definition of the metre,” Metrologia 19, 163–177 (1984); T. J. Quinn, “Mise en pratique of the definition of the metre,” Metrologia 30, 523–541 (1992).
  2. E. Engelhard, “Precise interferometric measurement of gauge blocks,” in Proceedings of the Symposium on Gauge Blocks, August 1955, Natl. Bur. Stand. (U.S.) Circ.581, 1–20 (1957); H. Damedde, “High-precision calibration of long gauge blocks using the vacuum wavelength comparator,” Metrologia 29, 349–359 (1992).
  3. International Organization for Standardization, International Standard ISO 3650:1998(E), “Geometrical product specifications—length standards—gauge blocks” (International Organization for Standardization, Geneva, 1998).
  4. J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34, 479–493 (1997).
    [CrossRef]
  5. B. G. Vaucher, R. Thalmann, “CCDM comparison of gauge block measurements,” Metrologia 35, 97–104 (1998).
    [CrossRef]
  6. A. Titov, I. Malinovsky, H. Belaïdi, R. S. França, C. A. Massone, “Sub-nanometer precision in gauge block measurements,” presented at the Conference on Precision Electromagnetic Measurements, Washington, D.C., July 1998.
  7. I. Malinovsky, A. Titov, J. A. Dutra, H. Belaïdi, R. S. França, C. A. Massone, “Toward subnanometer uncertainty in interferometric length measurements of short gauge blocks,” Appl. Opt. 38, 101–112 (1999).
    [CrossRef]
  8. L. Miller, Engineering Dimensional Metrology (Arnold, London, 1962), p. 96.
  9. I. Malinovsky, A. Titov, C. Massone, “Fringe-image processing gauge block comparator of high-precision,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 92–100 (1998).
    [CrossRef]
  10. A. Titov, I. Malinovsky, C. Massone, “Study to realize subnanometer accuracy level in gauge block measurements,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 82–91 (1998).
    [CrossRef]
  11. C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Austr. J. Phys. 8, 224–240 (1955);“Obliquity effects in interferometry,” Opt. Acta 4, 127–135 (1957).
    [CrossRef]
  12. R. K. Leach, A. Hart, K. Jackson, “Measurement of gauge blocks by interferometry: an investigation into the variability in wringing film thickness,” (National Physical Laboratory, Teddington, UK, 1999).
  13. International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization, Geneva, 1993), pp. 2–28.
  14. K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
    [CrossRef]

1999 (1)

1998 (1)

B. G. Vaucher, R. Thalmann, “CCDM comparison of gauge block measurements,” Metrologia 35, 97–104 (1998).
[CrossRef]

1997 (1)

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34, 479–493 (1997).
[CrossRef]

1994 (1)

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

1984 (1)

N. a., “Documents concerning the new definition of the metre,” Metrologia 19, 163–177 (1984); T. J. Quinn, “Mise en pratique of the definition of the metre,” Metrologia 30, 523–541 (1992).

1955 (1)

C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Austr. J. Phys. 8, 224–240 (1955);“Obliquity effects in interferometry,” Opt. Acta 4, 127–135 (1957).
[CrossRef]

Belaïdi, H.

I. Malinovsky, A. Titov, J. A. Dutra, H. Belaïdi, R. S. França, C. A. Massone, “Toward subnanometer uncertainty in interferometric length measurements of short gauge blocks,” Appl. Opt. 38, 101–112 (1999).
[CrossRef]

A. Titov, I. Malinovsky, H. Belaïdi, R. S. França, C. A. Massone, “Sub-nanometer precision in gauge block measurements,” presented at the Conference on Precision Electromagnetic Measurements, Washington, D.C., July 1998.

Birch, K. P.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Bruce, C. F.

C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Austr. J. Phys. 8, 224–240 (1955);“Obliquity effects in interferometry,” Opt. Acta 4, 127–135 (1957).
[CrossRef]

Decker, J. E.

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34, 479–493 (1997).
[CrossRef]

Downs, M. J.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Dutra, J. A.

Engelhard, E.

E. Engelhard, “Precise interferometric measurement of gauge blocks,” in Proceedings of the Symposium on Gauge Blocks, August 1955, Natl. Bur. Stand. (U.S.) Circ.581, 1–20 (1957); H. Damedde, “High-precision calibration of long gauge blocks using the vacuum wavelength comparator,” Metrologia 29, 349–359 (1992).

França, R. S.

I. Malinovsky, A. Titov, J. A. Dutra, H. Belaïdi, R. S. França, C. A. Massone, “Toward subnanometer uncertainty in interferometric length measurements of short gauge blocks,” Appl. Opt. 38, 101–112 (1999).
[CrossRef]

A. Titov, I. Malinovsky, H. Belaïdi, R. S. França, C. A. Massone, “Sub-nanometer precision in gauge block measurements,” presented at the Conference on Precision Electromagnetic Measurements, Washington, D.C., July 1998.

Hart, A.

R. K. Leach, A. Hart, K. Jackson, “Measurement of gauge blocks by interferometry: an investigation into the variability in wringing film thickness,” (National Physical Laboratory, Teddington, UK, 1999).

Jackson, K.

R. K. Leach, A. Hart, K. Jackson, “Measurement of gauge blocks by interferometry: an investigation into the variability in wringing film thickness,” (National Physical Laboratory, Teddington, UK, 1999).

Leach, R. K.

R. K. Leach, A. Hart, K. Jackson, “Measurement of gauge blocks by interferometry: an investigation into the variability in wringing film thickness,” (National Physical Laboratory, Teddington, UK, 1999).

Malinovsky, I.

I. Malinovsky, A. Titov, J. A. Dutra, H. Belaïdi, R. S. França, C. A. Massone, “Toward subnanometer uncertainty in interferometric length measurements of short gauge blocks,” Appl. Opt. 38, 101–112 (1999).
[CrossRef]

I. Malinovsky, A. Titov, C. Massone, “Fringe-image processing gauge block comparator of high-precision,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 92–100 (1998).
[CrossRef]

A. Titov, I. Malinovsky, H. Belaïdi, R. S. França, C. A. Massone, “Sub-nanometer precision in gauge block measurements,” presented at the Conference on Precision Electromagnetic Measurements, Washington, D.C., July 1998.

A. Titov, I. Malinovsky, C. Massone, “Study to realize subnanometer accuracy level in gauge block measurements,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 82–91 (1998).
[CrossRef]

Massone, C.

A. Titov, I. Malinovsky, C. Massone, “Study to realize subnanometer accuracy level in gauge block measurements,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 82–91 (1998).
[CrossRef]

I. Malinovsky, A. Titov, C. Massone, “Fringe-image processing gauge block comparator of high-precision,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 92–100 (1998).
[CrossRef]

Massone, C. A.

I. Malinovsky, A. Titov, J. A. Dutra, H. Belaïdi, R. S. França, C. A. Massone, “Toward subnanometer uncertainty in interferometric length measurements of short gauge blocks,” Appl. Opt. 38, 101–112 (1999).
[CrossRef]

A. Titov, I. Malinovsky, H. Belaïdi, R. S. França, C. A. Massone, “Sub-nanometer precision in gauge block measurements,” presented at the Conference on Precision Electromagnetic Measurements, Washington, D.C., July 1998.

Miller, L.

L. Miller, Engineering Dimensional Metrology (Arnold, London, 1962), p. 96.

Pekelsky, J. R.

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34, 479–493 (1997).
[CrossRef]

Thalmann, R.

B. G. Vaucher, R. Thalmann, “CCDM comparison of gauge block measurements,” Metrologia 35, 97–104 (1998).
[CrossRef]

Titov, A.

I. Malinovsky, A. Titov, J. A. Dutra, H. Belaïdi, R. S. França, C. A. Massone, “Toward subnanometer uncertainty in interferometric length measurements of short gauge blocks,” Appl. Opt. 38, 101–112 (1999).
[CrossRef]

I. Malinovsky, A. Titov, C. Massone, “Fringe-image processing gauge block comparator of high-precision,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 92–100 (1998).
[CrossRef]

A. Titov, I. Malinovsky, H. Belaïdi, R. S. França, C. A. Massone, “Sub-nanometer precision in gauge block measurements,” presented at the Conference on Precision Electromagnetic Measurements, Washington, D.C., July 1998.

A. Titov, I. Malinovsky, C. Massone, “Study to realize subnanometer accuracy level in gauge block measurements,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 82–91 (1998).
[CrossRef]

Vaucher, B. G.

B. G. Vaucher, R. Thalmann, “CCDM comparison of gauge block measurements,” Metrologia 35, 97–104 (1998).
[CrossRef]

Appl. Opt. (1)

Austr. J. Phys. (1)

C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Austr. J. Phys. 8, 224–240 (1955);“Obliquity effects in interferometry,” Opt. Acta 4, 127–135 (1957).
[CrossRef]

Metrologia (4)

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

N. a., “Documents concerning the new definition of the metre,” Metrologia 19, 163–177 (1984); T. J. Quinn, “Mise en pratique of the definition of the metre,” Metrologia 30, 523–541 (1992).

J. E. Decker, J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia 34, 479–493 (1997).
[CrossRef]

B. G. Vaucher, R. Thalmann, “CCDM comparison of gauge block measurements,” Metrologia 35, 97–104 (1998).
[CrossRef]

Other (8)

A. Titov, I. Malinovsky, H. Belaïdi, R. S. França, C. A. Massone, “Sub-nanometer precision in gauge block measurements,” presented at the Conference on Precision Electromagnetic Measurements, Washington, D.C., July 1998.

E. Engelhard, “Precise interferometric measurement of gauge blocks,” in Proceedings of the Symposium on Gauge Blocks, August 1955, Natl. Bur. Stand. (U.S.) Circ.581, 1–20 (1957); H. Damedde, “High-precision calibration of long gauge blocks using the vacuum wavelength comparator,” Metrologia 29, 349–359 (1992).

International Organization for Standardization, International Standard ISO 3650:1998(E), “Geometrical product specifications—length standards—gauge blocks” (International Organization for Standardization, Geneva, 1998).

L. Miller, Engineering Dimensional Metrology (Arnold, London, 1962), p. 96.

I. Malinovsky, A. Titov, C. Massone, “Fringe-image processing gauge block comparator of high-precision,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 92–100 (1998).
[CrossRef]

A. Titov, I. Malinovsky, C. Massone, “Study to realize subnanometer accuracy level in gauge block measurements,” in Recent Developments in Optical Gauge Block Metrology, N. Brown, J. E. Decker, eds., Proc. SPIE3477, 82–91 (1998).
[CrossRef]

R. K. Leach, A. Hart, K. Jackson, “Measurement of gauge blocks by interferometry: an investigation into the variability in wringing film thickness,” (National Physical Laboratory, Teddington, UK, 1999).

International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization, Geneva, 1993), pp. 2–28.

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Figures (12)

Fig. 1
Fig. 1

Inclination-correction measurements for the interferometer with a 100-mm block: experimental points and theoretical fits for the data versus the laser spot displacement from the center of the input diaphragm. Inset, the laser beam spot against the diaphragm as a background. (a) Curves 1 and 2, which correspond to a spot size difference of 25%, give the inclination corrections at the maximum of curves 0.32 nm and 0.97 nm, respectively. (b) More-accurate measurement in the vicinity of optimum tuning, that is, the maximum of the curve. The height of the squares in (b) corresponds approximately to random uncertainty.

Fig. 2
Fig. 2

Set of experiments 1–5 for precision length measurements of steel platens. For reproducible wringing of the slave block (SB), the length of the measured block (GB) is obtained as a difference of two differential measurement results (I 2 - I 4) and (I 3 - I 4) with respect to the numbering in the experiment set. Differential measurement (I 1 - I 4) is necessary for determination of the phase-change correction of the optical reflection; (I 5 - I 3) is used to control the wringing quality. Designations used: L opt and L m , optical and mechanical lengths of the block, respectively; I 1, noncorrected length measured by the interferometer in measurement 1 of the experiment set; ΔGP, wringing film thickness at the block center; δ G , δ P , the phase change for the block and the plate, respectively; d i , d p , wave-front error and platen flatness error, respectively.

Fig. 3
Fig. 3

Difference between two 3-D length profiles of a high-quality 5-mm gage block, corresponding to the reproducible wrings to a steel platen, which shows that the area of tight wringing is close to the center of the block and that the measurements are performed without Abbe error.

Fig. 4
Fig. 4

Left, bending deformation magnitudes for the steel block and platen and right, the ratio of these deformation magnitudes for the block and platen versus the nominal length value of the block. Inset, schematic of the method.

Fig. 5
Fig. 5

Effectiveness of the differential measurement (I 1 - I 4): Noncorrected central length measurements for a 5-mm block and the values, corrected for interferometer optics and deviation in base-platen curvature, as a function of distance from the block edge. Dimensions of the data points are approximately equal to the random uncertainty of the measurement.

Fig. 6
Fig. 6

Central length measurements of a grade K 30-mm block for different wrings to a steel platen, illustrating the spread of data for the standard method. 3-D length profiles of the block, corresponding to wrings 1 and 3, show that in case 3 some nonexcluded Abbe error is present.

Fig. 7
Fig. 7

Abbe error (offset) in block measurements. (a), (b) Cases of correctable Abbe error, indicated as A c ; (c) case of nonexcluded Abbe error, indicated as A n . The length (dashed lines) is shifted relative to the line at which scale is applied (solid lines) by a distance p. For (a) reproducible wringing and (b) nonreproducible wringing at the block center (white dots 1), the Abbe error can be corrected by measurement of the free platen. For (c) the Abbe error can be corrected only at the point of wringing (dark dots 2).

Fig. 8
Fig. 8

Deviations of central length from the nominal value for 6- and 7.5-mm steel blocks, obtained by (a), (d) the standard and (b), (e) the modified slave-block techniques and by (c), (f) differential measurement (I 1 - I 4) on a steel platen with corrections for interferometer optics and platen curvature. The difference between the values of the two methods gives the phase-change correction value ρ for the block relative to the platen. (See text for details.)

Fig. 9
Fig. 9

Deviations of central length from the nominal value for a 2-mm tungsten carbide block, obtained by (a) (e) wringing different faces of the block to a steel platen and by (b)–(d), (f) the modified slave-block technique, with similar 5- and 100-mm blocks used as slave blocks. The difference between the values of the two methods gives the phase change-correction value ρ for the tungsten carbide block relative to the steel platen. (See text for details.)

Fig. 10
Fig. 10

Central length measurements of a 5-mm tungsten carbide block obtained for wrings on different faces of the block: (a), (b) left face; (c), (d) right face. (a), (c) Measured by the slave-block technique; (b), (d) obtained by the differential measurement (I 1 - I 4) on the steel platen.

Fig. 11
Fig. 11

Central length measurements of a 50-mm steel block obtained for wrings on different faces of the block: (a), (b) is right face; (c), (d) left face. (a), (c) Measured by the slave-block technique; (b), (d) obtained by the differential measurement (I 1 - I 4) on the steel platen.

Fig. 12
Fig. 12

Length profiles for the 50-mm steel block for wrings to (a) the left face of the block and (b) to the right face. Data correspond to the same wrings as in Fig. 11.

Tables (1)

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Table 1 Length-Dependent Component of Combined Standard Uncertainty

Equations (13)

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u2c=u2x+0.0392L2,
I1=Lopt+δG+δP+ΔGP+di+dP*=Lm+ΔGP+di+dP*+δP-δG,
Lm=Lopt+2δG.
I4=di+dP,
I1-I4=Lm+ΔGP+dP*-dP+δP-δG=LD+δP-δG+dP*-dP,
LD=Lm+ΔGP.
I2=Lm+ΔGP+LS+ΔSG+di+dP*+δP-δS,
I3=LS+ΔSP+di+dP*+δP-δS.
I2-I3=Lm+ΔGP+ΔSG - ΔSP=LD+ΔSG - ΔSP.
I5-I3=Lm+ΔGS+δS-δG=LD+δS-δG.
I2-I3=LD.
I2-I3-I1-I4=δG-δP.
u2x=u2WS+u2WB+u2WD+u2WF=0.32+0.32+0.12+0.120.452,

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