Abstract

One important prerequisite for interferometric length measurements of high accuracy is autocollimation adjustment. This guarantees that the direction of the length scale represented by light waves is parallel to the length direction of the object investigated. First we describe the conventional visual autocollimation adjustment method used at Physikalisch-Technische Bundesanstalt since the beginning of interferometric length measurements. Then a new autocollimation method based on scanning the retroreflection from the interferometer is described. Check measurements are performed in order to investigate the quality of the adjustment. As a result of the method applied the uncertainty contribution originating from the cosine error could be reduced drastically for the interferometer used.

© 2004 Optical Society of America

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References

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  1. J. E. Decker, R. Schödel, G. Bönsch, “Considerations for evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry,” Metrologia 41, L11–L17 (2004).
    [CrossRef]
  2. R. Schödel, J. E. Decker, “Methods to recognize the sample position for most precise interferometric length measurements,” in Interferometry XII: Techniques and Analysis, W. Osten, E. Novak, eds., Proc. SPIE5532, 237–247 (2004).
  3. P. Cordiale, G. Galzerano, H. Schnatz, “International comparison of two iodine-stabilized frequency-doubled Nd:YAG lasers at 532 nm,” Metrologia 37, 177–182 (2000).
    [CrossRef]
  4. G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulas,” Metrologia 35, 133–139 (1998).
    [CrossRef]
  5. K. Creath, “Temporal phase measuring methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Bristol, U.K., 1993), pp. 99–112.
  6. C. F. Bruce, “The effect of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
    [CrossRef]
  7. R. Schödel, A. Nicolaus, G. Bönsch, “Minimizing interferometer misalignment errors for measurement of subnanometer length changes,” in Recent Developments in Traceable Dimensional Measurements II, J. E. Decker, N. Brown, eds., Proc. SPIE5190, 34–42 (2003).
    [CrossRef]
  8. G. Bönsch, “Simultaneous wavelength comparison of iodine stabilized lasers at 515 nm, 633 nm, and 640 nm,” IEEE Trans. Instrum. Meas. IM-34, 248–251 (1985).
    [CrossRef]
  9. A. Lewis, D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
    [CrossRef]

2004 (1)

J. E. Decker, R. Schödel, G. Bönsch, “Considerations for evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry,” Metrologia 41, L11–L17 (2004).
[CrossRef]

2000 (1)

P. Cordiale, G. Galzerano, H. Schnatz, “International comparison of two iodine-stabilized frequency-doubled Nd:YAG lasers at 532 nm,” Metrologia 37, 177–182 (2000).
[CrossRef]

1998 (1)

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulas,” Metrologia 35, 133–139 (1998).
[CrossRef]

1992 (1)

A. Lewis, D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

1985 (1)

G. Bönsch, “Simultaneous wavelength comparison of iodine stabilized lasers at 515 nm, 633 nm, and 640 nm,” IEEE Trans. Instrum. Meas. IM-34, 248–251 (1985).
[CrossRef]

1955 (1)

C. F. Bruce, “The effect of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
[CrossRef]

Bönsch, G.

J. E. Decker, R. Schödel, G. Bönsch, “Considerations for evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry,” Metrologia 41, L11–L17 (2004).
[CrossRef]

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulas,” Metrologia 35, 133–139 (1998).
[CrossRef]

G. Bönsch, “Simultaneous wavelength comparison of iodine stabilized lasers at 515 nm, 633 nm, and 640 nm,” IEEE Trans. Instrum. Meas. IM-34, 248–251 (1985).
[CrossRef]

R. Schödel, A. Nicolaus, G. Bönsch, “Minimizing interferometer misalignment errors for measurement of subnanometer length changes,” in Recent Developments in Traceable Dimensional Measurements II, J. E. Decker, N. Brown, eds., Proc. SPIE5190, 34–42 (2003).
[CrossRef]

Bruce, C. F.

C. F. Bruce, “The effect of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
[CrossRef]

Cordiale, P.

P. Cordiale, G. Galzerano, H. Schnatz, “International comparison of two iodine-stabilized frequency-doubled Nd:YAG lasers at 532 nm,” Metrologia 37, 177–182 (2000).
[CrossRef]

Creath, K.

K. Creath, “Temporal phase measuring methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Bristol, U.K., 1993), pp. 99–112.

Decker, J. E.

J. E. Decker, R. Schödel, G. Bönsch, “Considerations for evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry,” Metrologia 41, L11–L17 (2004).
[CrossRef]

R. Schödel, J. E. Decker, “Methods to recognize the sample position for most precise interferometric length measurements,” in Interferometry XII: Techniques and Analysis, W. Osten, E. Novak, eds., Proc. SPIE5532, 237–247 (2004).

Galzerano, G.

P. Cordiale, G. Galzerano, H. Schnatz, “International comparison of two iodine-stabilized frequency-doubled Nd:YAG lasers at 532 nm,” Metrologia 37, 177–182 (2000).
[CrossRef]

Lewis, A.

A. Lewis, D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

Nicolaus, A.

R. Schödel, A. Nicolaus, G. Bönsch, “Minimizing interferometer misalignment errors for measurement of subnanometer length changes,” in Recent Developments in Traceable Dimensional Measurements II, J. E. Decker, N. Brown, eds., Proc. SPIE5190, 34–42 (2003).
[CrossRef]

Potulski, E.

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulas,” Metrologia 35, 133–139 (1998).
[CrossRef]

Pugh, D. J.

A. Lewis, D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

Schnatz, H.

P. Cordiale, G. Galzerano, H. Schnatz, “International comparison of two iodine-stabilized frequency-doubled Nd:YAG lasers at 532 nm,” Metrologia 37, 177–182 (2000).
[CrossRef]

Schödel, R.

J. E. Decker, R. Schödel, G. Bönsch, “Considerations for evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry,” Metrologia 41, L11–L17 (2004).
[CrossRef]

R. Schödel, J. E. Decker, “Methods to recognize the sample position for most precise interferometric length measurements,” in Interferometry XII: Techniques and Analysis, W. Osten, E. Novak, eds., Proc. SPIE5532, 237–247 (2004).

R. Schödel, A. Nicolaus, G. Bönsch, “Minimizing interferometer misalignment errors for measurement of subnanometer length changes,” in Recent Developments in Traceable Dimensional Measurements II, J. E. Decker, N. Brown, eds., Proc. SPIE5190, 34–42 (2003).
[CrossRef]

Aust. J. Phys. (1)

C. F. Bruce, “The effect of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

G. Bönsch, “Simultaneous wavelength comparison of iodine stabilized lasers at 515 nm, 633 nm, and 640 nm,” IEEE Trans. Instrum. Meas. IM-34, 248–251 (1985).
[CrossRef]

Meas. Sci. Technol. (1)

A. Lewis, D. J. Pugh, “Interferometer light source and alignment aid using single-mode optical fibers,” Meas. Sci. Technol. 3, 929–930 (1992).
[CrossRef]

Metrologia (3)

J. E. Decker, R. Schödel, G. Bönsch, “Considerations for evaluation of measurement uncertainty in interferometric gauge block calibration applying methods of phase step interferometry,” Metrologia 41, L11–L17 (2004).
[CrossRef]

P. Cordiale, G. Galzerano, H. Schnatz, “International comparison of two iodine-stabilized frequency-doubled Nd:YAG lasers at 532 nm,” Metrologia 37, 177–182 (2000).
[CrossRef]

G. Bönsch, E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulas,” Metrologia 35, 133–139 (1998).
[CrossRef]

Other (3)

K. Creath, “Temporal phase measuring methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Bristol, U.K., 1993), pp. 99–112.

R. Schödel, J. E. Decker, “Methods to recognize the sample position for most precise interferometric length measurements,” in Interferometry XII: Techniques and Analysis, W. Osten, E. Novak, eds., Proc. SPIE5532, 237–247 (2004).

R. Schödel, A. Nicolaus, G. Bönsch, “Minimizing interferometer misalignment errors for measurement of subnanometer length changes,” in Recent Developments in Traceable Dimensional Measurements II, J. E. Decker, N. Brown, eds., Proc. SPIE5190, 34–42 (2003).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Derivation of the cosine error. The path difference of the two partial waves reflected at the end plate and the sample’s front face, reckoned from the common incident wave front through A and D to the reflected wave fronts through E, is compared with path length 2L.

Fig. 2
Fig. 2

Visual autocollimation adjustment scheme.

Fig. 3
Fig. 3

Schematic of PTB’s precision interferometer.

Fig. 4
Fig. 4

Light coupling of the interferometer and retroreflection scanning.

Fig. 5
Fig. 5

Retroreflection signal as a function of x and y; B, section in the x direction together with a theoretical curve obtained from the overlap of two circles as a function of displacement.

Fig. 6
Fig. 6

Length evaluation at different axial fiber positions away from the optimum, z = 0. Autocollimation was performed after z was set. The insets show the corresponding scan as density graphics (compare Fig. 5). The optimum z position was assigned to zero. The curve is theoretical (see text). An absolute sample length of almost 200 mm was subtracted.

Fig. 7
Fig. 7

Wave fronts of a spherical wave at two positions separated by one wavelength in the direction of propagation. For point P at a distance d from the axis, the separation of the wave fronts in the direction of the axis is increased to λ/cos β, where β = arcsin d/ R.

Fig. 8
Fig. 8

Length evaluation at different x and y positions of the fiber output, where the zero positions are based on retroreflection scanning with the green laser (532 nm): solid circles, measurement points with the green laser fitted by the solid curves; open circles, measurements with the red laser (633 nm) and fitted by the dashed curves. See text for details.

Fig. 9
Fig. 9

Length measurements (total length of a 200-mm sample being subtracted) made with different fringe adjustment by tilting the reference mirror. For illustration the measured fringe systems are shown as insets. Arrows indicate the measurement sequence.

Equations (5)

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L˜=L cos α α1 L1- 12α2.
α=arcsinδmax/fcoll α1 δmax/fcoll,
xc, yc= n=1,m=1N,Mxn, ymSxn, ym-S0n=1,m=1N,MSxn, ym-S0,
2Lλ1- 12d2R2
α=1/fcollx-x02+ y-y021/2

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