Abstract

A new and potentially cost efficient kind of vibration-tolerant surface measurement interferometer based on the Fizeau-principle is demonstrated. The crucial novelty of this approach is the combination of two optoelectronic sensors: an image sensor with high spatial resolution and an arrangement of photodiodes with high temporal resolution. The photodiodes continuously measure the random-phase-shifts caused by environmental vibrations in three noncollinear points of the test surface. The high spatial resolution sensor takes several “frozen” images of the test surface by using short exposure times. Under the assumption of rigid body movement the continuously measured phase shifts of the three surface points enable the calculation of a virtual plane that is representative for the position and orientation of the whole test surface. For this purpose a new random-phase-shift algorithm had to be developed. The whole system was tested on an optical table without vibration isolation under the influence of random vibrations. The analysis of the root-mean-square (RMS) over ten different measurements shows a measurement repeatability of about 0.004 wave (approximately 2.5nm for 632.8nm laser wavelength).

© 2011 Optical Society of America

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References

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  1. J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 504–505, 514–515.
  2. J. Hayes, “Dynamic interferometry handles vibrations,” in Proceeding of Laser Focus World, March 2002, pp. 109–113.
  3. L. Wizinowich, “Phase shifting interferometry in the presence of vibration: a new algorithm and system,” Appl. Opt. 29, 3271–3279 (1990).
    [CrossRef] [PubMed]
  4. C. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
    [CrossRef]
  5. J. E. Millerd, N. J. Brock, and J. B. Hayes, “Modern approaches in phase measurement metrology,” Proc. SPIE 5856, 14–22(2005).
    [CrossRef]
  6. H. Kihm, “A point-diffraction interferometer with vibration-desensitizing capability,” Proc. SPIE 6293, 62930B (2006).
    [CrossRef]
  7. R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 24, 361–364 (1984).
  8. J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
    [CrossRef]
  9. N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
    [CrossRef]
  10. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
    [CrossRef]
  11. B. Kimbrough, J. E. Millerd, J. C. Wyant, and J. B. Hayes, “Low coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).
  12. N. Doloca and R. Tutsch, “Random phase shift interferometer,” in Proceeding of Fringe 2005—The 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten, ed. (Springer Verlag, 2005), pp. 167–174.

2006 (2)

H. Kihm, “A point-diffraction interferometer with vibration-desensitizing capability,” Proc. SPIE 6293, 62930B (2006).
[CrossRef]

B. Kimbrough, J. E. Millerd, J. C. Wyant, and J. B. Hayes, “Low coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

2005 (2)

J. E. Millerd, N. J. Brock, and J. B. Hayes, “Modern approaches in phase measurement metrology,” Proc. SPIE 5856, 14–22(2005).
[CrossRef]

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

2004 (2)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

1992 (1)

C. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

1990 (1)

1984 (1)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 24, 361–364 (1984).

Brock, N.

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

Brock, N. J.

J. E. Millerd, N. J. Brock, and J. B. Hayes, “Modern approaches in phase measurement metrology,” Proc. SPIE 5856, 14–22(2005).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

Bruning, J. H.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 504–505, 514–515.

Doloca, N.

N. Doloca and R. Tutsch, “Random phase shift interferometer,” in Proceeding of Fringe 2005—The 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten, ed. (Springer Verlag, 2005), pp. 167–174.

Greivenkamp, J. E.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 504–505, 514–515.

Hayes, J.

J. Hayes, “Dynamic interferometry handles vibrations,” in Proceeding of Laser Focus World, March 2002, pp. 109–113.

Hayes, J. B.

B. Kimbrough, J. E. Millerd, J. C. Wyant, and J. B. Hayes, “Low coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

J. E. Millerd, N. J. Brock, and J. B. Hayes, “Modern approaches in phase measurement metrology,” Proc. SPIE 5856, 14–22(2005).
[CrossRef]

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

Kihm, H.

H. Kihm, “A point-diffraction interferometer with vibration-desensitizing capability,” Proc. SPIE 6293, 62930B (2006).
[CrossRef]

Kimbrough, B.

B. Kimbrough, J. E. Millerd, J. C. Wyant, and J. B. Hayes, “Low coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

Koliopoulos, C.

C. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

Millerd, J. E.

B. Kimbrough, J. E. Millerd, J. C. Wyant, and J. B. Hayes, “Low coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

J. E. Millerd, N. J. Brock, and J. B. Hayes, “Modern approaches in phase measurement metrology,” Proc. SPIE 5856, 14–22(2005).
[CrossRef]

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 24, 361–364 (1984).

North-Morris, M. B.

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

Novak, M.

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 24, 361–364 (1984).

Tutsch, R.

N. Doloca and R. Tutsch, “Random phase shift interferometer,” in Proceeding of Fringe 2005—The 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten, ed. (Springer Verlag, 2005), pp. 167–174.

Wizinowich, L.

Wyant, J. C.

B. Kimbrough, J. E. Millerd, J. C. Wyant, and J. B. Hayes, “Low coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

Appl. Opt. (1)

Opt. Eng. (1)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 24, 361–364 (1984).

Proc. SPIE (7)

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

N. Brock, J. B. Hayes, B. Kimbrough, J. E. Millerd, M. B. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005).
[CrossRef]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314(2004).
[CrossRef]

B. Kimbrough, J. E. Millerd, J. C. Wyant, and J. B. Hayes, “Low coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

C. Koliopoulos, “Simultaneous phase-shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

J. E. Millerd, N. J. Brock, and J. B. Hayes, “Modern approaches in phase measurement metrology,” Proc. SPIE 5856, 14–22(2005).
[CrossRef]

H. Kihm, “A point-diffraction interferometer with vibration-desensitizing capability,” Proc. SPIE 6293, 62930B (2006).
[CrossRef]

Other (3)

N. Doloca and R. Tutsch, “Random phase shift interferometer,” in Proceeding of Fringe 2005—The 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten, ed. (Springer Verlag, 2005), pp. 167–174.

J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 504–505, 514–515.

J. Hayes, “Dynamic interferometry handles vibrations,” in Proceeding of Laser Focus World, March 2002, pp. 109–113.

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Figures (13)

Fig. 1
Fig. 1

The experimental setup.

Fig. 2
Fig. 2

The mounting systems for reference and test plate. Both consist of a mechanical holder, but with a rigid postholder for the reference surface and a flexible postholder for the test plate.

Fig. 3
Fig. 3

(a) Detector system consisting of three photodiodes. (b) The three corresponding noncollinear measurement points P1, P2, and P3 on the test surface which define the oscillating plane Σ.

Fig. 4
Fig. 4

The simultaneous photodiode signals and the vibrometer signal indicating correlation between the main extreme values and the extreme positions of the oscillating test plate.

Fig. 5
Fig. 5

Deconvolution of the modulo π phase, resulting in the phase variation at the sampling point on the test plate.

Fig. 6
Fig. 6

Measured photodiode signal dependent on the aperture position of the calibration mask in front of the sensitive photo diode area. (a) Shows the signal with partial overlapping between aperture and sensitive photodiode area, (b) with maximum overlapping.

Fig. 7
Fig. 7

Measurement set with four sequentially recorded interference images with random phase shifts.

Fig. 8
Fig. 8

(a) Direct raw phase map solution 1234 of the algorithm given by the Eq. (11). (b) Wrapped phase map 1234 with values in the interval ( 0 , 2 π ) .

Fig. 9
Fig. 9

Phase map 4123 with the calculated nominator N and denominator D over a pixel column x i . The interval at which both N ( x i , y ) and D ( x i , y ) present small absolute values is characterized by nonaccurate data points.

Fig. 10
Fig. 10

Several modulo 2 π phase maps for different combinations of four out of six interference images. The last image illustrates the final unwrapped result.

Fig. 11
Fig. 11

Surface topography of the test plate, measured by random-phase-shift interferometry.

Fig. 12
Fig. 12

Surface topography of the test plate, measured by the manufacturer.

Fig. 13
Fig. 13

Distribution of the local RMS error, demonstrating the repeatability of random-phase-shift interferometry over two days.

Equations (16)

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I ( x , y , t ) = I ( x , y , t ) + I ( x , y , t ) cos [ ϕ ( x , y ) + δ ( x , y , t ) ] ,
I i ( t ) = I i + I i cos [ ϕ i + δ i ( t ) ] ; i = 1 , 2 , 3 ; δ i ( t ) = 4 π λ z i ( t ) ,
δ i j ( t ) = cos 1 I i ( t ) I i I i ; t { Δ t j } ,
δ i j ( t ) = cos 1 [ P i j N ( t ) ] ,
A · X + B · Y + C · Z = D ,
A = | 1 Y 1 Z 1 ( t ) 1 Y 2 Z 2 ( t ) 1 Y 3 Z 3 ( t ) | , B = | X 1 1 Z 1 ( t ) X 2 1 Z 2 ( t ) X 3 1 Z 3 ( t ) | , C = | X 1 Y 1 1 X 2 Y 2 1 X 3 Y 3 1 | , D = | X 1 Y 1 Z 1 ( t ) X 2 Y 2 Z 2 ( t ) X 3 Y 3 Z 3 ( t ) | .
Z ( X , Y , t ) = D A X B Y C .
M = | 1 y 1 δ 1 ( t ) 1 y 2 δ 2 ( t ) 1 y 3 δ 3 ( t ) | , N = | x 1 1 δ 1 ( t ) x 2 1 δ 2 ( t ) x 3 1 δ 3 ( t ) | , O = | x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 | , P = | x 1 y 1 δ 1 ( t ) x 2 y 2 δ 2 ( t ) x 3 y 3 δ 3 ( t ) | .
δ ( x , y , t ) = P M x N y O .
I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) + δ 1 ( x , y ) ] , I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) + δ 2 ( x , y ) ] , I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) + δ 3 ( x , y ) ] , I 4 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) + δ 4 ( x , y ) ] ,
ϕ ( x , y ) = tan 1 [ R ( x , y ) c 34 ( x , y ) c 12 ( x , y ) s 12 ( x , y ) R ( x , y ) s 34 ( x , y ) ] ,
R ( x , y ) = I 1 ( x , y ) I 2 ( x , y ) I 3 ( x , y ) I 4 ( x , y ) , c 12 = cos δ 1 ( x , y ) cos δ 2 ( x , y ) , s 12 = sin δ 1 ( x , y ) sin δ 2 ( x , y ) , c 34 = cos δ 3 ( x , y ) cos δ 4 ( x , y ) , s 34 = sin δ 3 ( x , y ) sin δ 4 ( x , y ) .
h ( x , y ) = λ 4 π ϕ ( x , y ) .
δ ( x , y , t 11 ) = δ ( x , y , t 1 ) δ ( x , y , t 1 ) = 0 , δ ( x , y , t 21 ) = δ ( x , y , t 2 ) δ ( x , y , t 1 ) , δ ( x , y , t 31 ) = δ ( x , y , t 3 ) δ ( x , y , t 1 ) , δ ( x , y , t 41 ) = δ ( x , y , t 4 ) δ ( x , y , t 1 ) .
N ( x , y ) = | R ( x , y ) c 34 ( x , y ) c 12 ( x , y ) | < 0.3 , D ( x , y ) = | s 12 ( x , y ) R ( x , y ) s 34 ( x , y ) | < 0.3 ,
RMS ( x , y ) = 1 N 1 i = 1 N [ h ( x , y ) h ¯ ( x , y ) ] 2 ,

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