Abstract

Considering the wavefront error of KH2PO4 (KDP) crystal is difficult to control through face fly cutting process because of surface shape deformation during vacuum suction, an error compensation technique based on a spiral turning method is put forward. An in situ measurement device is applied to measure the deformed surface shape after vacuum suction, and the initial surface figure error, which is obtained off-line, is added to the in situ surface shape to obtain the final surface figure to be compensated. Then a three-axis servo technique is utilized to cut the final surface shape. In traditional cutting processes, in addition to common error sources such as the error in the straightness of guide ways, spindle rotation error, and error caused by ambient environment variance, three other errors, the in situ measurement error, position deviation error, and servo-following error, are the main sources affecting compensation accuracy. This paper discusses the effect of these three errors on compensation accuracy and provides strategies to improve the final surface quality. Experimental verification was carried out on one piece of KDP crystal with the size of Φ270mm×11mm. After one compensation process, the peak-to-valley value of the transmitted wavefront error dropped from 1.9λ (λ=632.8nm) to approximately 1/3λ, and the mid-spatial-frequency error does not become worse when the frequency of the cutting tool trajectory is controlled by use of a low-pass filter.

© 2013 Optical Society of America

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References

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  1. J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
    [CrossRef]
  2. B. A. Fuchs, P. P. Hed, and P. C. Baker, “Fine diamond turning of KDP crystals,” Appl. Opt. 25, 1733–1735 (1986).
    [CrossRef]
  3. Q. Xu and J. Wang, “Analysis of the influence of vacuum chucking on the distortion of the KDP crystal,” Proc. SPIE 4231, 464–468 (2000).
    [CrossRef]
  4. G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on compensation of suction deformation error of potassium dihydrogen phosphate crystal,” Appl. Opt. 52, 110–116 (2013).
    [CrossRef]
  5. G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
    [CrossRef]
  6. Y. E. Tohme and J. A. Lowe, “Machining of freeform optical surfaces by slow slide servo method,” (2003), http://aspe.net/publications/Annual_2003/PDF/8EQCTRL/1283.PDF .
  7. C. Falldorf, C. Dankwart, R. Gläbe, B. Lünemann, C. V. Kopylow, and R. B. Bergmann, “Holographic projection based on diamond-turned diffractive optical elements,” Appl. Opt. 48, 5782–5785 (2009).
    [CrossRef]
  8. Zygo, http://www.zygo.com .

2013

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on compensation of suction deformation error of potassium dihydrogen phosphate crystal,” Appl. Opt. 52, 110–116 (2013).
[CrossRef]

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
[CrossRef]

2009

2004

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

2000

Q. Xu and J. Wang, “Analysis of the influence of vacuum chucking on the distortion of the KDP crystal,” Proc. SPIE 4231, 464–468 (2000).
[CrossRef]

1986

Baker, P. C.

Bergmann, R. B.

Borden, M. R.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Campbell, J. H.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Dai, Y.

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on compensation of suction deformation error of potassium dihydrogen phosphate crystal,” Appl. Opt. 52, 110–116 (2013).
[CrossRef]

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
[CrossRef]

Dankwart, C.

Falldorf, C.

Feit, M. D.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Fuchs, B. A.

Gläbe, R.

Guan, C.

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
[CrossRef]

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on compensation of suction deformation error of potassium dihydrogen phosphate crystal,” Appl. Opt. 52, 110–116 (2013).
[CrossRef]

Hackel, R. P.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Hawley-Fedder, R. A.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Hed, P. P.

Kopylow, C. V.

Lünemann, B.

Menapace, J. A.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Riley, M. O.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Runkel, M.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Song, B.

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
[CrossRef]

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on compensation of suction deformation error of potassium dihydrogen phosphate crystal,” Appl. Opt. 52, 110–116 (2013).
[CrossRef]

Stolz, C. J.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Tie, G.

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
[CrossRef]

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on compensation of suction deformation error of potassium dihydrogen phosphate crystal,” Appl. Opt. 52, 110–116 (2013).
[CrossRef]

Wang, J.

Q. Xu and J. Wang, “Analysis of the influence of vacuum chucking on the distortion of the KDP crystal,” Proc. SPIE 4231, 464–468 (2000).
[CrossRef]

Whitman, P. K.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Xu, Q.

Q. Xu and J. Wang, “Analysis of the influence of vacuum chucking on the distortion of the KDP crystal,” Proc. SPIE 4231, 464–468 (2000).
[CrossRef]

Yu, J.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Zhu, D.

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on compensation of suction deformation error of potassium dihydrogen phosphate crystal,” Appl. Opt. 52, 110–116 (2013).
[CrossRef]

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
[CrossRef]

Appl. Opt.

J. Mater. Process. Technol.

G. Tie, Y. Dai, C. Guan, D. Zhu, and B. Song, “Research on full-aperture ductile cutting of KDP crystals using spiral turning technique,” J. Mater. Process. Technol. 213, 2137–2144 (2013).
[CrossRef]

Proc. SPIE

Q. Xu and J. Wang, “Analysis of the influence of vacuum chucking on the distortion of the KDP crystal,” Proc. SPIE 4231, 464–468 (2000).
[CrossRef]

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Other

Zygo, http://www.zygo.com .

Y. E. Tohme and J. A. Lowe, “Machining of freeform optical surfaces by slow slide servo method,” (2003), http://aspe.net/publications/Annual_2003/PDF/8EQCTRL/1283.PDF .

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Figures (12)

Fig. 1.
Fig. 1.

Schematic for compensation cutting technique.

Fig. 2.
Fig. 2.

Photograph of evaluation of in situ measurement system.

Fig. 3.
Fig. 3.

Results of evaluation of in situ measurement system: (a) measurement curve for invariable signal and (b) measurement curve for 20 μm step signal.

Fig. 4.
Fig. 4.

Calculation schematic of position deviation error: (a) position deviation error between in situ surface shape and initial surface shape and (b) cutting tool adjustment error.

Fig. 5.
Fig. 5.

Bode diagram for the transfer function of Z axis.

Fig. 6.
Fig. 6.

Initial surface figure error of KDP crystal: (a) transmitted wavefront error and (b) GRMS error.

Fig. 7.
Fig. 7.

(a) In situ measurement surface figure error and (b) calculated surface figure error to be compensated.

Fig. 8.
Fig. 8.

Calculated results of surface figure error caused by position deviation: (a) error caused by unrepeated lamping and (b) error caused by cutting tool adjustment.

Fig. 9.
Fig. 9.

Z axis component of the tool path and its fast Fourier transform.

Fig. 10.
Fig. 10.

Compensation results: (a) transmitted wavefront error and (b) GRMS error.

Fig. 11.
Fig. 11.

PSD curve of transmitted wavefront error.

Fig. 12.
Fig. 12.

PSD curve of transmitted wavefront error after filtering the tool path.

Tables (2)

Tables Icon

Table 1. Sinusoidal Input for System Identification Experiment

Tables Icon

Table 2. Surface Roughness Data (RMS, nm) for Finished Surface

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Zcomp=Zin_situZinit.
δcal=Zinit(x,y)Zinit(x0,y0)=Zinit(R0cos(θ0Δθ)+Δx,R0sin(θ0Δθ)+Δy)Zinit(x0,y0),
δtool=Zcomp(X,C)Zcomp(X0,C0)=Zcomp((X0+Δx)2+Δy2,C0+Δθ+θ)Zcomp(X0,C0),
δposition(x0,y0)=δcal(x0,y0)+δcomp(x0,y0)d1(x0,y0)GRMSinit(x0,y0)+d2(x0,y0)GRMScomp(x0,y0),
xo(t)=L1{Xo(s)}=L1{H(s)L{xi(t)}},
δservo=xo(t)xi(t).

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