Abstract

Three-dimensional profile measurement is perceived as an indispensable process for deterministic fabrication of aspheric mirrors. In this work, we develop on-machine 3D profile measurement on a subaperture polishing machine, namely, JR-1800. The influences of mechanical errors, misalignments, output stability, temperature variation, and natural vibration are investigated in detail by calibration, mechanical alignment, and finite-element analysis. Two quantitative methods are presented for aligning the turntable, length gauge, and workpiece into together. An error compensation model is also developed for further eliminating misalignments. For feasibility validation, two prototypical workpieces are measured by JR-1800 and an interferometer. The results indicate that JR-1800 has an RMS repeatability of λ/30 (λ=632.8nm). The data provided by the two systems are highly coincident. Direct subtractions of the results from the two systems indicate that the RMS deviations for both segments are less than 0.07 μm.

© 2014 Optical Society of America

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References

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    [CrossRef]
  5. H. B. Cheng, Y. Yam, and Y. T. Wang, “Experimentation on MR fluid using a 2-axis wheel tool,” J. Mater. Process. Technol. 209, 5254–5261 (2009).
    [CrossRef]
  6. J. Burke, K. Wang, and A. Bramble, “Null test of an off-axis parabolic mirror. I. Configuration with spherical reference wave and flat return surface,” Opt. Express 17, 3196–3210 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).
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  16. F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
    [CrossRef]
  17. Z. C. Dong, H. B. Cheng, and H. Y. Tam, “Modified subaperture tool influence functions of a flat pitch polisher with reverse-calculated material removal rate,” Appl. Opt. 53, 2455–2464 (2014).
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2014

2013

Y. F. Wen, H. B. Cheng, and H. Y. Tam, “Modified stitching algorithm for annular subaperture stitching interferometry for aspheric surfaces,” Appl. Opt. 52, 5686–5694 (2013).
[CrossRef]

C. Gray, I. Baker, and G. Davies, “Fast manufacturing of E-ELT mirror segments using CNC polishing,” Proc. SPIE 8838, 88380k (2013).
[CrossRef]

2012

2011

P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60, 379–382 (2011).
[CrossRef]

2010

2009

J. Burke, K. Wang, and A. Bramble, “Null test of an off-axis parabolic mirror. I. Configuration with spherical reference wave and flat return surface,” Opt. Express 17, 3196–3210 (2009).
[CrossRef]

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc. SPIE 7426, 74260J (2009).
[CrossRef]

H. B. Cheng, Y. Yam, and Y. T. Wang, “Experimentation on MR fluid using a 2-axis wheel tool,” J. Mater. Process. Technol. 209, 5254–5261 (2009).
[CrossRef]

2007

2005

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

1997

1991

R. S. Breidenthal, “Measurement of large optical surfaces for fabrication using a non-optical technique,” Proc. SPIE 1618, 97–103 (1991).
[CrossRef]

Baker, I.

C. Gray, I. Baker, and G. Davies, “Fast manufacturing of E-ELT mirror segments using CNC polishing,” Proc. SPIE 8838, 88380k (2013).
[CrossRef]

Bramble, A.

Breidenthal, R. S.

R. S. Breidenthal, “Measurement of large optical surfaces for fabrication using a non-optical technique,” Proc. SPIE 1618, 97–103 (1991).
[CrossRef]

Burge, J. H.

P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc. SPIE 7426, 74260J (2009).
[CrossRef]

P. Zhou and J. H. Burge, “Optimal design of computer-generated holograms to minimize sensitivity to fabrication,” Opt. Express 15, 15410–15417 (2007).
[CrossRef]

Burke, J.

Chen, F. J.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

Cheng, H. B.

Cheng, K.

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

Comley, P.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60, 379–382 (2011).
[CrossRef]

Davies, G.

C. Gray, I. Baker, and G. Davies, “Fast manufacturing of E-ELT mirror segments using CNC polishing,” Proc. SPIE 8838, 88380k (2013).
[CrossRef]

Dong, Z. C.

Fan, Y. F.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

Fang, T.

Feng, Z. J.

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

Goodwin, E. P.

E. P. Goodwin and J. C. Wyant, Field Guide to Interferometric Optical Testing (SPIE, 2006).

Gray, C.

C. Gray, I. Baker, and G. Davies, “Fast manufacturing of E-ELT mirror segments using CNC polishing,” Proc. SPIE 8838, 88380k (2013).
[CrossRef]

Huang, H.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

Jing, H. W.

King, C.

Lambropoulos, J. C.

Morantz, P.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60, 379–382 (2011).
[CrossRef]

Oh, C. J.

P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc. SPIE 7426, 74260J (2009).
[CrossRef]

Ohmori, H.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

Parks, R. E.

P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc. SPIE 7426, 74260J (2009).
[CrossRef]

Shore, P.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60, 379–382 (2011).
[CrossRef]

Su, P.

P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc. SPIE 7426, 74260J (2009).
[CrossRef]

Tam, H. Y.

Tonnellier, X.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60, 379–382 (2011).
[CrossRef]

Walker, D.

Wang, K.

Wang, Y.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

Wang, Y. H.

P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).

Wang, Y. T.

H. B. Cheng, Y. Yam, and Y. T. Wang, “Experimentation on MR fluid using a 2-axis wheel tool,” J. Mater. Process. Technol. 209, 5254–5261 (2009).
[CrossRef]

Wang, Y. W.

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

Wen, Y. F.

Wyant, J. C.

E. P. Goodwin and J. C. Wyant, Field Guide to Interferometric Optical Testing (SPIE, 2006).

Xu, S.

Yam, Y.

H. B. Cheng, Y. Yam, and Y. T. Wang, “Experimentation on MR fluid using a 2-axis wheel tool,” J. Mater. Process. Technol. 209, 5254–5261 (2009).
[CrossRef]

Yin, S. H.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

Zhou, P.

Zhu, Y. J.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

Appl. Opt.

CIRP Ann.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60, 379–382 (2011).
[CrossRef]

Int. J. Mach. Tools Manuf.

F. J. Chen, S. H. Yin, H. Huang, H. Ohmori, Y. Wang, Y. F. Fan, and Y. J. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50, 480–486 (2010).
[CrossRef]

H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005).
[CrossRef]

J. Mater. Process. Technol.

H. B. Cheng, Y. Yam, and Y. T. Wang, “Experimentation on MR fluid using a 2-axis wheel tool,” J. Mater. Process. Technol. 209, 5254–5261 (2009).
[CrossRef]

Opt. Express

Proc. SPIE

R. S. Breidenthal, “Measurement of large optical surfaces for fabrication using a non-optical technique,” Proc. SPIE 1618, 97–103 (1991).
[CrossRef]

C. Gray, I. Baker, and G. Davies, “Fast manufacturing of E-ELT mirror segments using CNC polishing,” Proc. SPIE 8838, 88380k (2013).
[CrossRef]

P. Su, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM for aspherics,” Proc. SPIE 7426, 74260J (2009).
[CrossRef]

P. Su, Y. H. Wang, C. J. Oh, R. E. Parks, and J. H. Burge, “Swing arm optical CMM: self-calibration with dual probe shear test,” Proc. SPIE 8126, 81260 (2011).

Other

E. P. Goodwin and J. C. Wyant, Field Guide to Interferometric Optical Testing (SPIE, 2006).

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Figures (15)

Fig. 1.
Fig. 1.

Sketch map of aspheric surfaces.

Fig. 2.
Fig. 2.

Schematic illustration of JR-1800: (a) overall view; (b) lateral view of the metrology and fabrication units; (c) fabrication status; and (d) metrology status.

Fig. 3.
Fig. 3.

Calibration results of the systemic error of JR-1800 with (a) XC mode and (b) XY mode.

Fig. 4.
Fig. 4.

Coordinates of JR-1800 (a) with offset in XY direction and (b) aligned together precisely in XY direction.

Fig. 5.
Fig. 5.

Emulational measurement errors caused by tool misalignment (a) with different offsets and (b) with different F#.

Fig. 6.
Fig. 6.

Calibration model for misalignments of the length gauge in XY position.

Fig. 7.
Fig. 7.

Measurement error if the workpiece has offset error.

Fig. 8.
Fig. 8.

Output stability with increasing reading times.

Fig. 9.
Fig. 9.

Deformation diagram of the proposed system when temperature increases by 1°C.

Fig. 10.
Fig. 10.

First six mode vibration shapes and the corresponding natural frequencies.

Fig. 11.
Fig. 11.

Sketch map of tool radius compensation.

Fig. 12.
Fig. 12.

Schematic illustration of the error separation model.

Fig. 13.
Fig. 13.

Comparing the results of a plane measured with JR-1800: (a) first, PV=1.15λ, RMS=0.231λ; (b) second, PV=1.39λ, RMS=0.259λ; and (c) third, PV=1.24λ, RMS=0.244λ.

Fig. 14.
Fig. 14.

(a) Result of Zygo GPI laser interferometer: PV=1.25λ, RMS=0.231λ. (b) Direct subtraction of the measurement results of JR-1800 and Zygo interferometer, PV=248nm, RMS=42nm.

Fig. 15.
Fig. 15.

(a) Interferometric result with Zygo PGI laser interferometer: PV=2.88λ, RMS=0.459λ. (b) Result measured with JR-1800: PV=2.92λ, RMS=0.529λ. (c) Direct subtraction of the measurement results of JR-1800 and Zygo interferometer: PV=512nm, RMS=67.8nm.

Tables (2)

Tables Icon

Table 1. Mechanical Errors of XYZC Axis

Tables Icon

Table 2. Parameters of Materials

Equations (30)

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

Z(X,Y)=C(X2+Y2)1+1(K+1)C2(X2+Y2)+i=1nA2i(X2+Y2)i.
Z1(X,Y)=C(X12+(Y1y0)2)1+1(K+1)C2(X12+(Y1y0)2)z0,
|XYZ1|=|10000cos(θ)sin(θ)00sin(θ)cos(θ)00001||X1Y1Z11|,
AZ2+BZ+Q=0,
Z=B+B24AQ2A,
{A=C+KCcos2(θ)B=(2CYsin(θ)cos(θ)2Cy0sin(θ)2cos(θ)+(K+1)C(2z0cos(θ)+2Ysin(θ)cos(θ)))Q=2z0+2Ysin(θ)(K+1)C(z02+2Yz0sin(θ)+Y2sin2(θ))C(X2+Y2cos2(θ)+2Yy0cos(θ)+y02).
X2=2RZ,
dz=(X+dx)22RX22R=2Xdx+dx22RXdxR.
Z2=R02((X+dx)2+dy2)R02(X2+2Xdx),
Z2=R02X2,
δ=Z2Z2=2Xdx,
dx=13.6μm,dy=41.2μm.
dz=Cρcos(θ)1(K+1)C2ρ2dx+Cρsin(θ)1(K+1)C2ρ2dy,
S(dx,dy)=i=1n[Zidzi]2=i=1n[Zi(Uidx+Vidy)]2,
Sdx=Sdy=0,
|Ui2UiViUiViVi2||dxdy|=|ZiUiZiVi|,
Ui=Cρicos(θi)1(K+1)C2ρi2Vi=Cρisin(θi)1(K+1)C2ρi2.
ZUP=ZVPZVU=ZQZPZVU=Z((XP2+YP2)+Rtsin(γ),0)Z((XP2+YP2),0)Rt(1cos(γ)).
XA=XB,YA=YB.
dz=ZBZA,
|XBYBZB1|=([cos(β)sin(β)sin(α)sin(β)cos(α)dx0cos(α)sin(α)dysin(β)cos(β)sin(α)cos(β)cos(α)00001])1|XBYBZB1|.
(K+1)ZB2+2(KXBsin(β)KYBsin(α)R)ZB+XB2+YB22XBdx2YBdy2RXBsin(β)+2RYBsin(α)=0.
az12+bz1+c=0,
z1={b+b24ac2a(K1)c/b(K=1),
{dz=1K+1[(K+11(K+1)C2(x2+y2))ysin(α)(K+11(K+1)C2(x2+y2))xsin(β)]xdx+ydy1(K+1)C2(x2+y2)(K1)dz=[x(x2+y2)2R2x]sin(β)+[y+(x2+y2)2R2y]sin(α)CxdxCydy(K=1).
{si=Cxi1(K+1)C2(xi2+yi2)ti=Cyi1(K+1)C2(xi2+yi2)ui=1K+1(K+11(K+1)C2(xi2+yi2))yivi=1K+1(K+11(K+1)C2(xi2+yi2))xi.
dz=si*S+ti*T+ui*U+vi*V.
W(S,T,U,V)=i=1n[dzdz]2=i=1n[dz(siS+tiT+uiU+viV)]2.
WS=WT=WU=WV=0,
|si2sitisiuisivitisiti2tiuitiviuisiuitiui2uivivisivitiviuivi2||STUV|=|dzsidztidzuidzvi|.

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