Abstract

Considering the special characteristics of the removal function with the ring-shaped profile in fluid jet polishing (FJP), we present an effective method called the discrete convolution algorithm to compute the dwell function for controlling the figuring process. This method avoids the deconvolution operation, which usually fails to converge. Then an experimental confirmation of FJP figuring was demonstrated by machining a one-dimensional depth profile on a flat sample. The profile was figured from 0.914λ(λ=632.8  nm) peak to valley (PV) to 0.260λ. This experiment demonstrated the successful implementation of the algorithm to solve the dwell function in optical manufacturing.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. A. Cordero-Dávila and E. Luna-Aguilar, "Polishing TIM mirror segments with HyDra," in Future Giant Telescopes, J. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 604-611 (2003).
    [CrossRef]

2004 (1)

2003 (1)

A. Cordero-Dávila and E. Luna-Aguilar, "Polishing TIM mirror segments with HyDra," in Future Giant Telescopes, J. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 604-611 (2003).
[CrossRef]

2000 (1)

1999 (1)

O. W. Fähnle, "Fluid jet polishing: removal process analysis," in EUROPTO Conference on Optical Fabrication and Testing,Proc. SPIE 3739, 68-77 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

1995 (1)

T. W. Drueding, T. G. Bifano et al., "Contouring algorithm for ion figuring," Precis. Eng. 17, 10-21 (1995).
[CrossRef]

1972 (1)

Aspden, R.

Bifano, T. G.

Booij, S. M.

S. M. Booij, O. W. Fähnle, and J. J. M. Braat, "Shaping with fluid jet polishing by footprint optimization," Appl. Opt. 43, 67-69 (2004).
[CrossRef] [PubMed]

S. M. Booij, "Fluid jet polishing--possibilities and limitations of a new fabrication technique," Ph.D. dissertation (Delft University of Technology, 2003).

Braat, J. J. M.

Cordero-Dávila, A.

A. Cordero-Dávila and E. Luna-Aguilar, "Polishing TIM mirror segments with HyDra," in Future Giant Telescopes, J. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 604-611 (2003).
[CrossRef]

Cumbo, M. J.

Drueding, T. W.

T. W. Drueding, T. G. Bifano et al., "Contouring algorithm for ion figuring," Precis. Eng. 17, 10-21 (1995).
[CrossRef]

Fähnle, O. W.

Fang, H.

H. Fang, P. Guo, and J. Yu, "Research on the mathematical model of fluid jet polishing," presented at the 2nd SPIE International Symposium on Advanced Optical Manufacturing and Testing Technologies, Xian, China, 2-5 November 2005.

Fang, T.

Feinberg, M. R.

Frankena, H. J.

Funkenbusch, P. D.

Golini, D.

Guo, P.

H. Fang, P. Guo, and J. Yu, "Research on the mathematical model of fluid jet polishing," presented at the 2nd SPIE International Symposium on Advanced Optical Manufacturing and Testing Technologies, Xian, China, 2-5 November 2005.

Horenstein, M. N.

Jacobs, S. D.

Lambropoulos, J. C.

Luna-Aguilar, E.

A. Cordero-Dávila and E. Luna-Aguilar, "Polishing TIM mirror segments with HyDra," in Future Giant Telescopes, J. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 604-611 (2003).
[CrossRef]

McDonough, R.

Nitchie, F. R.

Sandri, G.

Shanbhag, P. M.

van Brug, H.

Xu, S.

Yu, J.

H. Fang, P. Guo, and J. Yu, "Research on the mathematical model of fluid jet polishing," presented at the 2nd SPIE International Symposium on Advanced Optical Manufacturing and Testing Technologies, Xian, China, 2-5 November 2005.

Appl. Opt. (6)

Precis. Eng. (1)

T. W. Drueding, T. G. Bifano et al., "Contouring algorithm for ion figuring," Precis. Eng. 17, 10-21 (1995).
[CrossRef]

Proc. SPIE (2)

A. Cordero-Dávila and E. Luna-Aguilar, "Polishing TIM mirror segments with HyDra," in Future Giant Telescopes, J. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 604-611 (2003).
[CrossRef]

O. W. Fähnle, "Fluid jet polishing: removal process analysis," in EUROPTO Conference on Optical Fabrication and Testing,Proc. SPIE 3739, 68-77 (1999).
[CrossRef]

Other (2)

S. M. Booij, "Fluid jet polishing--possibilities and limitations of a new fabrication technique," Ph.D. dissertation (Delft University of Technology, 2003).

H. Fang, P. Guo, and J. Yu, "Research on the mathematical model of fluid jet polishing," presented at the 2nd SPIE International Symposium on Advanced Optical Manufacturing and Testing Technologies, Xian, China, 2-5 November 2005.

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Figures (6)

Fig. 1
Fig. 1

Profile of material removal with normal incident angle.

Fig. 2
Fig. 2

Removal function.

Fig. 3
Fig. 3

Original surface curve of work piece before being polished.

Fig. 4
Fig. 4

Desired removal function.

Fig. 5
Fig. 5

Computed final surface curve.

Fig. 6
Fig. 6

Final surface curve after being polished.

Equations (14)

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d Z = k P K ν d t .
Δ Z ( x , y ) = k 0 t P ( x , y , t ) K ν ( x , y , t ) d t .
Δ Z ( x , y ) = D ( x , y ) R ( x , y ) .
Δ Z ˜ ( ξ , η ) = D ˜ ( ξ , η ) R ˜ ( ξ , η ) ,
D ( x , y ) = F 1 ( Δ Z ˜ ( ξ , η ) R ˜ ( ξ , η ) ) .
D ( x , y ) = R ( x , y ) B ( x , y ) - 1 ,
z i = h i d i .
z i = h i d i = k = 0 m h k d i k     ( i = 0 , 1 , , m + n ) .
[ h 0 0 0 0 h 1 h 0 0 0 0 h 2 h 1 h 0 0 0 h m h ( m 1 ) h ( m 2 ) h ( m n 1 ) h ( m n ) 0 h m h ( m 1 ) h ( m n ) h ( m n + 1 ) 0 h m h ( m n + 1 ) h ( m n + 2 ) 0 0 0 0 h m ] [ d 0 d 1 d 2 d n ] = [ z 0 z 1 z 2 z m z m + 1 z m + 2 z m + n ] .
H ( n + m , n ) D ( n , 1 ) = Z ( n + m , 1 ) .
D i + 1 = D i + k H ( Z i + 1 Z i ) .
K ν = ( ν ν 0 ) 2 = [ 1 + ( ω r ν 0 ) 2 ] .
K ν = ( ν ν 0 ) 2 = [ 1 + ( ω r ν 0 ) 2 ] = 1 + 0.0759 r 2 .
d i = d i K ν r .

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