Abstract

The global optimization threshold algorithm is reported to obtain the deformations of an optical surface. The advantage of these types of algorithm is that they can be solved for the correlation problem presented in Seidel polynomials. We obtain the 2D deformations of a surface test with the transversal aberration along one direction only. In order to apply this algorithm we used exact ray tracing to simulate the transversal aberration adapting the same mathematical theory for the Ronchi test. The error obtained in sagitta recovering deformation was 1  μm.

© 2006 Optical Society of America

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References

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    [CrossRef]
  16. A. Cordero, A. Cornejo, and O. Cardona, "Ronchi and Hartmann tests with the same mathematical theory," Appl. Opt. 31, 2370-2376 (1992).
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  17. J. J. Collins, M. Fanciulli, and R. G. Hohlfeld, "A random number generator based on the logit transform of the logistic variable," Comput. Phys. 6, 630-632 (1992).
    [CrossRef]

2005 (1)

2003 (2)

N. Bautista, C. I. Robledo, A. Cordero, and A. Cornejo, "Sensing a wave front by use of a diffraction grating," Appl. Opt. 42, 3737-3741 (2003).
[CrossRef]

Z. Peng, F. Qian, X. Wang, and X. Zhong, "Phase unwrapping with regularized phase-tracking technique based on simulated annealing algorithm," Optik 114, 175-180 (2003).
[CrossRef]

2002 (1)

1995 (1)

T. J. P. Penna, "Fitting curves by simulated annealing," Comput. Phys. 9, 341-343 (1995).
[CrossRef]

1994 (1)

1993 (1)

W. Ahmad and W. Abdullah, "Seeking global minima," J. Comput. Phys. 110, 320-326 (1993).

1992 (2)

J. J. Collins, M. Fanciulli, and R. G. Hohlfeld, "A random number generator based on the logit transform of the logistic variable," Comput. Phys. 6, 630-632 (1992).
[CrossRef]

A. Cordero, A. Cornejo, and O. Cardona, "Ronchi and Hartmann tests with the same mathematical theory," Appl. Opt. 31, 2370-2376 (1992).
[CrossRef]

1991 (1)

1989 (1)

1988 (1)

1983 (1)

G. Groisman, "Computer-assisted photometry using simulated annealing," Comput. Phys. 7, 87-96 (1983).
[CrossRef]

1980 (1)

W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 999-1006 (1980).
[CrossRef]

1979 (1)

Abdullah, W.

W. Ahmad and W. Abdullah, "Seeking global minima," J. Comput. Phys. 110, 320-326 (1993).

Ahmad, W.

W. Ahmad and W. Abdullah, "Seeking global minima," J. Comput. Phys. 110, 320-326 (1993).

Bautista, N.

Cabrera, V.

Cardona, O.

Caulfield, H. J.

Collins, J. J.

J. J. Collins, M. Fanciulli, and R. G. Hohlfeld, "A random number generator based on the logit transform of the logistic variable," Comput. Phys. 6, 630-632 (1992).
[CrossRef]

Cordero, A.

Cornejo, A.

Cuautle, J.

Cubalchini, R.

Fanciulli, M.

J. J. Collins, M. Fanciulli, and R. G. Hohlfeld, "A random number generator based on the logit transform of the logistic variable," Comput. Phys. 6, 630-632 (1992).
[CrossRef]

Feldman, M. R.

Fuentes, F. J.

Fuentes, O.

González, J.

Groisman, G.

G. Groisman, "Computer-assisted photometry using simulated annealing," Comput. Phys. 7, 87-96 (1983).
[CrossRef]

Guest, C. C.

Hohlfeld, R. G.

J. J. Collins, M. Fanciulli, and R. G. Hohlfeld, "A random number generator based on the logit transform of the logistic variable," Comput. Phys. 6, 630-632 (1992).
[CrossRef]

Kim, M. S.

Mahlab, U.

Malacara, D.

D. Malacara, Optical Shop Testing, Wiley Series in Pure and Applied Optics (Wiley1992), Chap. 9,pp. 321-366.

Navarro, R.

Nieto, M.

Peng, Z.

Z. Peng, F. Qian, X. Wang, and X. Zhong, "Phase unwrapping with regularized phase-tracking technique based on simulated annealing algorithm," Optik 114, 175-180 (2003).
[CrossRef]

Penna, T. J. P.

T. J. P. Penna, "Fitting curves by simulated annealing," Comput. Phys. 9, 341-343 (1995).
[CrossRef]

Qian, F.

Z. Peng, F. Qian, X. Wang, and X. Zhong, "Phase unwrapping with regularized phase-tracking technique based on simulated annealing algorithm," Optik 114, 175-180 (2003).
[CrossRef]

Robledo, C.

Robledo, C. I.

Sánchez, J. J.

Shamir, J.

Southwell, W. H.

W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 999-1006 (1980).
[CrossRef]

Vázquez, S.

Wang, X.

Z. Peng, F. Qian, X. Wang, and X. Zhong, "Phase unwrapping with regularized phase-tracking technique based on simulated annealing algorithm," Optik 114, 175-180 (2003).
[CrossRef]

Yatagai, T.

Yoshikawa, N.

Zhong, X.

Z. Peng, F. Qian, X. Wang, and X. Zhong, "Phase unwrapping with regularized phase-tracking technique based on simulated annealing algorithm," Optik 114, 175-180 (2003).
[CrossRef]

Appl. Opt. (5)

Comput. Phys. (3)

G. Groisman, "Computer-assisted photometry using simulated annealing," Comput. Phys. 7, 87-96 (1983).
[CrossRef]

T. J. P. Penna, "Fitting curves by simulated annealing," Comput. Phys. 9, 341-343 (1995).
[CrossRef]

J. J. Collins, M. Fanciulli, and R. G. Hohlfeld, "A random number generator based on the logit transform of the logistic variable," Comput. Phys. 6, 630-632 (1992).
[CrossRef]

J. Comput. Phys. (1)

W. Ahmad and W. Abdullah, "Seeking global minima," J. Comput. Phys. 110, 320-326 (1993).

J. Opt. Soc. Am. (2)

W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 999-1006 (1980).
[CrossRef]

R. Cubalchini, "Modal wave-front estimation from phase derivative measurements," J. Opt. Soc. Am. 69, 972-977 (1979).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

Optik (1)

Z. Peng, F. Qian, X. Wang, and X. Zhong, "Phase unwrapping with regularized phase-tracking technique based on simulated annealing algorithm," Optik 114, 175-180 (2003).
[CrossRef]

Other (2)

Ref. 1, Appendix 1, pp. 321-366.

D. Malacara, Optical Shop Testing, Wiley Series in Pure and Applied Optics (Wiley1992), Chap. 9,pp. 321-366.

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Figures (4)

Fig. 1
Fig. 1

Exact ray tracing to simulate the transversal aberration. PS is the point source; CC is the curvature center, and OP the observation plane.

Fig. 2
Fig. 2

Ronchigrams with data of Table 2: (a) simulated reference Ronchigram and (b) Ronchigram recovered with the threshold algorithm.

Fig. 3
Fig. 3

Ronchigrams with data of Table 3: (a) simulated reference Ronchigram and (b) Ronchigram recovered with the threshold algorithm.

Fig. 4
Fig. 4

Ronchigrams with data of Table 4: (a) simulated reference Ronchigram and (b) Ronchigram recovered with the threshold algorithm.

Tables (4)

Tables Icon

Table 1 Conic Constant for Different Surfaces

Tables Icon

Table 2 Data for Simulation of a Ronchigram a

Tables Icon

Table 3 Data for Simulation of a Ronchigram a

Tables Icon

Table 4 Data for Simulation of a Ronchigram a

Equations (20)

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Z ( x , y ) = Z con ( x , y ) + Z def ( x , y ) ,
Z con = c s 2 1 + 1 ( k + 1 ) c 2 s 2 ,
Z def = A ( x 2 + y 2 ) 2 + B y ( x 2 + y 2 ) + C ( x 2 + 3 y 2 ) + D ( x 2 + y 2 ) + E x + F y .
s ^ 1 = ( x α , y β , z γ ) / N ,
N ^ = ( Z x , Z y , 1 ) / O ,
Z x = x R 2 ( k + 1 ) s 2 + 4 A x ( x 2 + y 2 ) + 2 B x y + 2 C x + 2 D x + E ,
Z y = y R 2 ( k + 1 ) s 2 + 4 Ay ( x 2 + y 2 ) + B ( x 2 + 3 y 2 ) + 6 C y + 2 D y + F .
S ^ 2 = s ^ 1 - 2 ( s ^ 1 N ^ ) N ^ .
S 2 x = 1 N O 2 { ( x α ) O 2 2 Z x [ ( x α ) Z x + ( y β ) Z y ( z γ ) ] } ,
S 2 y = 1 N O 2 { ( y β ) O 2 2 Z y [ ( x α ) Z x + ( y β ) Z y ( z γ ) ] } ,
S 2 z = 1 N O 2 { ( z γ ) O 2 2 [ ( x α ) Z x + ( y β ) Z y ( z γ ) ] } .
X 0 x S 2 x = Y 0 y S 2 y = Z 0 z S 2 z .
X 0 = x + ( Z 0 z ) S 2 x S 2 z ,
Y 0 = y + ( Z 0 z ) S 2 y S 2 z .
J = k = 1 M ( X 0    ref X 0    rec ) 2 ,
Δ J < T .
P = P initial D n .
t n + 1 = 4 λ t n ( 1 t n ) ,
a l e a n = 2 π a s e n ( t n ) .
I ( x , y ) = 256 2 { 1 + cos [ 2 π X 0 ( x , y ) n l p ] } ,

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