Abstract

A simple interferometric method is presented for determining the parent radius of curvature (ROC) and conic constant (CC) of a conic surface. This method compares the test surface with a spherical reference wavefront having a ROC equal to the local sagittal, medial, or tangential ROC. The measured wavefront aberrations, particularly the astigmatism and coma, and local radii are used to determine the parent ROC and CC. This method does not require null optics or knowledge of the surface coordinate where the measurement is made.

© 2007 Optical Society of America

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References

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  1. K. Z. Smith, J. P. Schwenker, R. J. Brown, and J. F. Sullivan, Proc. SPIE 5494, 141 (2004).
    [CrossRef]
  2. D. Baiocchi and J. H. Burge, Proc. SPIE 4093, 58 (2000).
    [CrossRef]
  3. G. C. Dente, Proc. SPIE 429, 187 (1983).
  4. E. W. Young and G. C. Dente, Proc. SPIE 540, 59 (1985).
  5. O. Cardona-Nunez, A. Cornejo-Rodriguez, R. Diaz-Uribe, A. Cordero-Davila, and J. Pedraza-Contreras, Appl. Opt. 25, 3585 (1986).
    [CrossRef] [PubMed]
  6. V. N. Mahajan, Aberration Theory Made Simple (SPIE, 1991), Chap. 8, pp. 86.
  7. Optical Research Associates, 'CodeV online reference manual,' www.opticalres.com.

2004 (1)

K. Z. Smith, J. P. Schwenker, R. J. Brown, and J. F. Sullivan, Proc. SPIE 5494, 141 (2004).
[CrossRef]

2000 (1)

D. Baiocchi and J. H. Burge, Proc. SPIE 4093, 58 (2000).
[CrossRef]

1986 (1)

1985 (1)

E. W. Young and G. C. Dente, Proc. SPIE 540, 59 (1985).

1983 (1)

G. C. Dente, Proc. SPIE 429, 187 (1983).

Baiocchi, D.

D. Baiocchi and J. H. Burge, Proc. SPIE 4093, 58 (2000).
[CrossRef]

Brown, R. J.

K. Z. Smith, J. P. Schwenker, R. J. Brown, and J. F. Sullivan, Proc. SPIE 5494, 141 (2004).
[CrossRef]

Burge, J. H.

D. Baiocchi and J. H. Burge, Proc. SPIE 4093, 58 (2000).
[CrossRef]

Cardona-Nunez, O.

Cordero-Davila, A.

Cornejo-Rodriguez, A.

Dente, G. C.

E. W. Young and G. C. Dente, Proc. SPIE 540, 59 (1985).

G. C. Dente, Proc. SPIE 429, 187 (1983).

Diaz-Uribe, R.

Mahajan, V. N.

V. N. Mahajan, Aberration Theory Made Simple (SPIE, 1991), Chap. 8, pp. 86.

Pedraza-Contreras, J.

Schwenker, J. P.

K. Z. Smith, J. P. Schwenker, R. J. Brown, and J. F. Sullivan, Proc. SPIE 5494, 141 (2004).
[CrossRef]

Smith, K. Z.

K. Z. Smith, J. P. Schwenker, R. J. Brown, and J. F. Sullivan, Proc. SPIE 5494, 141 (2004).
[CrossRef]

Sullivan, J. F.

K. Z. Smith, J. P. Schwenker, R. J. Brown, and J. F. Sullivan, Proc. SPIE 5494, 141 (2004).
[CrossRef]

Young, E. W.

E. W. Young and G. C. Dente, Proc. SPIE 540, 59 (1985).

Appl. Opt. (1)

Proc. SPIE (4)

K. Z. Smith, J. P. Schwenker, R. J. Brown, and J. F. Sullivan, Proc. SPIE 5494, 141 (2004).
[CrossRef]

D. Baiocchi and J. H. Burge, Proc. SPIE 4093, 58 (2000).
[CrossRef]

G. C. Dente, Proc. SPIE 429, 187 (1983).

E. W. Young and G. C. Dente, Proc. SPIE 540, 59 (1985).

Other (2)

V. N. Mahajan, Aberration Theory Made Simple (SPIE, 1991), Chap. 8, pp. 86.

Optical Research Associates, 'CodeV online reference manual,' www.opticalres.com.

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Figures (1)

Fig. 1
Fig. 1

Layout of the test for a concave surface.

Tables (2)

Tables Icon

Table 1 Relationships between Aberration Coefficients

Tables Icon

Table 2 Comparison of Results from Theory and Code V Simulation

Equations (16)

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W ( ρ , φ ) = w 20 ρ 2 + w 22 ρ 2 cos 2 φ + w 31 ρ 3 cos φ + w 40 ρ 4 ,
w 20 = R r s 2 4 ( f # ) 2 ( 1 R r s + 1 R S ) ,
w 22 = R r s 2 4 ( f # ) 2 ( R 2 R S 3 1 R S ) = R r s 2 4 ( f # ) 2 ( 1 R T 1 R S ) ,
w 31 = R r s 3 32 ( f # ) 3 Q ( 3 R 2 + R S 2 ) R S 4 ,
w 40 = R r s 4 64 ( f # ) 4 [ 1 R r s 3 ( R 2 + R S 2 ) R r s 2 R S 3 + ( 4 Q 2 R S 2 + M R 2 ) ( 3 R 2 + R S 2 ) + M R S 2 ( R 2 + 3 R S 2 ) 8 R S 7 ] ,
Q = ± { ( R 2 R S 2 ) [ ( K + 1 ) R S 2 R 2 ] } 1 2 R S 2 ,
M = K + 2 R 2 R S 2 ,
W = W ( R , K ; R r s , R S , f # ; ρ , φ ) ,
w j = w j ( R , K ; R r s , R S , f # ) ,
z i = z i ( R , K ; R r s , R S , f # ) .
R = R S 2 + 4 ( f # ) 2 R S w 22 S ,
K = Q 2 R S 2 R 2 R S 2 + R 2 R S 2 1 ,
Q = 32 ( f # ) 3 R S w 31 S 3 R 2 + R S 2 .
w 22 T w 22 S = ( R S R ) 4 , w 22 S w 22 M = ( R R S ) 4 ( 1 + Δ R T S 2 R S ) 2 ,
R = Δ R T S 2 ( w 22 T w 22 S ) 1 4 [ ( w 22 T w 22 M ) 1 2 1 ] .
R S = R 2 K r 2 or R T = ( R 2 K r 2 ) 3 R 2 ,

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