Abstract

To test the ultra-deep conic surface in wide-field optical systems, a catadioptric null test method is researched in this paper. Equations of infinite conjugate null test system are established and solved using optical path length. The numeric results of a self-aligning mirror’s shapes are fitted by coefficients and validation is done in optical design software. The rms wavefront error is 0.0019λ (λ=632.8nm) in the example fitted by five coefficients. Furthermore, by adjusting spherical aberration distributions, an all-spherical finite conjugate null test system is designed, whose rms wavefront error is 0.0309λ. The test methods in this paper have been proven to be adaptive to many other similar ultra-deep surfaces, even with higher orders.

© 2013 Optical Society of America

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References

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  1. N. A. Agal’tsova, Atlas of Aerial photographic lenses “Russar” (Science, 2010).
  2. W. Yongzhong, Fish-eye Lens Optics (Science, 2006).
  3. S. Bambrick, M. Bechtold, and S. DeFisher, “Recent developments in finishing of deep concave, aspheric, and plano surfaces utilizing the ultraform 5-axes computer controlled system,” Proc. SPIE 7302, 73020U (2009).
    [CrossRef]
  4. D. Malacara, Optical Shop Testing (China Machine, 1983).
  5. T. Kim and J. H. Burge, “Null test for a highly paraboloidal mirror,” Appl. Opt. 43, 3614–3618 (2004).
    [CrossRef]
  6. R. Pursel, “Null testing of a f/0.6 concave aspheric surface,” Proc. SPIE 2263, 210–217 (1994).
    [CrossRef]
  7. J. Burge, “A null test for null correctors: error analysis,” Proc. SPIE 1993, 86–97 (1993).
    [CrossRef]
  8. A. Offner, “A null corrector for paraboloidal mirrors,” Appl. Opt. 2, 153–155 (1963).
    [CrossRef]
  9. L. Jones, “Reflective and catadioptric objectives,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, 1995), II p. 18.3.
  10. P. Jun-hua, Design, Machining and Testing of Optical Aspheric Surface (Science, 1994).
  11. ZEMAX Optical Design Program User’s Guide (ZEMAX, 2009).
  12. R. Kingslake, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

2009 (1)

S. Bambrick, M. Bechtold, and S. DeFisher, “Recent developments in finishing of deep concave, aspheric, and plano surfaces utilizing the ultraform 5-axes computer controlled system,” Proc. SPIE 7302, 73020U (2009).
[CrossRef]

2004 (1)

1994 (1)

R. Pursel, “Null testing of a f/0.6 concave aspheric surface,” Proc. SPIE 2263, 210–217 (1994).
[CrossRef]

1993 (1)

J. Burge, “A null test for null correctors: error analysis,” Proc. SPIE 1993, 86–97 (1993).
[CrossRef]

1963 (1)

Agal’tsova, N. A.

N. A. Agal’tsova, Atlas of Aerial photographic lenses “Russar” (Science, 2010).

Bambrick, S.

S. Bambrick, M. Bechtold, and S. DeFisher, “Recent developments in finishing of deep concave, aspheric, and plano surfaces utilizing the ultraform 5-axes computer controlled system,” Proc. SPIE 7302, 73020U (2009).
[CrossRef]

Bechtold, M.

S. Bambrick, M. Bechtold, and S. DeFisher, “Recent developments in finishing of deep concave, aspheric, and plano surfaces utilizing the ultraform 5-axes computer controlled system,” Proc. SPIE 7302, 73020U (2009).
[CrossRef]

Burge, J.

J. Burge, “A null test for null correctors: error analysis,” Proc. SPIE 1993, 86–97 (1993).
[CrossRef]

Burge, J. H.

DeFisher, S.

S. Bambrick, M. Bechtold, and S. DeFisher, “Recent developments in finishing of deep concave, aspheric, and plano surfaces utilizing the ultraform 5-axes computer controlled system,” Proc. SPIE 7302, 73020U (2009).
[CrossRef]

Jones, L.

L. Jones, “Reflective and catadioptric objectives,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, 1995), II p. 18.3.

Jun-hua, P.

P. Jun-hua, Design, Machining and Testing of Optical Aspheric Surface (Science, 1994).

Kim, T.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

Malacara, D.

D. Malacara, Optical Shop Testing (China Machine, 1983).

Offner, A.

Pursel, R.

R. Pursel, “Null testing of a f/0.6 concave aspheric surface,” Proc. SPIE 2263, 210–217 (1994).
[CrossRef]

Yongzhong, W.

W. Yongzhong, Fish-eye Lens Optics (Science, 2006).

Appl. Opt. (2)

Proc. SPIE (3)

R. Pursel, “Null testing of a f/0.6 concave aspheric surface,” Proc. SPIE 2263, 210–217 (1994).
[CrossRef]

J. Burge, “A null test for null correctors: error analysis,” Proc. SPIE 1993, 86–97 (1993).
[CrossRef]

S. Bambrick, M. Bechtold, and S. DeFisher, “Recent developments in finishing of deep concave, aspheric, and plano surfaces utilizing the ultraform 5-axes computer controlled system,” Proc. SPIE 7302, 73020U (2009).
[CrossRef]

Other (7)

D. Malacara, Optical Shop Testing (China Machine, 1983).

N. A. Agal’tsova, Atlas of Aerial photographic lenses “Russar” (Science, 2010).

W. Yongzhong, Fish-eye Lens Optics (Science, 2006).

L. Jones, “Reflective and catadioptric objectives,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, 1995), II p. 18.3.

P. Jun-hua, Design, Machining and Testing of Optical Aspheric Surface (Science, 1994).

ZEMAX Optical Design Program User’s Guide (ZEMAX, 2009).

R. Kingslake, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

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Figures (7)

Fig. 1.
Fig. 1.

Ultra-deep concave aspheric surface used in a wide-field optical system.

Fig. 2.
Fig. 2.

Ray tracing of an ultra-deep aspheric lens.

Fig. 3.
Fig. 3.

Surface sag of self-aligning mirror versus a radial coordinate.

Fig. 4.
Fig. 4.

Layout of infinite conjugated test system.

Fig. 5.
Fig. 5.

Wavefront error of infinite conjugated test system.

Fig. 6.
Fig. 6.

Layout of the all-spherical finite conjugate null test system.

Fig. 7.
Fig. 7.

Wave-front-error of all-spherical finite conjugate null test system.

Tables (1)

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Table 1. Surface Fitting Coefficients

Equations (22)

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Z(r)=cr21+1(1+K)c2r2,
ΔR=kx0,
|CyO|=1c+ΔRx0=1c(1+k)x0c,
tanφ=y0|CyO|=cy01c(1+k)x0,
φ1=φ=arctan[cy01c(1+k)x0],
φ1=arcsin[sinφ1n],
k1=tanθ1=tan(|φ1||φ1|).
{yy0=k1(xx0)y2+(x+Rl2)2=R2,
{x1=x0y0k1+y0+k1(l2Rx0+A)k1(k12+1)y1=y0+k1(l2Rx0+A)k12+1,
A=R2+2Rk1(y0+l2k1k1x0)l2k1(2y0+l2k12k1x0)k1x0(k1x02y0)y02.
φ2=θ1|arctan(y1R2y12)|,
φ2=arcsin(n·sin|φ2|),
k2=tanθ2=tan[|arctan(y1R2y12)|+φ2].
{x2=x1+d2Bk2y2=y1+d2B,
B=1k22+1.
n|PP1|+|P1P2|=|OO|+n|OO1|+|O1O2|,
d2=|P1P2|=|x0|+nl1+|O1O2|n|(x1x0)2+(y1y0)2|,
Z(r)=cr21+1(1+K)c2r2+a2r4+a3r6+a4r8.
SIt+SIc=0,
SI=[n(u+yc)]2y(unun),
SI=SI+y4c3K(nn),
SIt=SI+SI=7.416.

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