Abstract

Off-axis reflective imaging systems are widely used, but manufacturing issues are seldom considered in their design. This paper proposes a direct design method for cylindrical freeform imaging systems considering manufacturing constraints to facilitate ultraprecise raster milling. The initial freeform shapes of a well-restricted system configuration are constructed using feature data points and calculated based on the constant optical path length condition. An iterative process with coefficient adjustment of the surface expression is employed to optimize the freeform mirrors for both image quality and the degree of deviation from a reference surface. The method’s feasibility is validated by designing an off-axis three-mirror imaging system that operates at F/2.0 with a 100 mm entrance pupil diameter and a 4° × 4° field of view. The freeform surfaces are guaranteed to be distributed along a cylinder 150 mm in radius for ultraprecise raster milling.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Integrated manufacture of a freeform off-axis multi-reflective imaging system without optical alignment

Zexiao Li, Xianlei Liu, Fengzhou Fang, Xiaodong Zhang, Zhen Zeng, Linlin Zhu, and Ning Yan
Opt. Express 26(6) 7625-7637 (2018)

Design method of freeform off-axis reflective imaging systems with a direct construction process

Tong Yang, Jun Zhu, Wei Hou, and Guofan Jin
Opt. Express 22(8) 9193-9205 (2014)

References

  • View by:
  • |
  • |
  • |

  1. X. L. Li, M. Xu, X. D. Ren, and Y. T. Pei, “An optical design of off-axis four-mirror-anastigmatic telescope for remote sensing,” J. Opt. Soc. Korea 16(3), 243–246 (2012).
    [Crossref]
  2. A. Dubra and Y. Sulai, “Reflective afocal broadband adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(6), 1757–1768 (2011).
    [Crossref] [PubMed]
  3. W. J. Marinelli, C. M. Gittins, A. H. Gelb, and B. D. Green, “Tunable Fabry-Perot etalon-based long-wavelength infrared imaging spectroradiometer,” Appl. Opt. 38(12), 2594–2604 (1999).
    [Crossref] [PubMed]
  4. K. Fuerschbach, G. E. Davis, K. P. Thompson, and J. P. Rolland, “Assembly of a freeform off-axis optical system employing three φ-polynomial Zernike mirrors,” Opt. Lett. 39(10), 2896–2899 (2014).
    [Crossref] [PubMed]
  5. D. Cheng, Y. Wang, H. Hua, and M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48(14), 2655–2668 (2009).
    [Crossref] [PubMed]
  6. B. Yang, J. T. Mäkinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
    [Crossref]
  7. D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849(2), 78490Q (2010).
  8. R. A. Hicks, “Controlling a ray bundle with a free-form reflector,” Opt. Lett. 33(15), 1672–1674 (2008).
    [Crossref] [PubMed]
  9. G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
    [Crossref]
  10. F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces,” Opt. Express 20(10), 10839–10846 (2012).
    [Crossref] [PubMed]
  11. J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
    [Crossref] [PubMed]
  12. B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
    [Crossref]
  13. T. Yang, J. Zhu, X. Wu, and G. Jin, “Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method,” Opt. Express 23(8), 10233–10246 (2015).
    [Crossref] [PubMed]
  14. Z. Li, F. Fang, J. Chen, and X. Zhang, “Machining approach of freeform optics on infrared materials via ultra-precision turning,” Opt. Express 25(3), 2051–2062 (2017).
    [Crossref] [PubMed]
  15. C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
    [Crossref]
  16. Q. Meng, W. Wang, H. Ma, and J. Dong, “Easy-aligned off-axis three-mirror system with wide field of view using freeform surface based on integration of primary and tertiary mirror,” Appl. Opt. 53(14), 3028–3034 (2014).
    [Crossref] [PubMed]
  17. X. Zhang, H. Gao, Y. Guo, and G. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP. Ann-Manuf. Technol. 61(1), 519–522 (2012).
  18. Z. Li, X. Liu, F. Fang, X. Zhang, Z. Zeng, L. Zhu, and N. Yan, “Integrated manufacture of a freeform off-axis multi-reflective imaging system without optical alignment,” Opt. Express 26(6), 7625–7637 (2018).
    [Crossref] [PubMed]
  19. I. Sieber, T. Martin, and U. Gengenbach, “Robust design of an optical micromachine for an ophthalmic application,” Micromachines (Basel) 7(5), 85 (2016).
    [Crossref]
  20. Q. Meng, H. Wang, K. Wang, Y. Wang, Z. Ji, and D. Wang, “Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror,” Appl. Opt. 55(32), 8962–8970 (2016).
    [Crossref] [PubMed]
  21. J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31(11), 2401–2408 (2014).
    [Crossref] [PubMed]

2018 (1)

2017 (1)

2016 (2)

Q. Meng, H. Wang, K. Wang, Y. Wang, Z. Ji, and D. Wang, “Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror,” Appl. Opt. 55(32), 8962–8970 (2016).
[Crossref] [PubMed]

I. Sieber, T. Martin, and U. Gengenbach, “Robust design of an optical micromachine for an ophthalmic application,” Micromachines (Basel) 7(5), 85 (2016).
[Crossref]

2015 (2)

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

T. Yang, J. Zhu, X. Wu, and G. Jin, “Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method,” Opt. Express 23(8), 10233–10246 (2015).
[Crossref] [PubMed]

2014 (3)

2012 (3)

2011 (1)

2010 (1)

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849(2), 78490Q (2010).

2009 (3)

2008 (1)

2006 (1)

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

1999 (1)

1949 (1)

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[Crossref]

Aikio, M.

B. Yang, J. T. Mäkinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Benítez, P.

Brecher, C.

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

Chen, J.

Cheng, D.

Davis, G. E.

Dong, J.

Dubra, A.

Duerr, F.

Fang, F.

Fuerschbach, K.

Gao, H.

X. Zhang, H. Gao, Y. Guo, and G. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP. Ann-Manuf. Technol. 61(1), 519–522 (2012).

Gelb, A. H.

Gengenbach, U.

I. Sieber, T. Martin, and U. Gengenbach, “Robust design of an optical micromachine for an ophthalmic application,” Micromachines (Basel) 7(5), 85 (2016).
[Crossref]

Gittins, C. M.

Green, B. D.

Gross, H.

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

Guo, Y.

X. Zhang, H. Gao, Y. Guo, and G. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP. Ann-Manuf. Technol. 61(1), 519–522 (2012).

Hicks, R. A.

Hua, H.

Infante, J.

Ji, Z.

Jin, G.

Lange, S.

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

Li, X. L.

Li, Z.

Lin, W.

Lippmann, U.

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

Liu, X.

Ma, H.

Mäkinen, J. T.

B. Yang, J. T. Mäkinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Marinelli, W. J.

Martin, T.

I. Sieber, T. Martin, and U. Gengenbach, “Robust design of an optical micromachine for an ophthalmic application,” Micromachines (Basel) 7(5), 85 (2016).
[Crossref]

Meng, Q.

Merz, M.

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

Metzner, G. S.

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

Meuret, Y.

Miñano, J. C.

Muñoz, F.

Niehaus, F.

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

Notni, G.

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

Pei, Y. T.

Ren, X. D.

Richter, U.

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

Rolland, J. P.

Santamaría, A.

Satzer, B.

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

Sieber, I.

I. Sieber, T. Martin, and U. Gengenbach, “Robust design of an optical micromachine for an ophthalmic application,” Micromachines (Basel) 7(5), 85 (2016).
[Crossref]

Sulai, Y.

Talha, M. M.

Thienpont, H.

Thompson, K. P.

Wang, D.

Wang, H.

Wang, K.

Wang, W.

Wang, Y.

Q. Meng, H. Wang, K. Wang, Y. Wang, Z. Ji, and D. Wang, “Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror,” Appl. Opt. 55(32), 8962–8970 (2016).
[Crossref] [PubMed]

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849(2), 78490Q (2010).

D. Cheng, Y. Wang, H. Hua, and M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48(14), 2655–2668 (2009).
[Crossref] [PubMed]

B. Yang, J. T. Mäkinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Wassermann, G. D.

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[Crossref]

Weck, M.

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

Wenzel, C.

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

Winterschladen, M.

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

Wolf, E.

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[Crossref]

Wu, X.

Xu, M.

Yan, N.

Yang, B.

B. Yang, J. T. Mäkinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Yang, T.

Zeng, Z.

Zhang, G.

X. Zhang, H. Gao, Y. Guo, and G. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP. Ann-Manuf. Technol. 61(1), 519–522 (2012).

Zhang, X.

Zhu, J.

Zhu, L.

Appl. Opt. (4)

Biomed. Opt. Express (1)

CIRP Ann. Manuf. Tech. (1)

C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winterschladen, and M. Weck, “NURBS based ultraprecision free-form machining,” CIRP Ann. Manuf. Tech. 55(1), 547–550 (2006).
[Crossref]

CIRP. Ann-Manuf. Technol. (1)

X. Zhang, H. Gao, Y. Guo, and G. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP. Ann-Manuf. Technol. 61(1), 519–522 (2012).

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

J. Opt. Soc. Korea (1)

Micromachines (Basel) (1)

I. Sieber, T. Martin, and U. Gengenbach, “Robust design of an optical micromachine for an ophthalmic application,” Micromachines (Basel) 7(5), 85 (2016).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Optik (Stuttg.) (1)

B. Yang, J. T. Mäkinen, M. Aikio, G. Jin, and Y. Wang, “Free-form lens design for wide-angle imaging with an equidistance projection scheme,” Optik (Stuttg.) 120(2), 74–78 (2009).
[Crossref]

Proc. Phys. Soc. B (1)

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[Crossref]

Proc. SPIE (2)

B. Satzer, U. Richter, U. Lippmann, G. S. Metzner, G. Notni, and H. Gross, “Using the 3D-SMS for finding starting configurations in imaging systems with freeform surfaces,” Proc. SPIE 9626, 96260Y (2015).
[Crossref]

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849(2), 78490Q (2010).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1 (a) Machining configuration for freeform three-mirror system. (b) Geometric relationship between the freeform surfaces and the reference surface.
Fig. 2
Fig. 2 Flow chart of the entire design process.
Fig. 3
Fig. 3 Data points and feature rays defined before calculation. (a) Sampled feature points on a circular aperture. (b) Feature rays emitted from data points.
Fig. 4
Fig. 4 Feature rays should be redirected to their corresponding target point after reflection by the unknown freeform surface.
Fig. 5
Fig. 5 Feature rays intersect the wavefront plane, determining their starting points. The optical path length in every field of view is calculated according to these starting points.
Fig. 6
Fig. 6 Feature points Pi are calculated based on the constant OPL condition.
Fig. 7
Fig. 7 A search process is required to determine the feature points on the feature rays.
Fig. 8
Fig. 8 Flow diagram of the construction process. U denotes the number of freeform surfaces in the system. M denotes the number of fields sampled in the design process.
Fig. 9
Fig. 9 Flowchart of iterative optimization with coefficient adjustment. M denotes the number of fields sampled in the design.
Fig. 10
Fig. 10 Layout of the alignment-free off-axis three-mirror imaging system. (a) Initial structure of primary mirror M1 and the auxiliary point used to construct M1. (b) Ray tracing result after M1 has been constructed. (c) Layout after all mirrors have been constructed.
Fig. 11
Fig. 11 (a) RMS deviation of the optical system after M3, M2, and M1 are generated. (b) Degree of deviation from the cylinder (DDRS) of freeform surfaces after three steps.
Fig. 12
Fig. 12 (a) Convergence behavior of the RMS deviation for the two iteration types versus the number of iteration steps. (b) DDRSs of each surface after each type of iteration.
Fig. 13
Fig. 13 Layout of optical system after (a) coefficient iteration and (b) optimization using Zemax.
Fig. 14
Fig. 14 RMS spot diagram in Zemax.
Fig. 15
Fig. 15 Field curvature and distortion of the optimized optical system.
Fig. 16
Fig. 16 MTF of the optical system.

Tables (1)

Tables Icon

Table 1 Specifications of freeform alignment-free off-axis three-mirror imaging system

Equations (10)

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

σ D D R S = i = 1 N d i 2 N .
O P = n | S 0 P 0 | + n | P 0 T | ,
n | S i P i | + n | P i T | = O P .
O P = n | S 0 P 0 | + n | P 0 M 0 | + n | M 0 T . |
n | S i P i | + n | P i M i | + n | M i T | = O P ,
σ R M S = i = 1 N σ i 2 N ,
z ( x , y ) = c ( x 2 + y 2 ) 1 + 1 ( 1 + k ) c 2 ( x 2 + y 2 ) + i = 1 N A i x m y n ,
z ( x , y ) = i = 1 N A i x m y n .
y 2 + z 2 = R 2 ,
z ( x , y ) = A 1 y + A 2 x 2 + A 3 y 2 + A 4 x 2 y + A 5 y 3 + A 6 x 4 + A 7 x 2 y 2 + A 8 y 4 .

Metrics