Abstract

In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.

© 2017 Optical Society of America

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2017 (1)

2016 (5)

U. Fuchs and S. R. Kiontke, “Discussing design for manufacturability for two freeform imaging systems,” Proc. SPIE 9948, 99480L (2016).

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]

M. P. Chrisp, B. Primeau, and M. A. Echter, “Imaging freeform optical systems designed with nurbs surfaces,” Opt. Eng. 55(7), 071208 (2016).
[Crossref]

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

M. Maksimovic, “Optical design and tolerancing of freeform surfaces using anisotropic radial basis functions,” Opt. Eng. 55(7), 071203 (2016).
[Crossref]

2015 (5)

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

S. Gautam, A. Gupta, and G. Singh, “Optical design of off-axis Cassegrain telescope using freeform surface at the secondary mirror,” Opt. Eng. 54(2), 025113 (2015).
[Crossref]

S. Kim, S. Chang, S. Pak, K. J. Lee, B. Jeong, G. J. Lee, G. H. Kim, S. K. Shin, and S. M. Yoo, “Fabrication of electroless nickel plated aluminum freeform mirror for an infrared off-axis telescope,” Appl. Opt. 54(34), 10137–10144 (2015).
[Crossref] [PubMed]

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 (6)

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]

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]

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

J. Ye, Z. Gao, S. Wang, J. Cheng, W. Wang, and W. Sun, “Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture,” J. Opt. Soc. Am. A 31(10), 2304–2311 (2014).
[Crossref] [PubMed]

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

M. P. Chrisp, “New freeform NURBS imaging design code,” Proc. SPIE 9293, 92930N (2014).
[Crossref]

2013 (2)

C. Menke and G. W. Forbes, “Optical design with orthogonal representations of rotationally symmetric and freeform aspheres,” Adv. Opt. Technol. 2(1), 97–109 (2013).

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

2012 (3)

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

2011 (1)

2008 (4)

S.-B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

E. Hugot, G. R. Lemaître, and M. Ferrari, “Active optics: single actuator principle and angular thickness distribution for astigmatism compensation by elasticity,” Appl. Opt. 47(10), 1401–1409 (2008).
[Crossref] [PubMed]

R. N. Youngworth and E. I. Betensky, “Lens design with Forbes aspheres,” Proc. SPIE 7100, 71000W (2008).
[Crossref]

2004 (2)

R. Upton and B. Ellerbroek, “Gram-Schmidt orthogonalization of the Zernike polynomials on apertures of arbitrary shape,” Opt. Lett. 29(24), 2840–2842 (2004).
[Crossref] [PubMed]

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, “Curved ccds and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).
[Crossref]

2002 (1)

M. P. Lesser and J. A. Tyson, “Focal Plane Technologies for LSST,” Proc. SPIE 4836, 240 (2002).
[Crossref]

1998 (1)

M. Ferrari, “Development of a variable curvature mirror for the delay lines of the VLT interferometer,” Astronomy Astrophys. 128, 221–227 (1998).

Agócs, T.

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

Benítez, P.

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

Betensky, E. I.

R. N. Youngworth and E. I. Betensky, “Lens design with Forbes aspheres,” Proc. SPIE 7100, 71000W (2008).
[Crossref]

Borghi, G.

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

Brewer, P.

Buljan, M.

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

Catrysse, P. B.

S.-B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

Chambion, B.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Chang, S.

Channin, D. J.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, “Curved ccds and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).
[Crossref]

Chazallet, F.

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

Cheng, J.

Chrisp, M. P.

M. P. Chrisp, B. Primeau, and M. A. Echter, “Imaging freeform optical systems designed with nurbs surfaces,” Opt. Eng. 55(7), 071208 (2016).
[Crossref]

M. P. Chrisp, “New freeform NURBS imaging design code,” Proc. SPIE 9293, 92930N (2014).
[Crossref]

Cuby, J.-G.

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

Davis, G. E.

Delabre, B.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

Devilliers, C.

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

Dinyari, R.

S.-B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

Dohlen, K.

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

Dong, J.

Echter, M. A.

M. P. Chrisp, B. Primeau, and M. A. Echter, “Imaging freeform optical systems designed with nurbs surfaces,” Opt. Eng. 55(7), 071208 (2016).
[Crossref]

Ellerbroek, B.

Ferrari, M.

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

E. Hugot, G. R. Lemaître, and M. Ferrari, “Active optics: single actuator principle and angular thickness distribution for astigmatism compensation by elasticity,” Appl. Opt. 47(10), 1401–1409 (2008).
[Crossref] [PubMed]

M. Ferrari, “Development of a variable curvature mirror for the delay lines of the VLT interferometer,” Astronomy Astrophys. 128, 221–227 (1998).

Forbes, G. W.

C. Menke and G. W. Forbes, “Optical design with orthogonal representations of rotationally symmetric and freeform aspheres,” Adv. Opt. Technol. 2(1), 97–109 (2013).

Freeman, R.

Fuchs, U.

U. Fuchs and S. R. Kiontke, “Discussing design for manufacturability for two freeform imaging systems,” Proc. SPIE 9948, 99480L (2016).

Fuerschbach, K.

Gaeremynck, Y.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Gao, Z.

Gautam, S.

S. Gautam, A. Gupta, and G. Singh, “Optical design of off-axis Cassegrain telescope using freeform surface at the secondary mirror,” Opt. Eng. 54(2), 025113 (2015).
[Crossref]

Geary, K.

Getin, S.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Grabovickic, D.

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

Gray, M.

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

Guenter, B.

Gupta, A.

S. Gautam, A. Gupta, and G. Singh, “Optical design of off-axis Cassegrain telescope using freeform surface at the secondary mirror,” Opt. Eng. 54(2), 025113 (2015).
[Crossref]

Hammon, D.

Henry, D.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Herrera, G.

Hofmann, A.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Hou, W.

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

Hourtoule, C.

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

Huang, K.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

S.-B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

Hugot, E.

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

E. Hugot, G. R. Lemaître, and M. Ferrari, “Active optics: single actuator principle and angular thickness distribution for astigmatism compensation by elasticity,” Appl. Opt. 47(10), 1401–1409 (2008).
[Crossref] [PubMed]

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Hundley, J.

Iwert, O.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

Jahn, W.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Jeong, B.

Ji, Z.

Jin, G.

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]

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

Joshi, N.

Kaiser, S.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Keefe, A.

Kim, G. H.

Kim, S.

Kiontke, S. R.

U. Fuchs and S. R. Kiontke, “Discussing design for manufacturability for two freeform imaging systems,” Proc. SPIE 9948, 99480L (2016).

Laslandes, M.

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

Le Mignant, D.

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

Lee, G. J.

Lee, K. J.

Lemaître, G. R.

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

E. Hugot, G. R. Lemaître, and M. Ferrari, “Active optics: single actuator principle and angular thickness distribution for astigmatism compensation by elasticity,” Appl. Opt. 47(10), 1401–1409 (2008).
[Crossref] [PubMed]

Lesser, M.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

Lesser, M. P.

M. P. Lesser and J. A. Tyson, “Focal Plane Technologies for LSST,” Proc. SPIE 4836, 240 (2002).
[Crossref]

Lipp, S. A.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, “Curved ccds and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).
[Crossref]

Liu, J.

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

Lopez, C.

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

Ma, H.

Maksimovic, M.

M. Maksimovic, “Optical design and tolerancing of freeform surfaces using anisotropic radial basis functions,” Opt. Eng. 55(7), 071203 (2016).
[Crossref]

Mark, D. S.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, “Curved ccds and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).
[Crossref]

McKnight, G.

Meng, Q.

Menke, C.

C. Menke and G. W. Forbes, “Optical design with orthogonal representations of rotationally symmetric and freeform aspheres,” Adv. Opt. Technol. 2(1), 97–109 (2013).

Miña, J. C.

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

Miñano, J. C.

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

Mott, R.

Moulin, G.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Narasimhan, B.

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

Narasimhn, B.

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

Neil, I. A.

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

Nikitushkina, L.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Nikolic, M.

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

Nowak, A.

Ouellette, D.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

Pak, S.

Pascal, S.

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

Patterson, P.

Peumans, P.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

S.-B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

Primeau, B.

M. P. Chrisp, B. Primeau, and M. A. Echter, “Imaging freeform optical systems designed with nurbs surfaces,” Opt. Eng. 55(7), 071208 (2016).
[Crossref]

Ries, H.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Rim, S.-B.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

S.-B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

Rolland, J. P.

Rossi, M.

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

Schubert, R.

Sherman, E.

Shin, S. K.

Shu, R.

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

Singer, C.

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

Singh, G.

S. Gautam, A. Gupta, and G. Singh, “Optical design of off-axis Cassegrain telescope using freeform surface at the secondary mirror,” Opt. Eng. 54(2), 025113 (2015).
[Crossref]

Stoakley, R.

Sun, W.

Swain, P. K.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, “Curved ccds and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).
[Crossref]

Taylor, G. C.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, “Curved ccds and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).
[Crossref]

Thompson, K. P.

Tyson, J. A.

M. P. Lesser and J. A. Tyson, “Focal Plane Technologies for LSST,” Proc. SPIE 4836, 240 (2002).
[Crossref]

Unterhinninghofen, J.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Upton, R.

Valls-Gabaud, D.

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

Valsecchi, G.

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

Vandeneynde, A.

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

Vives, S.

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

Wang, D.

Wang, H.

Wang, J.

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

Wang, K.

Wang, S.

Wang, W.

Wang, X.

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

Wang, Y.

Wu, X.

Yang, L.

Yang, T.

Ye, J.

Yoo, S. M.

Youngworth, R. N.

R. N. Youngworth and E. I. Betensky, “Lens design with Forbes aspheres,” Proc. SPIE 7100, 71000W (2008).
[Crossref]

Zago, P.

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

Zhang, X.

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

Zhu, J.

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (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]

Zocchi, F. E.

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

Adv. Opt. Technol. (1)

C. Menke and G. W. Forbes, “Optical design with orthogonal representations of rotationally symmetric and freeform aspheres,” Adv. Opt. Technol. 2(1), 97–109 (2013).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

Astronomy Astrophys. (1)

M. Ferrari, “Development of a variable curvature mirror for the delay lines of the VLT interferometer,” Astronomy Astrophys. 128, 221–227 (1998).

J. Opt. (1)

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

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

Opt. Eng. (6)

M. Nikolic, P. Benítez, B. Narasimhan, D. Grabovickic, J. Liu, and J. C. Miñano, “Optical design through optimization for rectangular apertures using freeform orthogonal polynomials: a case study,” Opt. Eng. 55(7), 071204 (2016).
[Crossref]

M. Rossi, G. Borghi, I. A. Neil, G. Valsecchi, P. Zago, and F. E. Zocchi, “Electroformed off-axis toroidal aspheric three-mirror anastigmat multispectral imaging system,” Opt. Eng. 53(3), 031308 (2014).
[Crossref]

M. Laslandes, E. Hugot, M. Ferrari, C. Hourtoule, C. Singer, C. Devilliers, C. Lopez, and F. Chazallet, “Mirror actively deformed and regulated for applications in space: design and performance,” Opt. Eng. 52(9), 091803 (2013).
[Crossref]

S. Gautam, A. Gupta, and G. Singh, “Optical design of off-axis Cassegrain telescope using freeform surface at the secondary mirror,” Opt. Eng. 54(2), 025113 (2015).
[Crossref]

M. Maksimovic, “Optical design and tolerancing of freeform surfaces using anisotropic radial basis functions,” Opt. Eng. 55(7), 071203 (2016).
[Crossref]

M. P. Chrisp, B. Primeau, and M. A. Echter, “Imaging freeform optical systems designed with nurbs surfaces,” Opt. Eng. 55(7), 071208 (2016).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Proc. SPIE (10)

E. Hugot, X. Wang, D. Valls-Gabaud, G. R. Lemaître, T. Agócs, R. Shu, and J. Wang, “A freeform-based, fast, wide-field, and distortion-free camera for ultralow surface brightness surveys,” Proc. SPIE 9143, 91434X (2014).
[Crossref]

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

S. Pascal, M. Gray, S. Vives, D. Le Mignant, M. Ferrari, J.-G. Cuby, and K. Dohlen, “New modelling of freeform surfaces for optical design of astronomical instruments,” Proc. SPIE 8450, 845053 (2012).
[Crossref]

M. P. Chrisp, “New freeform NURBS imaging design code,” Proc. SPIE 9293, 92930N (2014).
[Crossref]

R. N. Youngworth and E. I. Betensky, “Lens design with Forbes aspheres,” Proc. SPIE 7100, 71000W (2008).
[Crossref]

M. Nikolic, P. Benítez, J. C. Miña, D. Grabovickic, J. Liu, B. Narasimhn, and M. Buljan, “Optical design through optimization using freeform orthogonal polynomials for rectangular apertures,” Proc. SPIE 9626, 96260V (2015).
[Crossref]

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, “Curved ccds and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).
[Crossref]

U. Fuchs and S. R. Kiontke, “Discussing design for manufacturability for two freeform imaging systems,” Proc. SPIE 9948, 99480L (2016).

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

M. P. Lesser and J. A. Tyson, “Focal Plane Technologies for LSST,” Proc. SPIE 4836, 240 (2002).
[Crossref]

Other (6)

S. Nikzad, M. Hoenk, and T. Jones, “Solid-state curved focal plane arrays,” (2010). US Patent 7,786,421.

J. M. Geary, Introduction to Lens Design: With Practical Zemax Examples (Willmann-Bell, 2002).

B. Chambion, L. Nikitushkina, Y. Gaeremynck, W. Jahn, E. Hugot, G. Moulin, S. Getin, A. Vandeneynde, and D. Henry, “Tunable curvature of large visible CMOS image sensors: Towards new optical functions and system miniaturization,” in Proceedings of IEEE 66th Electronic Components and Technology Conference (IEEE, 2016), pp.178- 187.
[Crossref]

R. Hentschel, B. Braunecker, and H. J. Tiziani, Advanced Optics Using Aspherical Elements (SPIE Publishing, 2008).

T. M. Apostol, Linear Algebra: A First Course, with Applications to Differential Equations (Wiley, 1997).

M. P. Chrisp, “Three Mirror Anastigmat Designed with NURBS Freeform Surfaces,” in Renewable Energy and the Environment: Postdeadline Papers, OSA Postdeadline Paper Digest (online) (Optical Society of America, 2013), paper FM4B.3.

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Figures (10)

Fig. 1
Fig. 1

Main optical parameters of existing freeform-based optical systems performance evaluation.

Fig. 2
Fig. 2

Polynomials modes defined over a unite square aperture: a – Legendre polynomials, b – square Zernike polynomials.

Fig. 3
Fig. 3

Layout of the freeform-based unobscured TMA telescope.

Fig. 4
Fig. 4

Image quality of the telescope using mirrors described by Legendre polynomials: a – spot diagrams, b – energy concentration in 10µm-size pixel. The labels correspond to angular coordinates of the FoV points.

Fig. 5
Fig. 5

Image quality of the telescope using mirrors described by square Zernike polynomials: a – spot diagrams, b – energy concentration in 10µm-size pixel. The labels correspond to angular coordinates of the FoV points.

Fig. 6
Fig. 6

Residuals after subtraction of BFS from the mirrors surfaces in the design with Legendre polynomials: a – primary mirror, b – secondary mirror, c – tertiary mirror. The units are microns (the units on colorbars are microns).

Fig. 7
Fig. 7

Residuals after subtraction of BFS from the mirrors surfaces in the design with square Zernike polynomials: a – primary mirror, b – secondary mirror, c – tertiary mirror (the units on colorbars are microns).

Fig. 8
Fig. 8

Sag of the curved detector used in the design with Legendre polynomials (the units on colorbar are microns).

Fig. 9
Fig. 9

Estimation of the detector shape influence on the telescopes image quality.

Fig. 10
Fig. 10

Comparison of optimization results with use of different polynomial sets.

Tables (5)

Tables Icon

Table 1 Explicit form of the 2D Legendre and square Zernike polynomials

Tables Icon

Table 2 General parameters of the telescope

Tables Icon

Table 3 Image quality indicators

Tables Icon

Table 4 Distortion of the telescopes in %

Tables Icon

Table 5 BFS parameters for the freeform mirrors

Metrics