Abstract

A design is proposed for a refracting optical element for forming a rectangular directional pattern for a compact radiation source. The calculation of the surfaces of the optical element reduces to solving trivial problems with cylindrical symmetry. The results of the numerical modelling of the calculated elements are presented. The rms error of the formation of equilibrium rectangular intensity distributions is less than 10% for angular sizes of the directional patterns of (120°-180°)×(10°-40°).

© 2009 Optical Society of America

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  1. P. Guan and X.-J. Wang , “On a Monge-Ampere equation arising in geometric optics,” J. Diff. Geom. 48, 205 (1998).
  2. I. Knowles and Y. Satio , “Radially symmetric solutions of a Monge-Ampere equation arising in the reflector mapping problem (with P. Waltman),” in Proceedings of the UAB International Conference on Differential Equations and Mathematical Physics, Lecture Notes in Math, Springer-Verlag, 1987, pp. 973-1000.
  3. V. Oliker and A. Treibergs , “Geometry and nonlinear partial differential equations,” Contemp. Math. 127, 1 (1992).
  4. L. L. Doskolovich and N. L. Kazanskiĭ , “Calculating a mirror for the formation of a single-parameter directional pattern,” Avtometriya 40, No. 5, 104 (2004).
  5. L. L. Doskolovich , N. L. Kazanskiy , and S. I. Kharitonov , “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52, 1529 (2005).
    [Crossref]
  6. L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].
  7. L. L. Doskolovich , N. L. Kazanskiy , and S. Bernard , “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54, 589 (2007).
    [Crossref]
  8. L. L. Doskolovich , N. L. Kazanskiĭ , and M. A. Trenina , “Calculating a mirror for shaping a directional pattern in the form of a line segment,” Avtometriya 42, No. 4, 67 (2006).
  9. J. Muschaweck and H. Ries , “Tailored freeform optical surface,” J. Opt. Soc. Am. A 19, 590 (2002).
    [Crossref]
  10. J. Muschaweck and H. Ries , “Tailoring freeform lenses for illuminations,” Proc. SPIE 4442, 43 (2001).
    [Crossref]
  11. R. A. Hicks , “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. A 22, 323 (2005).
    [Crossref]
  12. S. Doyle , D. Corcoran , and J. Connell , “Automated mirror design using an evolution strategy,” Opt. Eng. 38, 323 (2001).
    [Crossref]
  13. A. A. Belousov and L. L. Doskolovich , “Gradient method of solving the problem of focusing in a two-dimensional region with an extended source,” Komp'yut. Opt. 31, No. 3, 20 (2007).
  14. A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].
  15. L. L. Doskolovich and M. A. Moiseev , “Calculating radially symmetric refracting surfaces allowing for Fresnel losses,” Komp'yut. Opt. 32, 201 (2008).
  16. W. B. Elmer , “Optical design of reflectors,” Appl. Opt. 17, 977 (1978).
    [Crossref]

2008 (2)

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

L. L. Doskolovich and M. A. Moiseev , “Calculating radially symmetric refracting surfaces allowing for Fresnel losses,” Komp'yut. Opt. 32, 201 (2008).

2007 (2)

A. A. Belousov and L. L. Doskolovich , “Gradient method of solving the problem of focusing in a two-dimensional region with an extended source,” Komp'yut. Opt. 31, No. 3, 20 (2007).

L. L. Doskolovich , N. L. Kazanskiy , and S. Bernard , “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54, 589 (2007).
[Crossref]

2006 (1)

L. L. Doskolovich , N. L. Kazanskiĭ , and M. A. Trenina , “Calculating a mirror for shaping a directional pattern in the form of a line segment,” Avtometriya 42, No. 4, 67 (2006).

2005 (3)

L. L. Doskolovich , N. L. Kazanskiy , and S. I. Kharitonov , “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52, 1529 (2005).
[Crossref]

L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].

L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].

R. A. Hicks , “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. A 22, 323 (2005).
[Crossref]

2004 (1)

L. L. Doskolovich and N. L. Kazanskiĭ , “Calculating a mirror for the formation of a single-parameter directional pattern,” Avtometriya 40, No. 5, 104 (2004).

2002 (1)

J. Muschaweck and H. Ries , “Tailored freeform optical surface,” J. Opt. Soc. Am. A 19, 590 (2002).
[Crossref]

2001 (2)

J. Muschaweck and H. Ries , “Tailoring freeform lenses for illuminations,” Proc. SPIE 4442, 43 (2001).
[Crossref]

S. Doyle , D. Corcoran , and J. Connell , “Automated mirror design using an evolution strategy,” Opt. Eng. 38, 323 (2001).
[Crossref]

1998 (1)

P. Guan and X.-J. Wang , “On a Monge-Ampere equation arising in geometric optics,” J. Diff. Geom. 48, 205 (1998).

1992 (1)

V. Oliker and A. Treibergs , “Geometry and nonlinear partial differential equations,” Contemp. Math. 127, 1 (1992).

1978 (1)

Belousov, A. A.

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

A. A. Belousov and L. L. Doskolovich , “Gradient method of solving the problem of focusing in a two-dimensional region with an extended source,” Komp'yut. Opt. 31, No. 3, 20 (2007).

Bernard, S.

L. L. Doskolovich , N. L. Kazanskiy , and S. Bernard , “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54, 589 (2007).
[Crossref]

Connell, J.

S. Doyle , D. Corcoran , and J. Connell , “Automated mirror design using an evolution strategy,” Opt. Eng. 38, 323 (2001).
[Crossref]

Corcoran, D.

S. Doyle , D. Corcoran , and J. Connell , “Automated mirror design using an evolution strategy,” Opt. Eng. 38, 323 (2001).
[Crossref]

Doskolovich, L. L.

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

L. L. Doskolovich and M. A. Moiseev , “Calculating radially symmetric refracting surfaces allowing for Fresnel losses,” Komp'yut. Opt. 32, 201 (2008).

A. A. Belousov and L. L. Doskolovich , “Gradient method of solving the problem of focusing in a two-dimensional region with an extended source,” Komp'yut. Opt. 31, No. 3, 20 (2007).

L. L. Doskolovich , N. L. Kazanskiy , and S. Bernard , “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54, 589 (2007).
[Crossref]

L. L. Doskolovich , N. L. Kazanskiĭ , and M. A. Trenina , “Calculating a mirror for shaping a directional pattern in the form of a line segment,” Avtometriya 42, No. 4, 67 (2006).

L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].

L. L. Doskolovich , N. L. Kazanskiy , and S. I. Kharitonov , “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52, 1529 (2005).
[Crossref]

L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].

L. L. Doskolovich and N. L. Kazanskiĭ , “Calculating a mirror for the formation of a single-parameter directional pattern,” Avtometriya 40, No. 5, 104 (2004).

Doyle, S.

S. Doyle , D. Corcoran , and J. Connell , “Automated mirror design using an evolution strategy,” Opt. Eng. 38, 323 (2001).
[Crossref]

Elmer, W. B.

Guan, P.

P. Guan and X.-J. Wang , “On a Monge-Ampere equation arising in geometric optics,” J. Diff. Geom. 48, 205 (1998).

Hicks, R. A.

R. A. Hicks , “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. A 22, 323 (2005).
[Crossref]

Kazanskii, N. L.

L. L. Doskolovich , N. L. Kazanskiĭ , and M. A. Trenina , “Calculating a mirror for shaping a directional pattern in the form of a line segment,” Avtometriya 42, No. 4, 67 (2006).

L. L. Doskolovich and N. L. Kazanskiĭ , “Calculating a mirror for the formation of a single-parameter directional pattern,” Avtometriya 40, No. 5, 104 (2004).

Kazanskiy, N. L.

L. L. Doskolovich , N. L. Kazanskiy , and S. Bernard , “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54, 589 (2007).
[Crossref]

L. L. Doskolovich , N. L. Kazanskiy , and S. I. Kharitonov , “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52, 1529 (2005).
[Crossref]

Kharitonov, S. I.

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

L. L. Doskolovich , N. L. Kazanskiy , and S. I. Kharitonov , “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52, 1529 (2005).
[Crossref]

L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].

L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].

Knowles, I.

I. Knowles and Y. Satio , “Radially symmetric solutions of a Monge-Ampere equation arising in the reflector mapping problem (with P. Waltman),” in Proceedings of the UAB International Conference on Differential Equations and Mathematical Physics, Lecture Notes in Math, Springer-Verlag, 1987, pp. 973-1000.

Moiseev, M. A.

L. L. Doskolovich and M. A. Moiseev , “Calculating radially symmetric refracting surfaces allowing for Fresnel losses,” Komp'yut. Opt. 32, 201 (2008).

Muschaweck, J.

J. Muschaweck and H. Ries , “Tailored freeform optical surface,” J. Opt. Soc. Am. A 19, 590 (2002).
[Crossref]

J. Muschaweck and H. Ries , “Tailoring freeform lenses for illuminations,” Proc. SPIE 4442, 43 (2001).
[Crossref]

Oliker, V.

V. Oliker and A. Treibergs , “Geometry and nonlinear partial differential equations,” Contemp. Math. 127, 1 (1992).

Ries, H.

J. Muschaweck and H. Ries , “Tailored freeform optical surface,” J. Opt. Soc. Am. A 19, 590 (2002).
[Crossref]

J. Muschaweck and H. Ries , “Tailoring freeform lenses for illuminations,” Proc. SPIE 4442, 43 (2001).
[Crossref]

Satio, Y.

I. Knowles and Y. Satio , “Radially symmetric solutions of a Monge-Ampere equation arising in the reflector mapping problem (with P. Waltman),” in Proceedings of the UAB International Conference on Differential Equations and Mathematical Physics, Lecture Notes in Math, Springer-Verlag, 1987, pp. 973-1000.

Treibergs, A.

V. Oliker and A. Treibergs , “Geometry and nonlinear partial differential equations,” Contemp. Math. 127, 1 (1992).

Trenina, M. A.

L. L. Doskolovich , N. L. Kazanskiĭ , and M. A. Trenina , “Calculating a mirror for shaping a directional pattern in the form of a line segment,” Avtometriya 42, No. 4, 67 (2006).

Wang, X.-J.

P. Guan and X.-J. Wang , “On a Monge-Ampere equation arising in geometric optics,” J. Diff. Geom. 48, 205 (1998).

Appl. Opt. (1)

Avtometriya (2)

L. L. Doskolovich and N. L. Kazanskiĭ , “Calculating a mirror for the formation of a single-parameter directional pattern,” Avtometriya 40, No. 5, 104 (2004).

L. L. Doskolovich , N. L. Kazanskiĭ , and M. A. Trenina , “Calculating a mirror for shaping a directional pattern in the form of a line segment,” Avtometriya 42, No. 4, 67 (2006).

Contemp. Math. (1)

V. Oliker and A. Treibergs , “Geometry and nonlinear partial differential equations,” Contemp. Math. 127, 1 (1992).

J. Diff. Geom. (1)

P. Guan and X.-J. Wang , “On a Monge-Ampere equation arising in geometric optics,” J. Diff. Geom. 48, 205 (1998).

J. Mod. Opt. (2)

L. L. Doskolovich , N. L. Kazanskiy , and S. I. Kharitonov , “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52, 1529 (2005).
[Crossref]

L. L. Doskolovich , N. L. Kazanskiy , and S. Bernard , “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54, 589 (2007).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Muschaweck and H. Ries , “Tailored freeform optical surface,” J. Opt. Soc. Am. A 19, 590 (2002).
[Crossref]

R. A. Hicks , “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. A 22, 323 (2005).
[Crossref]

Komp'yut. Opt. (2)

A. A. Belousov and L. L. Doskolovich , “Gradient method of solving the problem of focusing in a two-dimensional region with an extended source,” Komp'yut. Opt. 31, No. 3, 20 (2007).

L. L. Doskolovich and M. A. Moiseev , “Calculating radially symmetric refracting surfaces allowing for Fresnel losses,” Komp'yut. Opt. 32, 201 (2008).

Opt. Zh. (1)

L. L. Doskolovich and S. I. Kharitonov , “Calculating the surface shape of mirrors for shaping an image in the form of a line,” Opt. Zh. 72, No. 4, 34 (2005) L. L. Doskolovich and S. I. Kharitonov ,[J. Opt. Technol. 72, 318 (2005)].

Opt. Eng. (1)

S. Doyle , D. Corcoran , and J. Connell , “Automated mirror design using an evolution strategy,” Opt. Eng. 38, 323 (2001).
[Crossref]

Opt. Zh. (1)

A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov , “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” Opt. Zh. 75, No. 3, 30 (2008) A. A. Belousov , L. L. Doskolovich , and S. I. Kharitonov ,[J. Opt. Technol. 75, 161 (2008)].

Proc. SPIE (1)

J. Muschaweck and H. Ries , “Tailoring freeform lenses for illuminations,” Proc. SPIE 4442, 43 (2001).
[Crossref]

Other (1)

I. Knowles and Y. Satio , “Radially symmetric solutions of a Monge-Ampere equation arising in the reflector mapping problem (with P. Waltman),” in Proceedings of the UAB International Conference on Differential Equations and Mathematical Physics, Lecture Notes in Math, Springer-Verlag, 1987, pp. 973-1000.

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