Abstract

It was previously demonstrated by Bäuerle et al. [Opt. Express 20, 14477 (2012)] that the computation of ray paths through the optical system (ray mapping) can be used to design multisurface freeform optical elements creating a prescribed irradiance pattern for a zero-étendue source. The procedure outlined there uses the heuristic step of reducing the ray mapping’s curl to improve adherence to surface integrability criteria. This Letter formally derives a quantitative estimate for the limitations of this approach in the collimated case and shows the key factors influencing the quality of the final optics.

© 2013 Optical Society of America

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References

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  1. A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, Opt. Express 20, 14477 (2012).
    [CrossRef]
  2. W. A. Parkyn, Proc. SPIE 3482, 389 (1998).
    [CrossRef]
  3. S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Int. J. Comput. Vis. 60, 225 (2004).
    [CrossRef]
  4. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, Opt. Express 18, 5295 (2010).
    [CrossRef]
  5. H. Ries and J. Muschaweck, J. Opt. Soc. Am. A 19, 590 (2002).
    [CrossRef]
  6. A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
    [CrossRef]
  7. P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
    [CrossRef]
  8. J.-C. Miñano and P. Benítez, Proc. SPIE 5529, 87 (2004).

2012

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, Opt. Express 20, 14477 (2012).
[CrossRef]

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
[CrossRef]

2010

2004

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

J.-C. Miñano and P. Benítez, Proc. SPIE 5529, 87 (2004).

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Int. J. Comput. Vis. 60, 225 (2004).
[CrossRef]

2002

1998

W. A. Parkyn, Proc. SPIE 3482, 389 (1998).
[CrossRef]

Angenent, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Int. J. Comput. Vis. 60, 225 (2004).
[CrossRef]

Bäuerle, A.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
[CrossRef]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, Opt. Express 20, 14477 (2012).
[CrossRef]

Benítez, P.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

J.-C. Miñano and P. Benítez, Proc. SPIE 5529, 87 (2004).

Blen, J.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

Bruneton, A.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
[CrossRef]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, Opt. Express 20, 14477 (2012).
[CrossRef]

Cassarly, W. J.

Chaves, J.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

Dross, O.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

Falicoff, W.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

Fournier, F. R.

Haker, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Int. J. Comput. Vis. 60, 225 (2004).
[CrossRef]

Hernández, M.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

Loosen, P.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
[CrossRef]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, Opt. Express 20, 14477 (2012).
[CrossRef]

Miñano, J.-C.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

J.-C. Miñano and P. Benítez, Proc. SPIE 5529, 87 (2004).

Mohedano, R.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

Muschaweck, J.

Parkyn, W. A.

W. A. Parkyn, Proc. SPIE 3482, 389 (1998).
[CrossRef]

Ries, H.

Rolland, J. P.

Stollenwerk, J.

Tannenbaum, A.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Int. J. Comput. Vis. 60, 225 (2004).
[CrossRef]

Traub, M.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
[CrossRef]

Wester, R.

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
[CrossRef]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, Opt. Express 20, 14477 (2012).
[CrossRef]

Zhu, L.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Int. J. Comput. Vis. 60, 225 (2004).
[CrossRef]

Int. J. Comput. Vis.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Int. J. Comput. Vis. 60, 225 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

P. Benítez, J.-C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, Opt. Eng. 43, 1489 (2004).
[CrossRef]

Opt. Express

Proc. SPIE

W. A. Parkyn, Proc. SPIE 3482, 389 (1998).
[CrossRef]

J.-C. Miñano and P. Benítez, Proc. SPIE 5529, 87 (2004).

A. Bruneton, A. Bäuerle, M. Traub, R. Wester, and P. Loosen, Proc. SPIE 8485, 84850H (2012).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Single-surface setup with a collimated source.

Fig. 2.
Fig. 2.

Irradiance pattern as found by ray tracing for the case of an irrotational mapping.

Tables (1)

Tables Icon

Table 1. Residual Curl of the Surface Normal Field for Various Geometrical Configurations, in Units of 105mm1

Equations (14)

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

u  :Ω0Ω1,(x,y)(tx,ty)withμ0=|Du|μ1u.
ut=1μ0Du(Δ1divu)withu|t=0=u˜,
C=N·(×N)=0.
n1N×I=n2N×O.
N=N/NwithN=n1In2O,
C=(n1In2O)·(n1×In2×O).
C=n12I·(×I)+n22O·(×O)n1n2(I·(×O)+O·(×I)).
I·(×O)=0,
t=u(x0,y0)+z1ez
O=tS=u(x0,y0)x0exy0ey+(z1z0)ez.
I·(×O)=I·(O×1O)=I·(O×O×(×O)+(O·)OO3)=(O×I).(O·)OO3=(O×I).(O·)OO.
CTRD.
1A=1A·A=A×(×A)+(A·)AA3.
1A=(A·)AA3.

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