Abstract

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576–5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat’s principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

© 2012 OSA

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References

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  1. F. Duerr, P. Benítez, J.C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20, 5576–5585 (2012).
    [CrossRef] [PubMed]
  2. 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, 24036–24044 (2009).
    [CrossRef]
  3. P. Benítez, J.C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489 (2004).
    [CrossRef]
  4. D. Grabovičkić, P. Benítez, and J.C. Miñano, “Free-form V-groove reflector design with the SMS method in three dimensions,” Opt. Express 19, A747–A756 (2011).
    [CrossRef]

2012

2011

2009

2004

P. Benítez, J.C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489 (2004).
[CrossRef]

Benítez, P.

Blen, J.

P. Benítez, J.C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489 (2004).
[CrossRef]

Chaves, J.

P. Benítez, J.C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” 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, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489 (2004).
[CrossRef]

Duerr, F.

Falicoff, W.

P. Benítez, J.C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489 (2004).
[CrossRef]

Grabovickic, D.

Hernández, M.

P. Benítez, J.C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489 (2004).
[CrossRef]

Infante, J.

Lin, W.

Meuret, Y.

Miñano, J.C.

Mohedano, R.

P. Benítez, J.C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489 (2004).
[CrossRef]

Muñoz, F.

Santamaría, A.

Thienpont, H.

Supplementary Material (1)

» Media 1: AVI (4078 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Exemplary lens calculated with the previously published two-dimensional design method that couple three rays sets; (b) rotational symmetric lens constructed from such two-dimensional design; (c) free-form lens design designed in this paper to couple three ray sets in three dimensions

Fig. 2
Fig. 2

Introduction of all necessary initial values and functions to derive the conditional equations from Fermats principle in three dimensions

Fig. 3
Fig. 3

Exemplary single-frame excerpts from a ray tracing animation of calculated solutions ranging from meniscus lenses (a) to biconvex lenses (b) ( Media 1)

Fig. 4
Fig. 4

RMS spot radius plotted against the incident angle for m1 = −0.065 (a) and for m1 = 0.045 (b) and for corresponding free-form and rotational symmetric lenses

Equations (12)

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d1=v0(p1w0),d2=n2|p2p1|,d3=|p3p2|
d^1=v1(p^w0),d^2=n2|p^2p^1|,d^3=|p^3p^2|
D1=y(d1+d2)=0,D2=s(d2+d3)=0,D3=t(d2+d3)=0
D4=y(d^1+d^2)=0,D5=u(d^2+d^3)=0,D6=v(d^2+d^3)=0
f(x,y)=i=0j=0fi,j(xx0)iy2j,g(x,y)=i=0j=0gi,j(xx1)iy2j
s(x,y)=i=0j=0si,j(xx0)iy2j,u(x,y)=i=0j=0ui,j(xx0)iy2j
t(x,y)=i=0j=1ti,j(xx0)iy(2j1),v(x,y)=i=0j=1vi,j(xx0)iy(2j1)
f(x0,0)=z0,xf(x,y)|(x0,0)=m0,yf(x,y)|(x0,0)=0g(x1,0)=z1,xg(x,y)|(x1,0)=m1,yg(x,y)|(x1,0)=0s(x0,0)=x1,u(x0,0)=x1,t(x0,0)=0,v(x0,0)=0
limxx0limy0nxnmymDi=0(i=1,3,4,6),{n=0,m|oddnumberm}
limxx0limy0nxnmymDi=0(i=1,3,4,6),{n𝕅1,m𝕅|oddnumberm}limxx0limy0n1xn1m+1ym+1Di=0(i=2,5),{n𝕅1,m𝕅|oddnumberm}
My(f0,m+1g0,m+1t0,mv0,m)=b(0,m)
Mxy(fn,m+1gn,m+1sn1,m+1tn,mun1,m+1vn,m)=b(n,m)

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