Abstract

In this paper, a design method of surface contour for a freeform imaging lens with a wide linear field-of-view (FOV) is developed. During the calculation of the data points on the unknown freeform surfaces, the aperture size and different field angles of the system are both considered. Meanwhile, two special constraints are employed to find the appropriate points that can generate a smooth and accurate surface contour. The surfaces obtained can be taken as the starting point for further optimization. An f-θ single lens with a ± 60° linear FOV has been designed as an example of the proposed method. After optimization with optical design software, the MTF of the lens is close to the diffraction limit and the scanning error is less than 1μm. This result proves that good image quality and scanning linearity were achieved.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013

2012

2011

2010

2009

2007

2005

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for free form optics,” Proc. SPIE5874, 58740A, 58740A-11 (2005).
[CrossRef]

1992

Y. Wang and H. H. Hopkins, “Ray-tracing and aberration formulae for a general optical system,” J. Mod. Opt.39(9), 1897–1938 (1992).
[CrossRef]

1949

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B62(1), 2–8 (1949).
[CrossRef]

Benítez, P.

Bruegge, T.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for free form optics,” Proc. SPIE5874, 58740A, 58740A-11 (2005).
[CrossRef]

Cakmakci, O.

Chen, K.

Cheng, D.

Dow, T.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for free form optics,” Proc. SPIE5874, 58740A, 58740A-11 (2005).
[CrossRef]

Duerr, F.

Garrard, K.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for free form optics,” Proc. SPIE5874, 58740A, 58740A-11 (2005).
[CrossRef]

He, Q.

He, X.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Hicks, R. A.

R. A. Hicks, “Direct methods for freeform surface design,” Proc. SPIE6668, 666802, 666802-10 (2007).
[CrossRef]

Hoffman, J.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for free form optics,” Proc. SPIE5874, 58740A, 58740A-11 (2005).
[CrossRef]

Hopkins, H. H.

Y. Wang and H. H. Hopkins, “Ray-tracing and aberration formulae for a general optical system,” J. Mod. Opt.39(9), 1897–1938 (1992).
[CrossRef]

Hua, H.

Infante, J.

Jin, G.

Li, H.

Li, L.

Liang, P.

Lin, W.

Liu, Q.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Liu, X.

Ma, T.

Meuret, Y.

Miñano, J. C.

Muñoz, F.

Rolland, J.

Santamaría, A.

Shi, G.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Sohn, A.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for free form optics,” Proc. SPIE5874, 58740A, 58740A-11 (2005).
[CrossRef]

Talha, M. M.

Thienpont, H.

Wang, C.

Wang, L.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Wang, Q.

Wang, T.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Wang, Y.

Wassermann, G. D.

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B62(1), 2–8 (1949).
[CrossRef]

Wolf, E.

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B62(1), 2–8 (1949).
[CrossRef]

Xu, L.

Yi, A. Y.

Yu, J.

Yu, S.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Zhang, B.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Zhang, F.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Zhang, X.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Zheng, L.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

Zheng, Z.

Appl. Opt.

J. Mod. Opt.

Y. Wang and H. H. Hopkins, “Ray-tracing and aberration formulae for a general optical system,” J. Mod. Opt.39(9), 1897–1938 (1992).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. Phys. Soc. B

G. D. Wassermann and E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B62(1), 2–8 (1949).
[CrossRef]

Proc. SPIE

D. Cheng, Y. Wang, and H. Hua, “Free form optical system design with differential equations,” Proc. SPIE7849, 78490Q, 78490Q-8 (2010).
[CrossRef]

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE8486, 848607, 848607-10 (2012).
[CrossRef]

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for free form optics,” Proc. SPIE5874, 58740A, 58740A-11 (2005).
[CrossRef]

R. A. Hicks, “Direct methods for freeform surface design,” Proc. SPIE6668, 666802, 666802-10 (2007).
[CrossRef]

Other

T. Hisada, K. Hirata, and M. Yatsu, “Projection type image display apparatus,” U.S. Patent, 7,701,639 (April 20, 2010).

1stOpt Manual, 7D-Soft High Technology Inc. (2012).

Code V Reference Manual, Synopsys Inc. (2012).

D. Knapp, “Conformal Optical Design,” Ph.D. Thesis, University of Arizona (2002).

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Figures (14)

Fig. 1
Fig. 1

Layout of a freeform single lens and its starting point. (a) Layout of a freeform single lens. (b) The front surface (the surface contour in the tangential plane) is taken as the starting point for further optimization.

Fig. 2
Fig. 2

The change of the overlap area of neighboring fields with increasing field angle. When the field angle is small, the beams of neighboring fields with fixed intervals generally have overlap area on the front surface. When the field angle is increasing, the overlap area of neighboring fields is getting smaller, and finally disappears.

Fig. 3
Fig. 3

The rays of different pupil coordinates specified in each field. The three rays are the chief ray and two marginal rays from the top and the bottom of the entrance pupil.

Fig. 4
Fig. 4

The definition of the feature rays used in each field group to calculate the data points on the freeform surface. (a) When the two neighboring fields have overlap area on the unknown surface, two data points (point 1 and 2) are calculated in one field group using three feature rays (①②③). (b) When the light beams are separated, two data points (point 1 and 2) on the surface are calculated in one field group with only two feature rays (①②).

Fig. 5
Fig. 5

The constraint to establish the geometric relationships between neighboring field groups using the normal vector at each data point. P3 and P4 are the data points to be calculated in the current field group, P1 and P2 are the data points already calculated in the previous field group. The direction vector e23 from P2 to P3 is constrained to be perpendicular to the unit normal N3 at P3, and the direction vector e34 from P3 to P4 is constrained to be perpendicular to the unit normal N4 at P4.

Fig. 6
Fig. 6

The stairs-distribution of data points. The line connecting the two data points in each group is approximately parallel to the one in the neighboring group, which is shown in (a) and (b). It causes the stair-distribution of data points shown in (c).

Fig. 7
Fig. 7

The stairs-distribution elimination constraint. The intersection Pi of the two lines which connect the two data points in each group is expected to be between P2 and P3. The y coordinate Piy of Pi is constrained to be between the y coordinates of P2 and P3, and the z coordinate Piz of Pi is constrained to be between the z coordinates of P2 and P3.

Fig. 8
Fig. 8

The calculation of the data points on the contour of the front surface (the starting point). The whole algorithm starts from the group of the first two fields containing the marginal field of the system. When the coordinates of data point 1 and 2 in this group are obtained, field #2 and the next neighboring field #3 are taken as the next group, and data point 3 and 4 can be then obtained. The same procedure is done for the group containing field #3 and #4 to obtain data point 5 and 6. The mentioned method is repeated until the all the fields are calculated. The yellow areas on the front surface stand for the overlap areas of the neighboring fields.

Fig. 9
Fig. 9

The irregularly data points calculated by the method when the geometric relationships between neighboring groups are not established.

Fig. 10
Fig. 10

The effect of the two constraints used during the calculation of the data points that can generate a smooth link line. (a) The point distribution after adding the constraint to establish the geometric relationships between neighboring field groups using surface normal. The data points do not distribute irregularly in the tangential plane, but the stairs-distribution is obvious. (b) The point distribution when the stairs-distribution elimination constraint is finally added. The stairs-distribution is removed and the data points can generate a smooth link line.

Fig. 11
Fig. 11

Design result of the starting point of the system (a) Layout of the starting point (front surface). (b) The scanning error of each field of the starting point.

Fig. 12
Fig. 12

Layout of the f-θ single lens.

Fig. 13
Fig. 13

Image quality analysis of different fields (a) MTF plot. (b) Spot diagram.

Fig. 14
Fig. 14

Scanning error of different fields.

Tables (1)

Tables Icon

Table 1 Design result of the single f-θ lens.

Equations (15)

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Δω= ω k .
N 3 e 23 =0,
N 4 e 34 =0.
( P 2y P iy )( P 3y P iy )<0,
( P 2z P iz )( P 3z P iz )<0.
n'(r'×N)=n(r×N),
n'β'nβ=j(n'cosI'ncosI),
n'γ'nγ=k(n'cosI'ncosI),
cosI=(rp)=βj+γk,
cosI'= 1 n' n ' 2 n 2 + n 2 cos 2 I .
tanθ= β γ .
y= 210 60 θ=3.5θ.
Δh= h h,
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)= c( x 2 + y 2 ) 1+ 1(1+k) c 2 ( x 2 + y 2 ) + A 2 y+ A 3 x 2 + A 5 y 2 + A 7 x 2 y + A 9 y 3 + A 10 x 4 + A 12 x 2 y 2 + A 14 y 4 + A 16 x 4 y+ A 18 x 2 y 3 + A 20 y 5 .

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