"Design and optimization of compact freeform lens array for laser beam splitting: a case study in optimal surface representation", in Optical Modelling and Design III, Frank Wyrowski; John T. Sheridan; Jani Tervo; Youri Meuret, Editors, Proceedings of SPIE Vol. 9131 (SPIE, Bellingham, WA 2014), 913107.

1. 1
Design and optimization of compact
freeform lens array for laser beam splitting
Milan Maksimovic
Focal -Vision and Optics,
Enschede, The Netherlands
Brussels, Belgium, 14 - 17 April 2014

2. 2
Outline
• Introduction: free-form optics and beam shaping
• Motivation: laser beam multiplexing
• Design Method
• Design Examples: simulations results and analysis
• Concluding remarks

3. 3
Introduction
• Freeform optics: no rotational invariance, surfaces with arbitrary shape and regular or
irregular global or local structure:
• enhanced flexibility in design,
• boost in optical performances,
• combining multiplefunctionalities into single component,
• simplifying complex optical systems by reducing element count,
• lowering costs in manufacturing,
• reducing stray-light
• easing system integration and assembly
• Laser beam shaping (splitting) to achieve parallelism
• Lens array archives this purpose by the geometrical aperture splitting using the pupil division by
individual lenslets residing within sub-apertures
• Other optical elements are used and needed to obtain functions such as beam focusing,
combining or collimating

4. 4
Motivation: design of 1x laser diode to 3x
fibers coupler
• High-power LD (elliptical) beam splitting into 3 fibers with equalized energy per
channel
• System components: Individual lenses
• Collimatorlens
• Single focusing lens element per spot
• Manufacturing cost high (number of components)
• Assembly tolerances (for many elements) are critical

5. 5
Element representation:
• Low order aspheric + specific aperture on input
• Low order aspheric lenslet in the focusing lens array
Design and optimization (using standard software packageZemax):
• Custom merit function using real ray coordinates: explicit specification of in-out
relationship per each channel (spot)
• Pupil sampling (grid) define sampling rays f0r merit function
• Multi-parameter optimization
• Local optimizer (DLS or OD):
-> Initial starting point critical !
• Free-form surface representation:  
2 2
2 2 2
( )
( , ) ,
1 1 ( )
i i
i
c x y
z x y w x y
Kc x y

  
  

where c=1/R is base curvature, K is base conic
constant, wi is weight in expansion and Φ is suitable
basis function in expansion
Compact beam splitter: design method

6. 6
Compact beam splitter: design method
Compact beam splitter with regular lens array: 1x3 (left) and 1x 5 (right)
Optical layouts for: collimator (left), single lenslet (center) and 1x3 lens array (right).
Fixed input parameters (example):
• Object and image distance : 50mm
• Entrance pupil diameter: 30mm
• Rectangular aperture of 10x30 mm
• Lens array 10x10 mm,
(replicated in vertical direction)
Merit Function based on
real ray position @ image plane!
Pupil sampling grid defines input
ray position sampling !

7. 7
Different pupil sampling grids used
to compute merit function
Fibonacci sampling grid:
• Deterministic
algorithm based on
Fibonacci spiral
• Uniform and isotropic
resolution
• Equal area
(contribution) per each
grid point

8. 8
Compact design of 1x3 beam splitter
using regular lens array
Composite Fibonacci pupil sampling grid used in merit function , layout with rays
generated in the merit function, 3D model and multi-spot surface plot in the image
pane (left to right respectively).

9. 9
Compact design of 1x3 beam splitter
using regular lens array
Surface sag map (left) and cross-section (right) of lens array surface
Optimization with radius and conic as variables :
-> R=-22.9954mm and K=-2.1314

10. 10
Compact beam splitter design using
general freeform surface
Extended Polynomial surface representation
Surface sag map (left) and sag cross-section (right)
(Extended Polynomial surface after the optimization with 150 variables)
2 2
2 2 2
,
( )
( , )
1 1 ( )
m n
mn
m n
c x y
z x y c x y
Kc x y

 
  


11. 11
Compact beam splitter design using
general freeform surface
Merit function vs. number of variables used in optimization
with different size of pupil sampling grids:
0 50 100 150
0.5
1
1.5
2
2.5
3
Number ofVariables
MeritFunction
Extended Polynomial Representation
17 points per segment
51 points per segment
153 points pr segment

12. 12
Compact beam splitter design using
general freeform surface
Zernike surface representation :
Surface sag map (left) and sag cross-section (right) of Zernike surface after the
optimization with 37 variables
2 2
2
2 2 2
1...8 1..37
( )
( , ) ( , )
1 1 ( )
i
i j j
i j
c x y
z x y r A Z
Kc x y
  
 

  
  
 

13. 13
Compact beam splitter design using
irregular lens array
Motivation/ Application: different power ratio per spot!
Beam splitter 1x3 design with irregular lens array: layout (left) and 3D model (right)
Surface intensity plot in the entrance pupil (left) and multi-spot surface intensity
plot in the image plane (right)

14. 14
Compact beam splitter design using irregular
lens array: smoothing using image
processing technique
Surface sag map of irregular lens
array after smoothing
Sharp transitions removal:
Gaussian filter followed by Median filter
in the transition region (local smoothing!)

15. 15
Compact beam splitter design using
irregular lens array: CAD model smoothing
CAD model post-processing
• heuristic approach
• CAD surface representation often implies less
accurate ray tracing!
• Iterative procedure: (Zemax->CAD->Zemax)
Example of successful design iteration:

16. 16
Concluding remarks
• We demonstrated feasibility of freeform design of compact beam splitting element
that combines both functions of collimation and beam splitting into one (both regular
and irregular structure is possible)
• Design relaying on multi-parameter optimization + custom design merit function based
on real ray coordinates at target location works, but:
• Standard free-form surfaces often fail to produce design directly and with small number
of variables-> inefficient design process!
• Open questions: optimal free-form representation
• Pupil sampling method based on Fibonacci grid (highly structured grid and having
features usually associated with random grids) improves convergence in local
optimization procedure
• Designs often require post-processing for manufacturing constraints (smoothing)
• Application of local filtering techniques borrowed from image processing produce
smoothed versions of surfaces with discontinuities
• Possible applications of similar designs are in laser fiber coupling and off-axis multi-spot
generation where power splitting ratio can be arbitrarily predefined.

17. 17
Thank you for the attention!