 Astronomy
 Biomedical Optics & Medical Imaging
 Defense & Security
 Electronic Imaging & Signal Processing
 Illumination & Displays
 Lasers & Sources
 Micro/Nano Lithography
 Nanotechnology
 Optical Design & Engineering
 Optoelectronics & Communications
 Remote Sensing
 Sensing & Measurement
 Solar & Alternative Energy
 Sign up for Newsroom EAlerts
 Information for:
Advertisers




Lasers & Sources
Development of largeaperture diffractive optical elements for beam smoothing
YongPing Li, XiaoBo Zhang, Wei Zhang, FangJie Shu, and Rong Wu
A multistep diffractive optical element (MDOE), developed using a hybrid algorithm, has been shown to perform laserbeam smoothing well.
19 May 2006, SPIE Newsroom. DOI: 10.1117/2.1200602.0007
Uniform illumination has become a popular topic in recent years.^{1} For example, improvement in laserirradiation uniformity is now an important issue for those developing highpowerlaser output systems.^{2–3} Diffractive optical elements (DOEs) have been widely used to solve this problem,^{4} but the manufacture of these elements—especially large DOES—is very difficult.
In our group, we used a DOE with an axisymmetric continuous profile^{5} because of its relativelyhigh design index and because it can be fabricated using a rotary etching facility.^{6} However, in practice, it is very difficult to match the design of this kind of continuous profile using this kind of fabrication. The accumulation of etching errors can make the experimental DOE far worse than the design index. However, this problem can be solved using a multistep diffractive optical element (MDOE) that has a stepped phase structure that can be fabricated easily using multiplemask etching.
To improve the design index and save computing time, we have developed a mixed algorithm for MDOE design that inserts a quasioptimum process in every GS (GerchbergSaxton)^{7} iterative loop. Initially, though we could quickly get a convergent result by using the GS algorithm, the illumination uniformity was not as good as we expected. This was because the feedback was too limited to carry enough information to control the change of phase distribution. Also, occasionally, selftrapping and oscillation would prevent the GS algorithm from working properly.^{8}
We decided to solve these problems by making the feedback carry more effective information in each loop. We did this by adding two adjustable parameters and using a quasioptimum process to set their value in each iteration. This reformative mixed method can be described using the equations below.
Here, a_{k} is the outputamplitude feedback coefficient and β_{k} is the inputphase feedback coefficient. In every iterative loop, quantities are randomly generated for a and β, and each set of values gives a different U^{(k+1)}_{i}. We choose the best values for a_{k} and β_{k} as those that give the minimum deviation from the ideal.
In practice, the selftrapping and oscillation effects can be effectively suppressed using this reformative method. Furthermore, it is faster (in terms of computing time) and produces a better design result than the GS and IO algorithms shown in Figure 2.
In Figure 1, the top profile error (TPE) is that defined in Equation 2 to evaluate the quality of the output distribution. I_{avg} is the average flattop intensity, and N and I_{real} are the number of samples and the flattop intensity distribution, respectively.
Figure 1. The phase distribution of an MDOE: (a) phase distribution in twodimensions, (b) phase distribution in onedimension along the diametric.
Figure 2. The outputbeam pattern on the focal plane: (a) simulated result, (b) experimental result.
To prove the validity of our new method, a largeaperture MDOE was designed for beam smoothing using the reformative mixed algorithm. The MDOE has a 70mm diameter and the uniform illumination area is a 600μm spot at the focal plane. We set phase values with 16 steps ranging from π/8rad to 2πrad (see Figure 2).
This kind of structure can easily be realized using multiplemask etching. The simulated intensity of the output beam is shown in Figure 2a. The TPE of the MDOE in our design was 8.34%. We fabricated the MDOE with K9 glass, and there were 1080nm depthetch errors during fabrication (as measured by a stepdepth meter, see Table 1).

Mask 1 
Mask 2 
Mask 3 
Mask 4 
Etch Depth (nm) 
1040 
520 
260 
130 
Min Etch Error (nm) 
+14 
16 
+13 
+7 
Max Etch Error (nm) 
+59 
62 
+13 
+7 
Table 1. Etch depth and error for each mask step: for positive values the actual etch depth is deeper than the ideal, for negative values it is shallower.
The focalplane pattern is shown in Figure 2b. The spot diameter is about 600μm, matching our design data well. We again used TPE to evaluate the uniformity of the flat top, and the experimental result is about 19%: a little inferior to the design because of high etch errors. We can see that, although the actual depth errors of the first two etches are much more than 20nm, the MDOE still smooths the beam effectively at the focal plane.
The simulated and experimental results show that the new reformative algorithm is indeed useful for MDOE design. In practice, the stepped phase structure of MDOEs are easily realized with multiplemask etching. Although the etching error makes the experimental TPE inferior to that of design, the error can be dealt with within the design process.
Authors
YongPing Li, XiaoBoZhang, Wei Zhang, FangJie Shu, and Rong Wu
University of Science and Technology of China
HeFei, China
References:
1. M. A. Kutay, H. W. Ozoktas, Optimal filtering in fractional Fourier domains,
IEEE Trans. Sign. Proces,
Vol: 45, no. 5, pp. 11291143, 1997.
2. S. N. Dixit, J. K. Lawson, J. K. Manes, Kinoform phase plates for focal plane irradiance profile contra,
Opt. Lett.,
pp. 417419, 1994.
3. H. Thomas, R. Bett, M. Stevenson, M. R. Taghizadeh, Diffractive optic development for application on highpower solid state lasers,
Proc. SPIE,
Vol: 2633, pp. 129140, 1995.
4. Y. Lin, T. J. Kessler, G. N. Lawrence, Distributed phase plates for SuperGaussian focal plane irradiance profiles,
Optics Letter,
Vol: 20, no. 7, pp. 764771, 1995.
5. Wang Wei, Li Tao, Li Yongping, A hybrid algorithm for the design of DOE in uniform illumination,
Optics Communications,
Vol: 181, pp. 261265, 2000.
6. Wang Wei, Li Tao, Liu Li, Li Yongping, Hong Yilin, Xu Xiangdong, Huo Tonglin, Fu Shaojun, Design of largecaliber phase elements used in ICF,
Chinese J. Lasers,
Vol: 26, pp. 395399, 1999.


