This article demonstrates how to design a simple refractive beam shaper that converts a Gaussian intensity profile into a top-hat profile. Sample files are provided, which can be downloaded from the last page of this article.
Beam shaping optics transform input intensity distributions into some desired output distribution. A common example is to take the Gaussian irradiance distribution produced by a laser and transform it to a Top Hap (flat top) output.
An efficient way of optimizing the sag of such a lens is to use geometrical ray targets in the merit function. In this approach, we compute where in the output plane a given input ray should land, and express this through ray targets entered into thte Merit Function Editor.
The diagram below represents such a system with output top hat beam of K radius and input Gaussian beam of W waist.
First, we need to determine analytically the output radial distance S for a given input coordinate X such that the encircled energy B at the output is the same as the encircled energy A at the input.
Our desired output profile is a uniform distribution of maximum extent K from an input Gaussian of 1/e2 width W. The input distribution has irradiance Pexp{-(2R2/W2)} and the output distribution is a step-function of irradiance H and maximum radial width K
Now that we can calculate the output coordinate value S for every input coordinate X, we can use the REAY optimization operand to specify an array of input ray coordinates and their respective output target values in the merit function editor. In the REAY operands we will specify the normalized input coordinates and the corresponding targets at the image plane. Instead of inserting the operands manually, we will write a ZPL macro to automatically generate the merit function and optimize the lens.
The following macro will insert the REAY operands in the merit function editor and will then optimize the system. The macro can be downloaded from the zip file at the end of this article.
Save the included macro file Beam Homogenizer.ZPL from the last page of the article to your {rootZEMAX}/Macros folder.
Open the included Beam_Homogenizer.ZMX lens file.
The sample system is a single plano-convex lens with an Even Aspheric front surface. The variables are radius, conic and the even aspheric coefficients. The system wavelength is 0.623 um (HeNe) and the glass type is N-BK7.
In the main menu, click Macros/Beam Homogenizer.
Notice that the input ray apodization is Gaussian but the output is uniform. The spacing between the rays at the image surface is very uniform indicating that the irradiance distribution should be close to ideal Top Hat.
The illumination scan analysis (Analysis...Illumination...Illumination XY Scan) shows a Gaussian profile at surface #1, and a Top Hat profile at the image surface.
If, in the illumination analysis settings, we increase the number of rays to 100E6 with smoothing of 1, you will get a much better signal-to-noise ratio (shown below). It took only a few minutes to update the analysis on my single processor 3.4 GHz Pentium 4 machine,
For other values of input waist W and output radius K, you can change the corresponding variable values in the macro.
This article has shown how to use the geometrical rays to optimize the beam homogenizer. Geometrical rays allow fast optimization and result shows good irradiance uniformity at the image plane.