Laser image uniformity can be achieved from a process of homogenizing, which is the process of converting a gaussian laser beam profile into a uniform (or near-uniform) intensity distribution. This is commonly used in applications such as laser materials processing, medical lasers, and imaging systems. Several methods including diffusers, aspherical lens, lenslet array, and diffractive optical elements, can achieve beam homogenization, and Zemax can be used to model these methods.

A Gaussian laser beam has an intensity profile that follows a Gaussian distribution, meaning that the intensity is highest at the center of the beam and decreases symmetrically as you move away from the center. Profile of Gaussian beam is presented in figure below. Gaussian beams are common in laser applications because many lasers naturally emit beams with this profile.

In Zemax, a Gaussian beam can be modeled with wavelength λ, beam waist w0, and divergence angle θ, following the beam description equations below:

- The beam size is a function of the distance from the waist. Zemax uses the half width or radius to describe beam width.
- For large distances the beam size expands linearly. The divergence angle θ of the beam is given by
*z*is the Rayleigh range of the beam given by_{R }- The phase radius of curvature of the beam is a function of the distance from the beam waist,
*z*, as below

Rays in geometric optics are imaginary lines which represent normals to the surfaces of constant phase, or the wavefront. For a paraxial Gaussian beam, beam size changes very slowly. In this case, beam can be modeled as collimated ray bundle. Beam size changes linearly with propagation distance, so beam can be modeled as a point source. This is shown in the drawings below.

Here we simulated a laser beam with output characteristics below. Key parameters include typical beam diameter of 5.0 mm and beam divergence of 0.3 mrad.

With geometrical calculation, the emission point of the laser can be regarded as 1.8 x 10^{4} mm away from the emission point. With the series of input in Zemax, the output beam profile with 1000-pixel resolution is shown below:

Here we propose to reshape the laser beam at the image plane, to form a thin profile no larger than 0.2 mm, with a uniform distribution at the output profile. An even aspherical surface is proposed to reshape the beam. The target coordinate at image plane is defined as below.

K is the target illumination radius, while W is the laser beam waist. A sample size of 40 is used in merit function, these 40 samples are defined with operator REAY, to reflect the real ray output in y coordinate at the image surface. A part of merit function is shown below:

The incident light profile the front surface of the aspherical is shown below. The geometrical diameter is ~5 mm and the RMS diameter is ~3.4 mm.

The even aspherical lens in Zemax Sequential mode reforms the light profile to a image plane at ~1 meter away. The basic radius and each of the aspherical terms are set as variables.

This reshaping lens the even aspherical surface is designed with 4^{th} to 16^{th }order. 2^{rd} order is ignored to match manufacturer’s template. With running the merit function above, the aspherical lens terms are optimized as below:

The aperture of this aspherical lens is controlled at 5 mm to avoid difficulty of manufacturing. The light profile at the image plane is shown below.

The encircled energy in is shown below, which suggests almost 100% light is enclosed in a 0.9 radius circle.

The optimized aspherical lens is shown below, as well as the overall reform system. Not at the laser source is not shown here to avoid irrelevance appearance.

In summary, laser reshaping with homogenous light profile reshaping is achievable in Zemax with even aspherical lens. Laser profile definition and aspherical lens structure are key factors for design success. With consider of manufacturing feasibility and convenience, design should be compromised in aspherical orders in the lens.

August 19, 2024