Top Hat Distribution | The African Exponent.

Laser systems are used in many fields of industry and research. Some of the most common applications are in materials processing in which the high-power density of a focused laser beam can be harnessed for ablation or marking in metals, for instance. Following the same rationale, a laser focused spot is also used in medical applications for skin treatments or even in surgical procedures.

 A hindrance encountered in most laser systems used in these types of applications is that the laser beam does not have a uniform radiance distribution when coming out of the laser cavity. Consequently, when the beam is brought to a focus by a suitable optical lens, that non uniformity of the beam is also present in the final spot on the target. In fact, the most common type of natural emission profile from lasers is the Gaussian distribution which derives its name from a particular set of polynomials that solve the wave equation. 

The most basic of these polynomials is a wave mode in which the radiance has a peak at the centre and then slowly diminishes as the radial coordinate increases. According to the underlying equation describing the Gaussian beam, the radiance expands indefinitely. As mentioned above, when the beam is focused this same distribution is kind of replicated onto the target. Due to this, there is always a finite percentage of light falling outside the desired target spot.

A more convenient type of radiance, or irradiance, distribution would be one in which there is an area of constant energy density which is well bounded by hard edges. Such radiance distribution is referred to as the Top Hat distribution. It receives the name from the fact that its one-dimensional profile resembles the erstwhile cylinder hat from two centuries ago.

With a Top Hat distribution, the process involving laser systems becomes much more efficient. The spot of interest is radiated more uniformly and the losses induced by light leaking into surrounding areas, as it is indeed the case for Gaussian beams, are now mostly avoided.

To convert a Gaussian radiance distribution into a Top Hat distribution it is necessary to introduce an extra element. When the laser light is single mode and monochromatic, this extra element can be a diffractive optical element which has the required complex transformation encoded onto its pixels. Such a diffractive optical element is referred to as a specific type of diffractive beam shaper.

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