1. Field of the Invention
The present invention relates to the field of optics. More particularly, the present invention relates to an optical system that transforms a light beam having any axially-symmetric intensity distribution to a light beam having another axially-symmetric intensity distribution.
2. Description of the Related Art
Lasers emitting collimated beams of coherent light have many applications in optical science and technology, including lithography, spectroscopy, communications and display technology. Due to fundamental properties of light propagation in optical resonators, most lasers emit beams having a light intensity that is extremely inhomogeneous. Specifically, the light intensity frequently follows a Gaussian distribution, such as EQU I(r)=(2P/.pi.w.sup.2)e.sup.-2r.sup..sup.2 .sup./w.sup..sup.2 , (1)
where I(r) denotes the optical power per unit area measured at a distance r from the axis of the beam, P denotes the total power of the beam, and w is the beam waist parameter, which sets the length scale over which the optical intensity declines from its maximum value to zero. The same distribution also describes, to a good approximation, the intensity profile of a beam that emerges from a single-mode optical fiber, such as is used extensively in the optical industry for conveying coherent light.
For many applications, it is desirable that some area of interest be illuminated as uniformly as possible. For example, optical lithography, which is used to fabricate microelectronic devices, requires that the light fluence over an entire exposed region conform to tight tolerances. Laser users, therefore, frequently encounter the problem of transforming a beam having a Gaussian intensity profile to a so-called flat-top profile, which has a uniform intensity over a region of arbitrary radius a.
Many solutions have been proposed for transforming a Gaussian beam to a flat-top beam. All conventional solutions, however, have significant drawbacks. For example, the conceptually-simplest conventional method uses an element having radially-varying absorption for removing excess intensity from the center of a beam. Such an approach is inherently inefficient because it can be shown that, in the best case, the fraction of the incident beam power that emerges in the apodized beam is 1/e, or approximately 37%. Moreover, in this conventional approach, the absorptive element only subtends the central part of the incoming beam, having an aperture or other discontinuity located at a point where the light intensity is an appreciable fraction of the peak intensity.
When using spatially coherent light sources, including most lasers, any aperture that truncates the beam also diffracts light into the central region. Accordingly, interference of the diffracted and transmitted light reduces the uniformity of the beam. Yet another drawback of this conventional approach is that stable, well-characterized absorptive materials are required, which are not available for the technologically-important ultraviolet wavelengths.
Another conventional approach uses lithographically or holographically fabricated phase gratings for reshaping a Gaussian beam by diffraction. Holographic gratings suffer from limited diffraction efficiency of only about 30%, as well as a lack of materials that are suitable for ultraviolet applications. Lithographically-fabricated phase gratings can have high efficiency, but are expensive to fabricate and only work as designed for a single wavelength. Additionally, it is exceedingly difficult to avoid diffraction into unwanted orders, leading to undesirable effects, such as non-uniformity of the output beam at high spatial frequencies and "hot spots" on the beam axis.
Conventional refractive solutions have been proposed that use either spherical or aspheric optical elements for aberrating and then recollimating a laser beam. The solutions with conventional spherical optics are physically bulky and relatively inefficient because the spherical surfaces introduce limited aberrations. More compact and efficient conventional designs have been proposed that use either aspheric or gradient-index lenses. Nevertheless, use of a gradient index accomplishes essentially the same result as an aspheric surface, but having a drawback that no gradient-index glasses are available for ultraviolet applications. All aspheric and gradient-index solutions that until now have been analyzed in detail have used a negative first element and a positive second element in a configuration resembling a Galilean telescope. Unfortunately, such designs require lenses having large deviations from sphericity and are difficult to fabricate. Fabrication problems are especially acute for the concave surface of the first lens in the Galilean design.
Another serious problem with most conventional aspheric and gradient-index solutions is that such solutions are only valid for the central region of an incident beam, thereby entailing an aperture for the other discontinuity at a point where there is appreciable input beam intensity, at least 1/e.sup.2 times the peak intensity. As previously mentioned, truncating an input beam causes diffraction and interference fringes that reduce the uniformity of the output beam.
What is needed is a way to efficiently transform a light beam having any axially-symmetric intensity distribution to a light beam having another axially-symmetric intensity distribution.