What is Wavefront Distortion?
WAVEFRONT
A wavefront can be described as a set of photon points, a locus, moving in unison through a transparent medium. The wave has a sinusoid shape and variation with time. The medium must, of course, be at least partly transmissive for the wavefront of interest. Different materials transmit different frequencies of light waves. For visible light those may be such things as air, water, glass, crystals, even some metals. Does anyone remember “transparent aluminum” from Star Trek IV? It really does exist. Just ask Google!
Gold can be pounded so thin that it is able to transmit light. Several metal oxides are transparent. That allows them to be used as thin film optical coatings to enhance the performance of eyeglasses, camera lenses, building windows, lasers, and much more.
A few materials are transparent to visible light plus infrared and ultraviolet light. Most, however, have a limited range of transparency. Some that the eye cannot see through will, however, permit ultraviolet or infrared light to pass through.
A perfectly generated wave may be plano or spherical. What happens to it as it travels may alter that perfect shape. This circumstance is called wavefront distortion. There are a number of factors that cause such aberration. All amount to a variation in the index of refraction. The index of refraction is a dimensionless number that relates to the speed of light in a particular medium. The velocity varies with the local refractive index. That velocity variation amounts to a bend in a wavefront passing through. The higher the index change, the greater is the bending effect. The exception? Vacuum, which has an index of 1.0000. By contrast air is about 1.0003. Even that small number changes with pressure, humidity, temperature, and of course, wavelength. The same is true of water, with an average index of 1.333.
LOCAL INDEX CHANGE
The index of refraction for a material is NOT a single number. It is continuously variable by wavelength of light, increasing as the wavelength grows shorter. But even for a single material transmitting a single wavelength (think laser light), the index can have variation. In glass it can be a function of mixing, stirring, or cooling differential as the molten material hardens. In optical crystals there may be defects of a type that change the index around the defect volume. Inconsistency of the index can also be the result of temperature difference, internal stress, or an applied load. It requires good design to not stress a lens in its mount, for instance.
Local index change is virtually always undesirable—it distorts an otherwise good wavefront and is the whole reason for writing this article. Good wavefronts generally originate from a point source. If unaltered that results in an expanding spherical wave. A high-quality lens or combination of lenses can produce a plano, flat wavefront. Light transmitted from a point source will hence be collimated, that is, neither expanding or contracting, neither diverging nor focusing. That property is important for many optical system designs, including common laser applications.
What are the Effects of Wavefront Errors?
Worse than a poor quality spherical or plano wave is one with local “micro” errors. Those can result in poor contrast, scattering, reduced image quality, and hot spots in laser beams. GAMDAN Optics' crystals are grown with an absolute minimum of defects or inclusions. Any that occur are “mapped” and avoided when cutting out crystal blanks. If any remain those blanks are discarded or used for experiments.
Figure 1: Irregular part with local discontinuities. Source: https://www.researchgate.net/figure/a-Image-of-the-object_fig4_228712678
Wavefront Errors on the Macro Scale
Other errors affect the overall wavefront and are also undesirable. The most common flaw is departure from flatness of either or both the polished surfaces. This will cause a collimated beam to expand or begin to focus and cause a distortion in an image that is described as spherical aberration, in the most common case. A cylindrical surface leads to astigmatism as seen in figure 2. There can also be higher order and more complicated shapes. To limit these errors, surfaces are typically specified to be within some fraction of a wave. A common specification for laser optics and other demanding applications is the requirement that their surfaces be within one-tenth wave of the ideal form. The surfaces are generally flat (plano) or spherical. For the most used red test laser, the wavelength is 633 nanometers, approximately 0.6 microns (25 millionths of an inch). That is like splitting a hair one hundred times! GAMDAN Optics uses a phase shifting interferometer which is capable of making repeatable measurements of one-twentieth wave.
Figure 2: Astigmatism (saddle shaped) with smooth distortion. Source: https://www.semanticscholar.org/paper/Distortion-matrix-approach-for-ultrasound-imaging-Lambert-Cobus/2ef9346361f4f687d72cfeed30ff34d6cbe5ae99/figure/3
GAMDAN Optics Nonlinear Crystal Quality
Tight control of crystal growth, sophisticated selection of material, near compulsive attention to detail in manufacturing and polishing combine with discriminating inspection practices to ensure that GAMDAN Optics products are free of transmissive wavefront errors. Add that to demonstrated efficiency, long lifetime, and industry leading laser induced damage resistance make GAMDAN Optics your natural source for nonlinear frequency shifting crystals.
Figure 3: Interferogram showing one-half fringe (quarter wave) spherical distortion.
Figure 4: Slightly convex part with low depression in center and rolled down edge. A “Hole with a Roll”
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DENNIS J. GARRITY, AUTHOR
Dennis is an engineer with over 45 years of experience in fabrication, testing, and material evaluation for high precision optics, with extensive hands-on experience. More on the author can be found here.