In our previous articles we learned that optical materials are defined by their ability to refract and disperse light, as well as, the physical characteristics of the material itself. Using these properties, an optical designer determines which material, or often times several different materials, best suit the intended purpose of their system. But choosing a material is only the first step in the process. More often than not, a simple polished surface that is smooth and defect free to the unaided eye, would cause any number of unwanted optical effects when assembled into a fully integrated system. It is important to remember, optics work by manipulating wavelengths of light whose scale is measured in nanometers or billionths of a meter. At these incredibly small distances, even the smallest imperfection, those that are vastly outside the ability of the human eye to perceive, can send light off in unintended directions causing distortion or degradation of the overall signal or image quality. To prevent this from happening, optical designers have a list of individual terms which define an optic’s overall surface form or in layman’s terms, just how precisely polished the surfaces need to be. In this article, we will begin to dissect these terms by specifically examining plano optics, that is, optics with flat surfaces. But first, we must touch upon two fundamental aspects of optical fabrication, aspect ratio and clear aperture.
One of the most important characteristics of an optic is its aspect ratio. Simply defined, the aspect ratio is the proportion of an optics longest diagonal measurement across the surface in relation to its thickness. For example, a square with sides that are 50.8mm long has a diagonal measurement, derived using the Pythagorean Theorem, of approximately 72mm. If this same square has a thickness of 10mm, the ratio of the diagonal to thickness is 72:10 or 7.2 to 1. In optics, while not a firm rule, generally the difficulty in fabricating a precision surface increases substantially when the aspect ratio surpasses 5:1. Any ratio larger than this creates a circumstance where the part’s thickness no longer provides enough stability to consistently hold the precision of its surface form.
Clear aperture is defined as the functional portion of an optic over which its surface form is guaranteed. Using the same 50.8mm square described above, an optical designer may specify that 90% of the surface must meet all required specifications. By simple math, we derive that 90% of a 50.8mm square is 45.72mm. Overlaying the 45.72mm square onto our optic demonstrates that an optical fabricator has only 2.54mm of distance from the edge of the optic before the surface form must be certified to meet all specifications. Clear aperture is therefore one of the fundamental parameters in determining whether an optic can be manufactured to the required level of precision.
As the term implies, flatness is a measurement of deviation from a theoretically perfect plano surface. We learned from our previous article that opticians use a tool called an interferometer to measure subtle nanometer-scale differences between a known reference and an optical surface of unknown precision. Since an interferometer uses the wave properties of light as its diagnostic tool, it is fitting that opticians specify the flatness of a surface in terms of waves. For example, on a plano surface, the flatness may be defined as one wave. As most modern interferometers use the 632.8nm laser wavelength, a surface requiring one wave accuracy may have no more than 632.8nm of distance between the highest peak and lowest valley across the usable clear aperture. Not surprisingly, in optical terminology, this is defined as an optic’s peak-to-valley flatness or P-V for short.
However, it is important to note that flatness is more than a simple measurement of the microscale features on an optical surface. To truly verify the precision of flatness, an interferometer takes into account two important aspects, the power and irregularity. Simply defined, in plano optics, power is a measurement of the overall curvature along the surface and can be thought of as bow or warping on the larger scale of the entire optic. It demonstrates a deviation from true flat. One term commonly used in optical fabrication facilities is that an optic exhibits a “potato chip” effect whereby the center may appear flat but towards the edges the surface either curves up or downward, much like can be seen on a potato chip. This represents a type of spherical anomaly that normally requires correction.
Irregularity, on the other hand, takes into account the small scale variations on an optical surface. Whereas the overall peaks and valleys may be very consistent in one area of an optic, a specific portion may exhibit a much larger deviation which also requires correction.
Opticians therefore combine both the power (curvature) and irregularity (consistency) to yield an overall flatness measurement and as the level of required precision increases, the flatness becomes fractions of a wave. Consider for a moment that if an optical flatness is specified as 1/10 wave at 632.8nm, it follows that the largest distance between the greatest peak and valley on a surface can be no more than 63.28nm while still taking into account the overall curvature!
At times, an optical surface may be defined using what opticians call fringes. This term is derived from the interferometric pattern of light and dark lines created when an optic is tested against a known reference surface. One fringe is equal to ½ wave and can be thought of as seeing either the peak or valley of a light wave as its frequency completes one cycle. Two fringes combined is therefore one complete wave.
A consistent straight fringe pattern demonstrates exceptional flatness while deviation in the pattern shows an unflat optical surface.
Transmitted Wavefront Distortion (TWD)
Transmitted wavefront distortion is a measurement of light deviation when passing through an optic. Just like flatness, TWD is defined in terms of waves or fringes. As the term implies, a window with poor TWD will distort the light path and degrade the clarity of an image. As such, TWD is a common specification used in imaging applications where the quality of signal or image is paramount to the function of an optical system.
Many aspects affect TWD including a material’s purity, homogeneity, internal stress, as well as, how parallel the two optical surfaces are in relation to one another.
An optic placed in front of a reference transmission flat demonstrates the distortion of the fringe pattern as light travels through the optic.
RMS vs. P-V Flatness
When discussing flatness, irregularity, and transmitted wavefront distortion, it is important to discern the two methods by which they may be defined. The first is an absolute value. For example, if an optic is defined as being 1 wave flat, there can be no more than 1 wave difference between the highest and lowest point on the optical surface. The second method is to specify the flatness as 1 wave RMS (root mean squared) or average. In this interpretation, an optical surface defined as 1 wave RMS flat may, in fact, have peaks and valleys that are in excess of 1 wave, however, when examining the full surface, the overall average flatness must fall within 1 wave. As a general rule, an RMS value is 1/5 as stringent as flatness when compared side by side, i.e. 1/10 wave flat P-V is equivalent to approximately 1/2 wave RMS.
An optic’s surface roughness is closely related to the polishing process and material type. Even if the optic is deemed exceptionally flat with little irregularity across the surface, on close-up inspection, an actual microscopic examination may reveal a great deal of variation in the surface texture. A good analogy of this artifact is to compare surface roughness to sandpaper grit. While the finest grit size may feel smooth and regular to the touch, the surface is actually composed of microscopic peaks and valleys determined by the physical size of the grit itself. In the case of optics, the “grit” can be thought of as microscopic irregularities in the surface texture caused by the quality of the polish. Unlike flatness, power and irregularity, which are measured in waves or fractions of a wave, surface roughness, due to its extreme close-up focus on surface texture, is measured on the scale of angstroms and always in terms of RMS. For comparison, it takes ten angstroms to equal one nanometer and 632.8 nanometers to equal one wave. Optical designers pay close attention to roughness when working with high power lasers. Surfaces without tightly controlled roughness may scatter a laser beam, decreasing the coherence of its signal.
A computer-generated surface roughness map from a Zygo NewView Surface Profiler.
As unparallel faces on a plano optic can affect the direction of light throughput, opticians go to great lengths to minimize any variation in the physical distance between the two surfaces. Parallelism is most often specified in terms of angular deviation. For example, an optic may require the faces to be
< / = 1 arc minute parallel across the entire clear aperture. The easiest way to understand this specification is to picture a typical door wedge. While this is a grossly over-exaggerated comparison, two unparallel faces of an optic do, in fact, exhibit this effect when viewed on extremely small scales. Across a 1” diameter optic, a call-out of
< / = 1 arc minute of wedge equates to 0.00029” of total allowable deviation from true parallel. At such incredibly small distances, an interferometer once again becomes the workhorse as an optician’s diagnostic tool.
Related to parallelism is total thickness variation or TTV for short. TTV helps control wedge by examining individual sections of an optic’s parallelism. Remembering that an optic’s power may demonstrate the above referenced “potato chip” effect, TTV looks at wedge in multiple directions where an optic’s localized curvature may cause the parallelism to meet specification in one direction, while in another be out of spec.
We’ve covered a number of specifications used by opticians to define the precision of a plano optic’s surface form. By comparing the physical aspect ratio and clear aperture to an optic’s flatness, power, irregularity, transmitted wavefront distortion, surface roughness and parallelism, opticians can determine the feasibility and level of difficulty presented in manufacturing these highly precise surfaces.
Esco’s team of sales and manufacturing engineers have decades of combined experience working with these challenging aspects of optical fabrication. We welcome the opportunity to work with our customers, providing feedback on cost-saving considerations, while still achieving the world-class precision our clients demand.
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