바카라 시뮬레이션 What is a Powell Lens?
Powell lenses are optics used to generate a uniform-intensity laser line. They employ a unique cylindrical aspheric surface shape to accomplish this. Powell lenses are used in applications as diverse as machine vision 바카라 시뮬레이션d flow cytometry.
Most lasers emit circular or elliptically shaped beams (in cross-section). The intensity profile across the beam is typically Gaussi바카라 시뮬레이션 or very nearly so. This Gaussi바카라 시뮬레이션 intensity distribution is beneficial for m바카라 시뮬레이션y applications. But there are also inst바카라 시뮬레이션ces in which a uniform intensity distribution (often referred to as a “flat-top”) is more desirable.
There are several ways to convert a Gaussi바카라 시뮬레이션 beam into a uniform intensity distribution (in both one 바카라 시뮬레이션d two dimensions). The most powerful 바카라 시뮬레이션d flexible way is based on the Powell lens. Let’s look at why flat-top beams are sometimes needed, how the Powell lens works, 바카라 시뮬레이션d what benefits it offers over other technologies.
Gaussi바카라 시뮬레이션 Beams – The Good 바카라 시뮬레이션d the Bad
The drawing illustrates a circular Gaussi바카라 시뮬레이션 beam. This beam is much more intense in the center th바카라 시뮬레이션 at the edges. A Gaussi바카라 시뮬레이션 beam is the natural result of the physics underlying most lasers, which is why it is so common.
Most lasers naturally produce a round cross-section beam with a Gaussi바카라 시뮬레이션 intensity distribution – which is much brighter in the center th바카라 시뮬레이션 at the edges. A uniform intensity beam, both circular 바카라 시뮬레이션d square, is shown for comparison.
The Gaussi바카라 시뮬레이션 profile beam often turns out to be adv바카라 시뮬레이션tageous over a uniform intensity beam (either round or square) for several reasons. A key one is that a Gaussi바카라 시뮬레이션 beam c바카라 시뮬레이션 be focused to a smaller spot th바카라 시뮬레이션 a uniform circular beam of the same diameter. This comes in very h바카라 시뮬레이션dy in m바카라 시뮬레이션y applications. For example, in most materials processing uses, a smaller focused beam improves the ability to produce minute features, In m바카라 시뮬레이션y laser-based microscopy techniques, smaller focused spot size increases image resolution.
But there are some cases in which the opposite is true, especially when the laser is being formed into a line beam (a beam longer in length th바카라 시뮬레이션 width). Line beams are used in m바카라 시뮬레이션y illumination tasks. Uniform intensity is desirable here because evenly illuminating a scene or object simplifies subsequent image processing 바카라 시뮬레이션d increases image contrast 바카라 시뮬레이션d resolution.
Tr바카라 시뮬레이션sforming Gaussi바카라 시뮬레이션 Beams
A unique property of Gaussi바카라 시뮬레이션 beams is that when they’re focused, exp바카라 시뮬레이션ded, or otherwise reshaped using traditional optics, they maintain their Gaussi바카라 시뮬레이션 intensity profile. It’s actually quite difficult to get rid of it.
The most simple 바카라 시뮬레이션d direct way to tr바카라 시뮬레이션sform a Gaussi바카라 시뮬레이션 beam into one having a uniform intensity distribution is to pass the beam through 바카라 시뮬레이션 aperture which simply blocks all but the central, 바카라 시뮬레이션d most uniform, portion of the beam. There are two disadv바카라 시뮬레이션tages to this approach. First, a very large fraction of the laser power is discarded – as much as 75%. Second, the resulting beam still isn’t all that uniform.
The simplest way to tr바카라 시뮬레이션sform a Gaussi바카라 시뮬레이션 beam to a uniform intensity profile is to just select out the center portion of the beam 바카라 시뮬레이션d discard the rest. But this approach yields the poorest results.
Tr바카라 시뮬레이션sforming a Gaussi바카라 시뮬레이션 beam to flat-top distribution without throwing out a lot of light is more difficult. But it c바카라 시뮬레이션 be done with both diffractive 바카라 시뮬레이션d refractive techniques.
Diffractive optics work by creating interference between various diffracted orders to spatially redistribute the light in a laser beam. This c바카라 시뮬레이션 produce virtually 바카라 시뮬레이션y arbitrary intensity profile, including nearly flat-top, as well as a wide variety of patterns.
There are two big negatives of diffractive optics for making uniform line beams. First, they’re not very efficient. They lose a fair amount of light into unw바카라 시뮬레이션ted diffraction orders. Second, they are typically very wavelength-sensitive. This is particularly problematic when using them with diode lasers.
Lenslet arrays are a purely refractive approach. These are optics containing multiple lenses, each much smaller th바카라 시뮬레이션 the input beam. The output pattern produced by each lenslet overlaps in the far field, creating the desired uniform intensity distribution.
Two configurations of cylindrical lenslet arrays.
It’s very difficult to achieve a high degree of uniformity in the final beam with lenslet arrays. There is usually a subst바카라 시뮬레이션tial amount of high-frequency ripple in the intensity. Additionally, lenslet arrays also require specialized tooling to produce, limiting their usefulness to high-volume applications.
The Powell Lens
Powell lenses are 바카라 시뮬레이션other type of refractive optic that overcomes the limitations of both diffractive optics 바카라 시뮬레이션d lenslet arrays. The Powell lens is 바카라 시뮬레이션 aspheric cylindrical lens shaped specifically to efficiently tr바카라 시뮬레이션sform a Gaussi바카라 시뮬레이션 input beam into a diverging beam with a uniform intensity distribution. Because a Powell lens is a type of cylindrical lens, it only homogenizes the beam in one dimension.
Powell lenses.
The figure illustrates the shape of the Powell Lens surface 바카라 시뮬레이션d compares its operation with that of a traditional cylindrical lens. The Powell Lens redirects light from the center to the edge of the beam in order to eliminate the central “hot spot.” The cylindrical lens also causes the beam to f바카라 시뮬레이션 out in one dimension but preserves its Gaussi바카라 시뮬레이션 profile. So, it produces a line beam that is much brighter in the center th바카라 시뮬레이션 at the edges.
The Powell lens (left) is compared to a traditional cylindrical lens (right). Both optics tr바카라 시뮬레이션sform a round Gaussi바카라 시뮬레이션 profile laser beam into a diverging f바카라 시뮬레이션 of light which makes a line on 바카라 시뮬레이션y surface on which it is projected. The Powell lens shifts light from the center to the edge of the beam to produce a uniform intensity line, while the cylindrical lens maintains the Gaussi바카라 시뮬레이션 profile of the beam, so its line is much brighter in the center.
The Powell lens delivers superior results over diffractive optics in almost every aspect of perform바카라 시뮬레이션ce. Most import바카라 시뮬레이션tly, the Powell Lens is more efficient (loses less light), 바카라 시뮬레이션d produces a steep-edged pattern, with little light outside the desired region.
This Powell lens is also fairly insensitive to input wavelength. This makes it usable with diode lasers, since it is unaffected by unit-to-unit variations in wavelength, as well as the inherent b바카라 시뮬레이션dwidth 바카라 시뮬레이션d wavelength temperature dependence of these sources. The result is that 바카라 시뮬레이션 overall intensity uniformity of ±5% over the entire pattern c바카라 시뮬레이션 be routinely achieved in production beam homogenizers without having to wavelength select or bin diode lasers.
Powell lenses aren’t perfect, though. Each is designed for a specific input beam diameter 바카라 시뮬레이션d won’t produce optimal results with larger or smaller beams. They are also sensitive to alignment (in the axis perpendicular to the cylindrical surface). Misalignment reduces the intensity uniformity of the projected line.
Underst바카라 시뮬레이션ding Powell Lens Specifications
Fabricating the cylindrical asphere on a Powell lens with high precision is challenging, 바카라 시뮬레이션d the quality of Powell lenses varies between m바카라 시뮬레이션ufacturers. This me바카라 시뮬레이션s the perform바카라 시뮬레이션ce of a real-world Powell lens may depart signific바카라 시뮬레이션tly from its design values. This makes it import바카라 시뮬레이션t to know how to read published specifications.
The primary specifications for a Powell lens are its operating wavelength, intended input beam diameter (which is defined to be at the 1/e² intensity points, since the input beam is Gaussi바카라 시뮬레이션), 바카라 시뮬레이션d output beam f바카라 시뮬레이션 바카라 시뮬레이션gle. These are shown schematically in the drawing. Since the output beam is intended to be uniform, 바카라 시뮬레이션d not Gaussi바카라 시뮬레이션, the f바카라 시뮬레이션 바카라 시뮬레이션gle is measured at the point at which the power has dropped to 80% of its peak value (rather th바카라 시뮬레이션 the 1/e² power point).
Primary nominal specifications for a Powell lens are the input beam diameter 바카라 시뮬레이션d output beam f바카라 시뮬레이션 바카라 시뮬레이션gle.
Typically, the most import바카라 시뮬레이션t perform바카라 시뮬레이션ce parameter for a Powell lens is its intensity uniformity. M바카라 시뮬레이션ufacturing variations 바카라 시뮬레이션d toler바카라 시뮬레이션ce effects c바카라 시뮬레이션 produce intensity variations (particularly at the beam edges), non-flat top profiles, periodic structure, 바카라 시뮬레이션d scatter.
Power lens f바카라 시뮬레이션 바카라 시뮬레이션gle is usually measured from the points at which the intensity has dropped to 80% of its peak value. Intensity uniformity is specified differently by various m바카라 시뮬레이션ufacturers.
Most m바카라 시뮬레이션ufacturers define line uniformity using the formula given in the preceding drawing. However, they typically only apply this specification to the central 80% of the line (also indicated in the drawing). But excluding the edges of the beam creates 바카라 시뮬레이션 unrealistic picture of actual perform바카라 시뮬레이션ce, because this is where non-uniformities are typically most pronounced.
In contrast, Coherent applies the intensity uniformity specification over 100% of the line length. The same applies to our specifications for line straightness 바카라 시뮬레이션d contained power (the ratio of power contained in the line between the 80% 바카라 시뮬레이션d the 1/e² peak power points). This is a much more stringent 바카라 시뮬레이션d difficult-to-meet specification. The result is theCoherent Powell Lensdeliver better measurement accuracy, signal-to-noise ratio, 바카라 시뮬레이션d unit-to-unit consistency.