Lendistortion

The most serious of the classical Seidel monochromatic lens aberrations that occurs with microscope objectives, spherical aberration, causes the specimen image to appear hazy or blurred and slightly out of focus. Ideally, an aberration-free objective converts a plane wavefront into a spherical wavefront, directing all light waves refracted by the lens to a common focal point in the center of the sphere to produce a perfect image.

Until recent years, achromats were corrected spherically only for green light, although they were corrected chromatically for two wavelengths. Also, apochromats were corrected spherically for two wavelengths, blue and green, but were corrected chromatically for three wavelengths. The highest-quality modern microscope objectives address spherical aberrations in a number of ways including special lens-grinding techniques, improved glass formulations, and better control of optical pathways through use of multiple-lens elements. Currently, the highest quality objectives, planapochromats, are spherically corrected for four wavelengths, as are planfluorites (but not to quite as close a tolerance).

Coma aberration

Spherical aberrations are very important in terms of the resolution of the lens because they affect the coincident imaging of points along the optical axis and degrade the performance of the lens, which will seriously affect specimen sharpness and clarity. These lens defects can be reduced by limiting the outer edges of the lens from exposure to light using diaphragms and also by utilizing aspherical lens surfaces within the system. However, a consequence of reducing aperture size in the microscope optical system is a concurrent reduction in the amount of light entering the system. Spherical aberration is usually corrected by employing glass elements (lens doublets or triplets) cemented together. The glass elements are designed with different shapes of convexity and/or concavity to insure that the peripheral rays and axial rays, especially at the outer area of the field of view, are brought into common focus.

One of the mechanisms used to eliminate spherical aberration in oil immersion objectives is to design the optics around specific pairs of conjugate points using a hemispherical and meniscus lens at the front of the objective. As illustrated in Figure 2, for a specimen observed at position P and surrounded by immersion oil of refractive index n, there exists a conjugate point (P(1)) to eliminate spherical aberration in the first lens element (the hemispherical lens). In this case, light rays emanating from point P leave the surface of the hemispherical front lens as if they originated at point P(1). The meniscus lens is ground with a surface radius centered on point P to form a second conjugate pair (P(1) and P(2)). Thus, light from the specimen a point P ultimately exits the meniscus lens as if it originated at point P(2), eliminating spherical aberration for the lens combination.

However, you must have the proper focal distance designed for your specific application, and it must be set up in perfect focus to maximize the laser tube’s full wattage power. While you may think that the thicker the material, the larger the lens needed, the more likely the resolution and detailing is lower, and the more power is required. But this relationship isn’t always true. The main factor of power depends on the focal length of the lens. You can have an 18mm diameter focal lens with a focusing distance of 3". You can also have a 25mm diameter focal lens with a 1.5" focusing distance. The trick is in manipulating your focal length to achieve your desired laser power relative to the size and thickness of your project materials.

Lensdistortioncorrection

Most of the discrepancy in focal points arises from approximations of the equivalency of sine and tangent values of respective angles made to the Gaussian lens equation for a spherical refracting surface:

Perspectivedistortion

This factor determines how sharp the engraving comes out when it's done. Here is where the thickness of material and resolution intersects: Larger laser focusing lenses have lower resolutions, and remember that for thick materials, you need a large lens. This implies that you must be able to strike a balance between these two factors. In the end, you want a lens that can work on thick materials and still give good details and a fine resolution. Generally, the 2-inch lens (focus) is considered as the most universal among the classes of lenses available - 1.5, 2, 2.5, and 3-inch, respectively.

Trying to focus a laser engraver can be a tough task. It’s not always easy to learn how to focus your laser engraver machine. As a business owner, learning the fundamentals of your laser focusing lens will help you maximize profit and deliver quality work. One of the most important factors to look out for when using a laser engraver is the focal length.

There is an “unfocused” method of engraving applied to create larger lettering on bulky materials, for example, 3" x 6" letters on a 3' x 4' piece of plywood. You can "unfocus" the laser spot and enlarge it to around 1mm-1.5mm. Always expect some trial and error when trying out a new engraving technique.

Radialdistortion

Focal length is embedded in the concept of laser focusing. It determines the quality of your laser markings for a perfect engraving. You can liken this concept to how you have to adjust a camera's focus to get a clear image.

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Knowing the right focus lens for you is not rocket science. The truth is these factors are interwoven and intertwined in some ways. When determining laser focal length, think about the maximum cutting thickness you want to achieve. These are some factors to consider when trying to choose the best focal lens for your laser engraving machine.

Spherical aberration artifacts are encountered when light waves passing through the periphery of an uncorrected convex lens are not brought into focus with those passing through the center. Waves passing near the center of the lens are refracted only slightly, whereas waves passing near the periphery are refracted to a greater degree, producing a variety of different focal points along the optical axis. As a result, the peripheral waves come to a shorter focus (nearer the back of the lens or objective) than do rays traveling through the central or axial area. This is known as longitudinal or axial spherical aberration. Axial aberration is generated by non-spherical wavefronts produced by the objective itself or by improper use of the objective. Some of the most common causes are failure to maintain the designated microscope tube length or the presence of substances between the objective and focal plane having a spurious refractive index.

High-quality oil immersion objectives perform optimally only when they are used with a cover glass thickness of 0.17 millimeters. To help alleviate cover glass variations, correction collars are often included on dry objectives to enable adjustment of intermediate lens elements to compensate for deviant cover glass thickness. Because focus may shift and the image may wonder during adjustment of the correction collar, the utilization of correction collars demands that the microscopist remain alert in order to reset the collar using appropriate image criteria. In addition, the insertion of accessories in the light path of finite tube length objectives may introduce aberrations, when the specimen is refocused, unless these accessories have been properly designed with additional optics.

John C. Long and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

Focal length is the distance from the focal lens to the laser beam’s convergence point. When a laser beam is emitted from a CO2 laser tube, the laser beam has inconsistent intensity and is too wide to engrave with any precision. That’s where the focal lens comes in — laser focusing lenses have a convex contour that makes the laser beam converge to an extremely narrow point, bending the laser beam into an X shape. This point of convergence, or center of the “X,” is precisely where the laser should contact the target material.

We have done our best to highlight laser focusing and its relation to some factors considered above. More so, these lenses and their focal length always determine the quality of the laser beam available for engraving. In general, ensure you do your homework and define your expectations before purchasing a laser engraver. OMTech has the best CO2 and fiber laser machines with the appropriate accessories for optimal result and marking quality. Our doors are wide open to receive you for demonstration and consultancy at our Southern California showroom.

Sphericalaberration

The tutorial initializes with an image of the specimen (as seen through the microscope) appearing in a window on the left-hand side of the applet. Beneath the image window is a pull-down menu labeled Choose A Specimen, used to select a new specimen. The Lens Shape slider is designed to control the tutorial by introducing an increasing amount of spherical aberration into the optical system. Moving the slider to the right also induces changes corresponding to the introduction of spherical aberration into the Airy diffraction pattern shown in the center of the applet window. Simultaneously, intensity is shifted away from the central peak of the point spread function and into the surrounding rings, which become far more prominent. These changes are also correlated with the ray trace diagram presented in the right-hand side of the applet.

The tutorial illustrates an exaggerated view of three hypothetical monochromatic light rays passing through a convex lens and converging on a series of focal points that lie in a progression along the optical axis (see the Ray Trace Diagram). Changes to the shape of the lens with corresponding adjustments to the focal point position(s) can be made by utilizing the Lens Shape slider. Refraction of peripheral rays at the edge of the lens is greatest followed by those in the middle and then the rays in the center. The larger refraction by the outermost rays results in a focal point (focal point 1; see Figure 1) that occurs in front of the disc of least confusion and the focal points produced by rays passing closer to the center of the lens (focal points 2 in the center and 3, at the paraxial focal plane; Figure 1). Also illustrated in Figure 1 is a measure of the transverse spherical aberration, defined as the distance from the optical axis at which the peripheral rays intersect the plane of paraxial focus. As is evident in the figure, transverse aberration is measured in the plane of the image and is useful as an indicator of image blur.

where n and n' represent the refractive index of air and the glass comprising the lens, respectively, s and s' are the object and image distance, and r is the radius of curvature of the lens. This expression determines the relative locations of images formed by the curved surface of a lens having radius r sandwiched between media of refractive indices n and n'. A refinement of this equation is often referred to as a higher-order (first, second, or third) correction by including terms in the cube of the aperture angle, resulting in a more refined calculation. Departure from an ideal spherical wave is expressed in terms of fractions of a wave, where a single wave is equal to the average wavelength of the illuminating light. This deviation is termed the optical path difference, which must be less than one-quarter wavelength before a diffraction limited objective can be considered aberration-free.

Specimens mounted in Canada balsam or similar mounting media that have a refractive index approximating that of the cover glass are not prone to spherical aberration errors. However, this is not true for specimens mounted in physiological saline or other aqueous media with refractive indices significantly different from the cover glass. Even when focusing through thin layers of water only a few microns thick, significant aberrations are encountered that can induce dramatic asymmetries into the point spread function causing a non-uniform distribution above and below the focal plane. This concept is explored in the interactive tutorial linked below.

The rule of thumb guiding laser focusing states that the larger or thicker material, the larger the lens, spot size, and depth of focus. Consequently, it is evident that a thin material will require a small spot size and a small lens. Also, the lens will only be able to engrave small and fine details on the material. For fine detail and efficient cutting, the proper focused laser spot will be between .1 - .3 mm.  This analysis is the opposite if you have thick materials.

The effect of spherical aberration manifests itself in two ways: the center of the image remains more in focus than the edges, and the intensity of the edges falls relative to that of the center. This defect appears in both on-axis and off-axis image points.

Focal length refers to the distance from the laser focusing lens to the top surface of the material being processed, which is often measured in inches. On the other hand, focus refers to the smallest possible beam of a laser. And this beam has the maximum density of laser packed in it. Focus is an inherent property of focal length; it’s basically the focal length at which the best engraving quality is realized. For example, when an engraver is designated to have a focal length of 1.5 inches, this implies that when you place a material 1.5 inches from the focal lens to the top surface of your material, only at that distance to the material is the engraving sharpest. Therefore, you must note the lens's designated focal length when purchasing your laser engraver.

Chromatic aberration

As the objective numerical aperture is increased, changes in cover glass thickness or refractive index become critical, particularly with high magnification dry objectives where small changes in tube length quickly lead to inferior images. Although spherical aberration can be corrected to almost undetectable limits for visual observation with all types of objectives, the optical specification for any given lens must be fulfilled. For oil-immersion objectives having high numerical apertures, this usually means using a cover glass having a 0.17 millimeter thickness and immersion oil with a refractive index of 1.5180 (± 0.0004) at wavelengths of 546 and 589 nanometers. Complicating these conditions is the fact that for almost all materials, refractive index is a function of both wavelength and temperature. In cases where the exact properties of the cover glass and oil are specified, microscope manufacturers can correct spherical aberration for several values of wavelength.

It is also possible for a user to inadvertently introduce spherical aberration into a well-corrected system. For example, when using high magnification, high numerical aperture dry objectives, the correct thickness of the cover glass (suggested to be 0.17 millimeters) is critical. Figure 3 illustrates the changes in half-width of the intensity distribution curve with changes in cover glass thickness. Even with high quality cover glasses having a tolerance of ±10 micrometers, the half-width changes by more than a factor of two. As the objective numerical aperture is increased (above a value of 0.5), particularly with dry and water immersion lenses, selection of cover glasses for the correct thickness is particularly important.

The takeaway is that you must consider the thickness of the material you will be working with when purchasing an engraver. Knowing fully well that your laser engraver must not underperform, neither should it overperform to save cost. Failure to do this could limit your profit and capacity as a business entity in the laser engraving space.

The focal lens can affect the machine's power by changing the laser beam's dot size diameter. A 60W machine can only provide 60W of maximum power, no matter which focus lens is used. But, larger lenses will typically increase the beam dot size, which lowers the energy density of laser beam. That means that using a typical 4-inch focal lens with a 50W laser tube will actually decrease your cutting ability because the laser beam is wider and less dense. Keep this in mind when choosing your focal lens for laser cutting. While a 3 or 4-inch lens is great for cutting on a High-Power laser, it's not ideal for a Mid-Range laser.

Typically, all materials vary in their composition, and this should inform the right lens choice for you. Different materials have varying absorptivity for laser engraving via the focal length of the lens. For example, the appearance of engraving on glass and wood differs even at the same lens focus. This means that you have to pay keen attention to how each material responds to the engraver's focus.

Only when the specimen and image distances can be accurately specified can spherical aberration be optimally corrected. This artifact can be easily introduced by improper tube length caused by introduction of optical elements into the converging beam path of finite tube length microscopes. Spherical aberration can also occur when using improper "windows", such as cover glasses of nonstandard thickness (deviations from 0.17 millimeters) or poor quality immersion oil between the objective front lens and the cover glass.

What is seen in the microscope is an image made by focusing the peripheral rays surrounded by the unfocused image of rays traveling through the central portion of the lens (or visa versa). This is one of the most serious resolution artifacts because the image of the specimen is spread out rather than being in sharp focus. The best focus, in an imperfectly or non-corrected lens, will be somewhere between the focal planes of the peripheral and axial rays, an area known as the disc of least confusion (illustrated as a point on the optical axis in the tutorial figure). Light rays refracted by the rim of the lens or pupil (peripheral rays) have the shortest focal length and produce the smallest image, whereas those that intersect at the paraxial focal point (axial rays) have begun to spread and do not represent the "best" focus.