# Aspheric lens with high precision

asphericon has specialized in the production and machining of high-precision aspheric lenses. Premium quality and repeatability are cornerstones of the products we develop for you – from individual aspheric lenses to mounted optics and complex systems.

The use of an aspheric lens in an optical system achieves several advantages. In the following comparison the aspheric lens is compared to the classical sphere. Advantages of the aspheric lens are:

• Correction of spherical aberration
• System miniaturization
• Weight reduction

### Correction of aberrations

Using spherical lenses, imaging errors, so-called spherical aberrations, inevitably occur (see figure on the left). This results in a slightly blurred, out-of-focus image because the light rays do not converge on the optical axis at one focal point. The rays are refracted to different degrees depending on their distance from the optical axis: those that pass through the edges of the lens are refracted more strongly. An aspheric lens is rotationally symmetric, with one or more non-spherical surfaces that deviate from the shape of a sphere. The surfaces change their radius of curvature with increasing distance from the optical axis. These properties allow the light rays to converge in one point and the spherical aberration to be corrected. Thanks to modern production technologies, asphericon is able to manufacture aspheric lenses with highest precision even in series.

### Reduction in size and weight of optical systems

Regarding optical design, the use of an aspheric lens allows the optical system to be reduced in size. An application that requires several spherical lenses can sometimes be replaced by one aspheric lens. This is made possible by the high correction value of aberrations. By eliminating single optics, the entire system becomes more compact and the overall weight can be reduced. An illustrative example of the reduction of an optical system can be found in beam expansion. The monolithic beam expander a|BeamExpander, consists of only one single aspheric lens per element. Due to the afocal character, the individual monoliths can also be connected in series. This allows a high variance in the range of beam expansion. Compared to conventional systems, such as the Kepler and Galilean telescopes, the overall length is reduced by up to 50% while maintaining the same magnification and quality. For the specific application, the three optical systems mentioned above are shown below with a 10x magnification. The result: With the aspheric system the overall size is reduced by up to 50%. In addition, the system works completely diffraction limited, even when combining up to 5 a|BeamExpanders.

Due to the different shape to the sphere, a more complex description of the rotationally symmetric aspheric lens is required. Traditionally, aspheric lens surface profiles can be described with the following formula.

$$z(h) = \frac {h^2}{R(1+\sqrt{(1-(1+k) \frac{h^2}{R^2}}} + \sum_{i=2}^{n} A_{2i} h^{2i}$$

z = Sag of surface
h = Distance perpendicular to the optical axis (height of incidence)
k = Conic constant
A2i = aspheric coefficients of the correction polynomial

If the respective aspheric coefficient of a rotationally symmetric asphere is zero, the resulting surface profile is considered conical. Depending on the conic constant k, one of the following conic sections serves as a surface shape description:

 Conical constant Conic section k = 0 Sphere k > -1 Ellipsoid k = -1 Parabola k < -1 Hyperbola

With ISO 10110, which was renewed in 2015, there is an alternative to the traditional description of aspheric surfaces. Based on orthonormal polynomials, it can be used to model the real difference in deflection to the best-fitted spherical shape of the aspheric lens. The new formula also includes the surface quotient Qm and reads:

$$z(h) = \frac {h^2}{R[1+\sqrt{1- \frac{h^2}{R^2}]}} + (\frac{h}{h_0})^2 \frac {[1- (\frac{h}{h_0})^2]}{\sqrt{1-(\frac{h}{R})^2}} \sum_{m=0}^{N} A_m*Q_m (\frac{h^2}{h_0^2})$$

The revised formula offers far-reaching advantages that simplify the surface description. One major advantage is that fewer significant digits are required to describe the surface profile. A further advantage is the maximum sag departure deflection deviation. This can be estimated by multiplying the largest coefficient Am by the maximum amplitude for the order of this coefficient.

The three most reported surface shape imperfections are:

• Surface form error,
• Waviness and
• Surface roughness.

They represent deviations of the real surface from the ideal surface, as for the aspheric lens. The parameters used to describe the surface profile allow a prediction of the quality of a manufactured lens profile after processing. A high surface quality can among other things be achieved by a high process stability.

 Surface parameters Form error Waviness Surface roughness Shape deviation

Figure 3: Comparison of the three most frequent surface form imperfections (form error, waviness, and surface roughness) according to shape and type of deviation

### Surface form error

The form error describes the difference between the lowest and highest point of the test surface. Metaphorically speaking, it refers from mountain to valley, therefore the form error is given by the PV value, peak-to-valley. The PV value is one of the most important surface specifications for inspecting the surface of an aspheric lens. It is evaluated in waves or in fringes. It is also possible to specify it as an RMS or micrometer deviation. The RMS value (Root Mean Square) describes the mean square difference between the ACTUAL and the TARGET surface, taking into account the area of the defect.

### Waviness

Waviness errors on an aspheric lens can be caused, for example, by polishing tools during the machining process. This surface deviation is therefore application specific. The waviness has a longer wavelength than the roughness, which is why the short wavelengths are filtered out for their examination. Only low frequencies may pass. It is often also referred to as the inclination error, which is examined over a defined length. A specification of waviness tolerances is only necessary if the waviness has an effect on the optical task of the aspheric lens.

### Surface roughness

Surface roughness describes smallest irregularities on the optical surface. Therefore, only the short wavelengths are examined for analysis and low frequencies are filtered out. Surface roughness is a dimension for the quality of polishing processes. The effect on optical applications of the aspheric lens can often be decisive. For example, a high degree of roughness can lead to a faster wear of the aspheric lens as soon as high powers, such as those of a laser, act on it. In addition, scattering reduces the quality of the measurement results, which is why low surface roughness is considered a high-quality feature. In industries such as metrology or aerospace this is of importance. The determination of surface roughness is part of the manufacturing process, especially for high-quality aspheric lenses.

asphericon has specialized in the production of aspheric lenses by grinding, polishing, diamond turning and high-end finishing. In this process a blank is subjected to various work steps:

• Grinding or diamond turning for shaping,
• Polishing the ground aspheric lens,
• Measurement for form and surface inspection,
• Measurement and processing by means of high-end finishing.

### Grinding and polishing

Blanks are already shaped lenses and the starting material for the further process to produce an aspheric lens. In the first work step, the blank is ground to give it its desired shape. Various grinding tools and technologies are used for this complex process. The ability to simulate the individual process steps using asphericon's unique CNC control software allows for an unprecedented realization, for high flexibility and reliability during the entire process. In the following, the polishing process is an important part in the production of an aspheric lens. Step by step, the surface is reworked to achieve the desired requirements (e.g. the surface shape deviation). Polishing can be done by machining with geometrically undefined, very fine grain, but also by chemical removal. A finished polished lens has a bright surface without pores and depth cracks as well as the desired shape accuracy and surface quality.

### Diamond Turning

The diamond turning process is an alternative machining method for shaping an aspheric lens. A monocrystalline diamond is used to machine the lens surface. In contrast to grinding tools, this is much smaller and more filigree. Due to its high hardness, ultra-precise machining of the lens is possible, resulting in an improved surface quality. By means of diamond turning, non-ferrous metals, nickel-phosphorus layers, crystals, and IR-glasses can be machined, in addition to an aspheric lens made of plastic.

The subsequent measurement of an aspheric lens is used to check the shape and surface to detect and correct any deviations. An aspheric lens can be measured tactile and optical or contactless, depending on the processing state and accuracy. The full-surface precise measurement of aspheric lenses and other optics at asphericon includes:

• Tactile measuring methods up to diameters of 260 mm
• Full-surface, non-contact measurement up to 420 mm
• Non-contact center thickness measurement
• Roughness measurement Ra < 0.5 nm RMS, measuring field up to 1x1 mm
• Measurement of freeforms, shape and positional tolerances, roughness
• Measurement/positional check of mounts, mounted aspheric lenses and complete systems
• Confocal 3D defect characterization

### Tactile measurement

With tactile measuring methods, the surface of an optical component is scanned with a probe. Differences in height between the scanned surface section and the nominal surface of the measured object are determined. The determined data of the height differences are then analysed and evaluated by a software. A rigid touch probe system and a contact pressure of the probe ball that is as constant as possible are required for the exact determination of the surface contour. Among more complex tactile measuring devices are the 3D coordinate measuring system and the form tester Mahr MFU, both used at asphericon.

### Interferometric measurement

Much more common are interferometric measuring methods for testing an aspheric surface. Interferometers are based on the principle of interference, i.e. the superposition of two coherent light waves (the test beam and the reference beam). A characteristic interference fringe pattern is produced which is used to evaluate the optical surface. The interference fringes are differences in intensity caused by a phase shift of the test wave to the reference wave. This means that surface deviations of the aspheric lens from the ideal shape become visible. To measure an aspheric lens, a computer-generated hologram (CGH) is sometimes additionally required to generate the aspheric reference wavefront. Such a measurement is repeated in phase-shifting measurement methods with several shifts of the reference surface, resulting in a full-surface error map of the aspheric lens to be measured. The MarOpto TWI 60 measuring system, which has been used by asphericon since 2017, is considered a pioneer in optical metrology and measures without CGHs. The modern interferometer measures using differently tilted wave fronts and thus inspects aspheric lenses and freeforms in seconds.

The last processing step within the production of an aspheric lens is the high-end finishing. This serves as the final correction step for even more precise surface processing. The ION-Finish™ technology developed by asphericon (= punctual processing of optical surfaces using a focused ion beam) and the magnetorheological finishing technology (MRF for short, as a mechanical polishing process using magnetorheological fluid consisting of magnetic particles, polishing agent and water) enable accuracies of λ/600 RMS on flat surfaces - even in series production. In addition, asphericon offers the Ångström polishing, a process for aspheric surfaces with roughness values of 5 Å (Rq according to ISO 10110). Based on CNC manufacturing, this finishing is fully automatically controlled and is especially recommended for processing optics used in applications with high laser power.

The use of an aspheric lens is mainly based on its advantages compared to a spherical lens. The biggest benefit is the correction of aberrations resulting in better imaging properties.

Telescopes today, for example, are almost always aspherical, especially those with larger diameters. Aspheric elements are also used in zoom lenses. Not only the system size is reduced but also the imaging quality is increased compared to applications with spherical lenses.

For star observation, but also in the aerospace industry, aspheric lenses can be used. The Sentinel-4 satellite, for example, contains aspheric optics from asphericon in its spectrometers. For use in space, the optics do not only need excellent optical properties, but also have to withstand extreme environmental conditions. Here you can learn more about Sentinel-4.

Another field of application is laser beam shaping, such as the generation of Top-Hat beam profiles. In a beam shaping system with two aspheric lenses for Top-Hat light distribution the first lens is used to redistribute the incoming laser beams (Gaussian distribution) in such a way that a homogeneous intensity distribution is achieved at a certain distance. The second lens collimates the beam and as a result, the characteristic Top-Hat distribution is created. These aspheric applications are of interest in material processing (e.g. cutting of metal) and also in medical applications (e.g. ophthalmology). A detailed description of laser beam shaping with aspheric lenses and other application examples can be found in our blog.

Imaging ophthalmological-instrumental procedures also work with aspheric lenses. Installed in special instruments, they support preventive and postoperative examinations, treatments, and diagnoses of the eye, such as ocular fundus examinations using a slit lamp or fundus camera. In addition to high-resolution imaging, aspheric lenses guarantee a more compact design of ophthalmological observation systems as well as very good imaging qualities.

In industrial areas such as manufacturing, quality control or robotics, high-quality camera systems are required. These are equipped with lenses, which can be based on aspheric lenses. Even under the most difficult conditions, such as high temperatures under constant use, the lenses must withstand. Their task is to focus the light scattered by the object onto a light-sensitive sensor. By passing through several different process steps, important data is transported to its destination.

A relatively new application for aspheric lenses on the market is the field of metrology. Their use can significantly reduce the total number of lenses used in a Fizeau transmission sphere and increases the measuring range. Another advantage: the transmission sphere is also significantly lighter thanks to the use of fewer lenses. For information on the use of aspheric lenses in transmission spheres, please refer to the reference for our aspheric Fizeau lens.

Choose an individual Custom solution or use the innovative diversity of our stocked aspheric lens from the StockOptics product line.

Customized aspheres*StockOptics Aspheres
Diameter4-300 mm10-100 mm
Diameter Tolerance+/- 0,03 mm+/- 0,05 mm
RMS irregularities (RMSi)20 nm≤ 300 nm
Surface Imperfections (Scratch/Dig)20-1020-20
Coating Customer specific4 standard coatings
Laser damage thresholdNA12 J/cm², 100 Hz, 6 ns, 532 nm**
Measurement (optional)Full-surface interferometricallyFull-surface interferometrically
Delivery timeFrom 3-4 weeksFrom 1 day

*Best-fit-specifications | **100 Hz, 6ns, 532 nm

## Aspheric lenses made by asphericon

Choose optical elements from asphericon and benefit from these advantages:

### Aspheric lens at the highest level

asphericon manufactures your desired products at the highest technological level. The worldwide unique control technology of our CNC machines guarantees a perfectly finished aspheric lens according to your requirements in almost any shape and size. We manufacture with the highest technological standards and achieve precision even at atomic levels.

### Surface optimisation with precision

An aspheric lens “made by asphericon” has optimized functional surfaces with unique properties, you won’t find anywhere else. Using various manufacturing processes, we are able to produce extremely precise surfaces that are guaranteed to meet your requirements.

Despite the technical challenges an aspheric lens presents to manufacturers, our asphericon ION-FinishTM and Magnetorheological Finishing-Technology® surpass international standards in high-end finishing.

### Know-how & Economy

Benefit from our expertise gathered in numerous projects while partnering with renowned scientific and industrial institutions. We can implement your individual challenging solutions precisely.

For small as well as large order quantities we work with the proven asphericon precision. At the same time, we work efficiently and economically, making your project a complete success!

#### In-house solutions for aspheric lenses

Discover the possibilities we offer in-house for your aspheric lenses:

Behind each asphericon optic, stands a team of well-trained experts. Their experience expands day by day from demands of customer projects. Suitable for your application you choose from a variety of different shapes and materials for all wavelengths, and we take care of the implementation.

asphericon also manufactures high-precision

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