Correction of aberrationsUsing spherical lenses, imaging errors, so-called spherical aberrations, inevitably occur (see figure on the top of this page). 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. Aspheric optics are 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.Mathematical description of an aspheric lensDue 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 ) = h 2 R ( 1 + 1 − ( 1 + k ) h 2 R 2 ) + ∑ i = 2 n A 2 i h 2 i z = Sag of surfaceh = Distance perpendicular to the optical axis (height of incidence)R = Radiusk = Conic constantA2i = Aspheric coefficients of the correction polynomialIf 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:k = 0 - Spherek > -1 - Ellipsoidk = -1 - Parabolak < -1 - HyperbolaWith 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 aspherical lens. The new formula also includes the surface quotient Qm and reads: z ( h ) = h 2 R [ 1 + 1 − h 2 R 2 ] + ( h h 0 ) 2 [ 1 − ( h h 0 ) 2 ] 1 − ( h R ) 2 ∑ m = 0 N A m ∗ Q m ( 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.Aspheric surface profileFigure: Comparison of the three most frequent surface form imperfections (form error, waviness, and surface roughness) according to shape and type of deviationThe 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 form errorThe 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.WavinessWaviness 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 roughnessSurface 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 aspherical 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.asphericons standards in the production of high-precision opticsasphericon 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 polishingBlanks 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 TurningThe 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.Measurement of the aspheric lensThe full-surface precise measurement of aspheric lens and other optics at asphericon includes tactile and optical methods. 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 characterizationTactile measurementWith 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 measurementMuch 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.Application examples of the aspheric lensThe 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.

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

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2. Ramsden eyepiece: This design features two plano-convex lenses with the convex sides facing away from each other. It offers a wider field of view compared to the Huygenian eyepiece and is commonly used in modern microscopes.

The eyepiece on a microscope, also known as an ocular lens, is the part of the microscope that is looked through to view the magnified specimen. It is located at the top of the microscope and is the lens closest to the eye of the observer. The eyepiece is designed to magnify the image produced by the objective lens, which is the lens closest to the specimen being observed.

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An eyepiece on a microscope, also known as an ocular lens, is the lens at the top of the microscope that you look through to view the specimen. It is the part of the microscope that is closest to your eye and is responsible for magnifying the image of the specimen. The eyepiece typically contains a set of lenses that work together to magnify the image produced by the objective lens, which is the lens closest to the specimen.

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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 polishingBlanks 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 TurningThe 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.

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From a modern perspective, the eyepiece on a microscope may also be designed to reduce eye strain and provide a comfortable viewing experience. Some eyepieces are equipped with adjustable diopter settings to accommodate individual differences in vision, and others may incorporate anti-glare or anti-reflection coatings to improve image clarity.

Overall, the eyepiece on a microscope plays a crucial role in magnifying and enhancing the image of the specimen, as well as providing a comfortable and effective viewing experience for the user.

In summary, the eyepiece on a microscope is a crucial component that contributes to the overall quality of the viewing experience. Its design and construction have evolved to prioritize optical performance, user comfort, and versatility, making it an essential part of modern microscopy.

From the latest point of view, advancements in microscope technology have led to the development of eyepieces with variable magnification power, allowing users to adjust the level of magnification based on their specific needs. Additionally, some modern microscopes are equipped with digital eyepieces that can capture and display images on a computer screen, enabling users to easily share and analyze the microscopic images. These digital eyepieces often come with software that allows for further image enhancement and analysis, expanding the capabilities of traditional eyepieces.

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Choose between asphericon a|High-NA, a|Low-NA and a|UV-grade fused silica as well as up to three different quality levels (Precision, Ultra and BeamTuning). Thanks to CNC polishing and grinding this aspheric lens meets the highest demands on production quality and tolerance:

The eyepiece, also known as the ocular lens, is the lens at the top of the microscope that you look through to view the specimen. It typically contains a magnifying lens that further enlarges the image produced by the objective lens. The eyepiece is usually removable and interchangeable, allowing for different magnifications to be achieved depending on the specific needs of the user.

Eyepiece design and construction have evolved over time to improve the quality and comfort of the viewing experience. Modern eyepieces are typically designed with multiple lens elements to minimize aberrations and distortions, resulting in a clearer and more accurate image. Some eyepieces also incorporate advanced coatings to reduce glare and improve contrast.

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Based on an unique technology, asphericon is able to produce aspherical optics with a surface form deviation (RMSi) from up to 0,01 µm. In cooperation with our customers we are developing and producing suitable solutions for a big variety of optical lenses – from the prototype to series. Choose an individual Custom solution or use the innovative diversity of our stocked aspheric lens from the StockOptics product line. a|Aspheres are available in our web shop with surface form deviations of RMSi ≤ 0.5 μm and RMSi <0.3 μm. Due to precise focusing properties, all optics and components from asphericon are suitable for a wide variety of applications.

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 form errorThe 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.WavinessWaviness 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 roughnessSurface 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 aspherical 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.

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Looking for a custom solution? Discover our customized aspheres with unsurpassed surface quality and following specifications::

RMSi [nm]Diameter [mm]EFL [mm]NAλDesign [nm]MaterialCoatingAllAllAllAllAllAllAllProduct CodeRMSi [nm]Wavefront RMS [nm]Diameter [mm]EFL [mm]NAf/dWD [mm]λDesign [nm]MaterialScratch-DigCoatingPrice uncoatedPrice coatedAHM12-10-U-U1007812.5100.550.807.6780S-LAH6460-40A / B / C479.00528.00Quote AHM15-12-U-U1007815120.550.809.0780S-LAH6460-40A / B / C504.00564.00Quote AHM18-15-U-U1007818150.530.8311.5780S-LAH6460-40A / B / C534.00609.00Quote AHM20-18-U-U1007820180.490.9014.0780S-LAH6460-40A / B / C560.00628.00Quote AHM25-20-U-U1007825200.540.8015.7780S-LAH6460-40A / B / C588.00659.00Quote ALM12-25-U-U1005112.5250.252.022.4780N-BK760-40A / B / C479.00528.00Quote ALM25-50-U-U1005125500.232.046.0780N-BK760-40A / B / C588.00659.00Quote AFM12-10-U-U30014012.5100.580.8335.7355Fused Silica20-20A / B / C / X / Y / K / L / M523.00571.00Quote AFM12-15-U-U30014012.5150.391.212.3285Fused Silica20-20A / B / C / X / Y / K / L / M514.00562.00Quote AFM12-20-U-U30014012.5200.291.617.3285Fused Silica20-20A / B / C / X / Y / K / L / M514.00562.00Quote AFM25-17-U-U3001402517.50.640.710.0355Fused Silica20-20A / B / C / X / Y / K / L / M737.00847.00Quote AFM25-20-U-U30014025200.560.812.6355Fused Silica20-20A / B / C / X / Y / K / L / M706.00816.00Quote AFM25-25-U-U30014025250.481.017.0285Fused Silica20-20A / B / C / X / Y / K / L / M684.00795.00Quote AFM25-30-U-U30014025300.391.223.3285Fused Silica20-20A / B / C / X / Y / K / L / M636.00709.00Quote AFM25-40-U-U30014025400.291.634.6285Fused Silica20-20A / B / C / X / Y / K / L / M636.00709.00Quote AFM25-50-U-U30014025500.232.045.1355Fused Silica20-20A / B / C / X / Y / K / L / M636.00709.00Quote AFM25-75-U-U30014025750.153.070.9355Fused Silica20-20A / B / C / X / Y / K / L / M618.00709.00Quote AFM25-100-U-U300140251000.114.096.3355Fused Silica20-20A / B / C / X / Y / K / L / M636.00709.00Quote AFM25-50-D-U201025500.232.045.1355Fused Silica20-20A / B / C / X / Y / K / L / M950.001058.00Quote AFM25-75-D-U201025750.153.070.9355Fused Silica20-20A / B / C / X / Y / K / L / M950.001058.00Quote AFM25-100-D-U2010251000.114.096.3355Fused Silica20-20A / B / C / X / Y / K / L / M950.001058.00Quote Prices are valid per piece and in USD. Sales only to commercial customers. All prices are exclusive of VAT.

Aspheres have much better imaging properties than spherical lenses thanks to the surface geometry that deviates from a sphere. The main benefit is the ability to correct spherical aberrations. The total number of optical elements in an optical system can be reduced by using an aspheric lens. This enables a significantly more compact and efficient setup than is the case for a comparable system with spherical lenses.

The latest point of view on eyepiece design emphasizes the importance of ergonomic design to reduce eye strain and improve user comfort during extended periods of use. This includes features such as adjustable eye relief and eyecups to accommodate different users and provide a more comfortable viewing experience. Additionally, advancements in materials and manufacturing techniques have allowed for the production of lightweight yet durable eyepieces that are well-suited for various applications.

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In recent years, there has been a growing interest in digital eyepieces, which incorporate digital imaging technology to capture and display the magnified image on a computer or other digital device. This allows for easier sharing of images and facilitates analysis and documentation of the specimens. Additionally, there has been a focus on ergonomic designs to improve user comfort and reduce eye strain during prolonged use. These advancements aim to enhance the overall microscopy experience and make it more accessible to a wider range of users.

In addition to magnification, the eyepiece also helps to focus the light rays coming from the objective lens and to direct them into the viewer's eye. This helps to create a clear and sharp image of the specimen under observation. The eyepiece also often contains a reticle or a graticule, which is a grid or scale that can be used to measure the size or dimensions of the specimen.

1. Huygenian eyepiece: This is a simple eyepiece design that consists of two plano-convex lenses with the convex sides facing each other. It provides a relatively narrow field of view and is commonly used in older microscopes.

The eyepiece on a microscope, also known as the ocular lens, is the lens at the top of the microscope through which the viewer looks. It is the lens closest to the eye when using the microscope. The primary function of the eyepiece is to magnify the image produced by the objective lens, which is the lens closest to the object being observed. This magnification allows the viewer to see a larger and more detailed image of the specimen.

The magnification power of the eyepiece is a measure of how much the image is enlarged when viewed through the microscope. This is usually expressed as a number followed by an "x" (e.g., 10x, 20x), which indicates the number of times the image is magnified. For example, if the eyepiece has a magnification power of 10x and the objective lens has a magnification power of 40x, the total magnification of the microscope would be 400x (10x multiplied by 40x).

3. Wide-field eyepiece: This type of eyepiece is designed to provide a larger and more comfortable viewing area, allowing the viewer to see more of the specimen at once. It is particularly useful for applications that require prolonged observation.

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An eyepiece on a microscope is a lens that is positioned at the top of the microscope and is used to view the magnified image of the specimen. It is also known as an ocular lens and is an essential component of the microscope's optical system. The eyepiece typically contains a set of lenses that further magnify the image produced by the objective lens, allowing the viewer to see a highly detailed and enlarged image of the specimen.

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