Lens aberrationtest

Wireless communication has witnessed remarkable advancements in recent years, driven by a growing demand for higher data rates and capacity. As traditional radio frequency (RF) and microwave technologies struggle to keep pace with these growing requirements, free-space optical communication (FSOC) has emerged as a frontrunner, to address bandwidth limitations and last-mile connectivity challenges (see Fig. 1).

Lens aberrationCorrection

VynZ Research’s report “Global Free Space Optics Market – Analysis and Forecast (2025-2030)”, forecasts a 30% compound annual growth rate (CAGR) for FSOC between 2025 and 2030, with the global market, led by the U.S., to reach a value of $1.9B, up from just $550M in 2023.

Because apochromatic objectives require elements of abnormal dispersion, their characteristics may not be ideal for some specific applications, such as fluorescence excitation in the near ultraviolet, differential interference contrast, and other forms of microscopy utilizing polarized light. For this reason, a fluorite objective is often more suitable, and Figure 4 illustrates how close these objectives are to the performance of apochromats.

With apochromat and fluorite objectives, the diffraction-induced spreading of the intensity distribution can also be virtually eliminated, as illustrated in Figure 4. An achromat still has substantial intensity in the first fringe, while the apochromat approaches the theoretical resolution limit where the longitudinal chromatic aberration is greater than the wave-optical depth of field.

Christian Rookes is VP of marketing at Phlux Technology, a manufacturer of avalanche photodiode (APD) infrared sensors based in Sheffield, U.K. He has more than 25 years’ experience in technical marketing in semiconductor and optical communication fields. Rookes holds a BSc in Engineering and Physics from Loughborough University and an MBA Essentials Certificate from the London School of Economics. He holds two patents, including one related to impedance matching for laser diode circuits.

Lens aberrationexamples

Chromatic aberration is very common with single thin lenses produced using the classical lens-maker's formula that relates the specimen and image distances for paraxial rays. For a single thin lens fabricated with a material having refractive index n and radii of curvature r(1) and r(2), we can write the following equation:

Brian O. Flynn and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

Lens corrections were first attempted in the latter part of the 18th century when John Dollond, Joseph Lister and Giovanni Amici devised ways to reduce longitudinal chromatic aberration. These pioneers introduced achromatic lenses to microscopy, dramatically reducing axial (longitudinal) chromatic aberration, and made bacteria visible for the first time in the optical microscope. By combining crown glass and flint glass (each type has a different dispersion of refractive index), they succeeded in bringing the blue rays and the red rays to a common focus, near but not identical with the green rays. The dispersion of flint glass is about twice that of crown, so by pairing a positive crown element with a negative flint element, the combined dispersions will be approximately equal and opposite, thus eliminating axial color spread (Figure 2). Note that the magnifying power of the crown glass is twice that of the flint in this combination, yielding a net power about half that of the crown element alone. Another advantage to this lens marriage is the correction for spherical aberration, which often occurs when a positive and negative element are utilized together in a lens group.

Astigmatismaberration

1550 nm is a commonly preferred wavelength for FSOC. It is a sufficiently longer wavelength than visible light, so it’s “eye safe” if people encounter the signal, and avalanche photodiodes (APDs)—based on indium gallium arsenide (InGaAs) APDs—exhibit peak sensitivity to IR light at this wavelength. The Fraunhofer Heinrich Hertz Institute states that 1550-nm beams are 50x safer than those at 850 nm, which were also proposed for FSOC.

A further benefit of FSOC is that wireless channels are either regulated or where not regulated are already densely populated. FSOC needs no license and due to its narrow transmission angle, it is less susceptible to interference from other signals.

This positive forecast is despite the acknowledged challenges of environmental interference and installation capital costs. The report highlights the need for devices with greater photon efficiency to mitigate some factors that could limit growth.

These advancements in APD technology are poised to significantly enhance the capabilities of satellite and terrestrial FSOC and potentially revolutionize space-based data transmission.

A proper combination of lens thickness, curvature, refractive index, and dispersion allows the doublet to reduce chromatic aberration by bringing two of the wavelength groups into a common focal plane (Figure 2). If fluorspar is introduced into the glass formulation used to fabricate a lens, then the three colors red, green, and blue can be brought into a single focal point resulting in a negligible amount of chromatic aberration. Such lens elements are known as apochromatic lenses and they are used to build very high-quality chromatic aberration-free microscope objectives.

In medical applications, FSOC technology shows promise for communication with subcutaneous implants, where skin-induced propagation loss can be mitigated.

The focal length f varies with the wavelength of light as illustrated in the tutorial window and Figure 1(a), which demonstrates the effects of chromatic aberration on a beam of white light passing through a simple lens. The component colors (wavelengths) are focused at varying distances from the lens (Figure 2) to produce an image having an arbitrary blur radius approximately 0.3 millimeters in diameter. It is relatively simple to demonstrate chromatic aberration using a thick, simple converging (biconvex, positive meniscus, or plano-convex) lens illuminated with a polychromatic point source, such as a flashlight or candle. When observing an image produced by the simple lens, the periphery of the image will appear blurred and tinted with an orange-red halo when the lens is close to the eye. At greater distances, the halo will become blue-violet.

A comparison of the longitudinal chromatic correction of an achromat with that of an apochromat objective is presented in Figure 3. Glasses of normal dispersion, which have an almost linear decrease in refractive index with increasing wavelength, are used to produce achromat objectives. Only two wavelengths can have the same focus (see Figure 3), and the remaining secondary spectrum produces greenish or purple fringes on images of sharp edges. The higher quality apochromat objectives use glasses having a partial dispersion where the refractive index changes with wavelength more rapidly in either the blue or red region. As a result, apochromats have a high degree of chromatic correction in which up to four wavelengths can have the same image location.

Chromatic aberrations are wavelength-dependent artifacts that occur because the refractive index of every optical glass formulation varies with wavelength. When white light passes through a simple or complex lens system, the component wavelengths are refracted according to their frequency. In most glasses, the refractive index is greater for shorter (blue) wavelengths and changes at a more rapid rate as the wavelength is decreased.

Types ofaberrationin lenses

The first high-capacity space-to-ground laser communication system was installed on the Bartolomeo platform of the International Space Station (ISS) as part of a collaboration between Airbus Defense and Space, the Institute of Communications and Navigation of DLR (German Aerospace Center), and Tesat-Spacecom GmbH & Co. KG. The 2018 project, called OSIRIS, was designed to provide direct-to-earth (DTE) technology with a data rate of 10 Gbit/s over a range of about 1,500 km.

Blue light is refracted to the greatest extent followed by green and red light, a phenomenon commonly referred to as dispersion. The inability of a lens to bring all of the colors into a common focus results in a slightly different image size and focal point for each predominant wavelength group. This leads to colored fringes surrounding the image. When the focus is set for the middle of the wavelength band, the image has a green cast with a halo of purple (composed of a mixture of red and blue) surrounding it.

Compared to wireless systems, FSOC can operate with lower power consumption—which reduces cost and environmental impact. Narrow FSOC beams are also more focused than wireless emissions, and it boosts the received signal strength and mitigates the need for high-power transmitters. And antenna designs can be more compact using optics compared to RF. This reduces installation space constraints and aesthetic impact, which can be important where there is local sensitivity toward their presence. For cases in which the security of communications is important, FSOC systems may be preferred over wireless links because eavesdropping on optical links is technically challenging and the risk of interception is relatively low.

where s and s' are defined as the object and image distance, respectively. In the case of a spherical lens, the focal length (f) is defined as the image distance for parallel incoming rays:

One of the key technical challenges with achieving Earth-to-satellite and terrestrial FSOC is that the IR signals used to transmit data are diffracted as they pass through the troposphere, the atmospheric layer closest to Earth. Variations in our atmosphere's air temperature, humidity, and turbulence cause fluctuations in the intensity and angle of incidence of IR signals. This makes the beam wander over the signal detector area, which limits performance. The issue is addressed by using large-area receptors comprising multiple IR sensors.

Comaaberration

The crown/flint combination is termed a lens doublet where each lens has a different refractive index and dispersive properties. Lens doublets are also known as achromatic lenses or achromats for short, derived from the Greek terms a meaning without and chroma meaning color. This simple form of correction allows the image points at 486 nanometers in the blue region and 656 nanometers in the red region to now coincide (Figure 1(b)). Defocus between the central wavelength (550 nanometers) and the common focus (blue and red) is residual aberration that is termed secondary axial color. Even though blur is reduced by a factor of 30 with bichromatic correction using flint and crown glasses (Figure 1(b)), the aberration cannot be completely eliminated with common glass formulations, which limits the image quality of achromatic objectives. Achromats are the most widely used objective lenses and are commonly found on both teaching and research-level laboratory microscopes. Objectives that do not carry a special inscription stating otherwise are likely to be achromats. Achromats are satisfactory objectives for routine laboratory use, but because they are not corrected for all colors, a colorless specimen detail is likely to show, in white light, a pale green color at best focus (secondary axial color).

In microscopes having a finite tube length, it is the compensating eyepiece, with chromatic difference of magnification just the opposite of that of the objective, which is utilized to correct for lateral chromatic aberration. Because this defect is also found in higher magnification achromats, compensating eyepieces are frequently used for such objectives, too. Indeed, many manufacturers design their achromats with a standard lateral chromatic error and use compensating eyepieces for all their objectives. Such eyepieces often carry the inscription K or C or Compens. As a result, compensating eyepieces have build-in lateral chromatic error and are not, in themselves, perfectly corrected. In 1976, Nikon introduced CF optics, which correct for lateral chromatic aberration without assistance from the eyepiece. Newer infinity-corrected microscopes either correct chromatic aberration fully in the objective or take advantage of the system objective plus tube lens to render a fully corrected intermediate image.

Finally, it is interesting to note that the human eye has a substantial amount of chromatic aberration. Fortunately, we are able to compensate for this artifact when the brain processes images, but it is possible to demonstrate the aberration using a small purple dot on a piece of paper. When held close to the eye, the purple dot will appear blue at the center surrounded by a red halo. As the paper is moved farther away, the dot will appear red surrounded by a blue halo.

The future of FSOC looks promising and ongoing research and development is targeting enhancing system performance and expanding its applications.

Opticalaberration

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, which can be used to select a new specimen. The Image Position slider is utilized to control the tutorial by shifting the focal plane along the optical axis of the virtual lens system illustrated as a ray trace pattern on the right-hand side of the applet. The initial position of the slider is the center of the focus range. When the slider is moved to the left, the focal plane is shifted to longer (red) wavelengths and the microscope image and point spread functions simultaneously change to illustrate the effect of chromatic aberration. Moving the slider to the right shifts the focal plane to shorter (blue) wavelengths and produces corresponding changes in the microscope image and point spread functions. A set of radio buttons positioned beneath the ray trace pattern allows the visitor to toggle between an uncorrected virtual optical path and one that has been corrected to simulate achromatic, fluorite, or apochromatic optical elements. Note that clicking on and activating a radio button other than the one labeled Uncorrected will deactivate the Image Position slider.

As FSOC evolves, it is poised to play an increasingly significant role in various sectors—from space exploration to medical devices, and 5G networks to next-generation data centers. As advances in IR sensor technology leverage its unique advantages, FSO technology has the potential to revolutionize connectivity across diverse environments to meet the growing demand for high-speed, secure, and efficient communication systems.

Until recently, the sensitivity of 1550-nm APDs was limited by the internal noise generated within the devices, which limited the range and data rates achievable in FSOC systems. But in early 2024, noiseless InGaAs APDs were announced by Phlux Technology. These sensors, which add an antimony alloy to the compound semiconductor fabrication process, can detect exceptionally low levels of light down to single photons, which helps maintain signal integrity over long distances and under varying atmospheric conditions. They advance the performance of FSOC systems, offering 12x the sensitivity of traditional InGaAs APDs, which represents a potential 10.79-dB improvement in link efficacy before other noise sources such as amplifiers are considered (see Fig. 4).

The technology also shows great potential for intra-data-center communication, where its low latency and high bandwidth are attractive attributes.

In 2024, a collaborative European initiative was launched to enhance Earth-to-FSOC technology. This project, supported by the European Space Agency (ESA), brought together a specialized sensor manufacturer, Phlux Technology, Airbus Defense and Space, and the University of Sheffield (U.K.). The primary objective of the ongoing work is to develop more efficient FSOC satellite terminals. The mid-range target is reliable 2.5-Gbit/s communication links operating at an IR wavelength of 1550 nm with low Earth orbit (LEO) satellites. The satellites typically orbit at altitudes up to 2,000 km above Earth's surface. Looking further ahead, the team aims to create systems capable of consistent 10-Gbit/s transmission rates. A radiation-hardened, integrated IR sensor and amplifier will be developed for the system.

Most analysts predict strong growth for the FSOC market driven by growing demand for LTE networks, a desire for an alternative to RF technology, the requirement for more secure high-speed communications, and to address the challenges of last mile connectivity in optical networks—for fiber-to-the-premises (FTTP) and fiber-to-the-home (FTTH) installations.

In terrestrial applications, FSOC promises to be a cost-effective alternative to fiber-optic systems for high-speed connections in multipoint scenarios, such as large organizations or remote areas. Furthermore, its high capacity and low latency make it a promising technology for 5G backhaul links. Some hybrid systems are evolving that combine RF and FSOC technologies to provide greater reliability by adapting to varying weather conditions and interference levels.

Atmospheric conditions have, until recently, been a limiting factor in distance and bandwidth capabilities in FSOC. But techniques to mitigate these, such as adaptive optics, are now used and result in improved data rates for a given bit error rate (BER).

Sphericalaberration

These IR sensors are crucial components in FSOC receivers. Better sensors detect weaker signals, which enable development of faster, higher-bandwidth links with reduced latency. In Earth-to-satellite communications, they also improve performance because higher sensitivity allows maintenance of link integrity over a wider angle as the satellites pass overhead—resulting in longer periods of operation.

The technology leverages the visible and infrared (IR) light spectrum, in contrast to the RF spectrum used by most wireless systems. This offers significant benefits, not least a vast unlicensed spectrum in which FSOC systems typically operate at near-infrared (NIR) wavelengths between 700 and 1600 nm.

Modern microscopes utilize this concept, and today it is common to find optical lens triplets made with three lens elements cemented together, especially in higher-quality objectives. For chromatic aberration correction, a typical 10x achromat microscope objective is built with two lens doublets. Many fluorite objectives, which are intermediate in correction between achromats and apochromats, are built using fluorspar (or a similar formulation) combined with an appropriate glass element to form a doublet that is achromatized at three wavelengths. Apochromat objectives usually contain two lens doublets and a lens triplet for advanced correction of both chromatic (up to four wavelengths) and spherical aberrations.

FSOC operates on a straightforward principle: the transmission of modulated laser light through the air between a transmitter and receiver. This process involves lenses or parabolic mirrors to narrow and project the light toward the receiver where it is captured and focused onto an optical detector, typically a semiconductor photodiode. The optical signal is converted into an electrical one for processing (see Fig. 2).

In addition to longitudinal (or axial) chromatic aberration correction, microscope objectives also exhibit another chromatic defect. Even when all three main colors are brought to identical focal planes axially (as in fluorite and apochromat objectives), the point images of details near the periphery of the field of view are not the same size. This occurs because off-axis ray fluxes are dispersed, causing the component wavelengths to form images at different heights on the image plane. For example, the blue image of a detail is slightly larger than the green image or the red image in white light, resulting in color ringing of specimen details at the outer regions of the field of view. Thus, the dependence of axial focal length on wavelength produces a dependence of the transverse magnification on wavelength as well. This defect is known as lateral chromatic aberration or chromatic difference of magnification. When illuminated with white light, a lens with lateral chromatic aberration will produce a series of overlapping images varying in both size and color. In a non-corrected system, the blue component at 436 nanometers may be imaged 1.4 percent larger than the red component at 630 nanometers. Lateral chromatic aberration is greater for objectives of short focal length and can range from 1.1 to 1.9 percent of the radial distance from the optic axis.

The space sector has recognized the potential of FSOC technology, particularly for satellite communications. The technology can be used for both earth-to-satellite and satellite-to-satellite communication. In the latter scenario, its performance is particularly impressive because atmospheric factors do not impede performance and in space, data rates can scale into the terabit-per-second (Tbit/s) range. As a result, the reduced weight, lower power consumption, and higher data rates of FSOC make it a particularly attractive alternative to RF systems in these applications (see Fig. 3).

The integration of FSOC technology with unmanned aerial vehicles (UAVs) could provide high-bandwidth communication in remote areas or during emergencies. For these applications, vertical-cavity surface-emitting lasers (VCSELs) may be preferred instead of APDs.