Chromatic Aberrations
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: image distortions caused by wavelength-dependent optical effects
More general term: optical aberrations
DOI: 10.61835/1u3 Cite the article: BibTex plain textHTML Link to this page LinkedIn
Chromatic aberrations are optical distortions – encountered in imaging optics, for example – which are caused by wavelength-dependent (actually frequency-dependent) effects. Most frequently, they arise from frequency-dependent refraction at air–glass interfaces of optical lenses. However, chromatic aberrations can also occur in the context of prisms and diffractive optics, for example.
Note that reflective optics generally do not exhibit chromatic aberrations. This holds also for dielectric mirrors, despite the wavelength dependence of the refractive index of the used multilayer materials. That wavelength dependence can only affect the reflectance and related aspects such as chromatic dispersion, but not the angular orientations of optical wavefronts. The absence of chromatic aberrations in reflective optics has already been recognized by Isaac Newton, who therefore developed the first reflecting telescope, called the Newtonian telescope in 1668.
Axial and Transverse Effects
A frequently encountered phenomenon is that the axial (longitudinal) position of a focus or a sharp image depends on the optical wavelength; such distortions are called axial chromatic aberrations. They are related to the wavelength dependence of the focal length (and thus the dioptric power) of an optical system. In photography, their impact can be reduced by working with an aperture of smaller size, i.e., a higher f-stop number.
As an example case, we consider collimated laser beams with an initial beam radius of 1 mm, hitting a biconvex lens made of BK7 glass. Both lens surfaces are assumed to have a radius of curvature of 103 mm. Due to the moderate chromatic dispersion of that crown glass, the focus positions vary substantially (see Figure 1) – the deviations are of the order of the Rayleigh length in this case.

Note that the also observed variation of beam radius in the focus is essentially not caused by the material dispersion, but by diffraction.
Figure 2 shows the same for an achromatic doublet made from BK7 crown glass and SF2 flint glass with a numerically optimized design. The wavelength dependence of the beam radius is essentially not caused by the material dispersion, but by diffraction.

There are also so-called transverse aberrations, denoting the wavelength dependence of transverse positions e.g. of image details. They can arise from the wavelength dependence of the image magnification or of distortions. Such effects do not occur at the center of an image and generally increase with the distance from that center. (In contrast, axial aberrations affect the whole image.) An increased f-stop number does not reduce transverse aberrations.
Use of Common Reference Wavelengths; the Abbe Number
Traditionally, chromatic aberrations in the visible spectral region are quantified based on measurements at three wavelengths:
- <$\lambda_\textrm{F}$> = 486.1 nm (blue Fraunhofer F line from hydrogen)
- <$\lambda_\textrm{D}$> = 589.2 nm (orange Fraunhofer D line from sodium)
- <$\lambda_\textrm{C}$> = 656.3 nm (red Fraunhofer C line from hydrogen)
These wavelengths span much of the visible spectral region, and the middle one (the D line) lies in the region of maximum sensitivity of the human eye. The refractive indices of the material at these wavelengths are called <$n_\textrm{F}$>, <$n_\textrm{D}$> and <$n_\textrm{C}$>, respectively. In some cases, somewhat different wavelength values corresponding to other Fraunhofer lines are used, e.g., 480.0 nm (F' line), 587.6 nm (d line) and 643.9 nm (C' line); note that light with some wavelengths is easier to produce in gas discharge lamps than other wavelengths.
An important parameter in the context of chromatic aberrations is the Abbe number, which is defined as
$${\nu _{\rm{D}}} = \frac{{{n_{\rm{D}}} - 1}}{{{n_{\rm{F}}} - {n_{\rm{C}}}}}$$Obviously, the Abbe number becomes small (rather than large) for materials with a strong wavelength dependence of the refractive index. Glasses with a relatively low Abbe number of less than 50 (i.e., with relatively strong dispersion) are called flint glasses, whereas glasses with a higher Abbe number are crown glasses. Typically, flint glasses have relatively high refractive indices, whereas crown glasses exhibit lower values. One might think that one should avoid the use of flint glasses to obtain low chromatic aberrations; in reality, however, proper combinations of crown and flint glasses are often used for realizing achromatic optics.
Calculation of Chromatic Aberrations
Abbe numbers appear in various formulas for the calculation of optical aberrations, e.g. of an axial mismatch of focus or image positions at certain wavelengths. Such equations can then also be used to calculate parameter combinations for which certain chromatic aberrations vanish (→ achromatic optics). Note that particularly for various kinds of transverse chromatic aberrations, related to the wavelength dependence of various types of imaging distortions, the required equations can become relatively complicated. Therefore, the optimization of optical systems often requires sophisticated numerical optimization strategies.
Of course, calculations based on only three optical wavelengths cannot provide complete information on chromatic aberrations over the whole visible spectral region or even on other spectral regions; the optimization of optical systems often requires one to take into account refractive index data for additional wavelength values.
Even achromatic optics typically achieve a perfect suppression of axial and/or transverse chromatic aberrations only for two or three different wavelengths, while exhibiting more less pronounced distortions at other wavelengths. Note also that a comprehensive optimization of an optical system requires a compromise between different qualities, of which the strength of chromatic aberrations is only one.
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Suppliers
The RP Photonics Buyer's Guide contains 71 suppliers for achromatic optics. Among them:
Ecoptik

Ecoptik offers achromatic coated lenses which are used to minimize spherical and chromatic aberrations. They are ideal for a range of applications, including fluorescence microscopy, image relay, inspection, or spectroscopy. Such a lens is often made by either cementing two elements together or mounting the two elements in a housing.
The achromatic coated lens can also be called an achromatic doublet lens or achromatic cemented lens. If you want to know more information, please contact us.
Shalom EO

Hangzhou Shalom EO is a professional supplier of a series of achromatic optics, including achromatic waveplates, super-achromatic waveplates, and achromatic doublet lenses.
Shalom EO offers off-the-shelf and custom achromatic waveplates and super-achromatic waveplates. Our standard diameter 25.4 mm achromatic waveplates are composed of one quartz plate and one MgF2 plate cemented together or with an air gap in between the plates, offering flat retardation response of a quarter wavelength or a half wavelength over three optional wavelength ranges including 450–650 nm, 690–1200 nm, and 900–2000 nm, while other custom wavelength ranges and retardation values are also available. The air spaced achromatic waveplates have an outstanding damage threshold greater than 500 MW/cm2, suitable for high power applications.
Shalom EO’s standard super achromatic waveplates consisting of six quartz and MgF2 plates cemented together deliver ultra-stable retardation over extensive spectral regions, 325–1100 nm and 600–2700 nm (for quarter waveplates), or 310–1100 nm and 600–2700 nm (for half waveplates), in addition to other custom wavelength ranges and retardation values, making our super achromatic waveplate excellent for the altering of polarization state in multi-spectrum context.
Shalom EO’s achromatic lenses or achromatic doublet lenses are available in stock and custom versions, as for the stock versions, selection: an abundant selection of focal lengths 7.5 mm to 1000 mm (for positive achromatic doublet lens) and –100 mm to –20 mm (for negative achromatic doublet lens) are accessible with the lenses in standardized sizes to ensure seamless integration into various optical systems. Coating options include 350–650 nm, 650–1050 nm, 1050–1580 nm AR coatings, or other custom coatings.
Knight Optical

Knight Optical's offers achromatic lenses used to minimise chromatic and spherical aberrations. These achromatic doublet lenses are available in focal lengths up to 500 mm and are ideal in imaging applications, laser collimation, and as objective lenses in telescopes and other instruments. Custom achromatic lenses are available upon enquiry including triplet lenses and additional coatings. We also offer achromatic waveplates suitable for 450–680 nm, 700–1000 nm, 950–1300 nm, and 1200–1650 nm wavelength ranges, with applied AR coatings for consistent phase retardation over the entire wavelength.
Sinoptix

We offer custom doublet lenses manufacturing solutions. We perform precise gluing and coating in order to guaranty a high quality of achromatic optics.
DayOptics

Dayoptics has specially designed achromatic waveplates, containing two pieces of plates. They are similar to zero-order waveplates, except that the two plates are made from different materials, such as crystal quartz and magnesium fluoride. The bandwidth of such achromatic waveplates is very wide, meaning a nearly constant retardance over a large range of wavelength.
Schäfter + Kirchhoff

We offer fiber couplers like the laser beam couplers series 60SMS/60SMF or the fiber collimators series 60FC or series 60FC-SF with super fine-focussing mechanism with achromatic and even apochromatic optics (corrected for 400 – 640 nm).
EKSMA OPTICS

EKSMA Optics offers achromatic air-spaced waveplates made from crystal quartz and MgF2 plates mounted with an air gap. Achromatic waveplates feature nearly constant retardation over a broad wavelength range.
Shanghai Optics

Shanghai Optics offers a large variety of custom achromatic lenses for our customers including achromatic spherical and aspherical lenses, achromatic singlets, doublets and triplets. Combined with one of our advanced AR coatings (covering 400–700 nm, 650–1050 nm, 1050–2500 nm), these optimized lenses are ideal for ensuring high resolution image quality and durability. With our in-house state-of the-art metrology and professional testing personnel, Shanghai Optics is able to provide a full range of inspection reports and CoC (Certificate of Conformance) for full optical characterization such as surface quality, dimensions, centricity, coating transmittance/reflectance (with SHIMADU UV3600 spectrophotometer), and overall/partial surface accuracy (with 6-inch ZYGO interferometer). FAI inspection reports are available upon request.
Avantier

An achromatic lens, often called an achromat, is a type of optical lens capable of correcting chromatic aberration, a distortion that occurs when glass splits white light into multiple wavelength components.
2021-12-24
What is the origin of chromatic aberrations of zone plates?
The author's answer:
That is the wavelength dependence of phase changes, as in other diffractive optical elements.