Achromatic Optics – lens doublets, apochromats ...

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Author: The esteemed photonics expert Dr. Rüdiger Paschotta

Achromatic optics encompass optical devices or configurations designed to minimize chromatic aberrations, enabling usage across various wavelengths. Most commonly associated with optical lenses or objectives, achromatic optical lenses are often referred to simply as achromats. The fundamental characteristic of achromatism—the property of being largely unaffected by changes in wavelength—is vital for these optics. Historically, doublet and triplet achromatic lenses have found application since the eighteenth century.

Parameters frequently referenced in discussions on chromatic aberrations are derived from the refractive index values at specific reference wavelengths. These values are instrumental in calculating Abbe numbers, such as <$V_\textrm{D}$> or <$V_\textrm{d}$>, which appear in formulas meant to evaluate the strength of chromatic aberrations. These established equations enable practitioners to determine parameter combinations (e.g., concerning material choices, radius of curvature, and spacing between optical elements) that can lead to the cancellation of axial and/or transverse chromatic aberrations, typically at two or three different wavelengths.

Example: Achromatic Doublet Lens

Standard singlet lenses typically do not qualify as achromatic, exhibiting significant chromatic aberrations.

For illustration, consider chromatic aberrations in a simple lens. A biconvex singlet lens made from BK7 glass, with curvature radii of 103 mm on both surfaces, serves as our case study. The significant chromatic aberrations of this configuration are depicted in Figure 1, which assumes a collimated laser beam with a starting beam radius of 1 mm impacting the lens. It is evident that the focus position demonstrates considerable dependence on wavelength.

Figure 1:

The variation of beam radius around the focus for three distinct wavelengths in the visible spectrum.

(Note that employing a biconvex lens for focusing a collimated beam has implications for spherical aberrations, but this factor is outside the current discussion.)

Figure 2:

Configuration of an achromatic lens doublet, composed of a crown glass element on the left and a flint glass element on the right.

To enhance performance, an achromatic lens doublet may be employed, consisting of two components (illustrated in Figure 2): a biconvex lens crafted from BK7 and a concave-convex lens fashioned from SF2 (a flint glass). The essential goal is to achieve an effective focusing system through the integration of a strongly focusing lens and a less focusing lens that presents higher chromatic dispersion. Even though the defocusing effect of the second lens is lesser than that of the first, its chromatic aberrations can counterbalance those of the first lens.

The described doublet lens configuration has been optimized numerically to yield a focal length of about 100 mm (measured from the midpoint of the lens at <$z$> = 2 mm) within the wavelength range of 400 nm to 800 nm. The curvature radius on one side is fixed at 60 mm, while the remaining two curvature radii undergo optimization. It is essential that the inner radii of curvature of both lenses coincide to facilitate contact (e.g., cementing them together), creating a unified optical component and minimizing reflection losses. Note that achieving the specified focal length necessitates a greater curvature for the double lens owing to the defocusing influence of the flint lens.

Figure 3 illustrates the resulting focal points, demonstrating that the focus positions align closely for three considerably different wavelengths.

Figure 3:

Focus positions after passing through an achromatic lens, exhibiting similarity in focus locations across three distinct wavelengths.

The calculations were performed using the RP Resonator software.

Figure 4 reveals the remaining wavelength dependence of the focal length, indicating that while chromatic compensation is effective, it is not perfect.

Figure 4:

Wavelength dependence of the focal length for the achromatic lens. A broader array of achromatic lens designs exists.

Additional arrangements for doublet lenses include plano-concave designs (flat on one side) and negative achromats for defocusing applications. In certain scenarios, a lens doublet may not be cemented but merely placed within a shared housing (air-spaced doublets). Moreover, cylindrical lenses may also be created as achromats.

With adept configuration, parameters can be fine-tuned such that axial chromatic aberrations are nullified for two wavelengths (typically red and blue spectral ranges). By utilizing three different materials to form aspheric triplets, apochromatic lenses (apochromats) can be produced, where chromatic aberrations are minimized across three varied wavelengths. Although the distortions at other wavelengths are not necessarily constrained by this approach, they tend to be lesser for an apochromat at least within a designated wavelength range.

Like other lenses, achromats can be tailored to meet additional criteria such as mitigating spherical aberrations and coma in particular scenarios and can feature anti-reflective coatings. There are also both mounted and unmounted achromats available.

Additional reading:
Where to buy aspheric optics
Understanding Concave Cylindrical Mirrors: Applications and Benefits Explained

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Superior performance concerning remaining chromatic aberrations can be achieved with superachromatic lens designs, utilizing fluoride glasses and demanding precise manufacturing tolerances.

Different types of achromatic lenses may also employ diffractive optics. In this configuration, the operational principle diverges significantly from that of lens doublets.

Achromatic Prisms

Achromatic optical prisms are available which maintain a consistent deflection angle irrespective of the optical wavelength.

Optical prisms are often utilized to achieve a wavelength-dependent deflection angle for the light beam. On some occasions, a steady deflection angle is preferred across a broad wavelength spectrum. This objective can be met using a principle akin to that of an achromatic lens doublet, where two prisms formed from different optical materials can be combined, possibly resulting in a single prism.

Moreover, composite prisms can be engineered in such a way that the average deflection angle in a specified wavelength range remains near zero, yet substantial wavelength dependence is achieved. However, such a design would not be classified as achromatic.

Achromatic Waveplates

Achromatic waveplates also exist, albeit addressing a distinct type of chromatic distortion: the wavelength dependence of optical retardance, or the differences in phase shifts experienced by two perpendicular polarization directions. Devices of this nature can be created by combining materials with varying chromatic dispersion traits (e.g., quartz and MgF2), which may yield almost constant retardance over an expansive spectral range (spanning hundreds of nanometers).

Applications of Achromatic Optics

Imaging is the most significant application sector for achromatic optics.

The primary use of achromatic optics, particularly chromatic lenses, lies within imaging systems such as those employed in photography, microscopy, and video recording. Often, relying on merely a doublet lens is inadequate; more complex objectives composed of multiple lenses are essential. The conventional strategy to compensate for the chromatic aberrations in such systems does not involve constructing them solely from achromats. Instead, the goal is to devise an optical design where the overall chromatic aberrations are mitigated to an acceptable extent. Chromatic aberrations are generally one of several distortion types requiring minimization, while additional criteria such as compactness and light throughput add complexity to achieving an optimal compromise among all these requirements.

When managing very broadband light or light with distinctly varying wavelength components, the necessity for achromatic optics becomes apparent.

Achromatic optics are essential not only within the visible spectrum but also in infrared and ultraviolet light applications. Particularly significant dispersion compensation is essential in the ultraviolet region, while applications in the infrared may involve multiple disparate wavelengths or an extensive range. For instance, achromats are advantageous when focusing or collimating output from supercontinuum sources or in scenarios involving ultrabroadband ultrashort pulses.

Use of Reflective Optics

In various applications, chromatic aberrations may be circumvented by utilizing reflective optics instead of lenses. Curved mirrors, which serve to focus a beam, are inherently achromatic; this characteristic holds even for dielectric mirrors despite the wavelength variations imposed by multilayer materials.

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