Graded-index optical elements made from a three material blend reduce chromatic aberrations
April 03, 2017
By ARL Guest Author Dr. Joseph N. Mait
When physics students are introduced to imaging, it is typically with reference to a single-lens imaging system. See Fig. 1. Optical rays, drawn as straight lines, show that a lens is capable of reproducing an object that exists in space.
Why then are real optical systems, like the camera lens represented in Fig. 2, so much more complex?
The simple answer is lens performance is limited by the material used to produce the lens as well as the shape and size of the lens. No lens is capable of producing an exact replica of a point.
Deviations of an imaged point from its ideal are referred to as aberrations. The more severe the aberrations, the larger the image of an object point. This, in turn, reduces the system's resolving power, i.e., the minimum distance at which two points on the object can be distinguished.
Aberrations generated by the shape and size of the lens are geometric. Aberrations generated by the lens' material properties are chromatic, i.e., lens performance is dependent upon the color of light incident upon it. This latter property is manifested in the material's index of refraction n(λ), where λ is the wavelength of light.
Rainbows produced when sunlight passes through rain showers and through glass are the most vivid examples of the dependence of a material's refractive index on wavelength. The angle that a ray is bent when it encounters a material surface depends upon the refractive index for the incident wavelength. Since sunlight contains all visible wavelengths and each wavelength sees a different index, the rainbow results from each wavelength being deflected by a different amount.
The change in refractive index across a band of wavelengths is called dispersion and is measured by the Abbe number V,
where λ1 and λ2 define the range of wavelengths and λ0 is the center of the waveband. Highly dispersive materials, i.e., materials whose refractive index changes a large amount across the waveband, have small Abbe numbers. Low dispersion materials have high Abbe numbers.
Putting aside the aesthetic appeal of a rainbow, if the goal is to create a near-perfect representation of a scene, the presence of a rainbow around edges or points in an image is unacceptable. Since the 1730s, the conventional approach to correcting chromatic aberrations is to use two lenses constructed from different materials. This combination of two lenses is known as an achromatic doublet. See Fig. 3. The positive lens, i.e., the lens with the convex profile, is constructed from the material that has the larger Abbe number of the two materials. The negative lens, the one with a concave profile, is constructed from the material that has the smaller Abbe number.
However, in the past few decades, an alternate solution to creating an achromatic lens has evolved that involves blending two materials and changing their volume ratio to create a spatial change in refractive index. The resulting structure is referred to as a graded-index (GRIN) lens. This solution is attractive for the simple reason that replacing two lenses with one halves the volume and weight of an achromatic lens system. For handheld imagers, e.g., binoculars and rifle scopes, this savings in size and weight reduces the burden on the individuals carrying them.
In a recent article, staff from the Army Research Laboratory and the Navy Research Laboratory published a procedure to design achromatic GRIN lenses.1 They also developed criteria for selecting material pairs that are well suited to achromatic design. A conventional achromatic doublet requires one material that has a large index and a large Abbe number, and a second one that has a lower index and lower Abbe number. In contrast, an achromatic GRIN lens requires two materials with refractive indices that are nearly equal but with Abbe numbers that are very different.
This initial work led to a theoretical study on the advantages of using three materials to design an achromatic GRIN lens.2 Indeed, blending three different materials allows a designer to control both the refractive index and the dispersion over a region in space. This additional degree of control allows a designer to reduce further the impact of color on optical performance.
The advantage of this control was highlighted in a study of deflectors. See Fig. 4. The conventional means for deflecting light is a prism. Since the angle at which light is deflected is a function of the refractive index, white light incident upon a prism produces a rainbow of colors; each wavelength is deflected at a slightly different angle. A GRIN deflector deflects light due to a linear change in refractive index.
The study examined the chromatic deflection properties of a conventional prism, a GRIN deflector made from a material pair, and a GRIN deflector made from a material triplet. The triplet was a mix of the conventional material and the binary GRIN blend. The height and width of each deflector were equal and the same for each type of deflector considered.
The results of the study are shown in Fig 5. The prism deflects visible light over a 1.5 degree spread of angles, from 41 to 42.5 degrees. The large angular offset is due to the prism's wedge shape. Note that the binary GRIN deflector exhibits a larger range of deflection, 2.5 degrees, from 12 to 14.5 degrees. In contrast, the triplet GRIN deflector exhibits only a small range of deflection angles, about 0.25 degrees, from 12.25 to 12.50 degrees. Thus, the triplet blend displays almost no rainbow of colors, whereas the binary blend displays a rainbow with the largest spread of the three.
By examining optical deflection through a GRIN element, the advantage of optics blended from a triplet of materials to control and improve chromatic performance is apparent. Preliminary work by the ARL-NRL team on achromatic lens design indicates it is possible to reduce chromatic aberrations considerably using a triplet blend of materials.
The study's conclusions, drawn from analysis and simulation, indicate the potential advantages of blending three materials to control chromatic aberrations. Nonetheless, considerable effort remains before this potential can be realized practically.
Most important is not just the demonstration of a ternary material blend with prescribed index and dispersion profiles, but also the demonstration of a fabrication process with sufficient precision and robustness to control the volumetric ratio of three materials. This is imperative if the process is to be commercially viable. Further, one must demonstrate that the improvement in chromatic control provided by a ternary blend of materials is sufficiently significant to outweigh the costs of its manufacture.
This imperative, to develop a cost-effective method to manufacture ternary blend GRIN elements on a large scale, can benefit the Warfighter by providing current imaging capabilities in a smaller package or by enhancing the capabilities of present imagers, for example, increasing their field-of-view or range, without increasing their size or weight.
1 J. N. Mait, G. Beadie, P. Milojkovic, and R. A. Flynn, "Chromatic Analysis of a First-order Radial GRIN Lens," Opt. Express 23, 22069-22086 (2015). (doi: 10.1364/OE.23.022069)
2 J. N. Mait, G. Beadie, R. A. Flynn, and P. Milojkovic, "Dispersion Design in Gradient Index Elements using Ternary Blends," Opt. Express 24, 29295-29301 (2016). (doi: 10.1364/OE.24.029295)