September 25, 2023
In the intricate world of optics, few components play as crucial a role as the lens. Nestled at the heart of devices ranging from the commonplace eyeglasses to the expansive telescopes that gaze into the cosmos, lenses define the quality and clarity of our visual experiences. Lens design is at the heart of multifaceted domain of optical design - where we can explore its foundational principles, the meticulous design process, and the challenges that designers confront in this ever-evolving field.
At its core, a lens operates through the principle of light refraction or bending of light. The extent to which this light bends is contingent upon two primary factors: the lens's shape and the material from which it is constructed. Broadly categorized, lenses fall into two types: Concave and Convex Lenses. Concave, or diverging lenses spread out parallel rays of light due to their thinner centers and exhibit a virtual focus for a collimated beam. Convex, or converging lenses focus parallel rays to a real focus, in front of the lens.
Embarking on the journey of lens design commences with a clear demarcation of specifications. It is imperative to define aspects such as the focal length, the field of view, and the aperture size, alongside the lens's intended application. Following this, the designer is faced with the task of selecting the optimal material and determination of geometric constraints. Given that different optical materials possess distinct refractive properties, this choice is pivotal to the lens's eventual performance.
After defining specifications, the "focus" shifts to geometric optimization, which is essentially the art of tweaking the lens's curvature and potentially aspheric coefficients to ensure desired performance over some previously defined field. In order to determine how well a lens performs in an imaging applications, there must be a performance metric which defines the performance of a lens. The two most popular metrics are defined: Spot size and Wavefront Error.
The Spot Size can be defined by how tightly rays come to focus at a particular plane. But what this metric fails to capture are diffractive effects, which are present in the Wavefront Error. There are several methods to calculating the Wavefront Error, and one of which is calculation of Seidel Coefficients from the development of a paraxial system. Wavefront errors can be corrected for via two methods "Annihilation/Elimination" or "Balancing". Using Annihilation we can aim to develop a surface which does not contain a particular wavefront error contribution by choosing its geometric properties carefully. This method was the original method used by early lens designers, but it was quickly found that this method is typically more difficult than the more popular "Balancing" method. The "Balancing" method does exactly what it sounds like, which is taking a positive wavefront coefficient and balancing this out with a negative wavefront coefficient from some other surface. If all terms are balanced and the total wavefront error is zero, then the system is still limited by the diffraction limit which specifies the minimum spot size to be limited by the Airy disk. Which limits the minimum focus for a particular f/# to be 1.22 λ f/#. Where the f/# = EFL/EPD.
However, the challenges in lens design are not limited in just the realm of aberrations. Designers often find themselves walking the tightrope, trying to strike a balance between aberration content and other competing demands. A classic dilemma could involve choosing between a larger aperture, which allows for faster f/#'s but might exacerbate aberrations and potentially add many more elements or complexity to an optical design. Whereas a slower f/# system is typically comparatively simpler and thereby lower cost. Moreover, the relentless march of technology constantly pushes the envelope. As sectors like virtual and augmented reality burgeon, they bring forth novel demands, pushing lens design into uncharted territories. Adding to these complexities are the inherent limitations of materials, with some resisting easy molding or introducing undesirable color variations.
In conclusion, lens design, while rooted in optical physics and materials science, transcends into the realm of art. It is a dance of precision, a quest for perfection, and a testament to human ingenuity. With technology's relentless pace, it is a field poised for groundbreaking innovations, promising a future where our visual experiences are only limited by the boundaries of imagination.
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