Key Points:
- Extended depth of focus (EDOF) lenses intentionally stretch the longitudinal focal region, which can be valuable in imaging, projection, and laser-based systems where sensitivity to defocus is a performance drawback or yield limitation during packaging
- Metasurfaces are a platform for EDOF optics because they offer high spatial resolution in the phase profile and can often combine multiple optical functions into a single surface
- EDOF components entail several performance tradeoffs, including reductions in contrast and the introduction of sidelobes, but with the right design approach, those tradeoffs can be worthwhile and can be engineered effectively using inverse-designed meta-optics
Overview
All focusing lenses have limits on the transverse and longitudinal size of their focal spots. Typically, designers aim to make these spot sizes as compact as possible in order to increase the resolving power of the system, but in some cases, it can be beneficial to elongate a focus axially (i.e., to extend its depth of focus). Components that fall under this category are called extended depth of focus lenses.
The design of these components can be based on closed form sag profiles or phase functions, or they can alternatively exploit inverse design algorithms to yield very large enhancements in depth of focus of potentially 10-100x or more. While other types of components can realize extended depth of focus, meta-optics offer a compelling platform in terms of degrees of freedom and their ability to maintain an extended focal range at relatively high NA, owing to their enhanced space-bandwidth product relative to coarser pitch diffractive optical elements
Optical designers often want to make focal spots as compact as possible, but an axially extended focus can be useful
A lens (metalens or otherwise) is typically designed to focus light down to as compact a spot as possible. In the transverse plane, this spot size directly influences the resolving power of the system, with a smaller spot enabling finer resolution in imaging systems. There are well-established limits on the size of this spot (e.g., the Abbe limit), with the smallest size being referred to as the diffraction-limited spot size.
Longitudinally (i.e., along the optical axis), there are also constraints on the “length” of a focal spot. There is a range over which you can consider the system to be in focus, and this is usually a multiple of the wavelength, with higher f/# systems exhibiting elongated focal spots. This is why “stopping down” in photography helps to increase depth of field, by reducing aperture size you are increasing the f/# which increases the extent of the focal spot longitudinally. This means that the range of object distances over which a sharp image is formed at the image plane is increased.
An extended depth of focus (EDOF) lens is a lens that by design exhibits a longitudinally elongated focal spot
An EDOF lens is a specialized optic that by design has an intentionally elongated focal zone for its given application. The magnitude of this extension can vary considerably depending on the design methodology and use case, with modest extensions on the order of 0.5-2x being more straightforward from a design standpoint, often based on closed form sag profiles or phase functions. Enhanced performance is often achievable with inverse design algorithms, and very large increases in depth of focus of 10-100x have been achieved experimentally.
EDOF optics are not a new concept, and they did not come about from a single domain of optical design. Over the years, designers have looked for ways to make imaging less sensitive to defocus, whether by reducing the effective aperture, using annular pupils or axicon-like elements, or intentionally introducing spherical aberration to stretch the focal region, often with some tradeoff in throughput, contrast, or lateral resolution. Ophthalmic lens designers were already developing presbyopia-correcting and multifocal intraocular lens (IOL) concepts by the 1980s. More recently, true EDOF IOLs were developed to produce an elongated focal region rather than several discrete focal points. EDOF IOLs have relied on diffractive, refractive, and hybrid elements over the years.
A separate shift came in the 1990s with computational imaging approaches such as wavefront coding, most notably the work of Cathey and Dowski, where a phase mask and digital reconstruction were used together to make blur less sensitive to defocus over a larger axial range. Today, meta-optics continue this development by encoding EDOF behavior into ultrathin nanostructured surfaces, sometimes alongside computational reconstruction, enabling compact imaging systems with functionality that previously required thicker or more complex optical assemblies.
Metasurfaces offer a versatile platform for engineering EDOF lenses
As subwavelength-pitch diffractive optics, metasurfaces offer more degrees of freedom than their coarser pitch diffractive optical element counterparts. In use cases where a high NA is necessary, finer pitch becomes necessary. As a platform, metasurfaces enable wavefront transformations at higher space-bandwidth product. In practice, this means that you can engineer focusing behavior with finer spatial resolution. For EDOF systems, this is equally true; they can help to maintain both a compact transverse beam and an enhanced longitudinal extent. While refractive aspheres also can support EDOF behavior, manufacturing complexity has the potential to be a bottleneck, with different surface slopes poentially requiring retooling or changes in equipment configuration. With metasurfaces, it typically only requires changing the mask layout to accommodate a different EDOF design.
This ability to support near-arbitrary phase masks can also facilitate collapsing multiple surfaces into one. While many EDOF systems rely on a radially symmetric lens paired with a separate element that will extend the depth of focus, with a metasurface these phase terms can often be collapsed into a single surface, and there are numerous experimental demonstrations of single-surface EDOF meta-optics. In these cases, the phase function comprises a power term added to a an extra phase modulation or aberration term that intentionally elongates the focus about the nominal focal plane.
Axicons can be considered a type of EDOF, but both can have distinct use cases
An axicon is specialized component that by design is radially symmetric and is intended to generate an approximation of a Bessel beam that is non-diffracting over a wide range. In practice, it produces an elongated “focus” over a wide range and (depending on who you ask) could be considered to be a type of EDOF lens. An axicon is essentially a beam deflector phase that has been turned into a radially symmetric version of itself, and the resulting interference pattern produces an elongated needle-like “focus”, which in the far-field looks like a ring. This ring-like far-field behavior and the specific intensity profile produced by an axicon has applications in laser processing and some imaging use cases. EDOF lenses in general do not produce this type of far-field pattern (it will depend on the exact phase profile) and there are often more design knobs to control the focal extent (both longitudinal and transverse) compared to the analytical form of an axicon. An axicon, however, is often a reasonable initial condition for designing an EDOF.
EDOF lenses have many practical use cases in both imaging and projection systems.
EDOF lenses have a number of practical applications. In imaging systems, the depth of focus is often a critical parameter that plays a role in lens assembly and sensor integration. If the depth of focus is quite narrow, and the opto-mechanical assembly has coarse tolerances, it’s not uncommon for integration to require an active alignment procedure, entailing live feedback during alignment to determine the best focal positions before UV curing of a resin to fix a lens assembly in place relative to the sensor. This is a common procedure, but doing so costs more than assemblies that can be packaged without requiring active alignment. Passive alignment of components, however, can limit yield, partly because it can be challenging to ensure the back focal length is set within the lens’ depth of focus. If set outside the depth of focus, there can be an unacceptable degradation in resolution. With an extended depth of focus, even a more modest enhancement of 0.5-2x can mitigate alignment complexity, enhancing yield in passively aligned camera systems.
Beyond mitigating alignment complexity during camera assembly, an EDOF can also be used to extend depth of field on the object side. Instead of relying on an autofocus mechanism utilizing a varifocal lens (e.g., via mechanical actuation with voice coils or via tunable liquid lens designs), one can leverage an EDOF to maintain an in-focus image over an enhanced object distance range.
In diffractive and meta-optical systems, EDOF capability also provides a means for circumventing chromatic aberration. Within the focal range of an EDOF, the system’s point spread function can exhibit a high degree of invariance as a function of wavelength, which can facilitate encoding spatial information into a computationally invertible blur kernel using standard deconvolution routines.
In non-imaging and projection systems, EDOF can also bring a number of advantages, especially in manufacturing applications. In laser processing, widely used for various cutting, engraving, and additive processes, both spot size and depth of focus are key parameters that directly impact the volume over which the incident beam interacts with the irradiated material, influencing the achievable resolution and throughput. Many similar considerations also apply for lithography systems. Analogous to the case of back focal length alignment for camera systems, depth of focus in projection systems can also influence the stage precision utilized for alignment of sources, optics, wafers, and masks.
Elongating the focal zone comes with tradeoffs in spot size and efficiency, but in some applications these tradeoffs are worth it
While promising for a number of applications, any designer considering utilizing EDOF meta-optics for their use case should be aware of several key tradeoffs. Meta-optics are of course wavelength sensitive, which will induce a longitudinal chromatic focal shift that will change the behavior of the system. Fortunately, owing to the EDOF itself, the impact of this chromatic focal shift may be tolerable because this form of defocus is exactly the type of aberration that EDOF is intended to mitigate (i.e., there will still be a chromatic focal shift, but because the focal line is already extended, there is a high likelihood there will still be a sharp focus at the intended image plane). Beyond chromatic behavior, the achievable spot size and MTF are other key considerations. In modifying the phase mask to extend the focus longitudinally, the spot size is necessarily increased, or some of the energy is shifted to sidelobes in the transverse focal profile. If the encircled energy in the focal plane must be highly confined within the diffraction-limited region, then an EDOF may be a poor fit; however, if some sidelobes are tolerable and the benefits of the longitudinal elongation of the central focal lobe are highly useful in the target application, then this tradeoff can be worth it.
How does one design an EDOF metalens?
As touched on earlier in this article, there are a number of closed form solutions for extended depth of focus optics. These include phase mask designs such as the log-asphere, shifted axicon, SQUBIC, and cubic phase profiles. The cubic phase profile is worth noting as an important phase profile in EDOF research. If a monomial functional form of a phase profile is assumed, it was mathematically proven by Cathey and Dowski that insensitivity to misfocus (i.e., functionally equivalent to an extended depth of focus) can only be achieved if and only if the phase function is a cubic phase. In practice, however, a monomial function is overly restrictive, and cubic phase elements can introduce asymmetric artifacts in resulting images based on these components.
Oftentimes, inverse design algorithms applied to higher order polynomial functions can provide superior EDOF performance with very large enhancements in depth of focus of 10x-100x or more. These inverse design algorithms often exploit adjoint or automatic differentiation techniques to apply gradient-descent based optimization of phase masks, which are highly tailorable across aperture sizes, target wavelength(s), and f/#. Phase masks are then converted into a layout of meta-optical nanostructures for fabrication in alignment with best practices for meta-atom design and process constraints.
Summary
EDOF lenses are designed to intentionally elongate the focal region, and while the concept has existed for decades across several branches of optics, meta-optics provide a particularly powerful platform for realizing these components. Compared to conventional refractive or coarse-pitch diffractive approaches, metasurfaces offer finer spatial control of the wavefront, making it possible to engineer EDOF behavior at relatively high numerical aperture and, in many cases, collapse what would otherwise require multiple optical surfaces into a single flat element. This can be useful in imaging, projection, and manufacturing systems, where an extended focal range can relax alignment sensitivity, increase usable object depth, or help manage chromatic aberrations (especially in computationally corrected imaging systems). These benefits do not come for free, however, as extending the focus typically involves tradeoffs in spot size, sidelobes, efficiency, and contrast. In practice, the decision to use an EDOF, as well as the type of EDOF design depends on the application, and inverse design methods give designers a flexible means to balance these tradeoffs while achieving EDOF performance beyond what is typically possible with simple closed-form phase profiles or existing refractive alternatives.
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