We welcome readers to this special section on long-range imaging. The purpose is to explore technologies that operate at or beyond the boundaries of current range performance across land, sea, air, and space. Though possibilities for this special section were vast, it would appear that atmospheric turbulence and refractive bending effects are chief among concerns for long-range imaging researchers, comprising 8 of 10 papers in the special section. The guest editors had similar perceptions and recognized the lack thus far of a venue to publish works that address this interesting and challenging problem. We are therefore glad of the response to this call, grateful for the thoroughness of the reviewers, and hope that Optical Engineering becomes a regular home for this technology area.

Image degradation due to turbulence and bulk refractive effects are consequences of variations in the refractive index of air. Random variations on a time scale of a few milliseconds and on spatial scales ranging from a few millimeters to tens of meters gives rise to turbulence. The observable effect of turbulence near an imaging aperture is blur along with global apparent motion, while turbulence that occurs closer to the target degrades imagery though space-varying warping and distortions. Turbulence, which is driven primarily by temperature fluctuations, varies significantly with time of day, altitude, wind speed, and a host of other environmental factors along the imaging path. The refractive index of air also exhibits variations over much longer and larger temporal and spatial scales. Variations on these scales tend to displace and stretch imagery, the effect of which is commonly experienced as a mirage. Modeling, measuring, and mitigating these effects have been enduring research topics since the foundational work of V. I. Tatarski in the 1960s.¹

Four of the papers in the special section deal with simulating the effects of turbulence and bulk refraction on imagery. Hardie et al. present an approach to simulating anisoplanatic imagery. This includes a new method for defining phase screen parameters and new validation techniques based on the statistics of apparent motion in the scene. The paper by Basu applies combined numerical weather mesoscale and ray-tracing models to explain a case of imaging the Milwaukee skyline from over three times the range set by the geometric horizon across Lake Michigan. Anzuola and Gladysz report on their new method to generate fast and accurate turbulent phase screens using a weighted sum of Karhunen–Loève polynomials that faithfully reproduce Kolmogorov spatial and temporal statistics. Lachinova et al. provide an extensive comparison of conventional Monte-Carlo wave optics turbulence simulations with their much more computationally efficient brightness function approach.

There are also four additional papers on measuring and/or mitigating turbulence effects on imagery. McCrae et al. discuss an approach for estimating the atmospheric coherence diameter from wavefront tilt variance due to turbulence using time-lapse imagery. Hardie et al. present an approach for restoration of imagery in the presence of anisoplanatic conditions that weights the aggressiveness of the restoration using image-based estimates of coherence diameter and confidence in distortion corrections. Kelmelis et al. draw on experience to survey the many considerations that must go into real-time turbulence restoration of imagery and, in a related paper, Kozacik et al. present a comparison of turbulence image restoration algorithms using the bispectrum speckle processing, lucky-region fusion, and blind deconvolution techniques.

The special section also includes two papers tackling other aspects of long range imaging. Hart et al. design and build a prototype multiaperture Fizeau interferometer for space-based infrared imaging. This prototype features carbon fiber reinforced polymer primary optics and a factor of three reduction in volume over equivalent conventional telescopes. Finally, the paper by Smith lays down a theoretical argument for substantially increasing the range of laser radars through the application of a quantum Bell state system.

This vast area has many unanswered or unrefined aspects, and we hope that beyond the works presented here, authors will consider publishing on the hot topics or imaging metrics that are applicable to turbulence-degraded imagery, how to handle the inherent lack of truth data in the imagery, novel imaging apparatus, and paradigms related to turbulence strength and imaging through turbid media, to name but a few. We look forward to reading future works in this journal addressing these and other facets of the problem that is long-range imaging.