Standardizing the resolution claims for coherent microscopy

Scientific development is founded on the use of precisely defined units and metrics. In microscopy, important metrics include the imaging system’s magnification, field of view, depth of field, and spatial resolution. While many of these are easy to define in an unambiguous manner, the measurement of resolution can be problematic. In this Commentary, we propose the adoption of a standard imaging target and outline good practice for reporting the spatial resolution of a coherent optical microscope (a system where the light emitted from the sample retains phase information with respect to the illumination). In an incoherent microscope, such as a fluorescence microscope, defining and reporting resolution is fairly straightforward. The connection between the optical intensity emitted from the sample and the intensity detected at the image plane is linear for incoherent systems1. As such, resolution can be quantified by measuring the intensity point spread function (iPSF) of the microscope2 and stating well-known features of it, such as the distance to the first minimum (Rayleigh limit), the distance at which two adjacent iPSFs show no intermediate dip (Sparrow limit), or the highest spatial frequency of the sample captured (Abbe limit). The Fourier transform of the iPSF, known as the optical transfer function, is another common measure. The situation is more complex for coherent imaging, as the microscope now has a linear response to the optical field and not its optical intensity, which is the usually measured quantity. This has led to ambiguity and widespread confusion about (1) the type of sample that should be used to accurately report coherent system resolution and (2) the type of measurement that should be reported. The ambiguity that arises in coherent imaging is well illustrated by the famous case of imaging two closely spaced features1,3. Consider two point sources separated by a small distance and emitting mutually incoherent light, which are resolved at the Rayleigh limit (that is, just separated by a clear dip in intensity) when imaged by a specific microscope. The same point sources in the same locations will not be resolved by the same microscope (that is, will appear as only one large spot) if the sources are instead emitting light that is coherent and in-phase. However, the two sources become fully ‘resolved’ when their emissions are in anti-phase (that is, shifted by π radians) to each other. This means that the intensity profile of an image rendered by a coherent imaging system is phase dependent. As such, simply measuring and reporting its intensity response is an unsuitable means to characterize resolution in an unambiguous manner. Further compounding the issue, many recent coherent imaging methods rely on computational post-processing, with a digitally manipulated image formation pipeline. Another factor that needs to be taken into account is the presence of noise, which can impact image quality and resolution limits4, but is challenging to encompass within a single measurement or scalar performance metric. With this context in mind, we believe that the establishment of a practical unambiguous resolution standard is highly desirable and would allow all users to transparently and reliably assess the merits of coherent microscope techniques. The proposed standard and guidelines described here (summarized in Box 1) can form a baseline criterion for imaging system characterization. Consideration of the following mathematical model is helpful to understand our suggested standard. It is possible to express the behaviour of a large class of coherent imaging systems in terms of a transfer function that relates input and output complex fields of the imaging system: