&nbrs;Beyond Resolution


Resolving 'Resolution'

A re-reading of ‘resolution’

Defining resolution
The meaning of the word resolution depends greatly on the context in which it is used. The Oxford dictionary for instance, differentiates between an ordinary and a formal use of the word, while it also lists definitions from the discourses of music, medicine, chemistry, physics and optics. What is striking about these definitions is that they read not just diverse, but at times even contradictory. In order to come to terms with the many different definitions of the word resolution, and to avert a sense of inceptive ambiguity, I will start this chapter with a very short etymology and description of the term.

A short Etymology of ‘resolution’
The word resolution finds its roots in the Latin word re-solutio and consists of two parts: re-, which is a prefix meaning again or back, and solution, which can be traced back to the Latin action noun solūtiō (“a loosening, solution”), or solvō (“I loosen”). Resolution thus suggests a separation or disentanglement of one thing from something it is tied up with, or “the process of reducing things into simpler forms.” The Oxford Dictionary places the origin of resolution in late Middle English where it was first recorded in 1412, as resolucioun (“a breaking into parts”), but also references the Latin word resolvere. Douglas Harper, historian and creator of the Online Etymology Dictionary, describes a kinship with the fourteenth-century French word solucion, which translates to division, dissolving, or explanation. Harper also writes that around the 1520s the term resolution was used to refer to the act of determining or deciding upon something by “breaking (something) into parts to arrive at a truth or to make a final determination.” Following Harper, Resolving, in terms of “a solving” (of a mathematical problem) was only first recorded in the 1540s, as was its usage when meaning “the power of holding firmly” (resolute). This is where to “pass a resolution” stems from (1580s). Resolution in terms of a “decision or expression of a meeting” is dated at around 1600, while a resolution made around New Year, generally referring to the specific wish to better oneself, was first recorded around the 1780s.

When a resolution is used in the context of a formal, legislative, or deliberative assembly, it refers to a proposal that requires a vote. In this case, resolution is often used in conjunction with the term motion, and refers to a proposal (also connected to “dispute resolution”). So while in chemistry resolution may mean the breaking down of a complex issue or material into smaller pieces, resolution can also mean the finding of an answer to a problem (in mathematics) or even the deciding of a firm, formal solution. This use of the term resolution – a final solution – seems to oppose the older definitions of resolution, which generally signify an act of breaking down. Etymologically however, these different meanings of the term all still originate from the same root.

Douglas Harper dates the first recording of resolution referring to the “effect of an optical instrument” back to the 1860s. The Oxford Dictionary does not date any of the different uses of the term, but it does end its list of definitions with: “5) The smallest interval measurable by a telescope or scientific instrument; the resolving power. 5.1) The degree of detail visible in a photographic or television image.”

Optical resolution
In optical systems, the quality of the rendered image depends on the resolving power and acutance of the technological assemblage that renders the image; the source or subject that is captured, the technologies and their affordances and the context and conditions in which the image is recorded. Here, the resolving power is an objective measure of resolution, which can for instance be measured in horizontal lines (horizontal resolution) and vertical lines (vertical resolution), line pairs or cycles per millimetre. While the image acutance refers to a measure of sharpness of the edge contrast of the image and is measured following a gradient. A high acutance means a cleaner edge between two details while a low acutance means a soft or blurry edge.

(a) Two monochromatic light sources pass through a small circular aperture and produces a diffraction pattern. (b) Two point light sources that are close to one another produce overlapping images because of diffraction. (c) Two light sources move so close together, that they cannot be resolved or distinguished.

Following this definition of optical resolution, digital resolution should - in theory - also refer to the pixel density of the image on display, written as the number of pixels per area (in PPI or PPCM). However, in a day-to-day use of the term, the meaning of digital resolution is constantly confused or conflated to refer only to a display’s standardized output or graphics display resolution: the number of distinct pixels the display features in each dimension (width and height). As a result, resolution has become an ambiguous term that no longer reflects the quality of the content that is on display. However, the use of the word resolution in this context is a misnomer, since the number of pixels in each dimension of the display (e.g. 1920 × 1080) says absolutely nothing about the actual pixel density, the pixels per unit or quality of the content on display, which may in fact be shown zoomed, stretched, or letter-boxed to fit the displays standard display resolution.

A resolution does not just mean a final rendition of the data on the screen, but also involves the processes involved in its rendition: the procedural affordances and tradeoffs inside the technological assemblage which record, produce and display the image (or other media, such as for instance video, sound or 3D data). The current conflation of the meaning of resolution within the digital - as a result of which resolution only refers to the final dimensions the image is displayed at or in - obscures the complexities and politics at stake in the process of resolving and as a result, presents a limit to the understanding, using, compiling and reading of (imaging) data. Further theoretical refinements that elaborate on the usage and development of the term resolution have been missing from debates on resolutions since it was ported from the field of optics, where it has been in use for two centuries.

To garner a better understanding of our imaging technologies, the word resolution itself needs to be resolved - it needs to be disentangled. In order to do so, I will first offer a more detailed description of the use of the term resolution in optics. I will then describe its deployment in the context of newer and more complex digital technologies. Finally the chapter concludes with a (re-)definition of digital resolution.

Rayleigh criterion
In 1877, the English physicist John William Strutt succeeded his father to become the third Baron Rayleigh. Rayleigh’s most notable accomplishment is the discovery of the inert (not chemically reactive) gas argon in 1895, for which he earned a Nobel Prize in 1904. But Rayleigh also worked in the field of optics, where he wrote a criterion that is still used today in the process of quantifying angular resolution: the minimum angle at which a point of view still resolves two points, or the minimum angle at which two points become visible independently from each other. In an 1879 paragraph titled Resolving, or Separating, Power of Optical Instruments, Lord Rayleigh writes: “According to the principles of common optics, there is no limit to the resolving power of an instrument.” In a paper written between 1881 and 1887, Rayleigh asks: “How is it, […] that the power of the microscope is subject to an absolute limit […]? The answer requires us to go behind the approximate doctrine of rays, on which common optics is built, and to take into consideration the finite character of the wave-length of light.”

When it comes to straightforward optical systems that consider only light rays from a limited spectrum, Rayleigh was right: in order to quantify resolution of these optical systems, contrast, the amount of difference between the maximum and minimum intensity of light visible within the space between two objects, is indispensable. Just like a white line on a white sheet of paper needs contrast to be visible (to be resolved), it will not be possible to distinguish between two objects when there is no contrast between these two objects. Contrast between details defines the degree of visibility, and thus resolution: no contrast will result in no resolution.

But the contrast between two points, and thus the minimum resolution, is contingent on the wave length-quality of light and any possible diffraction patterns between those two points in the image. This ring-shaped diffraction pattern of a point (light source), known as an Airy Pattern, named after George Biddell Airy, is the result of diffraction and is characterized by the wavelength of light illuminating a circular aperture. When two point lights are moved into close proximity, so close that the first Airy disks’ zero crossing falls inside the second Airy disks zero crossing, the oscillation within the Airy Patterns will cancel most contrast of light between them. As a result, the two points will optically be blurred together, no matter the lens' resolving power. The diffraction of light thus results in the fact that even the biggest imaginable telescope has limited resolving power.

Rayleigh described this effect in his Rayleigh criterion, which states that two points can be resolved when the center of the diffraction pattern of one point falls just outside the first minimum diffraction pattern of the other. When considered through circular aperture, he states that it is possible to calculate a minimum angular resolution as:

θ = 1.22 λ / D

In this formula, θ stands for angular resolution (which is measured in radians), λ stands for the wavelength of the light used in the system (blue light has a shorter wavelength which will result in a better resolution), and D stands for the diameter of the lens’ aperture (the hole with a diameter through which the light travels). Aperture is a measure of a lens’ ability to gather light and resolve fine specimen detail at a fixed object distance.

As stated before, an angular resolution is the minimum distance two points (light sources) need from each other to stay individually distinguishable. Here, a smaller resolution means there is a smaller resolution angle (and thus less space) necessary between the resolved dots. However, real optical systems are complex and suffer from aberrations, flaws in the optical system and practical difficulties such as specimen quality. Besides this, in reality, most often two dots radiate or reflect light at different levels of intensity. This means that in practice the resolution of an optical system is always higher (worse) than its calculable minimum.

All technologies have a limited optical resolution, which depends on for instance aperture, wavelength, contrast and angular resolution. When the optical technology is more complex, the actors that are involved in determining the minimal resolution of the technology become more diverse and the setting of resolution changes into a more elaborate process. In microscopy, just like in any other optical technology, angular and lateral resolution refer to the minimum amount of distance needed (measured in rads or in meters) between two objects, such as dots, that still make it possible to just tell them apart. However, a rewritten, mathematical formula defines the theoretical resolving power in microscopy as:

dmin = 1.22 x λ / NA

In this formula dmin stands for the minimal distance two dots need from each other to be resolved, or minimal resolution. λ stands again for the wavelength of light. In the formula for microscopy however, the diameter of the lens’ aperture (D) is swapped with NA, or Numerical Aperture, which consists of a mathematical calculation of the light gathering capabilities of a lens. In microscopy, this is the sum of the aperture of an objective and the diaphragm of the condenser, which have set values per microscope. Resolution in microscopy is thus determined by certain physical parameters that not only include the wavelength of light, but also the light-gathering power of objective and lenses.

Resolution and affordances
The definition of resolution in this second formula is expanded to also include the affordances and the attributed settings of strength, accuracy or power of the material agents that are involved in resolving the image, such as the objective, condenser and lenses. At first sight, this might seem like a minimal expansion and lead to dismissal of a simple rephrasing or rewriting of the earlier formula for angular resolution. However, the expansion of the formula with just one specific material agent, the diaphragm, and the attribution of a certain power of this material agent is actually an important step that illustrates how technology gains complexity. Every time a new agent is added to the equation, the agent introduces complexity by adding new settings and rules involving or influencing the behaviour of all other material agents. In photography for instance, the higher the aperture, the shallower the depth of field, the closer the lens needs to come to the object. This also introduces new possibilities for failure: if the diaphragm does not afford an appropriate setting for this equation, it might not be possible to resolve the image at all - the imaging technology might simply refuse or even state an ‘unsupported setting’ error message - in this case it will refuse to resolve an image entirely.

"Resolution." Douglas Harper: Online Etymology Dictionary. October 30, 2015. <http://dictionary.reference.com/browse/resolution>.

Oxford Dictionary of English. Edited by Angus Stevenson. third edition, Oxford University Press. 2010. p. 1512.

Lorentz, H. Nobel Lectures, Physics 1901-1921. Elsevier Publishing Company, Amsterdam: 1967.

Rayleigh, Lord. "XXXI. investigations in optics, with special reference to the spectroscope." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 8.49 (1879): 261-274.

John William Strutt, Baron Rayleigh. Scientific Papers. Vol II. 1881–1887. University Press, Cambridge: 1900. p. 410.

Microscope Research Center. Accessed: January 30, 2018 <http://www.olympusconfocal.com/theory/resolutionintro.html>.

Wolniak, Stephen M. “Principles of Microscopy” in: BSCI 427 Principles of Microscopy Fall 2004 Syllabus. University of Maryland, 2004.
Accessed: January 30, 2018. <http://www.life.umd.edu/cbmg/faculty/wolniak/wolniakmicro.html>.