Airy disc radius = 1.22 * N * light wavelength ( N = aperture size, light wavelength is commonly 546 or 550 nm or 0.550 um, a wavelength of green)

The distance between two Airy discs where they are still considered to be resolved separately is the radius of the disc - also called the Raleigh criterion. A smaller Airy disc means a smaller disc radius and a higher resolution. This distance is somewhat arbitrary as there is still a small amount of contrast remaining in the space between the discs at the Raleigh criterion. If the discs are moved any closer, the remaining contrast between the two objects will completely disappear. The point where all contrast is lost between the adjacent discs is called the Sparrow criterion and is the absolute limit of resolution. The Raleigh criterion is the most commonly used measure of resolution:

The resolution limit of a lens is really just a measure of the diffraction in the system. We will assume that the lens doesn't have significant aberrations limiting things further. To lessen the diffraction, you can do one of two things: 1) enlarge the aperture (lower f/number), 2) lower the wavelength of the light (blue should produce more resolution than red will). The Airy disc as described in the previous entry is the smallest point of light that can be focused by a lens at a particular aperture and represents the center of a diffraction pattern. The size of the disc is a direct determinant of image resolution. The resolution of a lens is defined as the closest that two objects can be to each other while still being separately resolved by the lens. The two objects in question are two Airy discs. As the two discs get closer and closer together they will start to merge and at a certain point the separation between them will be lost. Above: The top two are fully separated, the middle two are barely separated and near the resolution limit, the bottom two are not resolved

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Exceeding the upper and lower bounds of this temperature specification can degrade image quality and cause irreparable damage. When the glass elements within the lens exceed the upper limit of the temperature rating, the metal expands, causing stress from the metal retaining ring. On the other hand, exceeding the lower temperature bounds will cause the glass to become brittle and more susceptible to cracking. As temperature changes, the index of refraction of each lens element changes, as well as the size of elements, causing the lens assembly to need refocusing as temperatures fluctuate (Figure 1). It is important to consider the fluctuation speed in your imaging environment, as glass is not suitable for quick changes in temperature. If temperature changes too quickly, it can cause glass to crack and damage the optic. There is no rule of thumb for an acceptable rate of change since there are many different types of glass with their own characteristics and specs.

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Operating temperature defines the upper and lower bounds of the temperature limits for athermalized lenses, or lenses designed specifically to maintain performance throughout temperature swings. Athermal lenses do not require refocusing when temperature fluctuates within their operating temperature bounds. Exceeding the temperature limit or rapid fluctuation with athermal lenses will, however, have similar defocusing effects as those experienced by regular, non-athermalized lenses discussed above. Not all lenses will have an operating temperature specification, only athermal lenses.

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Figure 1: Illustration of how changing temperatures can lead to a shift in the focal length of a lens, requiring imaging lens assemblies to be refocused after undergoing temperature changes.

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When looking at Edmund Optics® Imaging Lenses, you may see two different temperature specifications: operating temperature and storage temperature. Utilizing lenses outside of their specified temperature environment can compromise the image quality and potentially damage your system. But what is the difference between these two specifications? To ensure you are properly using your lenses, please refer to the below descriptions for temperature rating.

Storage temperature provides the temperature range that the lens is capable of withstanding. This range also describes the environment in which the lens will perform best. All imaging lenses manufactured by Edmund Optics® will have a storage temperature specification.

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Ideally, an imaging environment that maintains a consistent temperature within the operating temperature range will be the best use case for optics that specify a storage temperature. For environments with extreme environments such as heating or cooling chambers where temperature fluctuation will occur more rapidly, athermal lenses should be used.

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Learn about focal length in photography and why it is arguably the most important factor in camera lens specifications.

Knowledge Center/ Application Notes/ Imaging Application Notes/ Operating vs. Storage Temperature of Imaging Lenses

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Above: The top two are fully separated, the middle two are barely separated and near the resolution limit, the bottom two are not resolved

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