National Aeronautics and Space Administration, Science Mission Directorate. (2010). Reflected Near-Infrared Waves. Retrieved [insert date - e.g. August 10, 2016], from NASA Science website: http://science.nasa.gov/ems/08_nearinfraredwaves

Numerical aperture and resolutioncalculator

Numerical aperture (abbreviated as ‘NA’) is an important consideration when trying to distinguish detail in a specimen viewed down the microscope. NA is a number without units and is related to the angles of light which are collected by a lens. In calculating NA (see below), the refractive index of a medium is also taken into account and by matching the refractive index of a slide or cell culture container with an immersion medium, then more of the detail of a specimen will be resolved. The way in which light behaves when travelling from one medium to another is also related to NA (and termed ‘refraction’).  This article also covers a brief history of refraction and how this concept is a limiting factor in achieving high NA.

Data from scientific instruments can provide more precise measurements than analog film. Scientists can graph the measurements, examine the unique patterns of absorption and reflection of visible and infrared energy, and use this information to identify types of plants. The graph below shows the differences among the spectral signatures of corn, soybeans, and Tulip Poplar trees.

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In theory, the maximum angular aperture of the light cone collected by the objective front lens would be 180°, which would give an α value of 90°. As the sine of 90 is one, this would mean that the theoretical NA of an objective which was able to collect 180° of the resultant light from a specimen in a medium of air would also be one. Clearly, the refractive index is the limiting factor in achieving the highest NA of an objective. Consequently, the high-NA objectives are those which use an immersion medium in place of air, such as oil or water. In reality, an NA of one with air between the specimen and the objective front lens is unachievable and therefore the highest NA of a ‘dry lens’ (i.e. a non-immersion objective) and is closer to 0.95. This is due to the fact that most lenses would not be able to collect 180° of light from the specimen and the widest angle is approximately 144°. The sine of 144° is 0.95 and as air has a refractive index of 1.0, the theoretical maximum NA is close to 0.95.

Color Infrared film can record near-infrared energy and can help scientists study plant diseases where there is a change in pigment and cell structure. These two images show the difference between a color infrared photo and a natural color photo of trees in a park.

In simple terms, the NA of a microscope objective is the ability of the lens to gather light at a fixed distance from the object on view. As light passes through a specimen, it enters the objective as an inverted cone. However, some of the light from the specimen is refracted (and reflected), but objectives with a high NA value permit increasingly oblique light waves to be gathered by the front lens which in turn will produce an image which is highly resolved and contains more detail and information than objectives which have lower NA.

Numerical apertureof microscope formula

This false-color composite of Jupiter combines near-infrared and visible-light data of sunlight reflected from Jupiter's clouds. Since methane gas in Jupiter's atmosphere limits the penetration of sunlight, the amount of reflected near-infrared energy varies depending on the clouds' altitude. The resulting composite image shows this altitude difference as different colors. Yellow colors indicate high clouds; red colors are lower clouds; and blue colors show even lower clouds in Jupiter's atmosphere. The Near Infrared Camera and Multi-Object Spectrometer (NICMOS) onboard NASA's Hubble Space Telescope captured this image at the time of a rare alignment of three of Jupiter's largest moons—Io, Ganymede, and Callisto—across the planet's face.

The image brightness and the image detail (resolution) which is collected and formed by an objective lens are related to the angular aperture. The light from the specimen continues through the air between the cover glass and the objective front lens or through an immersion medium.

In simpler terms, when light travels from one medium to another it changes speed- for example, when passing from air to water, light slows down. In addition, the change in speed results in change in direction for light which enters a medium at an angle other than 90°. It should be noted that the frequency of light doesn’t change, but the wavelength will be determined by nature of the medium.

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A portion of radiation that is just beyond the visible spectrum is referred to as near-infrared. Rather than studying an object's emission of infrared, scientists can study how objects reflect, transmit, and absorb the Sun's near-infrared radiation to observe health of vegetation and soil composition.

The NA of an objective is an important aspect and relates to the image resolution. In brief, the resolution is the ability of the objective to distinguish details in your specimen. Without a correspondingly high NA, an objective with a high magnification would be unable to resolve sample detail.

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Reflected near-infrared radiation can be sensed by satellites, allowing scientists to study vegetation from space. Healthy vegetation absorbs blue- and red-light energy to fuel photosynthesis and create chlorophyll. A plant with more chlorophyll will reflect more near-infrared energy than an unhealthy plant. Thus, analyzing a plants spectrum of both absorption and reflection in visible and in infrared wavelengths can provide information about the plants' health and productivity.

NASA explores the unknown in air and space, innovates for the benefit of humanity, and inspires the world through discovery.

Numerical aperture and resolutionin microscope

Near-infrared data can also help identify types of rock and soil. This image of the Saline Valley area in California was acquired by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) onboard NASA's Terra satellite.

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Science Mission Directorate. "Reflected Near-Infrared Waves" NASA Science. 2010. National Aeronautics and Space Administration. [insert date - e.g. 10 Aug. 2016] http://science.nasa.gov/ems/08_nearinfraredwaves

Numerical apertureof 100X objective lens

If you have a close look at the objectives on your microscope, you’ll see a variety of information and numbers engraved on the barrel. As well as the magnification and the optical correction, you will see another number which has no units. This is the Numerical Aperture (or ‘NA’) of the objective (s. Figure 1).

Data and imagery from the U.S. Geological Service (USGS) and NASA Landsat series of satellites are used by the U.S. Department of Agriculture to forecast agricultural productivity each growing season. Satellite data can help farmers pinpoint where crops are infested, stressed, or healthy.

The angular aperture is inversely proportional to the focal length of the objective. As focal length decreases, there is an increase in the amount of light which the objective front lens can gather. In other words, if the objective is very close to the specimen, then more oblique light rays can be collected by the objective lens. It should be said that the angular aperture is usually determined by the optics within the objective and each objective lens will have an optimal focal length. Metaphorically, think of it this way: if you are standing in front of a door with a key hole which leads into another room, then when you are at a distance, you will only be able to see a little of the light and objects within the room. If you press your eye against the key hole, you will then see more of the detail and light in the room as you have, in theory, increased the angular aperture of your eye.

Numerical apertureof microscope

Our eyes perceive a leaf as green because wavelengths in the green region of the spectrum are reflected by pigments in the leaf, while the other visible wavelengths are absorbed. In addition, the components in plants reflect, transmit, and absorb different portions of the near-infrared radiation that we cannot see.

The maximum longitudinal angle of the cone of light collected by the front lens of the objective is known as the ‘angular aperture’ (s. Figure 1). In addition to an increasing NA, image brightness is also proportional to the angular aperture. The angular aperture, which varies with the objective focal length, relates to the maximum angle of image-forming light rays emanating from the specimen that the objective front lens can capture when the specimen is focused.

Data from ASTER's visible and near-infrared bands at 0.81 µm, 0.56 µm, and .66 µm are composited in red, green, and blue creating the false-color image below. Vegetation appears red, snow and dry salt lakes are white, and exposed rocks are brown, gray, yellow, and blue. Rock colors mainly reflect the presence of iron minerals and variations in albedo (solar energy reflected off the surface).

In the above equation, ‘n’ is the refractive index of the medium between the cover glass and the front lens of the objective (for example; air, water or oil). The ‘α’ symbol relates to half of the angle of the cone of light which can be collected by the lens (i.e., the angular aperture; s. Figure 2).

Snell’s Law states that the ratio of the angles of incident and refracted light are equivalent to the reciprocal of the ratio of the refractive indices through which the light passes.

In order to fully understand NA, it is helpful to have an understanding of refraction. In optics and microscopy, refraction is a change in the direction of light waves passing through and coming from a specimen which is due to a change in the medium though which the light passes, be it air, glass, water or oil. Refraction is described in a formula known as ‘Snell’s Law’. Willebrord Snellius (1580-1626) was a Dutch mathematician and astronomer. As well as determining a new method of calculating the radius of the earth, he was also credited for mathematically describing refraction. However, he wasn’t the first to do so and it is more accurate to say that he ‘rediscovered’ diffraction as this had been described many centuries before by a Persian mathematician and physicist called Ibn Sahl. In his manuscript from 984, he described how curved lenses and mirrors bent and focused light.

A high magnification objective lens with low NA will consequently have low resolution. Many microscopy companies offer objectives with as high an NA as possible. So, if you are in the position of buying new lenses for your microscope, you should always consider buying those objectives which offer the greatest NA within your budget.

Air has a refractive index which is approximately 1.0, whereas the refractive index of water is 1.3 and some immersion oils used for optical microscopy have a refractive index as high as 1.52.