A multispectral imaging (MSI) system is similar to one that is hyperspectral but does have key differences. In comparison to the effectively continuous wavelength data collection of an HSI, an MSI concentrates on several preselected wavebands based on the application at hand. While not a direct example or comparison, common RGB sensors help illustrate this concept. RGB sensors are overlaid with a Bayer pattern, consisting of red, green, and blue filters. These filters allow wavelengths from specific color bands to be absorbed by the pixels while the rest of the light is attenuated. The bandpass filters have transmission bands in the range of 400-700nm and have slight spectral overlap. An example of this can be seen in Figure 3. The images captured are then rendered with false color to approximate what the human eye sees. In most multispectral imaging applications, the wavelength bands are significantly narrower and more numerous. The wavebands are commonly on the order of tens of nanometers and are not exclusively a part of the visible spectrum. Depending on the application, UV, NIR, and thermal wavelengths (mid-wave IR) can have isolated channels as well.4

Another challenge occurs when pairing these high-end sensors with the proper optical components. Spectral data recording heavily relies on bandpass filters, diffractive optics, such as prisms or gratings, and even liquid crystal or acousto-optic tunable filters to separate the light of differing wavelengths.7 Additionally, the lenses used for these cameras must be optimally designed and compatible across vast wavelength ranges and temperature fluctuations. These designs must have more optical elements, which increases cost and system weight. Elements will need to have different refractive indices and dispersive properties for broadband color correction. Differing glass types lead to varied thermal and mechanical properties as well. After selecting glasses that have the appropriate internal transmission spectra, it is imperative to apply broadband multi-layer anti-reflection coatings to each lens to ensure maximum light throughput. The multitude of unique requirements in these circumstances makes the design process of lenses for hyperspectral and multispectral imaging tedious and requires great skill. Certain application spaces also necessitate that the lens assemblies are athermal to ensure that a system will function the same whether used on the ground or in the upper atmosphere.

As a quick aside, a spectrometer collects wavelength information as well as relative intensity information for the different wavelengths detected.2 These devices typically collect light from a singular source or location on a sample. A spectrometer can be used to detect substances that scatter and reflect specific wavelengths, or material composition based on fluorescent or phosphorescent emissions. An HSI system takes this technology to the next level by assigning positional data to the collected light spectrums. A hyperspectral system does not output a 2D image, but instead a hyperspectral data cube or image cube.3

Machine vision sensors output arrays of grayscale values resulting in a 2D image of the object within a viewing area. The functional utility of this is generally feature recognition for the purposes of sorting, measuring, or locating objects. The vision system is unaware of the wavelengths that are being used for illumination unless optical filters areused. This is not true for sensors that have a Bayer Pattern (RGB) filter, but even then, each pixel is restricted to accepting light from a narrow band of wavelengths and the camera software is what ultimately assigns color. In a truly hyperspectral image, each pixel corresponds to coordinates, signal intensity, and wavelength information. For this reason, HSI is often referred to as imaging spectroscopy.1

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Hyperspectral and multispectral imaging are two similar technologies that have been growing in prominence and utility over the past two decades. The terms are often conflated to have the same meaning, but represent two distinct imaging methods, each with their own application spaces. Both technologies have advantages over conventional machine vision imaging methods, which utilize light from the visible spectrum (400-700nm). However, these benefits come with an increased system complexity in terms of lighting, filtering, and optical design.

Life sciences and remote sensing are just a few topics in which these technologies have made a large footprint. More specific market areas include agriculture, food quality and safety, pharmaceuticals, and healthcare.3 Farmers find these tools particularly useful, allowing them to determine the growth of their crops. Tractors and drones can be equipped with spectral imagers to scan over fields while doing a form of lower altitude remote sensing. The farmers then analyze spectral characteristics of the captured images. These characteristics help determine the general health of the plants, the state of the soil, regions that have been treated with certain chemicals, or if something harmful, like an infection, is present. All the information has unique spectral markers that can be captured, analyzed, and used to ensure the optimal production of produce.

When a lens is used to form an image of some object, the distance from the object to the lens u, the distance from the lens to the image v, and the focal length f are related by

For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses or mirrors (e.g. a photographic lens or a telescope), there are several related concepts that are referred to as focal lengths:

The corresponding front focal distance is:[6] FFD = f ( 1 + ( n − 1 ) d n R 2 ) , {\displaystyle {\mbox{FFD}}=f\left(1+{\frac {(n-1)d}{nR_{2}}}\right),} and the back focal distance: BFD = f ( 1 − ( n − 1 ) d n R 1 ) . {\displaystyle {\mbox{BFD}}=f\left(1-{\frac {(n-1)d}{nR_{1}}}\right).}

To render closer objects in sharp focus, the lens must be adjusted to increase the distance between the rear principal plane and the film, to put the film at the image plane. The focal length f, the distance from the front principal plane to the object to photograph s1, and the distance from the rear principal plane to the image plane s2 are then related by:

In typical machine vision applications, illumination used and captured by the sensor is in the visible spectrum. This part of the spectrum consists of the only light that the human eye can detect, ranging from roughly 400nm (violet) to 700nm (dark red) (Figure 1). Imaging lens assemblies and sensors typically have peak spectral sensitivities around 550nm. The quantum efficiency of a camera sensor is the ability to convert photons into an electric signal; this efficiency decreases significantly into the ultraviolet or the near infrared. In the simplest terms, hyperspectral imaging (HSI) is a method for capturing images that contain information from a broader portion of the electromagnetic spectrum. This portion can start with UV light, extend through the visible spectrum, and end in the near or short-wave infrared. This extended wavelength range can reveal properties of material composition that are not otherwise apparent.

Principalfocus ofconvex mirror

Although application spaces that benefit from HSI and MSI are large and increasing, limitations in the current technology have led to slow industry adoption. Currently, these systems are significantly more expensive compared to other machine vision components. The sensors need to be more complex, have broader spectral sensitivity, and must be precisely calibrated. Sensor chips will often require the use of substrates other than silicon, which is only sensitive from approximately 200-1000nm. Indium arsenide (InAs), gallium arsenide (GaAs), or indium gallium arsenide (InGaAs), can be used to collect light up to 2600nm. If the requirement is to image from the NIR through the MWIR, a mercury cadmium tellurium (MCT or HgCdTe) sensor, indium antimonide (InSb) focal plane array, indium gallium arsenide (InGaAs) focal plane array, microbolometer, or other longer wavelength sensor is required. The sensors and pixels used in these systems will also need to be larger than many machine vision sensors to attain the required sensitivity and spatial resolution.1

For an optical system in a medium other than air or vacuum, the front and rear focal lengths are equal to the EFL times the refractive index of the medium in front of or behind the lens (n1 and n2 in the diagram above). The term "focal length" by itself is ambiguous in this case. The historical usage was to define the "focal length" as the EFL times the index of refraction of the medium.[2][4] For a system with different media on both sides, such as the human eye, the front and rear focal lengths are not equal to one another, and convention may dictate which one is called "the focal length" of the system. Some modern authors avoid this ambiguity by instead defining "focal length" to be a synonym for EFL.[1]

1 f = ( n − 1 ) ( 1 R 1 − 1 R 2 + ( n − 1 ) d n R 1 R 2 ) , {\displaystyle {\frac {1}{f}}=(n-1)\left({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}+{\frac {(n-1)d}{nR_{1}R_{2}}}\right),} where n is the refractive index of the lens medium. The quantity ⁠1/f⁠ is also known as the optical power of the lens.

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For a spherically-curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. The focal length is positive for a concave mirror, and negative for a convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so

The optical power of a lens or curved mirror is a physical quantity equal to the reciprocal of the focal length, expressed in metres. A dioptre is its unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dioptre = 1 m−1. For example, a 2-dioptre lens brings parallel rays of light to focus at 1⁄2 metre. A flat window has an optical power of zero dioptres, as it does not cause light to converge or diverge.[10]

Principalfocus of lens

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For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens.

Camera lens focal lengths are usually specified in millimetres (mm), but some older lenses are marked in centimetres (cm) or inches.

The focal length of a lens determines the magnification at which it images distant objects. It is equal to the distance between the image plane and a pinhole that images distant objects the same size as the lens in question. For rectilinear lenses (that is, with no image distortion), the imaging of distant objects is well modelled as a pinhole camera model.[7] This model leads to the simple geometric model that photographers use for computing the angle of view of a camera; in this case, the angle of view depends only on the ratio of focal length to film size. In general, the angle of view depends also on the distortion.[8]

Determining the focal length of a concave lens is somewhat more difficult. The focal length of such a lens is defined as the point at which the spreading beams of light meet when they are extended backwards. No image is formed during such a test, and the focal length must be determined by passing light (for example, the light of a laser beam) through the lens, examining how much that light becomes dispersed/ bent, and following the beam of light backwards to the lens's focal point.

For an optical system in air the effective focal length, front focal length, and rear focal length are all the same and may be called simply "focal length".

Principalfocus ofconcavelensis real or virtual

Reflection vs Transmission Diffraction Gratings. Reflection or transmission is one of the most fundamental distinctions in diffraction grating terminology.

Partsofa convexlens

Some see MSI as a worse form of HSI, one with lower spectral resolution. In truth, the two technologies each present their own advantages that make them a preferred tool for different tasks. HSI is best suited for applications sensitive to subtle differences in signal along a continuous spectrum. These small signals could be missed by a system which samples larger wavebands. However, some systems require significant portions of the electromagnetic spectrum to be blocked to selectively capture light (Figure 4). The other wavelengths could present significant noise that would potentially ruin measurements and observations. Also, if there is less spectral information included in the data cube, the image capture, processing, and analysis can happen more quickly.

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In most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and a narrower angle of view; conversely, shorter focal length or higher optical power is associated with lower magnification and a wider angle of view. On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length (higher optical power) leads to higher magnification because the subject can be brought closer to the center of projection.

When a photographic lens is set to "infinity", its rear principal plane is separated from the sensor or film, which is then situated at the focal plane, by the lens's focal length. Objects far away from the camera then produce sharp images on the sensor or film, which is also at the image plane.

Principalfocus of lensdiagram

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There are four primary hyperspectral acquisition modes used, each with a set of advantages and disadvantages (Figure 2). The whiskbroom method is a point scanning process that acquires the spectral information for one spatial coordinate at a time. This method tends to offer the highest level of spectral resolution, but requires the system to scan the target area on both the x and y axes, significantly adding to the total acquisition time.1 The pushbroom method is a line scanning data capture in which a single axis of spatial movement is required as a row of pixels scans over an area to capture the spectral and positional information. These pushbroom systems can have “compact size, low weight, simpler operation and higher signal to noise ratio.”1 When utilizing this HSI method, it is critical to time the exposures just right. Incorrect exposure timing will introduce inconsistent saturation or an underexposure of spectral bands. The method called plane scanning images the entire 2D area at once, but at each wavelength interval and involves numerous image captures to create the spectral depth of the hyperspectral data cube. While this capture method does not require translation of the sensor or full system, it is critical that the subject is not moving during acquisition; the accuracy of positional and spectral information will be compromised otherwise. The fourth and most recently developed mode of hyperspectral image acquisition is referred to as single shot or snapshot. A single shot imager collects the entirety of the hyperspectral data cube within a singe integration period.1 Although single shot appears to be the preferred future of HSI implementation, it is currently limited by comparatively lower spatial resolution and requires further development.1

Secondaryfocus of lens

In the sign convention used here, the value of R1 will be positive if the first lens surface is convex, and negative if it is concave. The value of R2 is negative if the second surface is convex, and positive if concave. Sign conventions vary between different authors, which results in different forms of these equations depending on the convention used.

For the case of a lens of thickness d in air (n1 = n2 = 1), and surfaces with radii of curvature R1 and R2, the effective focal length f is given by the Lensmaker's equation:[5]

The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power.

The application spaces that require the uses of HSI and MSI continue to grow in number. Remote sensing, aerial imaging of the earth’s surface with the use of unmanned aerial vehicles (UAVs) and satellites, has relied on both HSI and MSI for decades. Spectral photography can penetrate through Earth’s atmosphere and different cloud cover for an unobscured view of the ground below. This technology can be used to monitor changes in population, observe geological transformations, and study archeological sites. In addition, HSI and MSI technologies have become increasingly critical in the study of the environment. Data can be collected about deforestation, ecosystem degradation, carbon recycling, and increasingly erratic weather patterns. Researchers use the information gathered to create predictive models of the global ecology, which drives many environmental initiatives meant to combat the negative effects of climate change and human influence on nature.6

Infinitefocus lens

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The distinction between front/rear focal length and EFL is important for studying the human eye. The eye can be represented by an equivalent thin lens at an air/fluid boundary with front and rear focal lengths equal to those of the eye, or it can be represented by a different equivalent thin lens that is totally in air, with focal length equal to the eye's EFL.

The main benefit of using optical power rather than focal length is that the thin lens formula has the object distance, image distance, and focal length all as reciprocals. Additionally, when relatively thin lenses are placed close together their powers approximately add. Thus, a thin 2.0-dioptre lens placed close to a thin 0.5-dioptre lens yields almost the same focal length as a single 2.5-dioptre lens.

As s1 is decreased, s2 must be increased. For example, consider a normal lens for a 35 mm camera with a focal length of f = 50 mm. To focus a distant object (s1 ≈ ∞), the rear principal plane of the lens must be located a distance s2 = 50 mm from the film plane, so that it is at the location of the image plane. To focus an object 1 m away (s1 = 1,000 mm), the lens must be moved 2.6 mm farther away from the film plane, to s2 = 52.6 mm.

Focal length (f) and field of view (FOV) of a lens are inversely proportional. For a standard rectilinear lens, F O V = 2 arctan ⁡ ( x 2 f ) {\textstyle \mathrm {FOV} =2\arctan {\left({x \over 2f}\right)}} , where x is the width of the film or imaging sensor.

Future development goals are to make HSI and MSI systems more compact, affordable, and user friendly. With these improvements, new markets will be encouraged to utilize the technology, and advance the markets that already do.

The same is true in the medical field. Non-invasive scans of skin to detect diseased or malignant cells can now be performed by doctors with the help of hyperspectral imaging. Certain wavelengths are better suited for penetrating deeper into the skin, allowing a more detailed understanding of a patient’s condition. Cancers and other diseased cells are now easily distinguishable from healthy tissue, as they will fluoresce and absorb light under the correct stimulation. Doctors are no longer required to make educated guesses based on what they can see and a patient’s description of symptoms. Sophisticated systems can record and automatically interpret the spectral data, leading to significantly expedited diagnoses and rapid treatment of the exact areas of need.5

Due to the popularity of the 35 mm standard, camera–lens combinations are often described in terms of their 35 mm-equivalent focal length, that is, the focal length of a lens that would have the same angle of view, or field of view, if used on a full-frame 35 mm camera. Use of a 35 mm-equivalent focal length is particularly common with digital cameras, which often use sensors smaller than 35 mm film, and so require correspondingly shorter focal lengths to achieve a given angle of view, by a factor known as the crop factor.

The focal length of a thin convex lens can be easily measured by using it to form an image of a distant light source on a screen. The lens is moved until a sharp image is formed on the screen. In this case ⁠1/u⁠ is negligible, and the focal length is then given by

A lens with a focal length about equal to the diagonal size of the film or sensor format is known as a normal lens; its angle of view is similar to the angle subtended by a large-enough print viewed at a typical viewing distance of the print diagonal, which therefore yields a normal perspective when viewing the print;[9] this angle of view is about 53 degrees diagonally. For full-frame 35 mm-format cameras, the diagonal is 43 mm and a typical "normal" lens has a 50 mm focal length. A lens with a focal length shorter than normal is often referred to as a wide-angle lens (typically 35 mm and less, for 35 mm-format cameras), while a lens significantly longer than normal may be referred to as a telephoto lens (typically 85 mm and more, for 35 mm-format cameras). Technically, long focal length lenses are only "telephoto" if the focal length is longer than the physical length of the lens, but the term is often used to describe any long focal length lens.