These small diameter Geltech® Molded Glass Aspheric Lenses are an economic choice for collimating or focusing light at high magnification.

Light is one type of electromagnetic (EM) wave. As noted earlier, EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation (see Figure 2). There are specific directions for the oscillations of the electric and magnetic fields. Polarization is the attribute that a wave’s oscillations have a definite direction relative to the direction of propagation of the wave. (This is not the same type of polarization as that discussed for the separation of charges.) Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. Thus we can think of the electric field arrows as showing the direction of polarization, as in Figure 2.

What is polarization of lightclass 12

Broad perspectives generally equip Autonomous Mobile Robots to navigate complex environments and avoid obstacles. A wide FOV also ensures that robots can detect and analyze their surroundings in real time, boosting their ability to move safely and operate in dynamic environments, such as warehouses, manufacturing floors, and public spaces. A large vertical FOV ensures that obstacles at any height are detected, allowing robots to navigate under hanging obstacles such as shelves or overhead conveyor. For warehouse AMRs, two cameras placed on opposing corners, each providing a 270° FOV, can offer complete situational awareness. This setup enables the AMR to navigate freely in all directions—left, right, forward, and backward—while also turning efficiently without worrying about blind spots or objects coming from behind.

e-con Systems has 20+ years of experience designing, developing, and manufacturing OEM cameras. That’s why we understand the nuances involved in selecting lenses with the right FOV for your application. We can expertly guide you through the entire process of selecting the lens rather than merely acting as a camera supplier.

[latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] gives [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}=\frac{1.333}{1.00}=1.333\\[/latex].

Industrial automation systems for functions like quality inspection rely on cameras with accurate FOV settings to scrutinize products on assembly lines. They capture imaging data required for thorough product inspection by detecting defects instantly. Moreover, manufacturers can optimize their inspection processes, reduce errors, and maintain consistent product standards.

Circularpolarization

When the intensity is reduced by 90.0%, it is 10.0% or 0.100 times its original value. That is, I = 0.100I0. Using this information, the equation I = I0 cos2 θ can be used to solve for the needed angle.

Figure 12. (a) Polarized light is rotated 90º by a liquid crystal and then passed by a polarizing filter that has its axis perpendicular to the original polarization direction. (b) When a voltage is applied to the liquid crystal, the polarized light is not rotated and is blocked by the filter, making the region dark in comparison with its surroundings. (c) LCDs can be made color specific, small, and fast enough to use in laptop computers and TVs. (credit: Jon Sullivan)

In this article, let’s explore the importance of FOV in embedded vision, the factors that determine FOV, as well as which applications rely on this the most.

The Sun and many other light sources produce waves that are randomly polarized (see Figure 4). Such light is said to be unpolarized because it is composed of many waves with all possible directions of polarization. Polaroid materials, invented by the founder of Polaroid Corporation, Edwin Land, act as a polarizing slit for light, allowing only polarization in one direction to pass through. Polarizing filters are composed of long molecules aligned in one direction. Thinking of the molecules as many slits, analogous to those for the oscillating ropes, we can understand why only light with a specific polarization can get through. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave (see Figure 5).

Please write to us at camerasolutions@e-consystems.com if you need expert help integrating cameras with different FOVs into your applications.

Brewster’s law: [latex]\tan\theta_{\text{b}}=\frac{{n}_{2}}{{n}_{1}}\\[/latex], where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light

Now let us discuss FOV calculation. In many applications, the required distance from an object and the desired field of view (which determine the size of the object seen in the frame) are known quantities. This information can be used to directly determine the required angular field of view (AFOV) as shown below.

Figure 1. These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of water. Part (b) of this Figure was taken with a polarizing filter and part (a) was not. As a result, the reflection of clouds and sky observed in part (a) is not observed in part (b). Polarizing sunglasses are particularly useful on snow and water. (credit: Amithshs, Wikimedia Commons)

Focal length is the defining property of a lens. Simply put, it is the distance between the lens and the plane of the sensor, and is determined when the lens focuses the object at infinity. It is represented in mm. Focal length depends on the curvature of the lens and its material. The shorter the focal length, the wider the AFOV and vice versa. Please have a look at the below image to understand this better:

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Figure 10. Artist’s conception of an electron in a long molecule oscillating parallel to the molecule. The oscillation of the electron absorbs energy and reduces the intensity of the component of the EM wave that is parallel to the molecule.

Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic waves (often visible light) that have an electric field parallel to the axis. This is accomplished with long molecules aligned perpendicular to the axis as shown in Figure 9.

Smart traffic systems utilize cameras with a wide FOV to seamlessly monitor and manage road traffic. Such cameras capture comprehensive views of large areas for performing real-time traffic flow analysis and incident detection. Covering wide road sections also means they can promptly identify traffic violations, accidents, and congestion. Additionally, the broader view empowers advanced features like vehicle counting, object classification and lane discipline monitoring. This provides crucial real-time data that helps optimize traffic flow and improve overall safety.

Figure 6. The effect of rotating two polarizing filters, where the first polarizes the light. (a) All of the polarized light is passed by the second polarizing filter, because its axis is parallel to the first. (b) As the second is rotated, only part of the light is passed. (c) When the second is perpendicular to the first, no light is passed. (d) In this photograph, a polarizing filter is placed above two others. Its axis is perpendicular to the filter on the right (dark area) and parallel to the filter on the left (lighter area). (credit: P.P. Urone)

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There is a range of optical effects used in sunglasses. Besides being Polaroid, other sunglasses have colored pigments embedded in them, while others use non-reflective or even reflective coatings. A recent development is photochromic lenses, which darken in the sunlight and become clear indoors. Photochromic lenses are embedded with organic microcrystalline molecules that change their properties when exposed to UV in sunlight, but become clear in artificial lighting with no UV.

Remote patient monitoring systems rely on cameras with an optimal FOV to provide accurate and complete observations of patients. These cameras ensure that all relevant movements and conditions are captured so that healthcare providers can monitor the health of patients. It leads to timely medical interventions and improved remote patient safety.

A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to 10.0% of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that, at an angle of 45º, the intensity is reduced to 50% of its original value (as you will show in this section’s Problems & Exercises). Note that 71.6º is 18.4º from reducing the intensity to zero, and that at an angle of 18.4º the intensity is reduced to 90.0% of its original value (as you will also show in Problems & Exercises), giving evidence of symmetry.

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Figure 3. The transverse oscillations in one rope are in a vertical plane, and those in the other rope are in a horizontal plane. The first is said to be vertically polarized, and the other is said to be horizontally polarized. Vertical slits pass vertically polarized waves and block horizontally polarized waves.

Photographs of the sky can be darkened by polarizing filters, a trick used by many photographers to make clouds brighter by contrast. Scattering from other particles, such as smoke or dust, can also polarize light. Detecting polarization in scattered EM waves can be a useful analytical tool in determining the scattering source.

Meanwhile, you could check out the article What are the crucial factors to consider while integrating multi-camera solutions? if you are interested in learning more about multi-camera integration.

Many modern-day embedded vision systems utilize multiple types of lenses and sensors with different feature sets and varying costs. The design of the camera systems integrated with these components plays a huge role in achieving the required image quality.

e-con Systems has led from the front when it comes to innovation in embedded vision. And one of our key strengths is the platform side expertise especially on the NVIDIA Jetson series. Leveraging this, e-con has designed many multi-camera solutions that offer an FOV of up to 360 degrees.

Having 2 or more cameras enables a higher resolution, prevents lens distortion, and offers a wider FOV. To achieve high imaging quality in multi-camera systems, a lens having an FOV of around 60-70 degrees is usually chosen. But it is important to note that this is determined by a multitude of factors. There is no ‘one-size fits all’ approach to this. It is recommended to take the help from an imaging expert like e-con Systems as you go about picking the right field of view and lens for your application. Please feel free to write to us at camerasolutions@e-consystems.com if you need a helping hand.

Polarization of lightnotes PDF

You also have an option to capture the same field of view with sensors of different size. This can be done using a lens with the appropriate focal length. As a result, the same FOV can be achieved using a small sensor with a short focal length lens and a large sensor with a long focal length lens.

What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by 90.0%?

Figure 7. A polarizing filter transmits only the component of the wave parallel to its axis, , reducing the intensity of any light not polarized parallel to its axis.

What is polarization of lightin physics

To examine this further, consider the transverse waves in the ropes shown in Figure 3. The oscillations in one rope are in a vertical plane and are said to be vertically polarized. Those in the other rope are in a horizontal plane and are horizontally polarized. If a vertical slit is placed on the first rope, the waves pass through. However, a vertical slit blocks the horizontally polarized waves. For EM waves, the direction of the electric field is analogous to the disturbances on the ropes.

Figure 9. Long molecules are aligned perpendicular to the axis of a polarizing filter. The component of the electric field in an EM wave perpendicular to these molecules passes through the filter, while the component parallel to the molecules is absorbed.

Figure 11. Polarization by scattering. Unpolarized light scattering from air molecules shakes their electrons perpendicular to the direction of the original ray. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction.

Having two or more cameras enables a higher resolution, prevents lens distortion, and offers a wider FOV. To achieve high imaging quality in multi-camera systems, a lens having an FOV of around 60-70 degrees is usually chosen.

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Also, let us consider a popular embedded vision application like autonomous mobile robots (AMR). These autonomous systems perform obstacle detection and obstacle avoidance (ODOA) to seamlessly navigate their environment. And many of these robots require FOVs in excess of 180 degrees. This ultra-wide FOV is achieved by using multi-camera systems.

What is polarization ofwaves in Physics

However, it is extremely important to understand that many factors determine this. There is no ‘one-size fits all’ approach to this. It is recommended that you seek help from an imaging expert like e-con Systems as you pick the right field of view and lens for your application.

Each embedded vision application has different sensor size requirements to get the best output. A small sensor will have a narrow field of view while a large sensor can provide a wide field of view.

And one of the most popular among those solutions is e-CAM130A_CUXVR_3H02R1 180° FOV camera – a synchronized multi-camera solution that can be directly interfaced with the NVIDIA® Jetson AGX Xavier™ development kit. This camera solution comprises of three 13 MP camera modules that are based on the 1/3.2″ AR1335 CMOS image sensor from onsemi®. These 4K camera modules are positioned inwards to create a 180° FOV as shown in the image below:

Glass and plastic become optically active when stressed; the greater the stress, the greater the effect. Optical stress analysis on complicated shapes can be performed by making plastic models of them and observing them through crossed filters, as seen in Figure 14. It is apparent that the effect depends on wavelength as well as stress. The wavelength dependence is sometimes also used for artistic purposes.

Generally for a sensor, FOV refers to the diagonal measurement – which is called DFOV or Diagonal FOV. Horizontal FOV (HFOV) and Vertical FOV (VFOV) will vary based on the aspect ratio of the image sensor used.

polarization: the attribute that wave oscillations have a definite direction relative to the direction of propagation of the wave

From the previous section, we understood the definition of FOV and its relation with several other lens parameters. Let us now discuss how to choose the right FOV for an embedded vision application.

Find Polaroid sunglasses and rotate one while holding the other still and look at different surfaces and objects. Explain your observations. What is the difference in angle from when you see a maximum intensity to when you see a minimum intensity? Find a reflective glass surface and do the same. At what angle does the glass need to be oriented to give minimum glare?

For example, imagine that the camera and the object are fixed at a working distance of 30cm. In this case, the HFOV and VFOV are measured manually using a scale (in mm) as shown below:

Only the component of the EM wave parallel to the axis of a filter is passed. Let us call the angle between the direction of polarization and the axis of a filter θ. If the electric field has an amplitude E, then the transmitted part of the wave has an amplitude E cos θ (see Figure 7). Since the intensity of a wave is proportional to its amplitude squared, the intensity I of the transmitted wave is related to the incident wave by I = I0 cos2 θ, where I0 is the intensity of the polarized wave before passing through the filter. (The above equation is known as Malus’s law.)

Figure 10 illustrates how the component of the electric field parallel to the long molecules is absorbed. An electromagnetic wave is composed of oscillating electric and magnetic fields. The electric field is strong compared with the magnetic field and is more effective in exerting force on charges in the molecules. The most affected charged particles are the electrons in the molecules, since electron masses are small. If the electron is forced to oscillate, it can absorb energy from the EM wave. This reduces the fields in the wave and, hence, reduces its intensity. In long molecules, electrons can more easily oscillate parallel to the molecule than in the perpendicular direction. The electrons are bound to the molecule and are more restricted in their movement perpendicular to the molecule. Thus, the electrons can absorb EM waves that have a component of their electric field parallel to the molecule. The electrons are much less responsive to electric fields perpendicular to the molecule and will allow those fields to pass. Thus the axis of the polarizing filter is perpendicular to the length of the molecule.

Prabu is the Chief Technology Officer and Head of Camera Products at e-con Systems, and comes with a rich experience of more than 15 years in the embedded vision space. He brings to the table a deep knowledge in USB cameras, embedded vision cameras, vision algorithms and FPGAs. He has built 50+ camera solutions spanning various domains such as medical, industrial, agriculture, retail, biometrics, and more. He also comes with expertise in device driver development and BSP development. Currently, Prabu’s focus is to build smart camera solutions that power new age AI based applications.

Field of view (FOV) is the maximum area of a scene that a camera can focus on/capture. It is represented in degrees. There are three ways to measure the field of view of a camera – horizontally, vertically, or diagonally as shown below.

Figure 14. Optical stress analysis of a plastic lens placed between crossed polarizers. (credit: Infopro, Wikimedia Commons)

Figure 13. Optical activity is the ability of some substances to rotate the plane of polarization of light passing through them. The rotation is detected with a polarizing filter or analyzer.

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What helps e-con stand out when it comes to this solution is our proprietary 180-degree stitching algorithm that can process images from multiple cameras to create a 180 degree image. To learn more about this solution, please visit the product page.

While you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, computer screens, cellphones, flat screen televisions, and other myriad places, you may not be aware that they are based on polarization. Liquid crystals are so named because their molecules can be aligned even though they are in a liquid. Liquid crystals have the property that they can rotate the polarization of light passing through them by 90º. Furthermore, this property can be turned off by the application of a voltage, as illustrated in Figure 12. It is possible to manipulate this characteristic quickly and in small well-defined regions to create the contrast patterns we see in so many LCD devices.

FOV also depends on the distance between the camera and the object. As discussed earlier, if the objects are closer to the camera, the FOV becomes wider. This is because shorter focal lengths require shorter working distances for proper focusing. Thus, the lens to sensor distance has to be designed based on the working distance.

Polarisation meaning in Physics

Figure 8. Polarization by reflection. Unpolarized light has equal amounts of vertical and horizontal polarization. After interaction with a surface, the vertical components are preferentially absorbed or refracted, leaving the reflected light more horizontally polarized. This is akin to arrows striking on their sides bouncing off, whereas arrows striking on their tips go into the surface.

Many crystals and solutions rotate the plane of polarization of light passing through them. Such substances are said to be optically active. Examples include sugar water, insulin, and collagen (see Figure 13). In addition to depending on the type of substance, the amount and direction of rotation depends on a number of factors. Among these is the concentration of the substance, the distance the light travels through it, and the wavelength of light. Optical activity is due to the asymmetric shape of molecules in the substance, such as being helical. Measurements of the rotation of polarized light passing through substances can thus be used to measure concentrations, a standard technique for sugars. It can also give information on the shapes of molecules, such as proteins, and factors that affect their shapes, such as temperature and pH.

Another interesting phenomenon associated with polarized light is the ability of some crystals to split an unpolarized beam of light into two. Such crystals are said to be birefringent (see Figure 15). Each of the separated rays has a specific polarization. One behaves normally and is called the ordinary ray, whereas the other does not obey Snell’s law and is called the extraordinary ray. Birefringent crystals can be used to produce polarized beams from unpolarized light. Some birefringent materials preferentially absorb one of the polarizations. These materials are called dichroic and can produce polarization by this preferential absorption. This is fundamentally how polarizing filters and other polarizers work. The interested reader is invited to further pursue the numerous properties of materials related to polarization.

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Conversely, if you know the FOV and the working distance, then you can calculate the dimension of the object using the below formula.

Figure 15. Birefringent materials, such as the common mineral calcite, split unpolarized beams of light into two. The ordinary ray behaves as expected, but the extraordinary ray does not obey Snell’s law.

In flat screen LCD televisions, there is a large light at the back of the TV. The light travels to the front screen through millions of tiny units called pixels (picture elements). One of these is shown in Figure 12 (a) and (b). Each unit has three cells, with red, blue, or green filters, each controlled independently. When the voltage across a liquid crystal is switched off, the liquid crystal passes the light through the particular filter. One can vary the picture contrast by varying the strength of the voltage applied to the liquid crystal.

However, selecting and evaluating sensors and lenses can be challenging. The right combination can help build a highly optimized embedded vision system that meets all your standards. Of course, when selecting a lens for an embedded camera, numerous factors, such as Field Of View (FOV), must be considered.

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FOV is one of the most critical parameters considered while integrating a camera into an embedded vision system. Whether it’s an intelligent transportation system, autonomous mobile robot, remote patient monitoring system, or automated sports broadcasting device, FOV plays a major role in ensuring the necessary details of the scene are captured. The FOV of the lens can be set as wide or narrow based on the end application requirements.

Polarizationby reflection

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Brewster’s angle for water and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either water or glass under similar circumstances. Light not reflected is refracted into these media. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted.

Let’s look at Autonomous Mobile Robots (AMR) as a reference. These autonomous systems perform obstacle detection and obstacle avoidance (ODOA) to seamlessly navigate their environment. Many of them require FOVs in excess of 180 degrees. This ultra-wide FOV is achieved by using multi-camera systems.

If you hold your Polaroid sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim. This is a clear indication that light scattered by air is partially polarized. Figure 11 helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction it is traveling. The electrons then radiate like small antennae. Since they are oscillating perpendicular to the direction of the light ray, they produce EM radiation that is polarized perpendicular to the direction of the ray. When viewing the light along a line perpendicular to the original ray, as in Figure 11, there can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to be a longitudinal wave. Along other directions, a component of the other polarization can be projected along the line of sight, and the scattered light will only be partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations.

Figure 6 shows the effect of two polarizing filters on originally unpolarized light. The first filter polarizes the light along its axis. When the axes of the first and second filters are aligned (parallel), then all of the polarized light passed by the first filter is also passed by the second. If the second polarizing filter is rotated, only the component of the light parallel to the second filter’s axis is passed. When the axes are perpendicular, no light is passed by the second.

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Brewster’s angle: [latex]{\theta }_{\text{b}}={\tan}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)\\[/latex], where n2 is the index of refraction of the medium from which the light is reflected and n1 is the index of refraction of the medium in which the reflected light travels

Figure 5. A polarizing filter has a polarization axis that acts as a slit passing through electric fields parallel to its direction. The direction of polarization of an EM wave is defined to be the direction of its electric field.

Most embedded camera applications require the FOV to be wider enough to cover a large viewing area. For instance, a fish-eye lens is characterized by a wider FOV and larger depth of field (DOF) and is hence suitable for surveillance applications. On the other hand, for a zoom/telescopic application, you might require a normal/narrow FOV.

Most of the embedded camera applications require the FOV to be wider enough to cover a large viewing area. For instance, a fish-eye lens is characterized by wider FOV and larger depth of field (DOF) and hence is suitable for surveillance applications. On the other hand, for a zoom/telescopic application, you might require a normal/narrow FOV.

Polaroid sunglasses are familiar to most of us. They have a special ability to cut the glare of light reflected from water or glass (see Figure 1). Polaroids have this ability because of a wave characteristic of light called polarization. What is polarization? How is it produced? What are some of its uses? The answers to these questions are related to the wave character of light.

17. (a) 2.07 × 10−2 °C/s; (b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.

Polarized and unpolarizedlight

By now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. You can check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter.

Figure 2. An EM wave, such as light, is a transverse wave. The electric and magnetic fields are perpendicular to the direction of propagation.

Automated sports broadcasting systems use cameras with a wide FOV to cover entire fields or courts. Hence, all the movements within the sporting area are captured, which means viewers can experience the game in an immersive way. A wide FOV is also important for capturing aspects such as player movements and strategic plays, which enhances the overall broadcasting quality. Furthermore, wider FOV cameras streamline production by potentially replacing multiple conventional cameras, reducing setup complexity and personnel needs.

Since the part of the light that is not reflected is refracted, the amount of polarization depends on the indices of refraction of the media involved. It can be shown that reflected light is completely polarized at a angle of reflection θb, given by [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex], where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light. This equation is known as Brewster’s law, and θb is known as Brewster’s angle, named after the 19th-century Scottish physicist who discovered them.

Figure 8 illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so that the reflected light is left more horizontally polarized. The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertical polarization would be like an arrow perpendicular to the surface and would be more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and would be more likely to be reflected. Sunglasses with vertical axes would then block more reflected light than unpolarized light from other sources.

All we need to solve these problems are the indices of refraction. Air has n1 = 1.00, water has n2 = 1.333, and crown glass has n′2=1.520. The equation [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] can be directly applied to find θb in each case.

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Figure 4. The slender arrow represents a ray of unpolarized light. The bold arrows represent the direction of polarization of the individual waves composing the ray. Since the light is unpolarized, the arrows point in all directions.

Similarly, for the calculation of VFOV and DFOV, instead of width (or horizontal F0V), corresponding height and diagonal dimensions of the object are substituted in the above formula respectively.