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Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

FOV plays an important part in VR applications. VR glasses with thick and heavy lenses provide a small focal length, which increases the FOV and delivers a more immersive user experience (UX). However, heavier equipment and larger lenses also cause color distortions and chromatic aberrations, so lighter headsets are required to prevent these issues. It can be difficult to achieve this balance. Nonetheless, VR technology is improving, and in the future, we may see lighter equipment and lenses and a larger FOV to deliver enhanced UX.

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We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

FOV is the range of the observable world visible at any given time through the human eye, a camera viewfinder or on a display screen. It refers to the coverage of an entire area rather than a single, fixed focal point. FOV also describes the angle through which a person can see the visible world.

Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

Finally, FOV calculations matter in drone photography. Drone photographs can capture large swathes of a landscape better with a larger FOV. Extra visibility can also make it easier to see obstacles from a first-person view for better control of the drone.

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We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

The human eye is the natural starting point to perceive the FOV. In human vision, the FOV is composed of two monocular FOVs, which the brain stitches together to form one binocular FOV.

In addition to monocular and binocular differences in vision, humans also have different FOV for different colors. Color saturation and perception are concentrated in the center of the FOV, so the image becomes more monochromatic on the edges or periphery of a person's vision.

How to Convert Inch to Millimeter ; 0.313, 5/16, 7.95 mm, 4.0 mm, 0.157 ; 0.375, 3/8, 9.53 mm, 4.3 mm, 0.169.

A larger sensor yields a larger FOV for the same working distance. Changing the sensor size can change the FOV. The sensor size depends on the number of pixels on the sensor and the size of the pixels. Larger sensors enable a better image and higher resolution, while smaller sensors have a smaller depth of field (DOF) -- sharpest point between closest and farthest point of an image -- resolution and pixel size.

Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

FOV to focal length calculator

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Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

In photography and filmmaking, the FOV refers to what is visible through the camera lens or optical viewfinder. Changing the lens changes the FOV. To increase FOV and capture more of a scene, a wide-angle lens -- which displays a wider field of view than our human vision -- is used. Similarly, to decrease the FOV, a zoom lens can be used. In general, a smaller focal length lens increases the angle and the FOV. Thus, the FOV can be controlled by changing out lenses with varying focal lengths.

According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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The FOV can also be changed by using a varifocal lens or zoom lens, both of which enable focal length adjustment and, therefore, FOV adjustment. However, these lenses are larger and more expensive and offer lower performance than fixed focal length lenses.

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For a given sensor size, a shorter focal length gives a wider AFOV and, therefore, a larger FOV and vice versa. Additionally, a shorter working distance is needed to obtain the same FOV compared to a longer focal length lens. However, short focal length lenses are associated with higher distortion, which can influence the FOV and cause variations in the angle with respect to the working distance.

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We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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Using Linear Aproximation to illustrate Chromatic Aberration We are going to find the matrices of a simple lens system and then determine the focal length with a given radii, distance between the lenses, and other information to shop that focal point differs for different wavelength The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

See also: first-person view, imaging, aspect ratio, stereoscopy, Digital Imaging and Communications in Medicine, IP camera, complementary metal-oxide semiconductor sensor and thermal imaging.

Each individual eye has a horizontal FOV of about 135 degrees and a vertical FOV of just over 180 degrees. Stitching together the monocular FOV yields a binocular FOV of around 114 degrees of view horizontally. This FOV is necessary for depth perception.

Typically, magnification is related to scaling up visuals or images to be able to see more detail, increasing resolution, using microscope, printing techniques, ...

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A person's peripheral vision makes up the remaining 60-70 degrees. However, this version is only monocular because only one eye can see those sections of the visual field. All these FOV measurements assume that the person's eyes are fixed on the observable world.

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The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

Further, short focal length lenses usually do not provide a high level of performance compared to longer focal length lenses. And shorter lenses may not cover medium-large sensor sizes, which can limit their usability.

According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

Chromatic Aberration occurs because of dispersion. Dispersion is the change in refractive index due to changing wavelength. The images formed from these different colours of light are not coincident. There are two effects of chromatic abberation 1) Longitudinal displacement of the image along the optic axis ( Longitudinal Chromatic Abberation) 2) Variation in image size with color (Lateral Chromatic Abberation) This figure shows that, according to Snell's Law, the angle of refraction differ for different indexes. A white object will not give rise to a white image but it will be distorted and have rainbow edges. Connecting Wavelength to Indexes Applying Huyen's Principle to Snell's Law : The wavelengths are in Armstrong unit. These are the lines that appeared in the solar spectrum that J. von Fraunhofer studied known as "Fraunhofer wavelength". The refraction index increased with an decreasing wavelengths. Using Linear Aproximation to illustrate Chromatic Aberration We are going to find the matrices of a simple lens system and then determine the focal length with a given radii, distance between the lenses, and other information to shop that focal point differs for different wavelength The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

FOV is an important foundational concept in optics. Anyone working with optics should be aware of FOV. This includes the following:

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The main difference between FOV and DOF is that DOF refers to the area of sharpness behind and in front of the subject. FOV is the area that can be seen through a lens or viewfinder at any particular moment. It determines how big the imaged area is. Thus, FOV is about image.

We are going to find the matrices of a simple lens system and then determine the focal length with a given radii, distance between the lenses, and other information to shop that focal point differs for different wavelength The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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Applying Huyen's Principle to Snell's Law : The wavelengths are in Armstrong unit. These are the lines that appeared in the solar spectrum that J. von Fraunhofer studied known as "Fraunhofer wavelength". The refraction index increased with an decreasing wavelengths. Using Linear Aproximation to illustrate Chromatic Aberration We are going to find the matrices of a simple lens system and then determine the focal length with a given radii, distance between the lenses, and other information to shop that focal point differs for different wavelength The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

A white object will not give rise to a white image but it will be distorted and have rainbow edges. Connecting Wavelength to Indexes Applying Huyen's Principle to Snell's Law : The wavelengths are in Armstrong unit. These are the lines that appeared in the solar spectrum that J. von Fraunhofer studied known as "Fraunhofer wavelength". The refraction index increased with an decreasing wavelengths. Using Linear Aproximation to illustrate Chromatic Aberration We are going to find the matrices of a simple lens system and then determine the focal length with a given radii, distance between the lenses, and other information to shop that focal point differs for different wavelength The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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When a camera lens is focused on a subject, the DOF determines how blurry or sharp the area around the subject is. When the DOF is shallow, only a small area is in focus. But, when the DOF is deep, the lens captures a larger area in focus.

Field of view (FOV) is the open, observable area a person can see through their eyes or via an optical device, such as a camera. In the case of optical devices, FOV is the maximum area that the device can capture. In other words, it answers the question: "How much can the device see?"

The fixed focal length lens can be focused for different working distances to obtain differently sized FOV, even though the viewing angle remains constant. Thus, the lens focal length defines the AFOV and FOV.

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With a small focus area and shallow DOF, the subject is in focus, while the background is blurred. This scenario is required for portrait photographs. When a larger area is in focus with a deeper DOF, everything in the image remains sharp and clear, including the background. This situation is ideal for landscape photography.

FOV is also a crucial consideration in computer games. Gamers prefer games that enable FOV adjustment because games without this option are not as natural or immersive as gamers would like. A low FOV may even cause motion sickness.

We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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A fixed focal length lens provides a fixed angular FOV (AFOV). AFOV is the angle of light that can be captured by the lens. It is required to calculate the overall FOV. A fixed focal length lens is not the same as a fixed focus lens, which can only be used at a fixed working distance.

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Connecting Wavelength to Indexes Applying Huyen's Principle to Snell's Law : The wavelengths are in Armstrong unit. These are the lines that appeared in the solar spectrum that J. von Fraunhofer studied known as "Fraunhofer wavelength". The refraction index increased with an decreasing wavelengths. Using Linear Aproximation to illustrate Chromatic Aberration We are going to find the matrices of a simple lens system and then determine the focal length with a given radii, distance between the lenses, and other information to shop that focal point differs for different wavelength The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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A wider FOV makes the viewing experience more realistic. But, regardless of the lens used, the angle is always smaller than the field of vision possible with the human eye. In other words, camera lenses cannot deliver the same kind of immersive viewing experiences possible with human eyesight.

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The wider the FOV, the more one can see of the observable world. It is measured horizontally, vertically and diagonally. The camera lens, its focal length and the sensor size all play a part in determining the FOV.

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The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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This figure shows that, according to Snell's Law, the angle of refraction differ for different indexes. A white object will not give rise to a white image but it will be distorted and have rainbow edges. Connecting Wavelength to Indexes Applying Huyen's Principle to Snell's Law : The wavelengths are in Armstrong unit. These are the lines that appeared in the solar spectrum that J. von Fraunhofer studied known as "Fraunhofer wavelength". The refraction index increased with an decreasing wavelengths. Using Linear Aproximation to illustrate Chromatic Aberration We are going to find the matrices of a simple lens system and then determine the focal length with a given radii, distance between the lenses, and other information to shop that focal point differs for different wavelength The Lens System Matrices Examples Example 1 Example 2 We have shown that the focal point is different for different colour due to the wavelength. Correcting Chromatic Abberation: Chromatic aberration can be eliminated by making multiple refracting elements with opposite power (Pedrotti). The most common solution is making a achromatic doublet, consisting a convex and a concave lens, of different glasses. For example, using a crown glass equiconvex lens to a negative flint glass lens. Design for thin len: The matrix for thin len convex len is: Let's apply the matrix to the matrix of a focus image, we get Let's simplify the equation We are going to apply these equation to the sample achromatic doulet and figure out the lens design. The Fraunhofer wavelength we are going to use is D - yellow colour. Therefore, the index of refraction n is for the wavelength D. The power of the two lens are Let K1 and K2 be constants, represent abberation for the curvatures. We know that the power of a doublet with a distance of L is Since we our doublet are cemented, L=0, the powers are According to Pedrotti(P. 101), chromatic aberration does not exist for yellow(D) wavelength if the power is independent of the wavelength or the derivative We take the derivative of the power and we get According to Blaker(p. 71), the dispersive power is v and dispersive constant V To determine the variation for n with lamda, in the area around the colour yellow, we have to take an approximation using the colour red and blue. We want We have to determine each individual len power in term of the desire power P Finally, from the equation above, we can now determine the curvature K and the four radii. Achromatizing thin lens will result in a nearly equal focal lengths(focal length for red nearly equal to focal length for blue), eliminate longitudinal and later aberration at the same time, i.e will coincide. But the problem with thick len is that equal focal lenghts may not coincide as thin len. If we change the focal lengths for red and blue, resulting in a different later magnification and therefore lateral chromatic aberration remains. According to Pedrotti, the condition to remove lateral chromatic aberration is "the coincidence of the principal planes for the corrected wavelengths" (Pedrotti, p.104).

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