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If your light is made up of a combination of s- and p-polarised light, then you treat each of these components separately and then add them back together when considering the reflected and transmitted light.

Line scan cameras have great advantages in scanning speed. Because the line scan camera only scans one line at a time, its scanning speed is very fast and can meet the demand for real-time inspection of items on high-speed production lines. The area scan camera needs to scan the entire image line by line, so the scanning speed is relatively slow and cannot meet the detection needs of high-speed moving objects.

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Line scan cameras have great advantages in scanning speed. Because the line scan camera only scans one line at a time, its scanning speed is very fast and can meet the demand for real-time inspection of items on high-speed production lines. The area scan camera needs to scan the entire image line by line, so the scanning speed is relatively slow and cannot meet the detection needs of high-speed moving objects.

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What happens to that other light when interacting with a surface, or passing through a polarizing filter? From my reading so far it seems that there is a mathematical way to reduce these other orientations to combinations of s- or p-polarized light. How does that work? For example, if the electric fields of a light ray are at an angle of 45 degrees from the incident plane, does half of it behave like p- and half like s-polarized light? In the case of Brewster's angle, would that ray be half-transmitted and half-reflected, or only transmitted?

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To select a suitable line scan lens, start by understanding the camera's specifications, including sensor size and resolution. Calculate the desired field of view and choose a lens with an appropriate focal length. Ensure compatibility with the camera's mount type and consider factors like aperture size and lens resolution. Check for optical distortion and consider any special requirements such as low-light performance. Test the selected lens with the camera to validate its performance before finalizing the choice.

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Line scan cameras capture images one line at a time and are suited for inspecting continuously moving objects, like those on a conveyor belt. They excel in applications such as web and surface inspection. In contrast, area scan cameras capture entire images at once, making them versatile for stationary scenes. Area scan cameras are commonly used in general photography and surveillance. Both camera types offer unique advantages tailored to specific imaging needs and applications.

A line scan camera is designed to capture images of objects or scenes one line at a time, as opposed to traditional area scan cameras that capture entire images at once. The primary function of a line scan camera is to produce high-resolution images of continuously moving objects or scenes with exceptional clarity and detail. It achieves this by capturing individual lines of pixels rapidly and sequentially, allowing for precise inspection, measurement, and analysis of objects in motion. Line scan cameras are commonly used in industrial applications such as web inspection, surface inspection, sorting, quality control, and printing, where fast-moving objects or continuous processes need to be accurately monitored and analyzed.

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I'm trying to understand Brewster's angle and am stuck on what the different types of polarization actually mean (I'm a total beginner in physics so I might have misunderstood some very basic concepts).

Any polarisation state for the incident light can be made up of a mixture of two polarisation states that are mutually perpendicular. Since you are free to choose these perpendicular directions (so long as they are also perpendicular to the wave-vector for transverse waves), it makes sense to have them parallel (p) or perpendicular (s) to the plane of incidence.

In your example of light polarised at 45 degrees to the plane of incidence, then it is an an equal, in-phase mixture of s- and p-polarised light. You can calculate how each of these components behaves at the interface and then add together the resulting reflected and transmitted components to see what has happened to the reflected and transmitted light.

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My textbook describes light as either $s$- or $p$-polarized or a mixture of both, depending on the orientation of the electric fields towards the plane of incidence. But the non-polarized incident light must also contain other types, that are not either perpendicular or parallel to the plane of incidence? Why do all the diagrams describing Brewster's angle only show two types of polarization then? Example, this diagram from Wikipedia:

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Unpolarised light would be modelled as an equal mixture of p- and s-polarised light with random, rapidly varying phase differences between them.

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Selecting the right lens for a line scan camera involves careful consideration of several factors to ensure optimal performance. Begin by understanding the camera's specifications, including sensor size, pixel size, resolution, and spectral sensitivity. Calculate the desired field of view (FOV) based on application requirements, object size, and working distance. Choose a lens with an appropriate focal length using the formula (Focal Length = Sensor Width × Working Distance / FOV). Ensure compatibility between the lens mount and the camera's mount type. Consider aperture size, lens resolution, optical distortion, and any special requirements such as low-light performance or environmental sealing. Test the selected lens with the camera to validate its performance before finalizing the choice. This systematic approach ensures the selected lens complements the line scan camera, delivering high-quality imaging results tailored to the application's needs.

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In the case of incidence at the Brewster angle, the reflection coefficient for the p-polarised light will be zero and the reflected light will contain only an s-polarised component. There is however a non-zero transmission coefficient for the p-polarised component.

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