It was the first space observatory to extend the observations from the far-infrared into submillimetre wavelengths and bridge the two. By tapping these unexploited wavelengths, Herschel could see phenomena beyond the reach of other observatories, and study others at a level of detail that had not been captured before.

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Parabolic geometry is the basis for such concentrating solar power (CSP) technologies as troughs or dishes. Parabolic trough is also considered one of the most mature and most commercially proven technologies in the utility scale CSP facilities (Mendelsohn et al., 2012), so we will look at the physical principles of parabolic concentrators in some more detail.

This figure above shows that the flatter the reflecting surface, the longer the focal length. The "flatness" of the shape of a finite parabola is typically characterized by the rim angle ( ϕ ). When rim angle increases (within the same aperture), the parabola becomes more curved, and the focal distance shortens.

The equations presented here can be used to estimate the size of the reflected light image on the receiver for different shapes of parabolic reflectors. The formulas include a as a chosen aperture of the reflector (width of the trough), and ( ϕ ) as a measure of parabolic curvature. Note that these are the minimal theoretical dimensions of the reflected image that would be produced by the ideal parabolic mirror that is perfectly aligned. If there are any flaws in the mirror surface or trueness of the angle, additional spreading of the image may occur. If you are interested in more explanation of how these formulas were derived, please refer to Duffie and Beckman, 2013 book (Section 7.9)

Please refer to the following reading to study the tools for image analysis via the nonuniform solar disk model, and be sure to study the example presented therein, which is very helpful.

The use of infrared technology in astronomy is now well advanced and the infrared revolution is in full swing. But the golden age of infrared astronomy has just begun.

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By definition of the focal point of the parabola, all incoming rays parallel to the axis of the parabola are reflected through the focus. This provides an opportunity for light concentration by using parabolic surfaces. If we assume that solar light arrives to the surface as essentially parallel rays, and apply the Snell's law (the angle of reflection equals the angle of incidence), we can assign the focal point as an ideal location for the receiver (Figure 2.7).

Book chapter: Duffie, J.A. Beckman, W., Solar Engineering of Thermal Processes, Chapter 7: Sections 7.9 and 7.10. pp. 351-358.

The larger the aperture, the more energy is concentrated within a certain image size. The smaller the focal length, the smaller the image size within which the energy is concentrated.

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Infrared radiation can help us learn much more about the young‚ distant Universe. The Universe has been expanding since the Big Bang — the event that formed it. There were no stars or galaxies to begin with, but they started to form relatively early. We now know that at half the Universe's present age, star formation was much more vigorous than it is today and that in the very beginning it was zero. So the rate of star formation rate varies in cosmic time.

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The chemical make-up of dust clouds and other interesting regions can be probed by looking at the spectra of their molecules, often only in the infrared. The reason is that most atoms and molecules emit radiation which has energy corresponding to the infrared range (emitted during rotation and vibration). Besides, infrared radiation is typical of cooler regions, for instance dust clouds, where more complex compounds such as organic molecules are often found. Infrared astronomy has made many interesting discoveries related to these more complex molecules in space.

ESA's Herschel mission, which launched on 14 May 2009, explored further into the far-infrared than ever before, studying otherwise invisible dusty and cold regions of the cosmos, both near and far. It was designed to observe infrared-dominated galaxies – which are mostly star-burst galaxies where stars from a thousand times faster than in the Milky Way at present, enabling us to observe these galaxies through the cosmic epochs when most of the stars that ever existed in the Universe formed.

Geometrically, a parabola is a locus of points that lie on equal distance from a line (directrix) and a point (focus) - see Figure 2.6. For each point of the parabola, DR = FR. The distance VF between the vertex and focus of the parabola is the focal distance (f). The line perpendicular to the directrix that passes through the focus is the axis of the parabola; the axis divides the parabola into two parts that are symmetrical.

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The superposition of these individual ellipses produced by each element of the reflector form the total image, which is not uniform, but rather has a distribution of light intensity. The focal length (which is related to the rim angle of the reflector) is responsible for image size, while the aperture is responsible for the total amount of energy concentrated by a collector. So, the total image intensity (brightness) at the receiver should be a function of a/f. The image brightness essentially reflects the energy flux concentration:

Observations in the infrared have revolutionised astronomy, revealing previously hidden aspects of the Universe that have changed our perception of the world around us. The Universe seen in the infrared has proved amazingly rich and diverse. It has given us keys to unlock the chemistry of the Universe, to explain how stars are born and to establish the origin of galaxies.

Knowing the angular width of the cone, the dimensions of the ellipse image can be theoretically derived and presented as a function of ϕ (angle of deviation from the parabola axis). Below are the equations describing the length of the minor and major axes of the ellipse.

Launched on 25 December 2021, it is already helping us to see farther into our origins: from the formation of stars and planets, to the birth of the first galaxies in the early Universe.

Parabolic trough (Figure 2.9) is a typical example of an imaging concentrator that utilizes the geometric relationships discussed above. Parabolic trough is one of the most widely implemented technologies for sunlight concentration at the utility scale. This type of collectors relies on sun tracking to ensure that the beam radiation is directed parallel to the parabolic axis.

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The James Webb Space Telescope (Webb) – an international partnership between NASA, ESA and the Canadian Space Agency (CSA) – is the next great space science observatory, designed to answer outstanding questions about the Universe and to make breakthrough discoveries in all fields of astronomy.

The particles can be hard or soft and come in many different shapes, but their size is usually less than 1 micron (one thousandth of a millimetre). The wavelength of visible light is much the same size as many dust particles, so it is easily blocked (scattered) by the dust, whereas longer-wavelength infrared radiation passes through unhindered and dust is therefore transparent to it. And in the far-infrared, we see the 'glow' from dust itself.

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Astronomers have used several different properties of infrared light to reveal more about the Universe. Although our eyes cannot see infrared radiation we can sense it — as radiant heat. Infrared radiation 'is' heat, and all objects, even the coldest ones, an ice cube for example, emit a certain amount of heat.

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where r is the distance between the focus and reflection point (local radius) on the parabolic mirror (r=f at the vertex); ϕ is the angle between the parabola axis and the ray, and 0.267o is the half-angle of the ray cone width.

Solar applications deal with a parabola of a finite height (Figure 2.8). The design of the parabolic reflector takes into account the available aperture size (a), focus location (f - i.e., where receiver would be placed), and height of the reflector (h). These parameters are interrelated via the equation (Stine and Harrigan, 1986):

The distribution of intensity of the energy flux within the concentrated image may have a profile similar to Figure 2.5. Different models have been applied to quantify that profile. For example, one of the approaches is called nonuniform solar disk, which suggests that the sunlight intensity coming out of the center of the solar disk is higher than that coming from its edges [Evans, 1977]. Without going into too much detail of this model, we can use the diagrams presented in the book by Duffie and Beckman (2013), which allow connecting various parameters of a parabolic concentrator with the local intensity on the receiver.

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Please answer the following quick questions to check your understanding of some of the basic points in this section. The parabola cheatsheet presents a useful summary for your notes.

The above-described geometrical concepts apply to the cross-section of a parabolic reflector. In reality, the reflector itself is a three-dimensional shape, i.e., a parabolic cylinder with a finite length (l). So, the cone-shaped ray reflected at a point on the surface of a parabolic reflector will produce an ellipse-shaped image on the focal plane. We can see that as the reflection point is moved away from the vertex towards the rim, the ellipse transforms from a circular to a more and more elongated shape (because the cone would be sectioned by the focal plane at greater and greater angle - Figure 2.11).

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A parabolic mirror produces an image of the sun on the surface of the receiver, so the receiver size needs to be matched to the image size. Consider Figure 2.10, which illustrates this idea. Since the sun is not really a point source, solar beam incident on the reflector is represented as a cone with an angular width 0.53o (so the half-angle between the cone axis and its side is 0.267o). Being reflected at a point on the parabolic surface, the beam hits the focal plane, where it produces an image of a certain dimension, centered around the focal point. The diameter of the cylindrical receiver (D), which would intercept the entire reflected image can be theoretically calculated using aperture width (a), and rim angle ( ϕ ) as follows (Duffie and Beckman, 2013):

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In fact, celestial objects with surface temperatures of about 2000°C — cold compared to the Sun which has a surface temperature of about 5500°C — radiate most of their energy at infrared wavelengths. The Universe is full of cool objects, including ageing stars, planets and dust, none of which generally shine brightly in the optical part of the spectrum and could not be observed directly until sensitive infrared detectors came along. The cool Universe is best studied in the infrared.

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When Herschel launched, it carried the largest telescope ever flown in space, with a main mirror measuring 3.5 m across. This was more than four times larger than any previous infrared space telescope and almost one and a half times larger than that of the Hubble Space Telescope.

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The main goal for this assignment is to understand how to estimate concentrated image parameters using model diagrams 7.10.1, 7.10.2, and 7.10.3.

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Dust is the bane of the optical astronomer's life, blocking the view of many interesting objects. The Universe is full of dust, microscopic particles of varied composition — carbon, silicon, water ice, minerals, frozen carbon monoxide, organic compounds, silicates — the list is almost endless.

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