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courses:ast201:6 [2023/08/13 03:38] – [5.3 Spherical aberration] asadcourses:ast201:6 [2023/11/25 23:43] (current) – asad
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 A **coherent** source emits all light in phase, and in this case the geometrical wavefronts also correspond to surfaces of constant phase called **phase fronts**. A **coherent** source emits all light in phase, and in this case the geometrical wavefronts also correspond to surfaces of constant phase called **phase fronts**.
 +
 +{{:courses:ast201:n-lambda.png?nolink|}}
  
 ==== - Reflection and refraction ==== ==== - Reflection and refraction ====
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 reflectance R=0R=0 for TM polarization and only the TE polarization is reflected. reflectance R=0R=0 for TM polarization and only the TE polarization is reflected.
  
-=== Spherical surface and interface ===+==== - Spherical interfaces ====
 {{:courses:ast201:reflection-spherical.png?nolink&650|}} {{:courses:ast201:reflection-spherical.png?nolink&650|}}
  
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 where P12P12 is the power in diopters. Positive PP tells you how strongly converging a lens is, and vice versa. where P12P12 is the power in diopters. Positive PP tells you how strongly converging a lens is, and vice versa.
  
-===== - Mirrors, lenses and antennae =====+===== - Mirrors and lenses =====
 {{:courses:ast201:thick-lens.png?nolink|}} {{:courses:ast201:thick-lens.png?nolink|}}
  
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 Optical fibres are used in astronomy for transferring light from the focal plane to somewhere else for further analysis. Sometimes putting a large spectrometer or detector or sensor at the focal plane is not practical as it obstructs the optical path, so optical fiber openings are placed at the focal plane instead. Optical fibres are used in astronomy for transferring light from the focal plane to somewhere else for further analysis. Sometimes putting a large spectrometer or detector or sensor at the focal plane is not practical as it obstructs the optical path, so optical fiber openings are placed at the focal plane instead.
  
-==== - Optical materials ==== 
-{{:courses:ast201:n-lambda.png?nolink|}} 
- 
-Surface coating can increase or decrease reflectance. A coating with 1/4 wavelength thick film will create two reflected waves that are exactly 1/2 wavelength out of phase with each other; they will destruct each other if they have the same amplitude. If the glass and the coating have indices nsns and ncnc, then the amplitude of the two reflected beams will be equal if 
- 
-nc=√nsnc=√ns. 
  
 ==== Prisms ==== ==== Prisms ====
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 For reflecting systems, chromatic aberration does not occur. But even monochromatic light (light of just one wavelength) can have differing focus after getting reflected from a mirror. For reflecting systems, chromatic aberration does not occur. But even monochromatic light (light of just one wavelength) can have differing focus after getting reflected from a mirror.
  
-{{:courses:ast201:wavefront-aberrations.png?nolink&700|}}+{{:courses:ast201:optical-planes.webp?nolink&800|}}
  
 The plane of the diagram (a) is called the **tangential** plane and the plane perpendicular to it is called the **sagittal** plane. The chief ray V′VF and the ray CFBFC are shown on the tangential plane. The test ray P′PF could be on a different plane than the tangential and sagittal. The plane of the diagram (a) is called the **tangential** plane and the plane perpendicular to it is called the **sagittal** plane. The chief ray V′VF and the ray CFBFC are shown on the tangential plane. The test ray P′PF could be on a different plane than the tangential and sagittal.
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 f(ρ)=R2−(1+K)[ρ24R+(3+K)ρ416R3+...] f(ρ)=R2−(1+K)[ρ24R+(3+K)ρ416R3+...]
  
-where the first term gives R/2 gives the Gaussian focus, ρ2 is a third-order aberration term and ρ4 is a fifth-order aberration term. The conic constant K=−e2.+where the first term gives R/2 gives the Gaussian focus, ρ2 is a third-order aberration term and ρ4 is a fifth-order aberration term. The **conic constant** K=−e2.
  
 The actual image is blurred and formed not in the Gaussian plane but in the **plane of least confusion**. The actual image is blurred and formed not in the Gaussian plane but in the **plane of least confusion**.
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 A Schmidt telescope modifies a spherical reflector to have minimal SA.  A Schmidt telescope modifies a spherical reflector to have minimal SA. 
 +
 +==== - Coma ====
 +Before the invention of photography, astronomers did not care about off-axis sources.
 +
 +Among the four off-axis aberrations, coma and astigmatism degrade image resolution, and the curvature of field and distortion only change the position of the course.
 +
 +Both coma and SA are problematic mainly for large apertures because of the large exponent of ρ.
 +
 +Coma depends on ρ3bcosϕ, so it increases with distance of the object from axis.
 +
 +{{:courses:ast201:coma.png?nolink&700|}}
 +
 +In this sagittal plane diagram, rays are coming off-axis at an angle θ, here we are talking about a constant distance from the vertex ρ. The rays form a ring-shaped offset from the Gaussian focus. The farther the ray (its meeting point on the Gaussian plane) is from the Gaussian focus, the bigger the ring. So the overall offset creates a shape like a comet, hence the name coma.
 +
 +The angular size of the blur due to coma
 +
 +L=AbD2f3=AθR−2
 +
 +where D is the diameter of the aperture, R is the focal ratio, and A depends on the shape of the surface.
 +
 +An optical system with neither SA nor coma is called **aplanatic** which can only be achieved by using multiple optical elements together.
 +
 +==== - Astigmatism ====
 +Astigmatism depends on b2ρ2cosϕ and, hence, it increases more rapidly than coma for off-axis points in an image.
 +
 +In the sagittal plane, ϕ=90∘ or 270∘ and, hence, coma is zero. It is maximum in the tangential plane (ϕ=0∘ or 180∘).
 +
 +{{:courses:ast201:astigmatism.png?nolink&800|}}
 +
 +The tangential rays focus on the Gaussian focus on the sagittal plane, and this focus is the tangential focus. The sagittal rays focus on a sagittal focal point S farther away. The compromise focus is somewhere in between.
 +
 +The image of a star at the compromise focus has a length due to astigmatism
 +
 +Lastig=Bθ2R−1
 +
 +where B depends on the detailed structure of the aperture surface.
 +
 +A Schmidt-Cassegrain system is anastigmatic aplanat.
 +
 +==== - Field curvature ====
 +{{:courses:ast201:field-curvature.png?nolink&500|}}
 +
 +If the previous aberrations are absent, image should be formed at the focal plane at a distance f=R/2 from the vertex. However, the actual imaging surface is not a //plane// but a //curved surface// called the **Petzval surface**. If the object is on-axis, there is no problem, but the off-axis sources are necessarily out-of-focus because they are not imaged on the focal plane, but on the curved Petzval surface. This is field curvature.
 +
 +The detector is usually placed on the Petzval surface. If the detector is small, the curvature can be ignored. But for large detectors, this cannot be ignored. In the past, glass photographic plates used to be bent to match the curvature of the Petzval surface. However, modern CCDs cannot be bent. So corrector plates or lenses are used.
 +
 +==== - Distortion ====
 +{{:courses:ast201:distortion.png?nolink|}}
 +
 +Straight lines on the sky become curved lines in the focal plane. The **pincushion** and **barrel** distortions are shown above.
 +
 +Below you see the visual representation of all the distortions for both on-axis and off-axis objects.
 +
 +{{:courses:ast201:spot-diagram.png?nolink|}}
  
courses/ast201/6.1691919482.txt.gz · Last modified: 2023/08/13 03:38 by asad
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