Types of Optical Telescopespca015000/PHYS_3380/... · 2019-10-07 · Four primary reasons reflecting telescopes are primary astronomical tools used for research: 1. Lens of refracting

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PHYS 3380 - Astronomy

Types of Optical Telescopes

PHYS 3380 - AstronomyRefracting Telescope

Uses lens to focus light from distant object - the eyepiece contains a small lens that brings the collected light to a focus and magnifies it for an observer looking through it.


The largest refracting telescope in the world is the at the University of Chicago’s Yerkes Observatory - it is 40 inches in diameter and 63 feet long.


Reflecting Telescope

The primary mirror focuses light at the prime focus. A camera or another mirror that reflects the light into an eyepiece is placed at the prime focus.


Types of Reflecting Telescopes

Each design incorporates a small mirror just in front of the prime focus to reflect the light to a convenient location for viewing.

PHYS 3380 - AstronomyThe Keck Telescopes

Keck telescopes on Mauna Kea in Hawaii. 36 hexagonal mirrors function as single 10-meter mirror.

Largest in the world is the Gran Telescopio Canarias in the Canary Islands which began operations in May 2009 – 10.4 m. The European Extremely Large Telescope (E-ELT) is planned to have first light in 2025. The E-ELT will measure close to 40 meters in diameter


The Hubble Space Telescope is 43.5 ft long and weighs 24,500 lbs. Its primary mirror is 2.4 m (7 ft 10.5 in) in diameter.

The Hubble Space Telescope


Remember: the focus is the point where light rays parallel to optical axis converge and the focal length is the distance from the focus to the

centerline of the lens

Optical axisFocus

Focal length


Focal Plane

l1 l2

o i

Geometry of a Simple Lens

f

Lens formula

Linear Magnification

Using the Gaussian form of the lens equation, a negative sign is used on the linear magnification equation as a reminder that all

real images are inverted

The focal plane is where incoming light from one direction and distance (object distance o greater than focal length) is focused.


The image formed by a single lens is inverted.


Focal length

Focal Plane

PHYS 3380 - Astronomy The Eye

The eye consists of pupil that allows light into the eye - it controls the amount of light allowed in through the lens - acts like a simple glass lens which focuses the light on the retina - which consists of light sensitive cells that send signals to the brain via the optic nerve. An eye with perfect vision has its focus on the retina when the muscles controlling the shape of the lens are completely relaxed - when viewing an object far away - essentially at infinity. Farsightedness/Nearsightedness - focus behind/in front of the retina


When viewing an object not at infinity, the eye muscles contract and change the shape of the lens so that the focal plane is at the retina (in an eye with perfect vision). The image is inverted as with a single lens - the brain interprets the image and rights it.


Geometry is similar for a concave mirror - image is inverted.

PHYS 3380 - AstronomyGeometry of a Concave Mirror

Vertex

Focal length

Focal plane


Refracting/Reflecting Telescopes

Refracting Telescope: Lens

focuses light onto the focal plane

Reflecting Telescope:

Concave Mirrorfocuses light onto

the focal plane

Almost all modern telescopes are reflecting telescopes.

Focal length

Focal length


Secondary Optics

In reflecting telescopes: Secondary mirror, to re-direct light path towards back or side of incoming light path.

Eyepiece: To view and enlarge the small image produced in the focal plane of the primary optics.

PHYS 3380 - AstronomyMagnification Using Two Lenses - Refracting Telescope

f1 = 0.5 mf2 = 0.1 m

f1 = 0.5 mf2 = 0.3 m

Refracting telescope - consists of two lenses - the objective and the eyepiece (ocular). Incident light rays (from the left) are refracted by the objective and the eyepiece and reach the eye of the person looking through the telescope (to the right of the eyepiece). If the focal length of the objective (f1) is bigger than the focal length of the eyepiece (f1), the refracting astronomical telescope produces an enlarged, inverted image:

magnification = f1 /f2

Similar for a reflecting telescope.

PHYS-3380 Astronomy

Four primary reasons reflecting telescopes are primary astronomical tools used for research:

1. Lens of refracting telescope very heavy - must be placed at end of telescope - difficult to stabilize and prevent from deforming

2. Light losses from passing through thick glass of refracting lens

3. Lens must be very high quality and perfectly shaped on both sides

4. Refracting lenses subject to chromatic aberration

Refracting vs Reflecting Telescopes

PHYS-3380 Astronomy

Lens and Mirror AberrationsSPHERICAL (lens and mirror)

Light passing through different parts of a lens or reflected from different parts of a mirror comes to focus at different distances from the lens.

Result: fuzzy image

CHROMATIC (lens only)

Objective lens acts like a prism.

Light of different wavelengths (colors) comes to focus at different distances from the lens.

Result: fuzzy image

PHYS-3380 Astronomy

Focal point for blue light

Focal point for red light

Focal point for all light

The problem

The solution

Simple lenses suffer from the fact that different colors of light have slightly different focal lengths. This defect is corrected by adding a second lens

Chromatic Aberration in Lenses

PHYS-3380 Astronomy

Simple lenses suffer from the fact that light rays entering different parts of the lens have

slightly difference focal lengths. As with

chromatic aberration, this defect is corrected with the addition of a

second lens.

One focal point for all light rays

The problem

The solution

Spherical Aberration in Lenses

PHYS-3380 Astronomy

Simple concave mirrors suffer from the fact that light rays

reflected from different locations on the mirror have slightly different focal lengths. This

defect is corrected by making sure the concave surface of the

mirror is parabolic

The Problem

The Solution

All light rays converge at a single point

Spherical Aberration in Mirrors

PHYS-3380 Astronomy

Reflecting Telescope

The primary mirror focuses light at the prime focus. A camera or another mirror that reflects the light into an eyepiece is placed at the prime focus.

PHYS-3380 Astronomy

Mirror Position and Focus Animation

Focus Inversion Animation

The image from an reflecting telescope is inverted.

The focus is adjusted by changing the secondary mirror position.

PHYS-3380 Astronomy

Types of Reflecting Telescopes

Each design incorporates a small mirror just in front of the prime focus to reflect the light to a convenient location for viewing.

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Cassegrain reflector - most common form

of astronomical telescope

- allows room for large instruments

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Schmidt-Cassegrain focus most common in small telescopes- uses catadioptrics - combines

optical advantages of both lenses and mirrors

- light enters through a thin aspheric Schmidt correcting lens- focal length increased by the magnification of the correcting

lens- lens carefully matched to the

primary concave mirror to correct for spherical aberration

- too slightly curved to introduce serious chromatic

aberration- shorter physical length

- lighter and more compact- easy to use

PHYS-3380 AstronomyThe Keck Telescopes

On Mauna Kea in Hawaii. 36 hexagonal mirrors function as single 10-meter mirror.

- segmented mirrors- more economical - segments can be made separately- weighs less- cools rapidly

- less distortion from uneven expansion and contraction

- optical shape maintained by computer-driven thrusters

PHYS-3380 Astronomy

Two Fundamental Properties of a TelescopeResolution

smallest angle which can be seen

θ = 1.22 λ / D

The angular resolution of a reflecting telescope is dependent on the diameter of the mirror (D) and the wavelength of the light being viewed (λ). Called Dawes’ Limit

Light-Collecting Area

think of the telescope as a “photon bucket”The amount of light that can be collected is dependent on the mirror area A = π (D/2)2

These properties are much more important than magnification which is produced by placing another lens - the eyepiece - at the mirror focus. Astronomers do not look through telescopes with their eyes - a light gathering detector (for instance a camera) records the image which can later on be magnified to any desired size.

PHYS-3380 Astronomy

Angular Resolution

• The ability to separate two objects.

• The angle between two objects decreases as your distance to them increases.

• The smallest angle at which you can distinguish two objects is your angular

resolution.

PHYS-3380 Astronomy

Angular Resolution of Car Lights Animation

The maximum angular resolution attainable by the human eye is about one arcminute - in other words two stars will appear distinct if they are separated by more than one arcminute - remember that Tycho Brahe produced the best naked eye star charts ever - had resolution of one

arcminute.

PHYS-3380 Astronomy Angular ResolutionResolving power: Wave nature of light

=> The telescope aperture produces fringe rings that set a limit to the resolution of the telescope.

amin = 1.22 (λ/D)

Resolving power = minimum angular distance amin between two objects that can be separated.

For optical wavelengths (assuming λ=550 nm), this gives

amin = 11.6 arcsec / D[cm]

min

=> Two point sources are just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other. If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved.

Airy disc

amin

amin is the the angle at which the first minimum occurs

Fully Resolved

Just Resolved

Unresolved


Note on the calculations of resolving power:

The formula amin = 1.22 (λ/D) gives it in radians. To get it in arc seconds (which all resolutions are given in) you need to multiply by 206,265 “/rad

The book gives slightly different formulas for resolving power:

𝜶 (arc seconds) = 2.06 X 105 (λ/D)

and

𝜶 (arc seconds)=0.113/D

These ignore the 1.22 factor and uses 206,000 “/rad instead of 206,265 “/rad

I don’t know why the book ignores the 1.22 factor. This really irritates me! Please use the correct number.

PHYS-3380 Astronomy

So: the angular resolution/resolving power of a reflecting telescope is dependent on the diameter of its mirror

Mirror Angular Resolution Animation

and the wavelength of the light

Wavelength Effect on Resolution

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Light Gathering Ability: Size Does Matter

1. Light-gathering power: Depends on the surface area A of

the primary lens / mirror, proportional

to diameter squared:

A = π(D/2)2

D

PHYS-3380 Astronomy

So: light collecting ability of a reflecting telescope is dependent on the area of the mirror

Light Collecting Area Animation

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Magnifying Power

Magnifying Power = ability of the telescope to make the image appear bigger.

The magnification depends on the ratio of focal lengths of the primary mirror/lens (Fo) and the eyepiece (Fe):

M = Fo/Fe

A larger magnification does not improve the resolving power of the telescope!

PHYS-3380 Astronomy

Interferometry

Recall: Resolving power of a telescope depends on diameter D: amin = 1.22 λ/D.

This holds true even if not the entire surface is

filled out.

• Combine the signals from several smaller telescopes to simulate one big mirror

→ Interferometry

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Types of Optical Telescopespca015000/PHYS_3380/... · 2019-10-07 · Four primary reasons reflecting telescopes are primary astronomical tools used for research: 1. Lens of refracting