Elementary Optics - Cornell Universityhosting.astro.cornell.edu/.../A525_01(Elem_Optics).pdfA6525: Lecture - 01 1 Elementary Optics Astronomy 6525 Lecture 01 Elementary Optics 2 A6526

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Elementary Optics

Astronomy 6525

Lecture 01

A6526 - Lecture 1Elementary Optics 2

Outline

The Perfect Telescope Diffraction-limited performance

Plate scale

The HST blunder Launched 1990, Fixed 1993

Simple optics

Telescope design

Types of telescopes

Ray Tracing

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What is a telescope?

Forms images of a distance object:

Key parameters: Collecting area

Effective focal length (f/# at focal plane)

Related parameters Plate scale (e.g. arcseconds/mm)

Image quality Geometric aberrations

Diffraction

Sensitivity: signal-to-noise ratio on a source Highly dependent upon instrument


The Perfect Telescope Collects photons with 100%

transmission No obscurations Zero thermal emission and zero scattered

light

No geometrical aberrations But diffraction always present =>

no “point” sources Called diffraction-limited performance

DFWHM λ03.1≅

DDλθ 2.1≅

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Obscured Telescope For an obscured telescope the PSF, normalized to a peak of

unity is given by:

, = 2 − 2 11 −Here is the first order Bessel function of the first kind, = and =where and are the telescope and obscuration diameters respectively. Nominally is entered in units of / .



0 0.5 1 1.5

0.2

0.4

0.6

0.8

x

Am

plit

ude

Diffraction Point Spread FunctionObscuration

10 %

4 %

0 1 2 3 4 5 6

0.06

0.04

0.02

0.0

Am

plit

ude

x (λ/D)

Obscuration is by area

None

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Diffraction PSF

No obscuration

10 %4 %

0 1 2 3 4 5 6

100

10-1

10-2

10-3

10-4

10-5

Am

plit

ude

x (λ/D)

Obscuration is by area


Encircled Energy

No obscuration

10 %

4 %

0 1 2 3 4 5 6

1.0

0.8

0.6

0.4

0.2

0.0

Enc

ircl

ed E

nerg

y

x (λ/D)Obscuration is by area

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yGaussian vs. Airy Function

0 2 4 6 8 10

100

10-1

10-2

10-3

10-4

10-5

Am

plit

ude

x (λ/D)

10-6

10-7

Dsec/Dpri = 0.2 (4% obscuration)

Dsec/Dpri = 0


Plate Scale

For Palomar: f/16 with 5 m primary

θ θx

f

diameterprimarylengthfocaleffectivef =#

f = focal lengthf # = f/D

x = θ f = θ D f #

mm388.0mm10516rad/"206265

"1 3 =×⋅=x

1” ↔ 0.388 mm Plate scale = 2.57”/mm in telescope focal plane

[Often reimaged to match detector pixel size.]

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When telescopes go bad HST: $2.5 billion and the optics were wrong! Very bad PR for NASA and Astronomy


HST Primary Figuring Error

Actual Hyperboloidal Mirror

194 μm

2 μm

DesignedHyperboloid

1/2 μmSphere

Paraboloid

Focus is different for different height light rays

Focus is the same for different height light rays

Spheriod Paraboloid

Paraboloid

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HST Encircled Energy

Pre-fix HST performance.


HST Spot Diagrams

0.2"

2"

Diffraction spot at 0.5 μm

As designed Actual (pre-fix)

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HST PSF Plots

Profiles of HST f/30 planetary camera normalized to thesame peak brightness for λ = 0.57 μm. The FWHM of thecore is 0.1” in both cases, but only 15% is contained in thespherically aberrated image core.


Optics

Motivation

Thin lens

Telescopes Mixing conic sections

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Motivation

Why should we know about optics?

User viewpoint (observer) You will get better results if you know how your

experiment works and what its limitations are.

Builder’s viewpoint (experimenter) If you have someone design a system and build it for

you, there is little incentive for them to keep it simple (and cheap).

Pragmatists viewpoint (wage earner) You can make more money!


Thin Lens Equations Thin Lens Formula:

fpq111 =−

p q

f

f = focal lengthp = object distance

(neg. when to left of lens)q = image distance

(pos. when to right of lens)

Newton’s Formula:2fyx =⋅

x y

ff

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Thin Lens Equations (cont’d) Lensmaker’s Formula:

( )

−−=

21

111

1

rrn

f

n = refractive indexr1, r2 = radii of curvature

r1 r2

( r > 0) r < 0

For a convex lens: r1 > 0, r2 < 0 => f > 0

concave lens: r1 < 0, r2 > 0 => f < 0


Telescopes

Refractors Chromatic aberration

Must be internally flaw free

Must support from the side

Reflectors (astronomers choice) Typically have central obscuration

Have spiders to support secondary (diffraction spikes)

Object Image

Object not at infinity!

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The Parabolic Mirror Consider light from a very distant spot on the optical axis

A

cd

A parallel wavefront passes A in phase. We want it to arrive at the focus still in phase. Therefore, all paths from A to the focus must be the same length.

A parabola is the locus of points equidistant from a point and a line. Therefore, c = d and the distance from A to the focus is a constant.


Parabolic Mirror (cont’d)

A parabola will form a perfect (geometric) image at the focus.

NOTE: This is only for rays parallel to the axis. Off-axis rays will not be as good.

Rays from off-axis source

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Other Conics

Ellipse (e < 1):

Sphere (e = 0):

Hyperbola (e > 1):

tangentline bisectsangle

F′ F

reflected ray

P


Gregorian Telescope Conic sections produce perfect (geometric) images and can

be strung together to form complex systems.

Parabolic primary produces a perfect image at #1.

Ellipsoidal secondary transfers a perfect image to #2.

An erect image is produced.

Focus #1Focus #2

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Cassegrain Telescope

Focus #1Focus #2

Parabolic primary produces a perfect image at #1.

Hyperbolic secondary relays the virtual image at #1 to a real image at #2.

Greater compactness than Gregorian telescope.

But - hyperbolic secondary is hard to make and off-axis performance is not terribly good.


Designing a Cassegrain Telescope Start by picking the aperture and final focal length.

This gives f-ratio (f#) and plate scale

The final focal length is fpm where m = magnification produced by the secondary. fp is the primary focal length. m = 1 for flat.

p q

pqm =

1

1

−+=

mmes

111

−

−=

qpfs ss fr 2=

Relational equations:

p, q > 0 (convex)

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Designing a Cassegrain (cont’d)

Effective focal length = focal length of telescope

feff = fpm

s b

b = backfocal distance(> 0 as shown)

bsq +=

sfp p −= pqm =

1+−

=m

bmfs p&


Cassegrain Examples

f/2.2 primary, f/13.4 telescope magnification: 6 plate scale: 15.4/D(m) ′′/mm

f/1.3 primary, f/13.4 telescope magnification: 10.3 plate scale: 15.4/D(m) ′′/mm

f/2.2 primary, f/4.6 telescope magnification: 10.3 plate scale: 44.8/D(m) ′′/mm

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Other Telescope designs

Dall-Kirkham: Make secondary mirror a sphere

Adjust “figure” of primary to compensate (remove spherical aberration)

Bad off-axis performance

Ritchey-Chrétien Telescope Design used for all large telescopes

Reduce off-axis aberrations by Slightly flattening primary (hyperbolic)

slightly flattening rim of secondary (hyperbolic)


Schematics of TelescopesNewtonian

Keplerian

Herschelian

Cassegrain,Ritchey-Chrétien,Dall-Kirkham

Mersenne

Gregorian

Schmidt Bouwers-Maksutov

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Telescope TypesType Primary Optics Secondary Optic

Keplerian Sphere or parabola None

Herschelian Off-axis parabola None

Newtonian Parabola Diagonal Flat

Gregorian Parabola Ellipse

Mersenne Parabola Parabola

Cassegrain Parabola Hyperbola

Ritchey-Chrétien Modified parabola Modified hyperbola

Dall-Kirkham Ellipse Sphere

Schmidt Aspheric refractor Sphere

Bouwers-Maksutov Refractive meniscus Sphere

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Elementary Optics - Cornell Universityhosting.astro.cornell.edu/.../A525_01(Elem_Optics).pdfA6525: Lecture - 01 1 Elementary Optics Astronomy 6525 Lecture 01 Elementary Optics 2 A6526