Optical Astronomy Optical Astronomy Telescope: Collects and - - PDF document

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Optical Astronomy Optical Astronomy Imaging Chain: Imaging Chain: Telescopes & Telescopes & CCDs CCDs

Telescope and Sensor Telescope and Sensor

• Telescope:

– Collects and focuses light to make the image – Generally a “reflecting” telescope

• X-ray, Ultraviolet, Optical (visible), IR, Radio
• No variation in image with wavelength (“color”)
• Sensor:

– Measures the light at each position – Generally a “charge-coupled device” (CCD)

• Converts light (“photons”) to electrons

Charge Charge-

• Coupled Device = CCD

Coupled Device = CCD

• Individual “Picture

elements” (= “Pixels”)

• Convert photons to

electrons

• Pixel Size ⇒ “Resolution” in

image

• Area of Pixels ⇒ “coverage”

Reflector telescopes: Reflector telescopes: basic principles basic principles

• For Reflection, we know that:

angle of incidence = angle of reflection (angle in = angle out)

• angles measured from “normal”

(perpendicular to surface)

θin θout

Reflector telescopes: Reflector telescopes: basic principles basic principles

• Easy to make concave mirrors with a

“spherical” profile

Grind mirror on second piece of glass – the “tool”

water & “grit” Force

top piece becomes concave sphere bottom piece becomes convex sphere

C

(“center of curvature”)

Spherical Mirror Spherical Mirror

Concave mirror on top Convex mirror on bottom Same “radius of curvature” R

R

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• Reflected rays from source at ∞ at

different “heights” do not “focus” (cross

• ptic axis) at same distance from mirror
• This is called “Spherical Aberration!”

– This is what plagued the Hubble Space Telescope

Concave Concave “ “Spherical Spherical” ” Mirror Mirror Works Poorly for Imaging Stars Works Poorly for Imaging Stars Correct Mirror Surface for Correct Mirror Surface for Object at Object at ∞ ∞

• Paraboloid!

– somewhat “shallower” curve than sphere

• z = kx2 for paraboloid

– parallel incident rays brought to common focus

paraboloid sphere

z x

Basic Designs of Optical Basic Designs of Optical Reflecting Telescopes Reflecting Telescopes

• “Prime focus”

– light is brought to focus by primary mirror only!

• “Newtonian”

– flat, diagonal secondary mirror deflects light out of tube

• “Cassegrain”

– convex secondary mirror reflects light through hole in primary

• “Nasmyth” (or coudé) focus

– tertiary mirror to redirect light to external instruments – “coudé” = “elbow” in French

F# (F F# (F-

• ratio) and

ratio) and “ “Plate Scale Plate Scale” ”

• – D = diameter

– f = focal length – must consider focal length of combination of primary & any secondary mirrors

• Determines “plate scale”

– angle increment of image per unit length at focal plane (e.g., arcsec per mm) – estimated from (our old friend): small-angle relation

# f F D =

S f θ =

1 1 plate scale # S f F D θ = = = ⋅

Example of Plate Scale Example of Plate Scale

• 10"-diameter f/16 telescope

1 plate scale # S F D θ = = ⋅ mm mm arcseconds 10 5 . 2 254 16 1 D F# 1 scale plate

4 −

× ≅ ⋅ = ⋅ =

Sensors with Sensors with “ “Pixels Pixels” ”

(different from (different from “ “emulsions emulsions” ”) )

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Basic Concepts of CCD Sensors Basic Concepts of CCD Sensors

• “Pixelated” ⇒ discrete picture elements

(“pixels”)

• Converts Photons to Electrons by

absorption and conversion of energy

• Sensitive over wide range of wavelengths

(“colors”)

• Pixels are “read out” in sequence

– cannot be randomly accessed!!

CCDs CCDs: : “ “pixel scale pixel scale” ”

• Example:

– assume plate scale of image = 50 arcsec per mm – CCD pixel size (linear dimension) = 25 microns = 25 µm = 0.025 mm = 25,000 nm ⇒ pixel scale = 1.25 arcsec per pixel pixel arcseconds 25 . 1 pixel mm 025 . mm arcseconds 50 scale pixel = × =

CCDs CCDs: : “ “field of view field of view” ”

• Example:

– CCD with 1,000,000 pixels (1 Mpixel) in 1000×1000 array – Each pixel is 25 µm × 25 µm – Pixel size is 1.25 arcsec

⇒ field of view is:

1000 pixels × 1.25 arcsec per pixel = 1250 arcsec ≅ 21 arcmin – could image most of Moon’s surface on this CCD through this telescope

CCDs CCDs: field of view : field of view

• Want to match CCD pixel scale to image

“blur” due to diffraction

• Recall main sources of image blur

– angular resolution of telescope due to “diffraction limit” – random variations in atmosphere ⇒ time- varying movement

• Ideal pixel scale: 2 CCD pixels ≥ width of
• ptical “blur”

⇒ Image field of view then limited by size of CCD (number of pixels) F CCD bi f ll i l i

Basic Principles of CCD Imaging in Astronomy

Based on Slides by Simon Tulloch: available from

http://www.ing.iac.es/~smt/CCD_Primer/CCD_Primer.htm

• “CCD” = “Charge-Coupled Device”
• Invented in 1970s, originally for:

– Memory devices – Arithmetic data processing (computer chips)

• Usually made of Silicon (“Si”)

⇒Has Same Light-Sensitive Properties as Silicon Light Meters

What is a CCD? What is a CCD?

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Spectral Response (sensitivity) Spectral Response (sensitivity)

• f Typical CCD
• f Typical CCD
• Response is large in visible region, falls off for

ultraviolet (UV) and infrared (IR)

300 400 500 600 700 800 900 1000

Incident Wavelength [nm]

Relative Response Visible Light IR UV

• Light-Sensitive Properties applied to Imaging
• Revolutionized Astronomical Imaging

– Improved Light-Gathering Power of Telescopes by nearly 100× (5 magnitudes!!)

• 2005 Amateur w/ 15-cm (6") Telescope + CCD can get

similar performance as 1960 Professional with 1-m (40") Telescope + Photography

• Now Considered to be “Standard” Sensor in

Astronomical Imaging

– Special Arrangements with Observatory Necessary to use Photographic Plates or Film

CCDs CCDs in Astronomy in Astronomy Film/Plates Still Useful!! Film/Plates Still Useful!!

• Large field of view
• Cheap!
• Crystal Form of Matter (typically Si)
• Converts “Light” to “Electronic Charge”

– Pattern of Charge = “Image”

• 1. “Digitized”

– Analog Measurements (“Voltages”) Converted to Integer Values at Pixels

• 2. “Digitized” Measurements Stored as

Computer File

What is a CCD? What is a CCD? Si Si Crystal Structure Crystal Structure

• Regular Pattern of Si

atoms

– Fixed Separations

• Atomic Structure

Pattern “Perturbs” Electron Orbitals

– Changes Layout of Available Electron States

http://www.webelements.com/webelements/elements/text/Si/xtal.html

Electron States in Electron States in Si Si Crystal Crystal

• Available States in Crystal Arranged in

Discrete “Bands” of Energies

– Lower Band ≡ Valence Band

• More electrons

– Upper Band ≡ Conduction Band

• Fewer electrons
• No States Exist in “Gap” Between Bands

Increasing energy

Valence Band of Electron States Conduction Band of Electron States

“Gap” ≈ 1.26 electron-volts (eV)

• - -
• “Gap”

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5 Action of Light on Electron States Action of Light on Electron States

• Incoming Photon with Energy ≥ 1.26 eV

– Excites Electrons From “Valence Band” to “Conduction Band”

• Electron in Conduction Band Moves in the

Crystal “Lattice”

• Excited Electron e- leaves “Hole” (“Lack of

Electron” = h+) in Valence Band

– Hole = “Carrier” of Positive Charge

Action of Action of “ “Charge Carriers Charge Carriers” ”

• Carriers are “Free” to Move in the

Corresponding Band

– Electron e- moves in Conduction Band – Hole h+ moves in Valence Band

• Charge Carriers may be “Counted”

Electronically

– Measure the Number of Absorbed Electrons ≈ Number of Absorbed Photons

Wavelength Wavelength λ λ corresponding to corresponding to E = 1.26 electron Volts E = 1.26 electron Volts

• 1 eV = 1.602 × 10-12 erg = 1.602 × 10-12 Joule

⇒ To Energize Electron in Si Lattice Requires λ < 984 nm ≅ 1 µm

( )

27 8 12 7

6.624 10 sec 3 10 sec 1.26 1.602 10 9.84 10 984 m erg hc erg E eV eV m nm λ

− − −

⎛ ⎞ × − ⋅ × ⎜ ⎟ ⎝ ⎠ = = ⎛ ⎞ × × ⎜ ⎟ ⎝ ⎠ = × =

Energy and Wavelength Energy and Wavelength

• If Incident Wavelength λ > 1 µm, Photon

CANNOT be Absorbed!

– Insufficient Energy to “Kick” Electron to Conduction Band

⇒ Silicon is “Transparent” to long λ ⇒ CCDs constructed from Silicon are Not Sensitive to Long Wavelengths

After Electron is Excited into After Electron is Excited into Conduction Band Conduction Band… …. .

• Electron and Hole Usually “Recombine” Quickly

– Charge Carriers are “Lost”

• Prevent by Applying External Electric Field to “Separate”

Electrons from Holes

• Field Attracts “Sweeps” Electrons and Holes in Opposite

Directions:

– Field “Sweeps” Electrons and Holes Apart ⇒They don’t recombine

• Maintains Population of Charge Carriers

– Allows Carriers to be “Counted” photon photon

Hole Electron Conduction Band Valence Band

Generation of CCD Carriers Generation of CCD Carriers

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Thermal Thermal “ “Noise Noise” ”

• BUT: Other Forms of Energy has Same Effect

as Light

• Thermally Generated Electrons are

Indistinguishable from Photon-Generated Electrons

– Heat Energy can “Kick” e- into Conduction Band – Thermal Electrons appear as “Noise” in Images

• “Dark Current”

– Keep CCDs COLD to Reduce Number of Thermally Generated Carriers (Dark Current)

How Do We How Do We “ “Count Count” ” the Charge the Charge Carriers ( Carriers (“ “Photoelectrons Photoelectrons” ”)? )?

• Must “Move” Charges to an “Amplifier”
• Astronomical CCDs: Amplifier Located at “Edge”
• f Light-Sensitive Region of CCD

– Most of CCD Area “Sensitive” to Light – Charge Transfer is “Slow”

• Video and Amateur Camera CCDs: Must

Transfer Charge QUICKLY

– Less Area Available to Collect Light

“ “Bucket Brigade Bucket Brigade” ” CCD Analogy CCD Analogy

• Electron Charge Generated by Photons is

“Transferred” from Pixel to “Edge” of Array

• Transferred Charges are “Counted” to

Measure Number of Photons

BUCKETS (PIXELS) VERTICAL COLUMNS

• f PIXELS

CONVEYOR BELT

(SERIAL REGISTER)

MEASURING CYLINDER (OUTPUT AMPLIFIER)

Rain of Photons

Shutter

Rain of Photons

CONVEYOR BELT

(SERIAL REGISTER)

MEASURING CYLINDER (OUTPUT AMPLIFIER)

Empty First Buckets in Column Into Buckets in Conveyor Belt

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CONVEYOR BELT

(SERIAL REGISTER)

MEASURING CYLINDER (OUTPUT AMPLIFIER)

Empty Second Buckets in Column Into First Buckets Empty Third Buckets in Column Into Second Buckets Start Conveyor Belt

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Measure & Drain

After each bucket has been measured, the measuring cylinder is emptied, ready for the next bucket load.

Measure & Drain

Empty First Buckets in Column Into Buckets in Conveyor Belt

Now Empty

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Empty Second Buckets in Column Into First Buckets Start Conveyor Belt

Measure & Drain

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Measure & Drain Measure & Drain

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Empty First Buckets in Column Into Buckets in Conveyor Belt

Start Conveyor Belt

Measure & Drain

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Measure & Drain Measure & Drain

Ready for New Exposure

Features of CCD Readout Features of CCD Readout

• Pixels are Counted in Sequence

– Number of Electrons in One Pixel Measured at One Time – Takes a While to Read Entire Array

• Condition of an Individual Pixel Affects

Measurements of ALL Following Pixels

– A “Leaky” Bucket Affects Other Measurements in Same Column

for this Pixel

“Leaky” Bucket Loses Water (Charge)

AND following Pixel ⇒ Less Charge Measured for This Column

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Structure of Astronomical Structure of Astronomical CCDs CCDs

• Image Area of

CCD Located at Focal Plane of Telescope

• Image Builds Up

During Exposure

• Image

Transferred, pixel-by-pixel to Output Amplifier

Connection pins Gold bond wires Bond pads Silicon chip

Package

Image Area

Serial register (Conveyor Belt) Output amplifier

CCD Manufacture CCD Manufacture

Don Groom LBNL

Fabricated CCD Fabricated CCD

Kodak KAF1401

1317 × 1035 pixels (1,363,095 pixels)

Charges ( Charges (“ “Buckets Buckets” ” are Moved are Moved by Changing Voltage Pattern by Changing Voltage Pattern

1 2 3 Apply Voltages Here 1 2 3

Charge Transfer Charge Transfer

1 2 3

+5V 0V

• 5V

+5V 0V

• 5V

+5V 0V

• 5V

Time-slice shown in diagram

1 2 3

Charge Transfer Charge Transfer -

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1

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1 2 3

+5V 0V

• 5V

+5V 0V

• 5V

+5V 0V

• 5V

1 2 3

Charge Transfer Charge Transfer -

• 2

2

1 2 3

+5V 0V

• 5V

+5V 0V

• 5V

+5V 0V

• 5V

1 2 3

Charge Transfer Charge Transfer -

• 3

3

1 2 3

+5V 0V

• 5V

+5V 0V

• 5V

+5V 0V

• 5V

1 2 3

Charge Transfer Charge Transfer -

• 4

4

1 2 3

+5V 0V

• 5V

+5V 0V

• 5V

+5V 0V

• 5V

1 2 3

Charge Transfer Charge Transfer -

• 5

5

1 2 3

+5V 0V

• 5V

+5V 0V

• 5V

+5V 0V

• 5V

1 2 3

Charge Transfer Charge Transfer -

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6

1 2 3

+5V 0V

• 5V

+5V 0V

• 5V

+5V 0V

• 5V

1 2 3

Charge Transfer Charge Transfer -

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CCDs CCDs: noise sources : noise sources

• “dark current”

– can be “removed” by subtracting image obtained without exposing CCD

• leave CCD covered: dark frame
• “read noise”

– detector electronics subject to uncertainty in reading out the number of electrons in each pixel

• “photon counting”

– Poisson statistics: if N photons are measured, the uncertainty in my photon count (the “noise”) is √N

CCDs CCDs: artifacts and defects : artifacts and defects -

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• “bad” pixels

– “dead,” “hot,” “flickering,” …

• methods for correcting:

– replace bad pixel with average value of the pixel’s neighbors – “dither” the telescope

• take series of images
• move telescope slightly between exposures
• ensures that image falls on good pixels at least some of

the time

CCDs CCDs: artifacts and defects : artifacts and defects -

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• pixel-to-pixel variation in “efficiency”

– “Quantum Efficiency” = “QE” – Some pixels are more sensitive than others

• Method for Correction:

– Construct a “flat field”

• Image of a uniformly illuminated scene
• Flat-field image measures efficiency of each

pixel

– Divide each image by flat field

CCDs CCDs: artifacts and defects : artifacts and defects -

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• Pixel “Saturation”

– a pixel can hold a limited amount of electric charge

• limited “well depth”

– once pixel is “saturated”, it stops detecting and counting new photons

• analogous to “overexposure” on photographic

emulsion

• charge loss occurs during pixel charge

transfer & readout

CCDs CCDs: artifacts and defects : artifacts and defects -

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• Charge loss

– during pixel charge transfer & readout

pixel boundary Photons

Charge Capacity of CCD pixel is Finite (Up to 300,000 Electrons) After Pixel Fills, Charge Leaks into adjacent pixels.

Photons Overflowing charge packet

Spillage Spillage

pixel boundary

CCD CCD “ “Blooming Blooming” ” -

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Flow of bloomed charge

Channel “Stops” (Charge Barrier) Charge Spreads in Column

• Up AND Down

CCD CCD “ “Blooming Blooming” ” -

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Charge Transfer Direction Bloomed Star Images with “Streaks” M42

CCD CCD “ “Blooming Blooming” ” -

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• Long Exposure for

Faint Nebulosity ⇒ Star Images are Overexposed

CCD Image Defects CCD Image Defects

• “Dark” Columns

– Charge “Traps” Block Charge Transfer – “Charge Bucket” with a VERY LARGE Leak

• Not Much of a Problem in

Astronomy

– 7 Bad Columns out of 2048 ⇒ Little Loss of Data

• 1. Bright Columns

– Electron “Traps”

• 2. Hot Spots

– Pixels with Larger Dark Current – Caused by Fabrication Problems

• 3. Cosmic Rays (γ)

– Unavoidable – Ionization of e- in Si – Can Damage CCD if High Energy (HST)

CCD Image Defects CCD Image Defects

Cosmic rays Cluster of Hot Spots Bright Column

M51

Dark Column Hot Spots, Bright Columns Bright First Row

• incorrect operation of

signal processing electronics

CCD Image Defects CCD Image Defects

Negative Image

CCD Image Processing CCD Image Processing

• “Raw” CCD Image Must Be Processed to

Correct for Image Errors

• CCD Image is Combination of 4 Images:
• 1. “Raw” Image of Scene
• 2. “Bias” Image
• 3. “Dark Field” Image with Shutter Closed
• 4. “Flat Field” Image of Uniformly Lit Scene

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Bias Frame Bias Frame

• Exposure of Zero Duration with Shutter

Closed

– “Zero Point” or “Baseline” Signal from CCD – Resulting Structure in Image from Image Defects and/or Electronic “Noise”

• Record ≅ 5 Bias Frames Before Observing

– Calculate Average to Reduce Camera Readout Noise by 1/√5 ≅ 45%

“ “Dark Field Dark Field” ” Image Image

• Dark Current Minimized

by Cooling

• Effect of Dark Current is

“Compensated” Using Exposures of Same Duration Taken with Shutter Closed.

• Dark Frames are

Subtracted from Raw Frames

Dark Frame

“ “Flat Field Flat Field” ” Image Image

• Sensitivity to Light Varies from Pixel to Pixel

– Fabrication Problems – Dust Spots – Lens Vignetting – …

• Image of “Uniform” (“Flat”) Field

– Twilight Sky at High Magnification – Inside of Closed Dome

[ ] [ ]

, , r x y d x y −

Correction of Raw Image Correction of Raw Image with Bias, Dark, Flat Images with Bias, Dark, Flat Images

Flat Field Image Bias Image Output Image Dark Frame Raw File

[ ]

, r x y

[ ]

, d x y

[ ]

, f x y

[ ]

, b x y

[ ] [ ]

, , f x y b x y − “Flat” − “Bias” “Raw” − “Dark”

[ ] [ ] [ ] [ ]

, , , , r x y d x y f x y b x y − − “Raw” − “Dark” “Flat” − “Bias”

[ ] [ ]

, , r x y b x y −

Correction of Raw Image Correction of Raw Image w/ Flat Image, w/o Dark Image w/ Flat Image, w/o Dark Image

Flat Field Image Bias Image Output Image Raw File

[ ]

, r x y

[ ]

, f x y

[ ]

, b x y

[ ] [ ]

, , f x y b x y − “Flat” − “Bias”

[ ] [ ] [ ] [ ]

, , , , r x y b x y f x y b x y − − “Raw” − “Bias” “Flat” − “Bias” “Raw” − “Bias”

Assumes Small Dark Current (Cooled Camera)

Filters Filters

• Because CCDs have broad spectral

response, need to use filters to determine e.g. star colors in visible

• broad-band: filter width is about 10% of filter’s

central wavelength

– example: V filter at 550 nm will allow light from 500 to 600 nm to pass through – astronomers use BVRI: blue, ‘visible’, red, IR

• narrow-band: filter width is <1%

– example: “H-alpha” covers 650 to 660 nm