astronomical cameras - uwyo.eduphysics.uwyo.edu/~aschwortz/lassi/files/lassi14oct24.pdf•the image...

Astronomical Cameras

I. The Pinhole Camera

• Whenever light passes through a small hole or aperture it creates an image opposite the hole

• This is an effect wherever aperturesoccur in nature

• Essentially, a pinholecamera consists oftwo components:

• An aperture

• A surface on which to project the image

• A designed pinhole camera is usually a light-proof box that is black other than the surface capturing the image

Pinhole Camera (or Camera Obscura)

• The image appears inverted (see diagram)

• The farther the source is from the aperture, the smaller the image appears. Why?

• what other everyday imagingdevice has a similar feature?

• Simplifying (e.g., ignore diffraction)

• A bigger aperture produces a brighter image

• A smaller hole produces a sharper image. Why?

• With a pinhole camera it is impossible to create an image that is bright and sharp

Pinhole Camera Properties

source

image

• The basic quantities for a pinhole camera are the aperture (or “pupil”) diameter (d ) and the focal length (f )

• The f-number is defined as f/d and isconfusingly written, e.g., f/2

• A 100mm focal length and a 5mmaperture has an f-number of f/20

• Note that increasing f decreases f-number!

• Devices can be built that change d(an “iris”) and f (a “focuser”)

• Then cameras can have adjustable f-ratios to let in morelight and change the size of the image

F-number

f

d

• For telescopes d is the diameter of the light-collector

• f-number is thena measure of fieldof view, and image resolution (of how sharp the image is)

• Telescopes with “large” f-numbers (e.g., f/20) are called slow and have large focal lengths and small fields of view

• Telescopes with “small” f-numbers (e.g., f/2) are called fast and have small focal lengths and large fields of view

F-number in telescopes

http://www.telescopenerd.com/telescope-astronomy-articles/how-fast-is-your-telescope.htm

d

f

f

slow - usually easy to design

fastd

fast - usually hard to design



• A point on a source P passesthrough a pinhole O to createa point on an image Q

• How can I make the image

• smaller by changing the camera?

• smaller by not changing the camera?

• not inverted?

Pinhole Camera Model

f

X

IMAGE

hole

Q

P

P

Q

f X

y = − fXx

http://hyperphysics.phy-astr.gsu.edu/HBASE/phyopt/raylei.html#c1

• When the image points of two source points overlap they are spatially unresolved (you can’t detect both)

• A diffraction limited image is when the minimum of one image overlaps the maximum of the other this is called the Rayleigh Criterion

Airy Disks and Rayleigh Criterion

Airy Disk

d is the aperture diameterλ is the wavelength of light

θR is theangularresolution




• If everything that passes through the aperture ends up in the central part of the Airy Disk or “spot” then the diameters of the aperture and spot would equate 2y = d

• The optimal pinhole diameter is about d ~ sqrt(2.44λf)

• Can a pinhole camera produce a bright and sharp image? What would happen to the size of the image?

Pinhole Camera Aperture Model

sinθR =1.22λd

(Rayleigh Criterion)

d

f

θR

y

tanθR =yf

For Small Angles :tanθR ~ sinθR ~θR

⇒ d = 1.22 fλy

Airy Disk

Angular Resolution for a Telescope

• For a telescope the angular resolution for a slit rather than a circular aperture is appropriate

• Again, d for a telescope is the diameter of the light-collector rather than the pinhole

• Most principles for astronomical cameras resemble pinhole cameras

Rayleigh Criterion

R = λd(R in radians)

• The pinhole camera does not capture an image permanently. What new component is needed for this?

Augmentations to the Pinhole Camera


• A light-sensitive image sensor (photo film, CCDs)




• A sensor exposed to too much light may saturate (record the same level of white light everywhere in the image). What new component can prevent this?





• A shutter





• A shutter

• With a pinhole camera it is impossible to create an image that is bright and sharp and big. Is there a new component that can help make this possible?





• A shutter

• With a pinhole camera it is impossible to create an image that is bright and sharp and big. Is there a new component that can help make this possible?

• A lens or a mirror


2. Focusing Light

• Light is deflected at the interface between two materials

• The angle to thenormal to the interface changes depending on what the materials are made of:

• n1sinθ1 = n2sinθ2, v2sinθ1 = v1sinθ2

• This is Snell’s Law where n is refractive index, v is velocity

• A prism will split out different colors of light because different wavelengths of light have slightly different velocities in most media (including in glass)

Refraction and Snell’s Law

• Lenses can replace a pinhole inorder to focus light with more control

• The collecting area of the lens is then the aperture and the distance from the lens to the focal point is the focal length

• Lenses can be used to help circumvent the fact that a pinhole can only make large images that are bright or sharp

Lenses

http://www.bigshotcamera.com/

Converging Lens

Diverging Lens

Compound Lens

f

d



• From the geometry of the situation it is possible to relate the image-lens and source-lens distances to f

• This is similar to the quick derivation for the pinhole camera, but with more triangles

• Lenses can be designed with anytheoretical focal length

• If an image is not in focus di > f, how can we bring it into focus?

• How will an image that is out of focus look? Why?

The (thin, convex) lens equation

http://www.alpcentauri.info

1di

+ 1do

= 1f



• It is always possible tocreate a mirror withequivalent optics to a lens

• The situation is very similarto the geometry of a lensexcept the optics stay on thesame side of a mirror

• There are several benefits to using a mirror to focus light for a telescoperather than a lens

• What are two advantages?

The (spherical, concave) mirror equation

http://www.aplusphysics.com

1di

+ 1do

= 1f

f



Plate Scale for a Telescope

http://ircamera.as.arizona.edu/astr_250/Lectures/Lec_10sml.htm

• The plate scale for a telescope is how an angle on the sky translates into a physical distance on the imaging surface

• It turns out that the plate scale (in radians) is just:

platescale= 1f



Refracting Telescopes: Lenses

• Problems: • Lenses focus

colors differently• Limited wavelengths• Requires longer

gap between objective lens and eyepiece as objective lens gets larger

• Sag:

• Large lens distorted as it hangs• Limits lens size

Bigger is BetterThe light gathering power of a telescope is just the area of the light collector (the primary lens or mirror)

Light Gathering Power = Area = πr2 = πd2

4

The Largest Refractor

•At Yerkes Observatory in southern WI

• 40 inch diameter lens, 63½ feet long!

•A 1-meter telescope, 20 meters long

•

The Largest Refractor

• External shot of Yerkes Observatory

A much larger telescope

•3.5-meter• (138-inch)•at APO

A much larger telescope

•2.5-meter• (98-inch)•external

shot at APO

3. Light Detection and CCDs

• We have discussed how to focus light to a surface but not how to make a permanent image from that light

• For many years, astronomy used photographic film to capture images, but now CCDs are almost exclusively used

• For what equation did Albert Einstein win the Nobel Prize in Physics?

Charge-Coupled Devices





K = h( f − f0 )




• This is called the photoelectric effect. It relates the kinetic energy of an electron ejected from a metal to the frequency of light that hits the metal


K = h( f − f0 )

• The photoelectric effect shows that particles of light (photons) can be used to produce electrons

• A CCD is basically a series of photoelectric sensors with individual capacitors placed beneath them

• Incident light causes electrons (charge) to be stored in the capacitors, which are simply devicesfor storing charge

• In a CCD, charge builds up in the capacitors proportional tothe number of photons (theintensity of light) that hits each sensor


photons

electrons

capacitors

Reading out the Charge

photons

http://coursewiki.astro.cornell.eduhttp://astro.unl.edu/classaction/animations/telescopes/buckets.html

• Moving charge is just electric current, and a seriesof voltages can be applied to shift the charge

• Over the CCD grid, charge is shifted horizontally then vertically until the amount of charge in each capacitor (bucket) has been read out

• We then know howmuch light fell on eachphotoelectric sensor cell

• The total readout time isimportant...long readout timescould delay subsequent images

http://coursewiki.astro.cornell.edu

http://coursewiki.astro.cornell.edu

• CCDs only measure the total amount of light that fell on each cell...not thecolor or wavelength of that light

• There are several ways to thenmake a color image

• multiple CCDs with a colorfilter in front of each CCD

• multiple telescopes each with its own CCD looking through a different color filter

• Interpolating across a series ofcolor filters laid out acrossa single CCD grid

How to make color images

The PROMPT array

SDSSCamera

• All colors of light can be determined by combining red, green and blue light

• The Bayer filter is a series of red, green and blue filters laid out across the surface of a CCD and combined to make any color

• Each photoelectric sensor cell then has a single color filter placed in front of it

• How would you populate theCCD grid to the right with red, green, blue filters to optimally measure red, green and blue light in each cell?

The Bayer Filter

• The Bayer filter is a layout of red, green and blue filters

The Bayer Filter

• The Bayer filter can be used to determine how many photons of light of each color fell on each cell of a CCD

• Let’s look at the cell pattern highlighted in yellow

The Bayer Filter

• What were the intensities of light (the numbers ofphotons of each color, red, green, blue) through the position in the CCD covered by the central green filter?

The Bayer Filter

150 110 100

140 140 160

200 130 110

• Let’s look at the cell pattern highlighted in yellow

The Bayer Filter

• What were the intensities of light (the numbers ofphotons of each color, red, green, blue) through the position in the CCD covered by the blue filter?

The Bayer Filter

130 100 150

180 130 200

190 120 170

A Far Less Intelligent Filter Pattern

4. Telescopes and Astronomical Cameras

• You now know all of the critical concepts to understand astronomical cameras and detectors

• field of view size is controlled by f-number; by the focal length and the size of the primary mirror (big mirrors have large fields of view unless the focal length is big)

• It is tough to focus the light from a big mirror so it is typical to have a larger focal length with a big mirror...but lenses and mirrors can be used to manipulate focal length

• the total amount of light collected is controlled by the size of the primary mirror (big mirrors collect more light)

• the angular resolution is controlled by the size of the primary mirror (big mirrors have better resolution)


• The Large Synoptic Survey telescope has a very large primary mirror (8.4m)

• What are two reasons why a large mirror is desirable?

• Look at the design to theright...why build a telescopewith 3 mirrors like this? What does f/1.23 at the sensor mean? Is the LSST fast or slow?

Some Modern Astronomical Cameras

Sensor@ f/1.23

• The Large Synoptic Survey telescope has a very large primary mirror (8.4m)

• What are two reasons why a large mirror is desirable?

• Look at the design to theright...why build a telescopewith 3 mirrors like this? What does f/1.23 at the sensor mean? Is the LSST fast or slow?


Sensor@ f/1.23

f

d The LSST has a 3.5o field of view (c.f. WIRO with a 2.3 meter primary mirror and a < 1o field of view)

• The Sloan Digital SkySurvey camera contains 30 CCDs arranged in 5 “columns” of different color filters (in the picture, columns run left-right!)

• The camera is fixed and the sky drifts over it, taking 5 minutes to cross the entire camera

• For what aspect of how CCDs function is the SDSS camera trying to compensate? Is CCD readout time important, here?


Sky Driftsthis way

• The Sloan Digital SkySurvey camera contains 30 CCDs arranged in 5 “columns” of different color filters (in the picture, columns run left-right!)

• The camera is fixed and the sky drifts over it, taking 5 minutes to cross the entire camera

• For what aspect of how CCDs function is the SDSS camera trying to compensate? Is CCD readout time important, here?


Sky Driftsthis way

The SDSS readout time was about 1 minute,

meaning each column could be read in real time

astronomical cameras - uwyo.eduphysics.uwyo.edu/~aschwortz/lassi/files/lassi14oct24.pdf•the image...

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