Astronomical Cameras

I. The Pinhole Camera

Pinhole Camera (or Camera Obscura) Whenever light passes through a small hole or aperture it creates an image opposite the hole This is an effect wherever apertures occur in nature Essentially, a pinhole camera consists of two 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 Properties The image appears inverted (see diagram) The farther the source is from the aperture, the smaller the image appears. Why? source what other everyday imaging device 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 image

F-number 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 is confusingly written, e.g., f/2 A 100mm focal length and a 5mm aperture 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 ) d f Then cameras can have adjustable f-ratios to let in more light and change the size of the image

F-number in telescopes For telescopes d is the diameter of the d slow - usually easy to design light-collector f-number is then a measure of field of view, and image resolution (of how sharp the image is) d f f fast - usually hard to design fast http://www.telescopenerd.com/telescope-astronomy-articles/how-fast-is-your-telescope.htm 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

Pinhole Camera Model A point on a source P passes through a pinhole O to create hole X P a point on an image Q Q y = f X x IMAGE f Q X How can I make the image smaller by changing the camera? smaller by not changing the camera? not inverted? f P

Airy Disks and Rayleigh Criterion http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html#c1 Airy Disk θr is the angular resolution d is the aperture diameter λ is the wavelength of light 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

Pinhole Camera Aperture Model sinθ R = 1.22λ (Rayleigh Criterion) tanθ R = y f d For Small Angles : tanθ R ~ sinθ R ~ θ R d = 1.22 f λ y d θr Airy Disk y If everything that passes through the aperture ends up in the f 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?

Angular Resolution for a Telescope For a telescope the angular resolution for a slit rather than a circular aperture is appropriate R = λ d (R in radians) Again, d for a telescope is the diameter of the light-collector rather than the pinhole Rayleigh Criterion Most principles for astronomical cameras resemble pinhole cameras

Augmentations to the Pinhole Camera The pinhole camera does not capture an image permanently. What new component is needed for this?

Augmentations to the Pinhole Camera The pinhole camera does not capture an image permanently. What new component is needed for this? A light-sensitive image sensor (photo film, CCDs)

Augmentations to the Pinhole Camera The pinhole camera does not capture an image permanently. What new component is needed for this? 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 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?

2. Focusing Light

Refraction and Snell s Law Light is deflected at the interface between two materials The angle to the normal to the interface changes depending on what the materials are made of: n 1 sinθ 1 = n 2 sinθ 2, v 2 sinθ 1 = v 1 sinθ 2 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)

Lenses Converging Lens Lenses can replace a pinhole in order to focus light with more control The collecting area of the lens is then the aperture and the distance from the Diverging Lens lens to the focal point is the focal length d Compound Lens Lenses can be used to help circumvent the fact that a pinhole can only make f large images that are bright or sharp http://www.bigshotcamera.com/

The (thin, convex) lens equation 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 any theoretical focal length If an image is not in focus di > f, how can we bring it into focus? http://www.alpcentauri.info 1 d i + 1 d o = 1 f How will an image that is out of focus look? Why?

The (spherical, concave) mirror equation It is always possible to create a mirror with equivalent optics to a lens f The situation is very similar to the geometry of a lens except the optics stay on the same side of a mirror There are several benefits to using a mirror to focus light for a telescope rather than a lens http://www.aplusphysics.com 1 d i + 1 d o = 1 f What are two advantages?

platescale= 1 f Plate Scale for a Telescope 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: http://ircamera.as.arizona.edu/astr_250/lectures/lec_10sml.htm

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 Better The light gathering power of a telescope is just the area of the light collector (the primary lens or mirror) Light Gathering Power = Area = πr 2 = πd 2 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

Charge-Coupled Devices 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? K = h( f f ) 0 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

Charge-Coupled Devices 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 devices for storing charge In a CCD, charge builds up in photons the capacitors proportional to the number of photons (the intensity of light) that hits electrons each sensor capacitors

Reading out the Charge Moving charge is just electric current, and a series of 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 how much light fell on each photoelectric sensor cell The total readout time is important...long readout times could delay subsequent images photons http://coursewiki.astro.cornell.edu http://astro.unl.edu/classaction/animations/ telescopes/buckets.html

How to make color images CCDs only measure the total amount of light that fell on each cell...not the color or wavelength of that light There are several ways to then make a color image multiple CCDs with a color filter in front of each CCD multiple telescopes each with its own CCD looking through a different color filter Interpolating across a series of color filters laid out across a single CCD grid The PROMPT array S D S S C a m e r a

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

The Bayer Filter Let s look at the cell pattern highlighted in yellow

The Bayer Filter What were the intensities of light (the numbers of photons of each color, red, green, blue) through the position in the CCD covered by the central green filter? 150 110 100 140 140 160 200 130 110

The Bayer Filter Let s look at the cell pattern highlighted in yellow

The Bayer Filter What were the intensities of light (the numbers of photons of each color, red, green, blue) through the position in the CCD covered by the blue filter? 130 100 150 180 130 200 190 120 170

A Far Less Intelligent Filter Pattern

4. Telescopes and Astronomical Cameras

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)

Some Modern Astronomical Cameras The Large Synoptic Survey telescope has a very large Sensor@ f/1.23 primary mirror (8.4m) What are two reasons why a large mirror is desirable? Look at the design to the right...why build a telescope with 3 mirrors like this? What does f/1.23 at the sensor mean? Is the LSST fast or slow?

Some Modern Astronomical Cameras The Large Synoptic Survey telescope has a very large Sensor@ f/1.23 primary mirror (8.4m) What are two reasons why a large mirror is desirable? f Look at the design to the right...why build a telescope with 3 mirrors like this? What does f/1.23 at the sensor mean? Is the LSST fast or slow? d The LSST has a 3.5 o field of view (c.f. WIRO with a 2.3 meter primary mirror and a < 1 o field of view)

Some Modern Astronomical Cameras The Sloan Digital Sky Survey camera contains 30 Sky Drifts this way 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?

Astronomical Cameras