ASTRONOMICAL BRIGHTNESS MEASUREMENTS

There is a reason for this that can be seen by understanding how a real detector detects!

 

(DISCLAIMER: If you haven’t had calculus, don’t worry about the details below  you don’t need to know calculus for this course)

 

 

 

 

 

Blackbody Radiation

 

Planck Law

 

The spectra of many stars are nearly that of blackbodies, which follow the Planck Law:

 

 

 

h = 6.627x10^-34 J s Planck’s constant

k = 1.381x10^-23 J K^-1 Boltzmann’s constant

c = 2.998x10⁸ m s^-1 speed of light

Wien’s Law

 

Stefan-Boltzmann Law

 

The total energy of a blackbody is just the area under the Planck curve  (for calc-types, the integral of B_ν(T)):

 

 

Limiting Approximations:

 

Okay, which “T do we use?

 

For a true blackbody, these are all identical, but for real stars, they may all be different! Then there is:

 

Kinetic T  the T that describes the velocities of atoms in the gas

Excitation T  the T that describes how “excited” the atoms are, in terms of their electrons & energy levels

Ionization T  the T that describes how ionized the gas is

Etc.

 

MAGNITUDES

 

 

where const(λ) is set by the photometric system.

 

Relative brightnesses of 2 stars at a given λ:

 

 

 

 

 

The relative brightnesses of a star at 2 different λs:

 

Measuring Stars at Different λs  “Alphabet Soup Photometry” - UBVRIJHKLMNQ

 

 

 

 

 

 

 

 

 

 

 

The Eye as a Detector

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Photomultiplier Tubes  1950’s

 

 

 

 

Photodiodes  light alters resistance

 

Photovoltaics  light induces EMF (voltage)

 

Bolometers  Light absorbed raises T that alters resistance

 

Charge-Coupled Devices  CCDs  light creates “electron” which is later read out

 

 

 

 

How CCDs Work

 

CCDs are nothing more than an elaborate series of light-sensitive regions built on top of a chip of silicon. One can think of these as a series of “light buckets” on conveyor belts. Each belt moves a series of buckets, say, horizontally. First each end bucket dumps its contents into a “readout” bucket, and the readout buckets advance vertically in sequence to a measuring bucket.

 

 

 

 

When light hits the active region in a CCD chip, an electron is released from the solid material’s lattice structure (the “vacancy” left behind, which acts like a positive charge, is called a “hole”).

 

CCDs are normally lit from above (left figure above). However, this causes the electronics to block the very light the CCD is built to detect! Metal-polymer composites which are partly transparent can be used to make the electronic contacts. For even higher sensitivity, the substrate the light-detecting layers sit on can be etched away with acid, and the CCD illuminated from the back side. These are often fragile and can suffer from distortions as they can have a mild “potato chip” shape!

 

With proper care, CCDs that have 97% quantum efficiency (detect 97 out of every 100 photons that hit them) can be achieved. Compare this to the mere 1% of typical film, and you can understand why CCDs are superior to film for most low-light applications.

 

 

Most CCDs are red-sensitive. To make them more blue sensitive, they may be coated with a dye that will fluoresce when hit by shorter-wavelength radiation. The sensitivity of the CCD camera chips on the Hubble Space Telescope have be extended to wavelengths as short as 120 nm using a coating not unlike that found in fluorescent yellow-green highlighter pens!

 

Once created, the charge has to be read somehow. This is done by sequentially altering the electrical voltage on a little plate nearby called a gate. By sending the right sequence of voltages to the gates, the little packet of charge can be transferred to the edge of the chip.

 

 

Once a column of charges has reached the edge of the chip, they are then read out in the perpendicular direction. These are then sequentially dumped onto a capacitor (small charge storage device), which changes its voltage. The voltage is detected and this number sent out as the “signal” that hit that one picture element, or pixel.

 

 

This readout process can be slow, especially for large chips. While reading out, the chip is still “busy” and light sensitive, s no exposing can be done.

 

To speed up the process, it is possible to mask half the pixels with a reflective material, expose the naked ones, shift then under the masked pixels, and read them out while the next exposure begins. Such schemes are useful for video cameras, when rapid readout is essential. But the blockage of 50% of the incoming light renders them less suitable for low-light applications.