Download Photometry

Photometry: The measurement of the
intensity, brightness, or other properties of
light.
Photons/sec
Count Photons
• Sounds simple, but
-- what if the measuring equipment misses
some because it is not 100% efficient?
-- what if the atmosphere or telescope don’t
transmit all of the photons?
-- what if some photons are from something
else like the sky which is not totally dark?
Comparison Sources
• Useful to compare an unknown source to a known reference -- this
is what you did to measure the luminosity of the Sun which was
compared to a known source, a 300-Watt light bulb
But this scheme has it limitations, too:
-- what about the temperature of the light bulb as compared
to the Sun?
-- is the Sun observed through the same air path as the light
bulb?
-- is your eye the most accurate recording device?
Compare an Unknown Star to a Known Star
• Another useful technique
is to measure a star in
comparison to another
star, very convenient
when looking for stars
that vary like Cepheids
• Using a comparison star
avoids the issues with
instrument and
Look through the same air path atmospheric
Also reduces problems due to
shortcomings
different temperatures
“Blinking” to Find Varying or Moving
Objects
• The homework
has you using a
simulated blink
comparator to
find variable stars
• Clyde Tombaugh
used a blink
comparator to
discover Pluto
Extra Sources of Photons
• When measuring a star you most likely would be measuring it
against a “background” that produces some photons (ie., the
night sky isn’t completely dark due to scattered light from
cities, etc)
• By measuring a region around the star, this level can be
subtracted from the star to get the brightness of the star
without any photons being included
Star = Inner Disc ave
– Outer Ring ave
= 6454.59 – 2334.49
= 4120.1
Complete Measurement
Brightness
• Take data on a pair of stars,
one of which is the star of
interest and the other of
which is a known reference
star (sometimes called a
standard or comparison
star)
• Correct each star’s data for
background counts
• Compare the star of interest
with the reference star
• Repeat many times if
looking for variable stars
Time
What to Believe
Brightness
Notice in the example from the previous slide that
comparison star’s data is not always exactly the same
value. Is it varying?
Probably not – need to understand “noise”
or uncertainty in a measurement.
Time
Noise from Counting
Anything that comes in indivisible units and has some probability of
occurring is subject to “counting statistics”.
For example, if you toss a coin 20 times, you would expect to get
heads 10 times, but will you actually get 10 heads?
-- sometimes, and sometimes not but if you repeat the
experiment of tossing a coin 20 times, on average you will get 10
heads
-- the spread in the number of heads is given by the square root of
the average value
Average = 10 heads
so expect to get any where from 10 - 10 to 10+ 10 heads
6.8 to 13.2 ( 10 = 3.2)
Any number is still possible, but some numbers of heads are very
unlikely: Probability of getting 20 heads = (.5)20 = 9.5 x 10-7 or just
under 1 in a million!
Other Examples of Counting Statistics
Sports: A basketball player doesn’t make every free throw she
tries. On average a player might make 85% of her throws but you
must be careful when making claims about a single game
performance.
For example: A player tries 10 throws in a game. On average she
would make 8.5 (but obviously you can’t have a half throw!). The
square root of 8.5 is 2.9 so one should expect to see a number of
throws made in the range of 8.5-2.9 to 8.5+2.9 or 5.6 to 11.4 so
making only 6 throws wouldn’t be so unusual.
Voter polls: Suppose 1000 people are sampled. The margin of
error as a percentage will be 1000 /1000 x 100% = 3.2% .
Two thirds of the time the true average will be within +/- the
margin of error and 95% of the time it will be within 2 time the +/margin of error.
Photon Counting
• Photons arrive in indivisible units and therefore are
subject to counting statistics
• The variation in the reference star noticed earlier
was due to the noise in counting photons -- if only
100 photons were counted, then the error would be
100 = 10 photons = 10% of the signal.
Beware that there is
also noise associated
with counting the
background photons!
Notice that the
averages of these two
blank sky regions are
not the same.