[Aavso-photometry] Photometric transformation coefficients -general concepts

[Steve Beckwith]

Tom,
This is an outstanding write-up on transformation coefficients.  A very
clear AND well written explanation/description!

Bravo Zulu,
- Steve

Beckwith Strings
Bolton, MA
978-779-5227
www.beckwithstrings.com

-----Original Message-----
From: aavso-photometry-bounces at aavso.org
[mailto:aavso-photometry-bounces at aavso.org] On Behalf Of Tom Krajci
Sent: Friday, June 19, 2009 12:38 AM
To: aavso-photometry at aavso.org
Subject: [Aavso-photometry] Photometric transformation coefficients -general
concepts

Below is something I wrote up to help get some general concepts across. 
Please feel free to use it.

Did I make any fundamental mistakes?

-- 
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Tom Krajci
Cloudcroft, New Mexico
http://picasaweb.google.com/tom.krajci

Center for Backyard Astrophysics (CBA)
http://cbastro.org/ CBA New Mexico

American Association of Variable Star
Observers (AAVSO): KTC http://www.aavso.org/
-------------------------------------------

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Photometric transformation coefficients - general concepts

There is no math in this post, only a discussion of general concepts.

We're gonna conduct some simple thought experiments to help explain 
concepts that are important to photometry.


Thought experiment 1

Step outside on a clear day near noon, and let sunlight fall on a piece 
of white paper. You'd say that bright white light is falling on the paper.

Do this again, but just before sunset. You'd say that fainter red light 
is falling on the paper.

What happened here? Did the sun change? No. But the sunlight traveled 
through much more atmosphere in the case just before sunset.

OK, then it should have been fainter *white* light, yes? Obviously it 
isn't, so something else is going on here.

Concept #1: Our atmosphere cuts down the amount of light that reaches us 
from space. This light travels through more atmosphere when the source 
appears closer to the horizon, so objects appear fainter when low, and 
brighter when high.

Concept #2: Our atmosphere does not cut down all colors of light 
equally. Red light is affected least (that's what you see in the sunset 
colors...it reaches your eyes), and blue is affected the most (little 
blue light reaches our eyes from light sources low on the horizon).



Thought experiment 2

Today it's clear, but the air is different. It may be a windy day dust 
storm, or smoke from a distant forest fire has drifted over you. Anyway, 
there's more stuff in the air today. Look at sunlight on white paper at 
noon, and just before sunset. What do you see? The noon light is not as 
bright as the 'transparent' day, and it may even have a yellow or orange 
tint. And sunset? If it's really heavy smoke/dust...the sun may be 
barely visible, and very deep red.


Concept #3: The amount of light that our atmosphere removes can change, 
depending on atmospheric conditions. (Not all clear days, or nights, are 
equal.)


Ouch! That darned atmosphere makes something simple, like observing our 
constant sun...change brightness and color...from hour to hour, and day 
to day! How can you measure brightness of stars when the atmosphere 
changes things so much? (There are 'work arounds' to this problem...and 
we'll get to them in a bit.)



Thought experiment 3

One clear night you're observing two stars that are close to each other 
- binoculars, telescope, it's not important. What's important is that 
these two stars are fairly close to each other...a couple degrees 
separation or closer. These stars are also the same color...both are 
orange, or both are bluish....doesn't matter. But to your eye they are 
the same brightness. You are observing them when they are high in the 
sky. Wait a few hours and observe them when they are much closer to the 
horizon...just before setting. Sure they look fainter, but how do they 
compare to each other? Are they still equal brightness? (We'll assume 
these are constant stars, not variable stars.)

Yes, they are fainter, but they are still equal to each other in 
brightness.


Solution #1: Compare the brightness of stars that are not widely 
separated. That will eliminate the negative effects of the atmosphere. 
(This is not a perfect solution...let's call it a 75% solution.) ('Close 
together' is less than one degree...which is fine for most telescopes. 
But camera lenses?...that's a problem because they cover wide fields. 
We'll stick with narrow angle telescopes for now and avoid the problem 
of wide angle camera lenses.)

NOTE: We are measuring brightness by making comparisons to other stars. 
This is known as differential photometry. (What's the absolute 
brightness of a star? We don't know. We just know how it compares to a 
nearby star. But that's a pretty good start in the world of measurement.)



Thought experiment 4

One clear night you're observing two stars that are close to each other 
- binoculars, telescope, it's not important. What's important is that 
these two stars are fairly close to each other...a couple degrees 
separation or closer. Also, these stars are *different* colors...one is 
orange, one is bluish. But to your eye they are the same brightness. You 
are observing them when they are high in the sky. Wait a few hours and 
observe them when they are much closer to the horizon...just before 
setting. Sure they are fainter, but how do they compare to each other? 
Are they still equal brightness? (We'll assume these are constant stars, 
not variable stars.)

No. The orange star now appears brighter than the bluish star.


Concept #4: As stars set, redder stars get fainter slowly, and bluer 
stars get fainter faster. (Conversely, as stars rise, redder stars get 
brighter slowly, and bluer stars get brighter faster.)


Double ouch! Thanks to our atmosphere, we're getting farther from our 
goal of measuring star brightness with any sort of confidence and accuracy.

What if the stars were the same color? In that case, they would get 
equally fainter as they set (and equally brighter as they rose).

But stars come in various colors...and you can't change that.


Well, here's one work around:
Solution #2: If possible, compare brightness between stars that are 
reasonably well matched in color. (Sometimes that's not easy. In the 
star-poor spring sky, such as Leo,...you may not find a nearby star of a 
similar color. You may have to use mis-matched stars, which is not a 
good solution. But it may be the only solution in some cases.)


NOTE: We are doing unfiltered photometry..and we need to be careful and 
try and match the color of the stars we study. If not, our accuracy 
suffers.


Perhaps you *can* can change the color of stars?



Thought experiment 5

You found some old glass filters from your (or your father's) 
film-photography days...red, green, blue. Look at a white star through 
the red filter - what does it look like? Red. Through the blue filter? 
Blue. And it looks green in the green filter.

That's not too surprising, because white light is all colors combined.

What about a reddish star? Through the red filter it looks red, in green 
it looks green (but a bit less bright), and in the blue filter it's 
blue...but even fainter.

And a blue star? Through the red filter it looks red (but somewhat 
faint), in green it looks green (but a bit brighter), and in the blue 
filter it's blue...but even brighter.


Concept #5: Stars (except exotic ones, which we'll ignore for now) of 
various colors still have some amount of light from all colors of the 
rainbow. (Neon signs, mercury vapor street lights...they only have one, 
or a few discrete colors. But stars, at a simple level, show all colors 
to some extent.)


Hmmmm, we may have found a way to 'force' stars to have the same 
color...use a filter. Now we can get them to behave the same way in 
terms of color/brightness, and how the atmosphere affects 
color/brightness as they rise and set.


Solution #3: Use a filter to 'force' all stars to have the same color. 
(This is not a perfect solution...let's call it a 90% solution.)



Thought experiment 6

You learn that there are standard photometric filters for science 
purposes, and you find some in the high school physics classroom, 
forgotten in a drawer. You learn that they have a V filter (passes green 
light), and B (blue) and R (red). You compare them to your 
film-photography red/green/blue filters. Looking through them, these two 
sets of filters are similar, but not identical. In your case, you find 
your film/green filter, compared to the photometry/V filter, passes a 
bit more red light, and a bit less blue light. In other words, your 
film/green filter is 'redder' than the photometric/V filter...it's 
bandpass is shifted toward the red end of the spectrum.

OK, make some careful measurements of stars with these two filters. What 
do you find? If the star is white, you'll find its brightness is pretty 
much equal in these two filters. If the star is red...you'll find your 
film/green filter shows that star a bit brighter than through the 
photometry/V filter. And if the star is blue, your film/green filter 
shows it as a bit fainter than through the photometry/V filter.

Why? For the example of red stars, they have a larger output of red 
light than other colors. And your film/green filter has a bandpass 
that's shifted toward the red. Compared to the photometry/V filter, your 
film/green filter passes more light from a red star. (And for blue stars 
it's the opposite. Those stars have more blue, and less red light. Your 
film/green filter passes less light compared to the photometry/V filter.)


Concept #6: Not all photometry filters are created identical/equal. 
Small differences exist...small deviations from the ideal definition. 
This will create small offsets in your measurements. (And the same can 
be said of your telescope optics, and CCD chip, and your 
atmosphere...they also introduce shifts/errors/deviations from the ideal.)

Where is this ideal place to do photometry? Above our atmosphere. And, 
using equipment that has the 'ideal' bandpass/response.

Fortunately, the deviation of your ground-based equipment from the 
standard is pretty much repeatable...at least if you're careful in using 
it.


Solution #4: Measure brightness of stars with your 'imperfect' 
filters/CCD/scope/atmosphere, and compare your results to 'catalog' 
values. Analyze the differences, and you'll probably find that they are 
repeatable and consistent. Then, apply a difference correction to your 
measurements and they should (pretty closely) match the 'catalog values.'

NOTE: This is the essence of transformed differential photometry. You've 
used good practices, and determined your small offsets from catalog 
values. You can produce well calibrated measurements...as if you were 
making measurements from above the atmosphere, with a perfect/ideal 
system. And, if other folks around the globe do similar calibration of 
their equipment...your measurements should be in very good agreement. 
That makes collaboration much easier.

This is not a perfect solution...let's call it a 98% to 99% solution.

Remember, different photometry projects require different amounts of 
calibration. In the beginning you work with the 75% solution...choose 
stars close to each other, and that have similar colors. Later, you can 
add filters, and that can improve your solution to 90%. Then you measure 
your filter deviations from the gold standard...and you can work at the 
98-99% level.

The history of measurement has examples for us. Centuries ago one inch 
was defined as three barleycorn. Later, the meter was defined as the 
distance between two thin scratches in a bar of low-expansion metal. 
These days length is defined in terms of light wavelenghs (of a precise 
color) in a vacuum. Photometry is the same way...with time and 
experience you learn to make more precise measurements.
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