[Aavso-photometry] Photometric transformation coefficients - general concepts

[Stan Walker]

Hi Tom,

Michael's post this morning reminded me that I read your one with 
considerable interest. In effect you described exactly what we worked out 
from Hardie's original paper/s but in a much simpler manner. I will probably 
include this in the Variable Stars South August Newsletter or - 
alternatively - have it placed on our web site when that's up and running.

Most books I've read seem to delight in describing the 'how' in a variety of 
ways, some very difficult to follow, but rarely the 'why'. Which is, I 
think, why so many people become stuck in unfiltered photometry of CVs, MPs 
etc., which are dramatically overobserved in this manner. Good to see the 
why explained in this way.

Regards,
Stan


----- Original Message ----- 
From: "Tom Krajci" <tom_krajci at tularosa.net>
To: <aavso-photometry at aavso.org>
Sent: Friday, June 19, 2009 4:37 PM
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?
>
> -- 
> -------------------------------------------
> 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/
> -------------------------------------------
>
> ====================================
>
> 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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