[Aavso-photometry] Determination and use of BVRI

Sat Jan 19 15:43:52 EST 2008

Brad,

Thanks for posting all that. There's a nice display of the equations in 
"real math", which may be easier to follow, in a paper that a grad student 
of mine and I wrote some years ago.  You can download it from the Harvard 
reprint server here:

    http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989PASP..101..849B&db_key=AST&link_type=ABSTRACT&high=431c8b327120719

Midway down the page, click the "Send PDF" button and wait ~30 seconds and 
you'll get it.

Michael Newberry

----- Original Message ----- 
From: "Brad Walter" <bswalter at hughes.net>
To: <aavso-photometry at mira.aavso.org>
Sent: Saturday, January 19, 2008 11:32 AM
Subject: Re: [Aavso-photometry] Determination and use of BVRI

> Two other points
> Your first equation is
> mdiff (star) = minst (star) - minst (ref) + mstd (ref)
>
> minst (star) is defined by your equation as being -2.5*Log (Flux(star)) -
> See below for the reason I use Flux instead of Int - leaving out the 
> detail
> of normalizing for the integration time. minst is an instrumental 
> magnitude
> that is not referenced to a known star. It is ofter called the "raw"
> instrumental magnitude. It will always be a negative number.
>
> However, mdiff, as you have defined it,  includes the zero point 
> correction.
> This is still called an instrumental magnitude but it isn't the value that
> you need for applying transformation coefficients. I would denote it m
> (star). The differential magnitude you need to apply extinction 
> coefficients
> is
> minst (star)- minst (ref)
>
> Your second equation is
> minst (ref) = -2.5 log (Int(ref))
> This is Ok with one small technical correction. You aren't actually 
> mesuring
> intensity you are measuring flux. I know that maxim calls it intensity. 
> For
> a point source of light,intensity is power per unit of wavelength per
> steradian of solid angle subtended by your telescope aperture. Since you 
> are
> not using correcting factors for the solid angle subtended and the width 
> of
> the bandpass, you are measuring flux which is simply power received by 
> your
> telescope aperture over whatever bandpass you get from the combination of
> atmosphere, telescope, filter and detector. For a given observing setup 
> the
> Intensity will be proportional to the flux reaching the telescope. 
> Therefore
> the second equation should really be
>
> minst (ref) = -2.5 log (Flux(ref))
>
> The problem with Maxim is that you only get the instrumental magnitude
> corrected for zero point in the output table. It doesn't give you
> minst(star) or minst(ref) so you don't have the basic data you need to do
> transformations. You would have to record that information manually from 
> the
> information window of the photometry tool enter that data into a 
> spreadsheet
> and do the math. If you are analyzing a few hundred images that becomes a
> mind numbing, time devouring chore.
>
> In an earlier e-mail, Sat, 12 Jan 2008 13:10:49 -0500, you asked what to 
> do
> about the zero points in the color index transformation equations. The 
> short
> answer is that the zero point terms cancel out in determining transformed
> Delta (B-V) between star and ref and transformed delta V between star and
> ref. The correct zeropoint for your session is added back when you add
> standard(B-V)ref or standard Vref back to the differential transformed
> magnitudes.
>
> The long answer is as follows.
>
> Going back to basic equations for photometry, using spreadsheet operators 
> to
> separate variables and changing nomenclature slightly to reduce typing
> v = vinst = -2.5*LOG(Flux/Integration Time)
> V (upper case) = vstd
>
> vo = extinction corrected raw magnitudes
> c (lower case) = a raw color index i.e. b(inst) - v(inst), v(inst) -
> r(inst), etc
> co = extinction corrected color index
> C (upper case) = the standard color, i.e. B-V, V-R, etc.
> Tc = Transformation coefficient for the color index
> k1c = first order extinction coefficient for the color index
> k2c - second order extinction for the color index
> Zc = zero point for the color
> Dc = c(star)-c(ref) (difference in color index betwee star and ref)
>
> The two basic equations for extinction correction and transformation of
> color indexes (colors) are
> co = c*(1 - k2c*X) - k1c*X
> C = Tc*co +Zc.
>
> The difference between extinction corrected instrumental colors is
> Dco = c(star) - c(ref) - k2c*X*(c(star)- c(ref))-k1c*X(star)+k1cX(ref)
>
> In the same FOV X(star) and X(ref) are essentially equal, therefore,
> Dco = Dc - Dc*k2c*X
>
> DC = C(star) - C(ref)
> DC = Tc*(co(star)-co(ref)) + Zc - Zc
>   = Tc*Dco
>   = Tc*(Dc - Dc*ksc*X)
>   = Tc*(c(star)-c(ref)-k2c*X*(c(star) - c(ref))
> or
> C(star) - C(ref) = Tc*(c(star)- c(ref))*(1-k2c*X)
> If you are not using second order extinction, this simplicies to
> C(star) - C(ref) = Tc*(c(star) - c(ref))
> C(star) = Tc*(c(star) - c(ref)) + C(ref)
>
> The Zc term is automatically included because the expression can be
> rewritten as
> C(star) = Tc*c(star) + C(ref)-Tc*c(ref)
> And C(ref) - Tc*c(ref) includes Zc
> Therefore even though you determned Tc using a particular reference star 
> in
> your M67 measurements, Tc doesn't depend on that star and the differential
> photometry process adds Zc back for the reference star you are using in 
> any
> particular session.
>
> Now we have the standard color index of interest for our target star. 
> Second
> order extinction coefficients are often omitted but should be included for
> color indexes if you are trying for high accuracy or high precision when
> taking data over a range of altitudes. 2nd order is more important for 
> color
> indexes than for V.
>
> To get Vstd(star) using the same small nomenclature changes
>
> The two basic equations for extinction and transformation in V are
>
> vo = v - k1v*X, omitting the usually very small second order extinction
> value
> V = vo + Tv*(B-V) + Zv
> Tv and Zv are the transformation coefficients and zero point for the V 
> band
>
> Dvo = v(star) - v(ref) -k1v*X(star) +k1v*X(ref) where
> k1v = first order extinction coefficient for V band
> Since X(star) and X(ref) are essentially equal when they are in the same 
> FOV
> the last two terms cancel leaving
>
> Dvo = v(star) - v(ref)
>
> using
> V = vo + Tv*(B-V) + Zv
> and defining
> D(B-V) = (B-V)(star) - (B-V)(ref)
> then
> DV = Dvo + Tv*D(B-V) (the Zv terms cancel out again)
>   = v(star) - v(ref) + Tv*D(B-V)
>
> Substituting for DV and vo
> V(star)-V(ref) = v(star) - v(ref) + Tv*((B-V)(star) - (B-V)(ref))
> V(star) = v(star) - v(ref) + Tv*((B-V)(star) - (B-V)(ref)) + V(ref)
>
> The zero point is again automatically taken care of by the difference
> between the transformed v(ref) and V(ref)
> V(star) = v(star) + Tv*(B-V)(star)  + ( V(ref) - v(ref) -Tv*(B-V)(ref))
> The last term in parenthesis adds Zv
>
> If you aren't taking data in B, you can use another color index and
> transformation coefficient Tv based on the bands you are using e.g. V-R or
> V-I.
>
>
>
>
>
>> Message: 1
>> Date: Tue, 15 Jan 2008 11:51:50 -0500
>> From: "Lionel Catalan" <lcatalan at lakeheadu.ca>
>> Subject: Re: [Aavso-photometry] Determination and use of BVRI
>> TransformationCoefficients with Maxim DL
>> To: <aavso-photometry at mira.aavso.org>
>> Message-ID: <E1JEoxn-0003a6-Do at mta2.lakeheadu.ca>
>> Content-Type: text/plain; charset="us-ascii"
>>
>> Thanks Brad for the suggestion about including the
>> integration time in the calculation of instrumental magnitudes.
>>
>> Lionel
>>
>>
>> -----Original Message-----
>> From: aavso-photometry-bounces at mira.aavso.org
>> [mailto:aavso-photometry-bounces at mira.aavso.org] On Behalf Of
>> Brad Walter
>> Sent: Tuesday, January 15, 2008 5:48 AM
>> To: aavso-photometry at mira.aavso.org
>> Subject: Re: [Aavso-photometry] Determination and use of BVRI
>> TransformationCoefficients with Maxim DL
>>
>>  Lionel, When computing your instrumental magnitudes I would
>> suggest that you use the form
>>
>> minst (star) = -2.5 log (Int(star)/Tint)
>>
>> Where Tint is the integration time of the image. Otherwise,
>> you will not be able to compare instrumental magnitudes
>> obtained with different integration times.
>>
>> Frequently the term differential magnitude is used to denote
>> Minst (star) -minst (ref) without adding mstd (ref) being
>> added. See the CBA submission format in the help document for
>> CCD/PEP Batch Upload in WebObs,
>> http://www.aavso.org/bluegold/webobs.html
>>
>>
>>
>> Message: 2
>> Date: Sun, 13 Jan 2008 22:49:48 -0500
>> From: "Lionel Catalan" <lcatalan at lakeheadu.ca>
>> Subject: Re: [Aavso-photometry] Determination and use of BVRI
>> transformation coefficients with Maxim DL
>> To: aavso-photometry at mira.aavso.org
>> Message-ID:
>> <58b78fe40801131949r4fa5458di30f0060e3d513be0 at mail.gmail.com>
>> Content-Type: text/plain; charset=WINDOWS-1252
>>
>> Based on comments from Arne and Gord Sarty, I thought that
>> the most straightforward way of using Maxim photometry data
>> to derive transformation coefficients would be to convert
>> Maxim's differential magnitudes into instrumental magnitudes.
>> This recognizes the fact that transformation equations are
>> written in terms of instrumental magnitudes.
>>
>> Because the photometry analysis tool in Maxim DL only
>> calculates differential magnitudes, a special procedure is
>> required to derive instrumental magnitudes. Differential
>> magnitudes in Maxim DL are calculated using a reference star
>> with known standard magnitude as
>> follows:
>>
>> mdiff (star) = minst (star) ? minst (ref) + mstd (ref)
>>
>> where mdiff, minst and mstd refer to differential,
>> instrumental and standard magnitudes, respectively. The
>> instrumental magnitude of the reference star can be
>> calculated as follows:
>>
>> minst (ref) = -2.5 log (Int(ref))
>>
>> where Int(ref) represents the intensity of the reference star
>> calculated as the sum of all pixel counts within aperture
>> less background. The value of Int(ref), which is simply
>> called "Intensity"
>> in Maxim DL, can be read from the information window in
>> aperture mode by centering the aperture on the reference star
>> while using the photometry analysis tool. One must be careful
>> to ensure that the centroid of the reference star has the
>> same coordinates when reading its intensity and when
>> calculating the differential maginutes of the other stars.
>>
>> Combining the two previous equations gives:
>>
>> minst (star) = mdiff (star) -2.5 log (Int(ref)) - mstd (ref)
>>
>> This equation is applied to magnitudes obtained with the B,
>> V, R, and I filters using Excel.
>>
>> Lionel
>>
>>
>>
>
>
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