[Aavso-photometry] Determination and use of BVRI
Michael Newberry
mnewberry at mirametrics.com
Mon Jan 21 11:04:16 EST 2008
Pierre,
Thanks, yes, in the equation, ADU is the number of counts ABOVE sky. Thank you for clarifying that.
Michael
----- Original Message -----
From: Pierre de Ponthiere
To: Michael Newberry
Sent: Monday, January 21, 2008 3:30 AM
Subject: Re: [Aavso-photometry] Determination and use of BVRI
Hi Michael,
In the equation you provided for the instrumental magnitude
m = K - 2.5 log (ADU * Gain / Time )
ADU should be replaced by the Co value (Co being the number of counts that are attributable to object i.e. after subtracting sky contribution) as per your equation (1) of your referenced article.
Pierre
--
Pierre de Ponthiere (Belgium)
AAVSO Member (American Association of Variable Star Observers)
CBA Lesve Observer (Center for Backyard Astrophysics)
CAB Member (Cercle Astronomique de Bruxelles)
AstroNamur Member (Regional astro club)
ACA Astronomie Centre Ardennes member
http://www.dppobservatory.net
=====================================
On Jan 20, 2008 7:32 PM, Michael Newberry <mnewberry at mirametrics.com> wrote:
Lionel and Brad,
I would make a correction in the "Long Answer" section. In the first
paragraph, you have
-2.5*LOG(Flux/Integration Time)
which should be just
-2.5*LOG(Flux)
since Flux is defined in the normal way as a quantity per unit time (or per
unit time, per unit area). Flux is a rate, not a quantity. Here it is
Signal/Time. So, strictly speaking, the Signal (in Counts, ADU, or DN)
should be divided by the exposure time to get Flux.
If working with a single image, using either Counts or Flux does not matter
since all Signal values will be divided by the same exposure time, and thus
the difference between -2.5log(ADU) and -2.5log(ADU/time) is accommodated by
the zero point constant. Choosing one or the other value in the log() will
make the zero points differ by a factor of 2.5 log(time). However, I like to
see how the zero point changes with time through the images and, if the
exposure times are not if comparing images, as in a time series, or if
comparing zero points between images, you want the fluxes to compare so you
would need to use the flux for each image.
Here's yet another thing to consider which may seem a little picky, but
that's not the case. That is including the value of the Gain, as electrons
per ADU, in the calculation. There are 2 reasons:
1) Working with an image set that came from different cameras or the same
camera using different Gain settings.
2) The photometric error, sigma(m), which is the magnitude uncertainty
(internal error) for each star is computed from using either the
instrumental parameters (gain, read noise, exposure time) or using the
standard deviation in the sky background in a fairly complex formula.
Calculated either way, it involves the value of the Gain. If the Gain is not
included in calculating the magnitude error, then the error is wrong. And
"How wrong?" depends upon the value of the Gain, the number of pixels in the
measuring aperture, and the ratio of the background standard deviation to
the object brightness.
Thus I have always used the full equation for instrumental magnitude, m,
like this:
m = K - 2.5 log (ADU * Gain / Time )
where K is the zero point magnitude.
You can find all this stuff (with all the gory details, plus how to optimize
the photometric results you will get and suggestions for improved CCD
imaging+calibration strategies) in a paper I published in 1991. It can be
downloaded here:
http://adsabs.harvard.edu/abs/1991PASP..103..122N
Choose "Send PDF" about midway down the page.
Michael Newberry
----- Original Message -----
From: "Lionel Catalan" <lcatalan at lakeheadu.ca>
To: <aavso-photometry at mira.aavso.org>
Sent: Sunday, January 20, 2008 5:53 AM
Subject: Re: [Aavso-photometry] Determination and use of BVRI
> Thanks Brad for taking the time to provide these thorough derivations.
> It took me some time to go through the math, but it's interesting to
> discover that one can in principle use Maxim DL data for
> transformation coefficients.
>
> Lionel
>
>
> 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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