[Aavso-photometry] Differential vs. absolute magnitudes

Sun Mar 9 03:36:40 EDT 2008

Hi Jeff,

But I showed that you indeed can increase precision using a B filter in the 
case that there is a good deal of light pollution from low pressure sodium 
lamps. The same result holds true for using a photomultipier tube, since the 
entrance diaphragm acts just like one big round pixel.

I've done a lot of photon counting PMT photometry too. One of the 
instruments I used was Gerard deVaucouleur's "Galaxymeter", a behemoth of an 
instrument which had a clone of Harold Johnson's tube and UBV filters from 
the same era. We had to painstakingly pack shaved dry ice into the chamber 
using a pencil eraser. PMT work was a lot of fun, except for standing 
outside in the cold all night trying not to fall off the platform. 
Reductions could be done the following day using graph paper, pencil, ruler, 
and calculator.

Michael

----- Original Message ----- 
From: "Jeff Hopkins" <phxjeff at hposoft.com>
To: "Michael Newberry" <mnewberry at mirametrics.com>; <gianlucaros at gmail.com>; 
<aavso-photometry at mira.aavso.org>
Sent: Saturday, March 08, 2008 5:26 PM
Subject: Re: [Aavso-photometry] Differential vs. absolute magnitudes

> Hi Michael,
>
> I think we are in different worlds. While I do CCD photometry most of my 
> work is with a single channel PMT based UBV photon counting photometer.
>
> BTW, I did not say a B filter would reduce precision, I said  "You cannot 
> increase your precision by adding a B filter. You might be able to 
> increase your accuracy, however."
>
> In my world error is signified by a standard deviation of three (or more) 
> determined magnitudes (for a short series on long period stars). For me 
> SNR is just that. There are other factors that can produce error and in 
> some cases significantly larger error. Taking three magnitudes, averaging 
> and taking the SD  of the three is a better indication, at least to me, 
> about how good the data is. I do this even with CCD data. If the resulting 
> SD is large, than it may point to something you are doing wrong, strange 
> sky conditions or something else that can be corrected. An error from SNR 
> will not show any of that.
>
> I have no argument that a higher SNR should produce better data, but by 
> itself SNR may not be a good indication as to the quality of the data.
>
> Jeff
>
> At 17:02 -0700 03/08/2008, Michael Newberry wrote:
>>Jeff,
>>
>>I am not disagreeing with what you say, but this brings up another point 
>>worth mentioning:
>>
>>It is not strictly true that a B filter would reduce the precision of the 
>>photometry. Of course, one benefit of using a B filter would be that the 
>>magnitude could be transformed to a standard system (at least 
>>theoretically and if he also had a V filter to get the transformation 
>>coefficients). But let's look at the issue of magnitude precision with and 
>>without the B filter.
>>
>>The magnitude precision is the random error the magnitude measurement 
>>which is simply related to the signal to noise ratio ("SNR") of the 
>>measurement. In equation form, this is Sigma(mag) = 1.0857 / SNR. Remember 
>>that we are measuring the object, not the (object+sky), so SNR is 
>>calculated using the net signal of the object without the sky whereas the 
>>noise includes noise from both the object and the sky underneath the star. 
>>The signal and noise are both summed inside the measuring aperture.
>>
>>The B filter does not pass the Sodium D lines near 5890A that comes from 
>>both light pollution and the natural sky background. So if someone has a 
>>heavily light polluted sky caused by low pressure sodium vapor lamps, then 
>>a B filter would dark the sky quite a bit. But the B filter reduces the 
>>energy from the star by an amount that is fixed by the bandpass, and that 
>>might be around a factor of 4 on a typical CCD.
>>
>>Two side notes: 1) The SNR is also affected by the aperture size (good 
>>seeing vs bad seeing). The larger the aperture, the more background is 
>>added to the starlight. 2) There is noise from the CCD's dark current. 
>>Even though the dark current is subtracted, its noise remains as part of 
>>the total noise underneath the star profile. In the same way that sky 
>>light is subtracted but leaves sky noise, the dark "light" is subtracted 
>>but leaves its dark noise. Therefore, observing in poor seeing or with a 
>>warm CCD will increase the noise and decrease the SNR. But I'm just 
>>talking about filters here.
>>
>>As an example, the B filter might reduce the sky brightness by a factor of 
>>10, 20, or even more but the star would be reduced by about 4x. It is true 
>>that the sky has to be pretty bright or the seeing pretty bad for the SNR 
>>to actually be improved by using a B filter, but it can happen. Let's look 
>>at some rough numbers. I am not going to include all noise sources because 
>>the sky is bright and its noise swamps these other sources.
>>
>>Consider a fairly light polluted urban sky so that, in the measuring 
>>aperture, the sky is 4 magnitudes brighter than natural sky. Suppose that, 
>>with the B filter, we have an exposure time and aperture size that gives 
>>1000e- from the star. Assume no dark current. We get the following:
>>
>>B filter:
>>Star = 1,000e- above sky
>>Sky = 1,000e- (no light pollution)
>>Star/Sky = 1.
>>Noise = sqrt(1,000+1,000) = 45e-
>>SNR = 1000 / 45 = 22.4, Sigma(mag) = 0.048.
>>
>>No filter:
>>Star = 4x brighter without B filter = 4,000e- above sky
>>Sky = 4 mag (40x) brighter = 40,000e-.
>>Star/Sky = 0.1
>>Noise = sqrt(40,000+4,000) = 210e-
>>SNR = 4000 / 210 = 19.1, Sigma(mag) = 0.057.
>>
>>Just for grins, suppose we expose 10x longer or we combine 10 images and 
>>measure that. Then we get a better result for both cases:
>>
>>B filter:
>>SNR = 70.7, Sigma(mag) = 0.015
>>
>>No filter:
>>SNR = 60.3, Sigma(mag) = 0.018
>>
>>BUT! The *ratio* of SNR obtained with and without the filter is identical 
>>to the case for shorter exposure. Hmmm.... what does this tell us? Answer: 
>>Exposing longer does not make the filtered/unfiltered comparison any 
>>different but it does give us higher precision in either case.
>>
>>As you can see, a measurement through the B filter can win when the sky is 
>>rather bright. On the flip side, a brighter star will provide more photons 
>>so the effect is not as dramatic. The critical factor is the ratio of 
>>star/sky brightness inside the measuring aperture.
>>
>>What I have described is the principle behind the so-called "nebular" 
>>filter. However it is not true that *any* filter will improve the SNR as I 
>>have shown. The signal in a given bandpass depends on the net transmission 
>>of the atmosphere, optical system, and filter combined with the response 
>>of the CCD and the spectrum of the star. Since the U filter is very dense 
>>and the CCD, atmosphere, and optics also ge worse below 4000A, the sky 
>>would have to be awfully bright at 5890A to win when using a U filter. But 
>>that is not the case for the B filter.
>>
>>Michael Newberry
>
>
> -- 
> Jeff Hopkins
> HPO SOFT
> Counting Photons
> http://www.hposoft.com/Astro/astro.html
> Hopkins Phoenix Observatory
> 7812 West Clayton Drive
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>
> 