[Aavso-photometry] Re: Scintillation tables
Wolfgang Renz
w_renz at onlinehome.de
Sat Dec 4 00:52:31 EST 2004
Hello Radu, hello Arne
I've followed the discussion on short-exposure photometry and scintillation
noise with interest. Thanks for posting the link to your tables.
I've found an online calculator "Transitsearch.org's Scintillation Noise
Calculator for Small Telescopes" by Dorian Bohler at
http://www.skywokker.com/scintillation.htm that is based on the same
formula.
Radu, your values are at AM > 1 slightly larger than in the online
calculator. But your values are much closer to the values I get when
I calculate the values myself (different probably just due to internal
rounding).
I also found the sources for the formula (see references below):
The used formula originally comes from Andrew T. Young. The
Dravins et.al. paper just changed some constants
Remarks on the the two fomulae:
- According to the Young paper, the typical S0 for apertures in inches is 0.05
and the corresponding S0 for apertures in cm is stated as 0.09. This value
is used in the Dravins et.al. paper.
But according to basic math 0.05*2.54 = 0.127 ?!
Do they have their own measure of 1.8 cm/inch down in Austin, Texas ?
- Reiger's 3/2 power of the air mass that fits the Young data well was set
in the Dravins et.al. paper to 1.75 (1.5 .. 2.0 dependant on the direction of
the wind).
- delta f = 1 / (2 * T) with T = "integration time in seconds" and
delta f = "low-frequency band of width delta f in Hz".
The 2 comes from the Sampling Theorem by Shannon (you must have at
least 2 data points during the period T to resolve a frequency f).
But isn't it just defined for delta f > 1 Hz (= 1 Hz .. 1+delta f Hz band) !?
Some more facts from the papers:
One major point is that the papers are about high-speed photometry
(http://www.astro.lu.se/~dainis/HTML/SCIPUBL.html). So the frequencies
of all measured data in these papers are at >= ~ 1 Hz. But the frequencies
that are of interest for bright star photometry with small scopes and are
<< 1 Hz ("often called variable extinction or transparency variations" !).
Extrapolating the integration times below 1 s to hundreds of seconds might
be possible but also might not give correct values. Unfortunately I haven't
found any measured scintillation sigmas for integration times >> 1 s yet.
I was wondering if the formula is also valid for smaller apertures (e.g. for
small scopes, camera lenses or even pin holes). The original Young paper
states that his formula should be good for apertures >= 4 inch. The smallest
apertures with measured data in the Dravins et.al. papers are 1.2 cm and
2.5 cm. It seems that the values converge to a constant value for apertures
below 5 cm ("become independent of aperture size" see Dravins et.al.
paper I, Fig. 3).
So it might be a good idea to set the aperture value to something around
5 cm (~= width of the flying shadows) for all apertures below 5 cm as the
D^(-2/3) factor in the formula will not fit the reality well and increase further
when D approches 0 (flying shadows are in fact not back and white but
brighter or darker grey).
E.g. my FL 8 mm f/3.5 camera lense for fire ball survey (D nominal: 2.3 mm,
D front lense: 58 mm) would give already pretty high scintillation sigma values
for the smaller nominal diameter. With D << 1 mm it gives values for the
scintillation sigma of > 1.0 and larger.
Recommendation to stop down aperture to allow longer integration times
on bright vars to not saturating the CCD:
-> Look at the D^(-2/3) * (2T)^(-1/2) factors in sintillation sigma formula:
If you half the diameter you must quadruple the integration time to collect
the same flux per image. If you do so you'll get a smaller sintillation sigma
as the gain due to the longer exposure time overwhelms the loss due to
the smaller aperture. E.g.:
D=20cm, T=10s corresponds to a factor of 0.030.
D=10cm, T=40s corresponds to a factor of 0.024.
But why not taking both advantages to minimize the sintillation sigma ?
Using the largest available aperture AND longer integration times by
using a filter instead of stopping down the aperture ?
D=20cm, T=40s + 25% transmission filter corresponds to a factor of 0.015.
Even using a grey filter should be better than stopping down the aperture
in respect of sintillation sigma.
Arne, you should probably change your recomondations to definitly favour
to "use a filter" over to "stopping down aperture" that should just be the
last back door.
-> When the CCD readout time is long it has an effect on the total collectable
flux during a certain time span. E.g. an unbinned ST-10XME has a readout
time of ~ 10 s. So 10 s exposures use just 50% of the time for collecting
flux while the other two use 80% of the time. But as the other two solutions
"waist" 3/4 of the collectable flux, stacking of short exposure time images
still gives a larger Poisson photon flux SNR (rel. flux 2.5 : 1 -> rel SNR factor
1.58 : 1).
However we are talking about bright star photometry, so Poisson photon
flux SNR isn't an issue as the sintillation noise is much larger than photon
flux noise for bright stars imaged near the usable full-well of a CCD.
Using different filters:
Scintillation sigma is just about SQRT(2) higher in the Johnson B band than
in the Cousins I band. So if there is no other reason that speaks against it,
imaging in a redder band gives lower scintillation sigmas. But with exo
planets there is a major reason as their amplitude is in the bluer bands
higher than in NIR.
Using "unsharp" telescope apertures:
Apodization slightly increases scintillation power at lower temporal frequencies
(probably caused by the decreased aperture). So do not use apodization for
photometry with longer integration times if possible.
Setting apertures and the gap width in aperture photometry:
Bad seeing (in Germany = heavy sintillation) will cause a larger FWHM
("irregular illumination pattern caused by the flying shadows diffracts into the
wings of focused stellar images"). So not just the radius of the apertures in
aperture photometry but also the gap between them should be increased.
If I've understood something wrong, please corret me.
Clear skies
Wolfgang
--
Wolfgang Renz, Karlsruhe, Germany
Rz.BAV = WRe.vsnet = RWG.AAVSO
A) 1997PASP..109..173D
Atmospheric Intensity Scintillation of Stars
I. Statistical Distributions and Temporal Properties
Dravins, Dainis; Lindegren, Lennart; Mezey, Eva; Young, Andrew T.
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1997PASP..109..173D
Abstract & Figures: http://www.astro.lu.se/~dainis/HTML/TEMPORAL.html
"naked-eye twickling (~= 5 mm aperture, a cutoff for frequencies above
~= 15 Hz), arises mostly from turbulence within 1 km of the ground"
"Mikesell (1955) and Protheroe (1955a) could correlate scintillation with the
wind speed at heights between 8-16 km, but not with that at lower levels.
Protheroe (1955b, 1964) also found the speed and direction of the 'flying
shodows' to correlate reasonably well with upper-air winds. The lifetime of
elements in the shadow pattern was found to be the order of 10 ms."
"Reiger (1963) [...] In his atmospheric model [...] more than 70% of the
scintillaion amplitude originates in the height range from 7 to 15 km."
+++
B) 1997PASP..109..725D
Atmospheric Intensity Scintillation of Stars.
II. Dependence on Optical Wavelength
Dravins, D.; Lindegren, L.; Mezey, E.; Young, A. T.
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1997PASP..109..725D
Abstract & Figures: http://www.astro.lu.se/~dainis/HTML/COLOR.html
"The intensity variance sigma^2 increases for shorter wavelengths, at small
zenith distances approximately consistent with a theoretical lambda 7/6
slope, but with a tendency for a somewhat weaker dependence" [measured
with a 2.5 cm aperture at 400, 550 and 700 nm at the astronomical
observatory on La Palma (Canary Islands)].
C) 1998PASP..110..610D
Atmospheric Intensity Scintillation of Stars.
III. Effects for Different Telescope Apertures
Dravins, Dainis; Lindegren, Lennart; Mezey, Eva; Young, Andrew T.
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1998PASP..110..610D
Abstract & Figures: http://www.astro.lu.se/~dainis/HTML/APERTURE.html
It discusses the "flying-shadow" properties well known from sun eclipses
before second and after third contact (directly noticable in scopes on
"multicolor high-speed (<~ 10 ms) photometry [...] over the spatially resolved
(<~ 10 cm) telescope entrance pupil").
"A central obscuration (secondary mirror) increases the scintillation power
[P(f) at higher temporal frequencies slightly], while apodization ["unsharp"
telescope apertures] decreases it [very sgnificant] for high temporal
frequencies [but increases the over-all scintillation power at lower temporal
frequencies]."
"For smaller apertures, the power [content P(f)*f.] distinctly shifts toward
higher frequencies. This trend continues until aperture diameters <~ 5 cm,
where the structures in the "flying shadows" begin to get resolved. [but
larger diameters still always give a lower power content]"
"In astronomical observations, scintillation normally constitutes a noise
source to be avoided. For larger telescopes (low-frequency) scintillation is
the dominant noise source for photometric broadband measurements of
stars brighter than mv ~= 12 or 13 near the zenith (assuming detectors of
high quantum efficiency; e.g., Gilliland et al. 1993). At large air masses, the
crossover to photon noise as the dominant one occurs at a few magnitudes
fainter. Scintillation also hinders highest definition imaging, since the
irregular illumination pattern caused by the flying shadows diffracts into the
wings of focused stellar images."
"Theoretical considerations provide an approximate scaling law for the rms
error due to the low-frequency component of scintillation (Young 1967,1974):
sigma = 0.09 D^(-2/3) * (sec(Z))^(1.75) * exp(-h/h0) / (2T)^(1/2) (10)
where D is the aperture diameter in centimeters, sec Z is the air mass, h
is the observer's height above sea level, h0 ~= 8000 m is the atmospheric
scale height, and T is the integration time in seconds. The air mass exponent
of 1.75 is an approximate value not far from the zenith; it equals 2 when
looking along the wind direction and 1.5 perpendicular to it. The rms
deviation sigma is then obtained in units of relative intensity deltaI/I.
This expression applies for timescales longer than those for flying shadows
to cross the telescope aperture, i.e., integrations on scales of seconds and
longer. [...] However, it is the low-frequency power in equation (10) that is
perceived as noise in ordinary photometry, and "limiting" accuracies for
ground-based photometry can be estimated from this expression (Brown
& Gilliland 1994; see also Young et al. 1991; Gilliland & Brown 1992;
Kjeldsen & Frandsen 1992; Heasley et al. 1996)."
"Classical 'brute-force' approaches [for high-speed photometry] by reducing
scintillation by averaging over larger apertures, and integrating for longer
times, do not seem especially promising for any order-of-magnitude
reduction of scintillation noise. Instead, we will now examine other schemes
for circumventing scintillation, doing exactly the opposite to classical
methods, avoiding all averaging by instead using very small (sub)apertures
and integrating over very short timescales. We want to treat scintillation as a
signal to be accurately determined and physically modeled, not as a random
noise that is averaged in larger data bins in the hope that it will eventually go
away. Following its accurate measurement, the photometric segregation of
the scintillation signal from that of the astrophysical source should become
feasible. Further, for imaging purposes (if a high photometric stability is not
required), a reduction of scintillation effects appears feasible in the sense of
real-time compensation for the inhomogenous pupil illumination cast by the
flying shadows."
D) 1967AJ.....72..747Y
Photometric error analysis.
VI. Confirmation of Reiger's theory of scintillation
Young, Andrew T.
http://cdsads.u-strasbg.fr/cgi-bin/bib_query?1967AJ.....72..747Y
"Combing all our results so far, we find that the ratio of rms intensity fluctation
to the mean (dc) intensity, measured in a low-frequency band of width delta f
Hz for a star observed through X (~~ secZ) air masses with a telescope of
aperture d inches at an altitude h meters above sea level, should be
S = Irms/Idc = S0 * d^(-2/3) * X^(3/2) * exp(-h/h0) * (delta f)^(1/2), (1)
where H0 ~~ 8000 m is the scale height of the atmoshere, and S0 is a measure
of the intensity of the scintillation. Equation (1) should be good for d >= 4 in. and
frequencies below the cutoff frequency.
In evaluating the importance of scintillation as a source of photometric error, we
need to know the typical range of values for S0. Table I gives data measured on
three different nights at McDonald Observatory (0.04, 0.05, 0.06).In addition
Reiger quotes 3% equivalent sine-wave modulation (~~ 2% rms modulation) as
an average value. (If d is measured in centimeters instead of inches,
the numerical value of S0 is 0.09.)"
----- Original Message -----
From: "Radu Corlan" <rcorlan at pcnet.ro>
To: "Brian Warner" <brian at minorplanetobserver.com>
Cc: <aavso-photometry at mira.aavso.org>
Sent: Tuesday, November 23, 2004 11:43 PM
Subject: Re: [Aavso-photometry] Scintillation tables
> On Tue, 23 Nov 2004, Brian Warner wrote:
> > You don't say in the table: what are the units for noise? magnitudes? >
> They are relative flux errors (which fortunately, for small errors are
> close to magnitude errors). I'll add this to the file.
>
> Radu
>
>
> > ----- Original Message -----
> > From: "Radu Corlan" <rcorlan at pcnet.ro>
> > To: <aavso-photometry at mira.aavso.org>
> > Sent: Tuesday, November 23, 2004 15:32
> > Subject: [Aavso-photometry] Scintillation tables
> >
> > > I've generated some scintillation tables (versus airmass, integration time
> > > and telescope aperture) that i think may be useful for observation
> > > planning. I found tables much easier to use than the formula.
> > >
> > > They are at:
> > > http://astro.corlan.net/gcx/scint.txt
> > >
> > > Enjoy,
> > > Radu
> > >
> > > --
> > > Radu Corlan Snail Mail: Bucuresti sect. 1,
> > > rcorlan at pcnet.ro str. Argentina nr. 28, Romania
> > > You can still escape the "Gates" of Hell!
> > > Use Linux!
----- Original Message -----
From: "Radu Corlan" <rcorlan at pcnet.ro>
To: "Michael Koppelman" <lolife at bitstream.net>
Cc: <aavso-photometry at aavso.org>
Sent: Tuesday, July 13, 2004 9:27 PM
Subject: Re: [Aavso-photometry] Short-Exposure Photometry
> On Tue, 13 Jul 2004, Michael Koppelman wrote:
>
> > Thanks to everyone would replied. Yes, it must be scintillation. That
> > sucks because I can't go longer or I'll saturate. I guess I can work in
> > B and see how that works out.
>
> I use the following formula for estimating scintillation (by Dravins i
> think):
> scint = (0.09 * A ^ 1.75) / (D ^ 0.66 * sqrt(2 * t))
>
> Where A is the airmass, D is the aperture in cm, t is the integartion time
> in seconds. This formula excludes a correction for altitude (which only
> becomes significant above 1000-2000m or so). Scintillation also depends on
> local conditions, of course - a factor of 0.5..3.0 could apply. But it;s
> never an order of magnitude better (or worse).
>
> Radu
----- Original Message -----
From: "Arne Henden" <aah at nofs.navy.mil>
To: "Michael Koppelman" <lolife at bitstream.net>
Cc: <aavso-photometry at aavso.org>
Sent: Tuesday, July 13, 2004 9:17 PM
Subject: Re: [Aavso-photometry] Short-Exposure Photometry
> Plenty of ways to defeat scintillation!
> 1. defocus
> 2. stop down your telescope aperture
> 3. wait for a poor seeing night
> 4. wait for a cirrusy night
> 5. take multiple exposures and average
> 6. don't work close to the horizon
> Arne
>
> Michael Koppelman wrote:
> > Thanks to everyone would replied. Yes, it must be scintillation. That
> > sucks because I can't go longer or I'll saturate. I guess I can work in
> > B and see how that works out.
> >
> > Thanks!
> > Michael
> >
> > On Jul 13, 2004, at 10:03 AM, <Arto.Oksanen at tietoenator.com> wrote:
> >
> >> Been there and seen the same. It is scintillation or twinking of the
> >> star by atmospheric turbulence. The shorter the exposure the more the
> >> star brighness seem to vary.
CCD Views #324:
4. BRIGHT STAR PHOTOMETRY
[Thanks to Arne Henden for much of the advice below.]
...
There are two main problems with high-precision short-exposure photometry
(SEP from here on out). First, bright sources tend to get overexposed,
especially if any nearby comparison star is fainter than the target.
Antiblooming gate (ABG) CCDs typically saturate at about 50% of their
full well depth, and many non-ABG chips saturate before the limit of
their Analog/Digital Converters (ADCs). Second, the atmosphere itself
conspires to degrade the photometry through a phenomenon called
scintillation, where the turbulent bubbles of gas act like lenses, increasing
or decreasing the amount of flux entering the front of your telescope.
The twinkling of naked eye stars is caused by scintillation.
To counteract saturation, first test your CCD camera to find out
the limits of its linearity and where full well occurs in the dynamic
range of your ADC. Then keep the signal level within the linear range
and below the full well. For very bright sources, you may reach a
limit where you cannot take a short enough exposure to prevent
saturation. Techniques to go even brighter include:
1. Stopping down the aperture of your telescope by using a mask
with a cutout hole. You can often place the cutout so that the
incoming light avoids the central obstruction and spiders.
2. Using a photometric filter, especially a blue one. The filter
decreases the bandwidth and therefore decreases the amount of
light reaching the CCD, enabling longer exposures. Using a
blue filter further moves the incoming light to a wavelength
regime where the CCD is less sensitive, enabling longer exposures.
3. Defocussing. While you don't want images with "donuts", you
can often increase the image profile by a factor of two or more,
thereby decreasing the central peak intensity.
4. Using a Barlow lens. Increasing the image scale spreads the
starlight over more pixels, decreasing the peak intensity.
5. Wait for a night of poor seeing!
6. Often a night with uniform cirrus can be used, since such
clouds decrease the incoming flux.
Scintillation can be tricky. It is stronger nearer the horizon where
you are looking through more atmosphere. It is also stronger for smaller
telescope apertures, where each blob of atmospheric gas is closer to
the telescope aperture size (bigger telescopes average many blobs).
It is also a function of wavelength (redder is better) and exposure time
(longer is better).
Tips to avoid scintillation:
1. Use relatively long exposures (10 seconds or longer). Use the
techniques listed above to increase exposure time if necessary.
2. Don't work close to the horizon. We usually recommend staying
above airmass 2.5 if possible.
3. Take multiple exposures and average to beat down the effects
of scintillation.
Here is a formula posted By Radu Corlan (CXR) for estimating
scintillation without taking altitude into consideration:
scint = (0.09 * A ^ 1.75) / (D ^ 0.66 * sqrt(2 * t))
Where A is the airmass, D is the aperture in cm and t is the integration
time in seconds.
It is taken from a series of papers by Dravins et al. that begin
with "Atmospheric Intensity Scintillation of Stars, I. Statistical
Distributions and Temporal Properties" 1997, PASP. 109, 173.
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