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How does the Madawaska Highlands Observatory compare with a high-end amateur
telescope? There are four key components to take into account
when trying to answer this question.
The most important component is the limiting magnitude, how
long does it take to reach a threshold magnitude for a defined
signal-to-noise ratio (s/n). This takes into account the entire
imaging train. Starting with the size of the main mirror and ending
up the performance of the camera which takes into account such
factors as quantum efficiency (QE), read noise, filter bandwidth,
filter transmission etc.
The second component is the field of view (FOV), the larger
the FOV the more of the sky the telescope can image for the same
exposure time. One way to view this is to compare a telescope
with a small FOV, say 20' (0.11 deg²), about 2/3 the size
of the moon, to a telescope with a large FOV, 2.22 degrees (4.94
deg²) , 4.5X the diameter of the moon. The difference in
FOV is about (4.94 / 0.11) = 44X, the large FOV telescope covers
44X more sky at the same time as the narrow FOV telescope. The
Pleiades, which has field of about 2 degrees would take about
40 images to be covered with the narrow FOV telescope, but could
be done with one image from the large FOV telescope!
The third component is the sky brightness. The brighter the sky
the longer it takes to get to the same limiting magnitude for
a given s/n. The observatory should be located in the darkest
possible sky. The Madawaska Highlands Observatory will be located in a sky of 21.82 mag/arcsec²,
compared to a sky of 18.5 (typical of urban skies) it would take
about 10X longer exposure to reach a star with a s/n of 20 with
the same telescope!
The fourth component is the seeing. The smaller the seeing disc
the shorter the exposure. This is because a larger seeing disc
spreads the starlight over a larger area thus it takes longer
to reach a given limiting magnitude. Although there is an inherent
atmospheric seeing of about 1 arcsec in Southern Ontario, the
seeing can be degraded quite substantially if the telescope and
dome are not properly designed. Observatories get in the 2-4"
range because of poor telescope and dome design. For example a
seeing of 2.5 arcsec would take double the exposure as compared
to a seeing of 1.25". This is dependent on the s/n and the
difference is much greater for a larger s/n.
Using the Madawaska Highlands
Observatory photometric tool, a table was assembled to
compare several commercially available telescope.
| Telescope |
Size |
Sky Brightness |
FOV |
FOV |
expos. 1.25" |
expos. 2.5" |
RATIO |
RATIO |
PSF |
Obs. Cost |
|
| |
" |
mag/arcsec² |
deg² |
ratio |
ratio |
ratio |
1.25" |
2.5" |
arcsec/pix |
|
|
| Meade SC |
16 f/10 |
21.7 |
0.05 |
102 |
60 |
109 |
6116 |
11133 |
0.40 |
$20,000 |
* |
| RCOS |
16 f/8.4 |
21.7 |
0.39 |
12 |
37 |
68 |
459 |
829 |
0.55 |
$75,000 |
** |
| Ceravolo |
12 f/4.9 |
21.7 |
2.06 |
3.38 |
47 |
82 |
158 |
276 |
1.26 |
$50,000 |
** |
| Dream |
24 f/3.5 |
21.7 |
0.99 |
4.94 |
9.9 |
19 |
48 |
94 |
0.87 |
$85,000 |
** |
| ASA |
16 f/2.63 |
21.7 |
4.00 |
1.21 |
13 |
23 |
15 |
28 |
1.76 |
$70,000 |
** |
| ASA |
12 f/2.63 |
21.7 |
7.14 |
0.67 |
26 |
47 |
18 |
32 |
2.35 |
$50,000 |
** |
| Dream |
12 f/2.5 |
21.7 |
7.90 |
0.61 |
29 |
50 |
14 |
25 |
2.48 |
$50,000 |
** |
| Dream |
20 f/2.3 |
21.7 |
16.00 |
0.25 |
13 |
24 |
3.3 |
6 |
1.57 |
$200,000 |
*** |
| MHO |
40 f2.5 |
21.7 |
4.94 |
1 |
0.73 |
1.53 |
1 |
2 |
0.76 |
|
+++ |
| |
|
|
|
|
|
|
|
|
|
|
|
| Meade |
16 f/10 |
19 |
0.05 |
102 |
98 |
244 |
10014 |
24844 |
0.40 |
$20,000 |
* |
| RCOS |
16 f/8.4 |
19 |
0.39 |
12 |
67 |
174 |
825 |
2132 |
0.55 |
$75,000 |
** |
| Ceravolo |
12 f4/9 |
19 |
2.06 |
3.38 |
146 |
375 |
494 |
1269 |
1.26 |
$50,000 |
** |
| Dream |
24 f.3.5 |
19 |
0.99 |
4.94 |
22 |
66 |
107 |
324 |
0.87 |
$85,000 |
** |
| ASA |
12 f/2.63 |
19 |
7.14 |
0.67 |
124 |
307 |
74 |
221 |
2.35 |
$50,000 |
** |
| Dream |
12 f2.5 |
19 |
7.90 |
0.61 |
143 |
343 |
71 |
145 |
2.48 |
$50,000 |
** |
| ASA |
16 f/2.63 |
19 |
4.00 |
1.21 |
58 |
150 |
71 |
181 |
1.76 |
$70,000 |
** |
| Dream |
20 f.23 |
19 |
16.00 |
0.25 |
26 |
74 |
6.6 |
9.9 |
1.57 |
$200,000 |
*** |
| DDO |
74 f/17.3 |
16.8 |
0.01 |
484 |
6.33 |
22.81 |
3063 |
11040 |
0.15 |
|
**** |
Calculation parameters:
*SBIG ST-4000XCM, QE=40%, read noise = 7.9e-
**FLI PL-16803, QE=60%, read noise = 9e-
***Fairchild CCD595 80.64 mm, QE=94%, Read noise 20e-
**** Kodak 4301E, 24u, 5e-, 2048x2048 (DDO does not image, for
reference only)
+++ reference (1.25" seeing)
Limiting magnitude = 20
Signal to noise (s/n) = 3
Zenith angle = 0 degrees
Filter color = visual
Filter transmission = 94%
Filter bandwidth = 89 nm
reaches magnitude 20 in less than 0.81s with a s/n=3, in the r'
(visual).
NHO has FOV = 4.94 degrees²
Radius of photometry aperture adjusted for maximum s/n.
The cost includes a fully equipped observatory, including telescope,
mount, and camera, etc.
The first item in the table is based on Meade 16" f/10 Schmidt
Cassegrain with an SBIG ST-4000XCM camera, this high-end setup
in a suburban locality of a fully equipped observatory would cost
around $20,000. This is the most common high-end setup. The sky
at a typical suburban location is about 19 mag/arcsec², compared
to the sky at the site which is measured at 21.9 mag/arcsec².
The ratio of the field of view (FOV) multiplied by limiting magnitude
(exposure) ratio yields a ratio of efficiency compared to the
Madawaska Highlands Observatory. In the case of a Meade 16 "
f/10 in a suburban location of 19 mag/arcsec² sky brightness
this number is an astonishing 10,000X! This implies that one hour
exposure on the Madawaska Highlands Observatory is equivalent
to 10,000 hours exposure on the 16" high end backyard scope.
Staggering to say the least. This is equivalent to more than 13
years continuous observing every clear night of the year for 13
years on the backyard scope.
For comparison the David Dunlap Observatory's 1.88 metre telescope
is included. You can see that even the largest telescope in Canada
cannot compare to the imaging capabilities of the Madawaska Highlands Observatory. Although
the DDO has a massive aperture, it has extremely bright skies,
and a very small field of view due to its extremely long focal
length. The DDO is used exclusively for spectroscopy as are all
major telescopes in Canada, without exception.
A number of other arrangements are also shown. Generally speaking
observing efficiency is closely related to field of view. The
table above is most appropriate for imaging rather than visual.
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