Detecting a dark spot -

Detecting a dark spot -

How would someone go about calculating the theoretical limit of the
smallest dark spot detectable (naked eye) for any given diameter
aperture? Not resolving two spots (as in using Dawes limits/Rayleigh
criterion ), but detecting one spot.

Meanings and some considerations:

Smallest - in diameter
Naked eye - assume 20/20 vision and dark adapted
Dark spot - e.g. small crater on the Moon or shadow of a Jovian moon
on Jupiter. No detail.
Detectable - above the lower limit (however small) of visibility
Seeing - excellent
Collimation - perfect
Optics - diffraction limited
Magnification - highest usable 40X/in
Contrast - black on well illuminated white
Planets - all lined up in a row. IOW, best case scenario, optimal gear
and conditions.

Thankx.

Errol
www.pasnola.org

On Mar 10, 7:17 pm, "Starboard" wrote:
Detecting a dark spot -

How would someone go about calculating the theoretical limit of the
smallest dark spot detectable (naked eye) for any given diameter
aperture? Not resolving two spots (as in using Dawes limits/Rayleigh
criterion ), but detecting one spot.


Errol,

It has become sort of a rule of thumb that a point source
of about 0.1 of the Dawe's Limit can be detected.

I say "about" because you are dealing with information
input that is subject to a fistful of variables.

Case in point: During the 2003 Mars opposition I was judging
my resolution by those two fingerlike projections that extend
from the Mare Cimmerium out into the Cerberus region. I call
them the "Cimmerium Dactyls" and CCD images take them
down very well. I had them pretty well resolved one evening
when a pocket of still air drifted across my FOV and for about
five seconds I could see three craters *inside* of the boundaries
of the dactyls.
It was shocking. It was one of those "moments" you read
about in S & T that introjects itself into the memory and stays
with you.
The price was about 250 hrs of observation for those five
seconds. Was it worth it? Yeah. (Did 152 drawings for the
2003 opposition)
Anyway there's nothing to compare with a moment of perfect
seeing and I feel like the rule of thumb is justified:

0.1 x Dawes Limit (about)

Ben, 90.126 n 35.539

PS: Those weren't "floaters" either - they faded out just
as the boundaries of the dactyls did. (10" @ 400x)

Well, from the book AMATEUR ASTRONOMER'S HANDBOOK (J.B. Sidgwick)

OBSERVATIONAL EXAMPLES OF RESOLUTION OF CERTAIN EXTENDED DETAIL
(from AMATEUR ASTRONOMER'S HANDBOOK, by J.B. Sidgwick, p.49-50)
("r" is Dawes Limit = 4.56/D in arc seconds with D the aperture in inches)
(NOTE: those specifically interested in the minimum aperture necessary to
resolve the Cassini and Encke divisions from their adjacent ring edges
should pay close attention to "C" below.)

A. BLACK SPOT ON A WHITE BACKGROUND:
i. W.H. Pickering, while testing his 10 inch reflector under good seeing
conditions in Jamaica, found that a circular spot became visible if its
angular diameter exceeded 0.20" arc (r/2.3).
ii. Experiments by W.H. Steavenson showed that r/3 is a fair average figure.
iii. The naked-eye visiblity of sunspots whose diameter is less than r is
well known.

B. SINGLE DARK LINE ON A WHITE BACKGROUND:
i. Cassini Division, width of about 0.5" arc was discovered with about a 2.5
inch aperture (r/3.5).
ii. Experiments by W.H. Steavenson yielded about r/5 as an average figure.
iii. During testing of an 11 inch refractor at Harvard, a human hair was
visible against a light-toned ground at a distance of nearly 1/4 of a mile
where it subtended 0.029" arc (r/14).
iv. W.H. Pickering glimsed a dark line 0.03" wide with his 10 inch (r/15).

C. PARALLEL LINES ON A LIGHT BACKGROUND:
i. W.H. Pickering: minimum separation for resolution with a 10 inch reflector
was 0.63" arc (1.4r).
ii. A similar performance was given by the Arequipa 15 inch, which resolved
a pair of parallel lines when their separation was increased past 0.42" arc
(1.4r), in good seeing; slight atmospheric deterioration immediately raised
the threshold to about 2r. At less than 0.42" arc, the lines appeared as a
grey band of width about 1.5 times their separation.
iii. Resolution of the lines at 12" arc with a 0.4 inch Object Glass (1.1r).

Clear skies to you.
--
David W. Knisely
Prairie Astronomy Club: http://www.prairieastronomyclub.org
Hyde Memorial Observatory: http://www.hydeobservatory.info/

**********************************************
* Attend the 14th Annual NEBRASKA STAR PARTY *
* July 15th-20th, 2007, Merritt Reservoir *
* http://www.NebraskaStarParty.org *
**********************************************

How would someone go about calculating the theoretical limit of the
smallest dark spot detectable (naked eye) for any given diameter
aperture? Not resolving two spots (as in using Dawes limits/Rayleigh
criterion ), but detecting one spot.
Errol

It has become sort of a rule of thumb that a point source
of about 0.1 of the Dawe's Limit can be detected.
I say "about" because you are dealing with information
input that is subject to a fistful of variables.
Ben

Thanks Ben.

Night before last, two friends and I brought some scope stuff to a
local school having a science camp (approx 100 kids and 30 adults).
My scope (12" Dob) stayed fixed on Saturn at 400X for 3 1/2 hours
(very labor intensive). Seeing and transparency were excellent.
Everyone who looked at Saturn was in total shock and awe as usual. The
most common comment of the night was, "is that real?"

Anyway, so we're talking about Saturn and one of my friends says he's
seen Encke in a three inch refractor. I told him I thought that he
should go have his eyes checked, have his head checked, and to keep
his delusions to himself when in public. I was thinking that it should
be pretty much impossible to see Encke in a three inch scope. Then I
got to thinking that I was basing my guess off of Dawes limit; which,
in hind sight, was not correct - as *detecting* a feature is not the
same as *resolving* two features from one another.

However, it appears that even using the adjusted formula, it is still
impossible to do with 3 incher.

Case in point: During the 2003 Mars opposition I was judging
my resolution by those two fingerlike projections that extend
from the Mare Cimmerium out into the Cerberus region. I call
them the "Cimmerium Dactyls" and CCD images take them
down very well. I had them pretty well resolved one evening
when a pocket of still air drifted across my FOV and for about
five seconds I could see three craters *inside* of the boundaries
of the dactyls.
Ben

Amazing. Thanks again.

Errol

David Knisely wrote:
Well, from the book AMATEUR ASTRONOMER'S HANDBOOK (J.B. Sidgwick)
....
OBSERVATIONAL EXAMPLES OF RESOLUTION OF CERTAIN EXTENDED
DETAIL

David,

Thanks for the data.

Errol