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Frank wrote-

" suppose we replace the eye with a camera. Now Venus is easy every time.
With a decent camera and the right settings, how many stars and planets can
you see in daylight? Jupiter? Yes. Sirius? Probably. How about Vega,
Arcturus, Capella...? How faint can you go? If the number of visible stars
averages more than three at a time, that completely changes the name of the
game. Imagine getting three-star fixes all day long."

Is Frank, here, discussing what's presently possible, in a navigational
context, from the deck of a vessel, in ordinary sea-conditions? Is he
claiming that daylight shots are possible, in such conditions, that show
such stars or planets when at a respectable altitude, with a clear horizon
below in the same shot? With angular accuracy and resolution of, say, a
(very) few arc-minutes, in the angle between them? In ordinary, clear-sky,
weather, with no special requirement for extraordinary crystal-clarity of
the sky?

If so, then he is right, that a useful tool is becoming available. But if
not, before being carried away with enthusiasm, it would be worth
considering any such limitations in terms of the restrictions they impose
on its use, for a navigational purpose.

========================

I agree with Frank's assessment of the calibration of lens / array
geometry, when applied to a non-zoom infinity-focussed system. A lens will,
in general, be axially symmetrical, in an (r, theta) plot, and the only
thing that really matters for astro is the plot of off-axis image angle
against off-centre pixel radius. However, this differs from the way that
lens distortions usually seem to be expressed, as a plot of off-centre
radial displacement on a distant plane object, against displacement from
the centre of the pixel array.  Those two plots differ by a factor of
exactly tan (angle), which should be easy to allow for. Being axially
antisymmetric in an (x,y) plot, it can involve only odd powers of pixel
off-centre displacement.

But, to use such a camera for our astro purposes calls for highly accurate
calibration, perhaps more accurate than the camera maker ever envisaged.
Although the maker's calibration curve might well be sufficient in terms of
its shape, if the aim is to even approach the precision of a sextant, it's
likely to be necessary to calibrate the overall scale-factor of each
individual instrument. Even if the pixel array is exactly uniform, is the
array pich exactly the same in x and y directions? Is the lens-to-array
spacing exactly reproducible, between cameras? Here, we're seeking an
exactness of one part in many thousands. And as temperatures change, does
that spacing change exactly in proportion to dimensions of the array
itself?

These are matters which over many years have been though about, and dealt
with, in the case of the sextant, but may never have even been considered
seriously for common  usage of a camera.

But such a calibration should not be difficult to make A single shot of a
night-sky image should provide all that's needed.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

===================
----- Original Message -----
From: "Frank Reed" 
To: 
Sent: Saturday, September 11, 2010 12:12 PM
Subject: [NavList] Digital camera: stars in daylight

Paul Jackson's daytime Venus observations reminded me of a topic I meant to
bring up back in July. Finding Venus by eye in daylight is a real
challenge. Without a pre-set sextant or a mounted telescope, you can stare
right at it for minutes and never "see" it. But suppose we replace the eye
with a camera. Now Venus is easy every time. With a decent camera and the
right settings, how many stars and planets can you see in daylight?
Jupiter? Yes. Sirius? Probably. How about Vega, Arcturus, Capella...? How
faint can you go? If the number of visible stars averages more than three
at a time, that completely changes the name of the game. Imagine getting
three-star fixes all day long... In order to be useful, this would require
some sort of software that can scan through an image looking for the
"little white dot". That's easy enough in principle. Does that software
exist anywhere? This would probably require analyzing "raw" image files
rather than compressed jpegs, but most mid-range "prosumer" digital SLRs
can output those easily.
By the way, a few months ago when I did not have much time for NavList,
there was another running discussion of camera calibration. I think it
might be worth noting that is a solved problem. People have been making
highly accurate angular measurements with digital cameras for over a
decade. You can even use a fisheye lens and still get accurate angles from
the images. This is not rocket science. The trouble, from the perspective
of a navigation enthusiast, is that these "well-known" algorithms are
generally deeply buried in various software tools, from standalone products
to photoshop plug-ins. The tools will spit out a calibration matrix (or a
set of coefficients) when fed a series of standardized calibration images
like photos of a checkerboard in various orientations, but if you want to
do it yourself, you'll probably have to dig through the original technical
literature. Some useful search terms: "camera calibration" (but that also
includes things like color calibration), "camera resectioning",
"photogrammetry" and "digital photogrammetry" (this is the process of
producing 3d models from a series of photos taken from various
angles --one-tenth of a minute of arc accuracy was considered reasonable
even seven or eight years ago), and "amateur astrometry"
(professional-quality astrometric results have been possible with mid-range
digital cameras and backyard telescopes for over a decade). The problem of
calibration for celestial navigation involves large angles and a very small
number of objects all at effectively infinite distance visible at any one
time. This problem falls somewhere in between the photogrammetry problem
(which deals with objects in a wide field of view at various distances from
the camera while celestial deals only with objects at infinity) and the
astrometric problem (which usually depends on field stars with known
angular positions in a smaller field of view).

   

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