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Brightness Calculator -> Custom Exposure Tables
This program builds custom results in the same style as our simpler
canned Easy
Exposures tables. It outputs the same kind of table. Required
input is more detailed, but is not restricted to "canned
objects". It allows us to "roll our own" exposure
tables. We can interconvert Apparent Magnitude, Brightness and
absolute magnitude,
but at least one still has to be known. The object's "apparent
diameter" must be known for the viewing date, else, the
program can calculate it from planetary radius and distance from
the Earth. That kind of data is supplied by the Starry
Night Pro program and similar resources; see Notes.
HELP consists
of (a) a test-drive demo that walks you through the steps for several
different "scenarios" - click the ? icon
above - , and (b) more-detailed notes and formulas in NOTES on
the bottom half of this page.
Usage: An asterisk (*) indicates
data required for any calculation. An (OR) indicates two or more
options are offered for data entry, and only one is needed. To
resolve any conflict of extra entries, the program uses only the
first non-blank field.
The US Naval Observatory publishes MICA,
software for PC and Mac, to obtain common astronomical data. You
can Test Drive the
software with a web version to obtain apparent diameter and apparent
magnitude m" (select topocentric illumination calcs), and many
other physical ephemeris. Date range is restricted on the USNO
Web version.
Notes
The published Covington tables give us both surface brightness
m" and photographic brightness B. For custom tables, for other
objects or apparent diameters, we start the calculation with a
B value. We may just convert m" to B as a starting point.
Approximate formulas are:
Brightness
B = 2.512(9.0
- m")
m" = 9.0 - 10.086
ln B (natural log, to base e)
where:
B = brightness of object being
photographed, as input or calculated.
m" or m-double-prime = surface brightness spread over
one square arc-second
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Given m" and the object's apparent diameter d, we can solve
for a more appropriate value of B than with a simple conversion.
Values of m" for the planets are in published data such as
the MICA software program, or the Astronomical
Almanac.
Apparent Magnitude and Apparent Diameter
m" = m + 2.5 log10(pi/4)(d2)
m = m" - 2.5 log10(pi/4)(d2)
where:
m" = surface brightness spread
over one square arc-second
m = total or "apparent" magnitude
d = apparent diameter, in arc-seconds
pi = constant 3.1415926535897932
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Filter Factors
The custom program page corrects for filter
factors when the value is supplied in the form.
Otherwise a value of '1' (no filter) is assumed. The adjustment
calculation (by hand, or by supplying in the form) is:
B (adjusted) = B/filter factor
A web-check of established amateur astronomy dealers indicates
that this filter factor isn't published at all. For example,
OPT and Orion both offer the #25A Red filter at "14%
transmission". What does that mean?
We think it means 14/100
= 1/x, or x=7.14, which agrees closely with the industry
Kodak Wratten values published by Covington. For a #25A,
these are a filter factor of 8 for most films, or 3 for Tech
Pan or CCD cameras. We build into the program the Kodak Wratten
values, and we offer a
choice for either film or digital camera.
How much of a practical difference between filter factor
3 and 8 is there? At f/10 ISO 25 if your shutter speed is
1/8 second for filter factor 3, it will be 1/4 second for
filter factor 8. One f-stop's difference -- there's greater
variation in the moon's surface brightness.
Solar filters are
built with greater densities, often expressed as logarithmic
densities. A filter factor of 1,000,000 (one million, or
1 x 106) is a logarithmic density of 6; 1,000
(1 x 103) is a log density of 3. Our One-Step
program emulates the Covington published tables with typical
solar filter factors of 1,000,000 100,000 and 10,000.
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Film vs. CCD Cameras
Digital: In
time-exposure situations over a few seconds at most, digital
camera pixels are subject to thermal noise pixillation problems.
These CCD's are optimized for daylight conditions. This causes
white speckles or "fake stars" on the finished
image. The Nikon D100 manual lists a conservative 1/2-second
limit, though I have seen published D100 photos with longer
values. Since each CCD has a unique "signature" pattern
of affected pixels, some astronomers have learned to "mask" out
CCD noise, though of course this does not recover the lost
information in the masked pixels.
While lacking the megapixel and color depth of camera CCD's,
a dedicated astrophotography CCD is built for long exposures
in the night sky. CCD devices are not subject to "reciprocity
failure" in long time exposures, but that is a moot
point with digital consumer cameras if they are inherently
limited to exposures of about a second or less. Good dedicated
astrophotography CCD's still go for several thousand dollars,
but they are MUCH "faster" than film.
Films: film is
capable of exposures of hours' duration. Over exposures of
about 1 second, it cumulatively starts taking more than 1
unit of light to expose the film by one more unit; "reciprocity
failure" is a well known controlled variable in the
film world. It is easily accounted for by the formula
t(corrected) = (t+1)(1/p) -
1
where
t is the exposure time (over 1 second)
p is a correction factor called the Schwarzschild exponent,
typically 0.9 for newer slow films, 0.8 for older slow
films or newer fast films, and 0.7 for older fast films.
Check the "film camera" checkbox if you want this
calculation factor built into shutter speed results over
1 second.
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Afocal Method (camera through eyepiece)
You can rig the camera to "see" through the
eyepiece with a special camera mount (Orion SteadyPix™).
Or, you can mount the camera on its own tripod and position
it for the best view through the eyepiece. Or, (horrors!)
you can snap a fast and dirty shot of the Moon through the
eyepiece by hand. Always use a shutter release extension
for steadiest results.
System focal ratio is the f-ratio of the telescope by itself,
times the system magnification:
f = f1 x M
where system (total) magnification is the ratio of the two
lenses, camera to eyepiece:
M = camera lens focal length
FC / eyepiece focal length F2
So, if you had a 50mm eyepiece and a 50mm camera lens, the
total magnification factor would be 1 x the telescope f-ratio.
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Projection Method
"Projection Coupling" allows connecting the
camera body to the telescope system through an extension
tube and T-ring. This system is almost always connected to
or through an eyepiece, affording magnification not available
in prime-focus photography (which is taken at the telescope
back).
Formulas for prime-focus photography are those for the telescope
itself; the eyepiece "projects" the image onto
the film plane, and this changes system f-ratio. We are using
the formula
M = (s2 - F2)/F2;
where
M = projection magnification
s2 = distance from objective to film plane, i.e. 75mm
F2 = eyepiece focal length, i.e. 18mm eyepiece
FC = camera lens focal length in mm (if any)
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How much of a deviation from
the "ideal" exposure is acceptable? Covington
notes that "a x1.4 difference is usually unnoticeable. Some
films tolerate exposure differences of x8 or more." Our
own early experiments with the lunar eclipse of 05-15-2003 bear
this out!
What about my camera's f-stop? We'll
quote Covington here: "The camera lens must always be wide
open; you cannot adjust it to change the exposure."
I have an auto SLR camera.
Can't I just use the built-in exposure metering? Yes -- if the
object fills the viewfinder and if the
light is strong enough for the camera's computer to allow the
shot to be taken. This pretty well restricts this amenity to
the Moon. Modern SLR computer exposure control is hooked to the
lens to obtain f-stop (and lens or zoom f-ratio), and probably
will not work at all without the lens. My Nikon D-100 locks up
without the lens in prime focus photography, if I've forgotten
to set it to Manual, which is easier for me anyway. The camera's
computer has its own built-in
set of f-ratio and brightness limitations; at best, we're "pushing
the envelope" in night sky photography.
I have a nice digital camera
with a non-removable zoom lens. Astronomy magazine
regularly publishes stunning photos taken with consumer digitals.
You'll note that most are brightly-lit compared to a black night
sky: the Moon, aurora borealis, eclipses, twilight scenes. If
your digital allows manual settings, so much the better, and
exposure tables may still help you in any situation your camera's
computer can't handle -- up to a few seconds' exposure time,
anyway. OPT sells couplings to attach better digital cameras
directly to the back of telescopes (wherever the eyepiece normally
goes), camera lens and all. But, if the camera viewfinder doesn't "see" through
the camera lens, focusing the telescope becomes a special challenge.
Buy a book and see how it can still be done.
Our calculators will help you set up a custom Appendix A Exposure
Table for an object when:
- You know some of the variables, but need to calculate others
- You know all of the variables, but some are different from
the "canned" tables. For example, you have the published
values of object "MARS", but you will be using a filter.
- Or, you have the values, but by August 27th the apparent diameter
will jump to four times average -- from about 6 to 25.1 arc-seconds.
You want to know the effect on exposure time (answer: about one
stop; not that much!)
- You want to build an exposure table for a different object
or one with different values.
algorithm library (Perl subroutines)
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