A couple of months ago I posted a formula I derived for working out how long you could take a photo on a fixed tripod and retain star images that look stationary.
Quote:
Revised rule for DSLR's
These rules or formulae are based on a set of starting assumptions and have been kicking around for a long time.
In the old days of 35mm film where very fast films used for tripod astrophotography had very course grains and so a bigger movement could pass off as no drift. It was based on someone looking at a 8x10inch enlargement at normal reading distance perceiving trails as almost stationary. The eye can resolve about 1 arc minute so it can in fact resolve approximately 200 microns on a print which scales back to 25 microns on the film. However the number 700 corresponds to a trail length of about 50 microns. This is about 9 pixels on a modern DSLR. But today, we mostly look at screen based images and images that are highly reduced from full size.
The number is related to how much drift you find acceptable. So I've derived a revised formula, modernized for DSLRs.
max exposure time(s) = [14*N*P] / [FL*cos(d)]
where
N..........Number of pixels of drift
to work this out load any full frame image from your camera and scale it to the size you want to view on screen. Look at the scale percentage. Number of pixels drift = 100 / percentage
P..........Pixel size (microns) Most DSLR's are between 5 and 8 microns. You can look it up in your manual or just split the difference and make it 6.5
FL.........Focal length(mm)
cos(d)...cos of the declination. Use the declination of the stars in the field that are closest to the celestial equator in the camera field
Example : Using a 14mm lens, 5 pixels drift, on an APS-C sensor with 5.4µm pixels pointed at the celestial equator can take a 27 sec exposure. Pointed at the SCP the lens will see 45 degrees each side of the pole extends the time to 38 seconds.
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Between a new job and lots of cloud I haven't had much time and only tested it out a couple of weeks ago. The attached image pushes this technique to its limits.
N=12 pixels drift because the image is displayed at 12.5% of full scale so the star images are 1.5 pixels long.
Pixel size = 5.4microns
FL = 300mm
declination = 40 S
max exposure time(s) = [14*N*P] / [FL*cos(d)]
max exposure time(s) = [14 x 12 x 5.4]/[300 * cos(40)] = 4s
The image was taken with a 300mm f4 lens DSLR set to ISO 12500 on a tripod with no guiding. It is processed in Lightroom 3 / Photoshop CS3 from a single exposure of 4s in length.
This technique doesn't pretend to compete with high quality guided images, just intended to give beginners without tracking gear and experienced astrophotographers traveling without tracking gear some options to play with. The formula updates outdated tables and rules of thumb based on 35mm film output. This formula allows you to find the maximum exposure for a particular pixel pitch and specific output display size.
Cheers
Joe Cali