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06-18-2017, 09:52 PM - 2 Likes   #1
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Easy Determinations of Camera Scale Factors (arcseconds per pixel)

In the past, I have analyzed star fields by hand to determine the scale (arcseconds per pixel) for various body and lens combinations. The process is straightforward, but tedious.

I have found a much better - i.e. easier and faster! - way to do this, and you can do it, too, if you want to measure your own camera+lens combinations. This easy way uses a web site to which you submit your camera images (best done with some extra information I’ll describe below). In a few minutes, the results come back, giving (among other things) the scale of the image in arcseconds per pixel.

The site is nova.astrometry.net

(It is partially supported by the US National Science Foundation, the US National Aeronautics and Space Administration, and the Canadian National Science and Engineering Research Council, so you can put some of your tax dollars to work.)

After some experimentation, here is what I think is a good approach to use this site with your images:

1) You need to take some pictures of a star field at night. This is a lot easier than you might think. The hardest part for non-astronomically inclined folks might be picking which star(s) to aim at. Even though I am a (retired) professional astronomer, I find it very convenient to use the freeware program Stellarium (go to stellarium.org to get it) to see what stars are “up” at any given time. Find a bright star that will be nicely up at the time you want to take frames. An elevation of 30 degrees or more is desirable to prevent refraction distortion across the field. While in Stellarium, write down the position in astronomical coordinates of your star (click on the star - a little circle will surround it, and various coordinates will be listed on the screen. You want the “RA/DE (of date)” - the line should look something like

RA/DE (of date): 5h56m2s/+7o24'32"

This is data for the star Betelgeuse in the constellation Orion. These are the “right ascension” (RA) and “declination” (DE) of the star - its astronomical coordinates on the sky, very similar to latitude and longitude on the earth. The numbers will be useful when you upload your image file to the astrometry site (“astrometry” is the science of measuring stellar positions).

2) Go take several images of the sky, centered on your star. You should use a tripod or some other support for your camera so it won’t move during an exposure. For starters, try an exposure something like f/4, ISO 3200, and 4 seconds. This should give you a reasonable number of stars. The astrometry program is quite happy with fewer than 100 stars in a frame.

The hardest part here may be getting a good focus on stars at infinity. If you haven’t discovered already, very few lenses actually focus exactly on infinity when the focus ring is set on the infinity symbol or turned all the way to the distant focus end, so you need to focus on your star. DO NOT USE AUTOFOCUS! Even the best of cameras won’t do very well trying to autofocus on a star. Use manual focus and Live View on your LCD to get the best focus on that central star. If you have a Live View zoom option, use it. For all but very wide angle lenses, you should be able to see and focus on a bright star this way. Aiming the camera so your bright star is in the center of the field will help with focus and when it comes to submitting your images for analysis.

Use the self timer delay (and perhaps mirror lock up) when you take your pictures. This minimizes vibration.

Don’t worry about tracking the stars to compensate for the Earth’s rotation. For short exposures, even with a telephoto lens, any blurring won’t affect analysis.

3) Once you have some images, use your favorite post-processing program to convert them to black and white. This isn’t necessary, but it will cut down on the file sizes you submit. I also found it useful to adjust the levels to bring up the star images. It may also be helpful to clip the bottom of your histogram to zero out any noise pixels. Noise spots can confuse the analysis program, which tries to associate them with (non-existent!) stars.

For very wide angle frames, you may find it desirable to crop and submit just the center of the frame. The analysis program did not do very well with my uncropped 10mm and 20mm frames. I don’t know if it doesn’t deal well with the considerable field curvature at the edges of these frames, or just finds so many stars that it is overwhelmed.

4) Submit your frames to nova.astrometry.net for analysis: Go to the web site. If you are so inclined, I guess you can create an account (I just used it in anonymous mode). Click on the Upload button. Once on that page, you can select your image file for analysis. The program seems fairly sophisticated, and it might work to just submit your file. However, analysis will proceed faster (and perhaps better) if you click on Advanced Settings before clicking upload, and supply a few numbers. The important settings are

Scale - the more-or-less overall size in degrees of the field of view (FOV) of your frame
For most camera images, selecting “wide field (1 to 180 degrees)” should suffice
a 300mm lens will have a FOV of a few degrees
a 10mm lens will have an FOV approaching 100 degrees or more
These values depend on whether you have a crop sensor

Parity - how your image relates to up/down & left/right on the sky
use negative for regular camera images
Pictures taken with a telescope and attached camera may well have the sky appearing to be flipped or inverted.
(Your camera actually takes such images, but the internal processor flips them back, so they look “normal”!)

Limits - put here the position of your central star
A good value here will speed up the analysis - the program knows where to start.
You need to do a bit of arithmetic first. The “RA” value that you wrote down needs to be converted to degrees. To do this, multiply the first number (hours) by 15 (there are 15 degrees in one hour), then divide the second number (minutes) by 4 to find how many more degrees there are and add that to the hours converted-to-degrees value. You can ignore the seconds value. For my Betelgeuse example above (5h56m2s), you should get 5x15 + 56/4 = 89 degrees (don’t worry about fractions - the idea here is to get within the nearest degree or so. Since we care only about the nearest degree, you can just take the leading value for the DE coordinate, which is already in degrees. So, for Betelgeuse (+7o24'32"), you can just take 7 (if the declination is negative, retain the minus sign). If the minutes value is bigger than 30, you can round up if you want. You can also put in a Radius - this is an estimate of how close your field center really is to your (assumed) central star. If you are reasonably centered, 5o is fine here.

Downsample - I have left this at 2 with no problems. If you have
a really sharp lens, are very accurately focused, and are
using some kind of tracking system so your stars are not blurred by earth rotation, you may want to set this at 1.

After setting these few parameters, browse to find the file you want to submit and send it in by clicking “Upload.” After a few minutes, you should be advised of success. (or failure! Try cropping your image.) Click on the “Go to results page” to see the results. You’ll see an image with some of the stars in the field identified and over on the right-hand side some numbers. Under Calibration, the 6th value will be your camera+lens scale in arcseconds/pixel - the goal of this whole exercise.

The process is really quite easy and simple. After you’ve submitted a few files, you can do it almost in your sleep.

Try it!

I have compared this program with some of my own analysis results, and the agreement is as good as the 3-digit precision implied by the astrometry.net results. With care, by hand I can get almost another decade of precision.

If you have questions or problems, please pm me.


Last edited by AstroDave; 06-18-2017 at 11:06 PM. Reason: Fix a typo
6 Days Ago   #2
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Yes, I have a question which I think is related to your post. I've been trying K1 astrotracer with the DFA150-450 @ 450mm but it did not work. Then I tried to look at the maximum duration of the astrotracer (displayed in bulb mode) using the DFA24-70. I was expecting that the max duration of astrotracing would be inversly proportional to the focal length since the displacement of the sensor is limited, but the maximum duration of astrotracing does not change with the lens focal length. Am I missing something?
6 Days Ago   #3
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Join Date: May 2007
Location: Flagstaff, Arizona
Posts: 121
Original Poster
QuoteOriginally posted by biz-engineer Quote
Yes, I have a question which I think is related to your post. I've been trying K1 astrotracer with the DFA150-450 @ 450mm but it did not work. Then I tried to look at the maximum duration of the astrotracer (displayed in bulb mode) using the DFA24-70. I was expecting that the max duration of astrotracing would be inversly proportional to the focal length since the displacement of the sensor is limited, but the maximum duration of astrotracing does not change with the lens focal length. Am I missing something?
I have not tried astrotracer yet (I have a real tracking mount!) , but it is on my list of things to do. So, I can't say much about your problem. I would tend to agree with your logic, though.
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