Linear Regression

Hi there, Long time no see, sorry I have been rather quite taken with various business ventures and so I have not been working on my projects as much as I should have. As I have had a lot of downtime recently as the semester winds down I have been taking my free time at work to learn some celestial mechanics.

The notes I am using are great and so I will link to them here.  It starts off with a primer on numerical methods, one of the things he asks you to do is create a program which will compute the  least squares solution to an overdetermined system, then apply that program to create a least squares fit to a set of data. This was the method Gauss used to create tables of ephermrides for asteroids, but it presents and interesting set of computational problems,

1) how does one represent a matrix in memory
2) how does one solve a system of linear equations in a finite number of steps
3) how does one then use that solution as a polynomial to evaluate a coefficent of determination.

This has occupied my time on and off for the past couple of weeks. It suffices to say I learned a lot about representing mathematical objects in a computer. Polynomials are really quite facinating actually. For example it is possible to compute a polynomial at any unknown value in Ω(n) time where n is the degree of the polynomial.

Another interesting question is how does one test a linear least squares code once its been written. The answers are found in my github repository. Here I will only present my results:

The test data and fit

Polynomial model: 
Degree: 1
Coefficients:
a_1: 7.939715
a_0: 1438.362123
r: 0.997310
r²: 0.994628

Motor turning!

More arduino fun!

Post observing report 12/23/2014

Hi all,

I thought last night was a lost night. First I forgot all of the manuals for my equipment at home, then it seemed that the telescope would not point, ever. Here is a summary of what I learned. 

Balance is crucial

The mount would not pont properly due to a wild imbalance in the declination axis, this resulted from balancing the tube with the camera attached but without the finder attached. The resulting imbalance caused the telescope to swing wildly when slewing in the declination direction. 

Need more power, Captain!

The night ended as a result of the Canon SL1 loosing power, this was after I had spent two hours charging it to make sure it was fully charged. The obvious solution is to power the Canon from the 12v SLA AGM battery which is not at all discharged even after running both the telescope and laptop from the begining of the night to when we packed it in. 

The best eyepiece is a Canon Camera

I cannot over emphasise how impressed with the Back Yard EOS software I am. I was able to get closer to good polar alignment than I ever have before using the camera to drift align the telescope. The thing is that now even if I wanted to do something with another imager, I think I would use the cannon first to align everything. 

As I have said in the past, many times, murphy's law goes double in Astronomy. At various times, the software for pointing the telescope, EQMOD, would not take input from a gamepad, or would claim to be pointing the wrong direction, these issues in and of themselves were not fatal, and that is progress. 

The final piece of good news from the night was that we were able to catch decent images of Albireo, and while there is significant coma at the edge of the field the images of the double star itself are still impressive. But the best image of the lot is one with a meteor in it:

Finally I have revamped the astrophotography page for the blog.

The interminable list of things to do.

Hi All,

Now that the semester is nearly over, I have a couple of announcements. First, I am not going to be returning to my Mathematics PhD program at ASU. For all of my friends still working toward their piled higher and deeper degree, I wish you the best of luck, and who knows I may drop by from time to time when I am tutoring on campus.

Now that that announcement is out of the way. I am currently working on a project with my little (read: younger) brother which may or may not result in more money coming my way. In any case, I am now as busy as I have ever been working on various projects.

OpenAIP is still alive and well though the code is still in rough shape, it probably still compiles though their is a lot of learning I need to do before I return too it. Unfortunately, my coding time has been hijacked by the project with my brother.

The telescope is still in boxes, for the most part I have not had time during the busy semester to use it and now that my time is clearing up the weather is not cooperating. I am still looking to get the equipment together I need to go camping, which should happen some time early next year.

I am still hoping to work on a focuser for my telescope, using my Arduino. I don't think I posted the videos from dipping my toes into Arduino programming so here they are:

Hopefully over the break I will be getting some more pieces, specifically a stepper motor, a driver and some optoisolators. If I can get that working I will post it. Also I have decided to start a Go Fund Me page because I am shameless and all of my projects seem to be out of my price range.

Dreams Deferred

Hi all,

The plan has been on indefinite hold for awhile now, my wants were bigger than my stomach and as a result I need to pay down some debt. I have also started to work on a new venture, as a result I am unable to acquire the things that I need to go on the first expedition.

Stay tuned though, hopefully I will be announcing a trip to Alamo Lake soon.

-Aaron

The next thing

So first light was a success, I was able to get a pretty good polar alignment and take some out of focus star images to run through WinRodder. For perspective here is a 1second black and white image of a star field from first light.

The bright star at the bottom of the frame is Vega.

I know what you're asking why would you want to take an image of an out of focus star. Well WinRoddier is software which attempts to reconstruct the wavefront of light coming through the telescope optics from Vega, the result is a reconstruction of the optical aberrations, or optical imperfections, of the mirror. In short this software will tell you if your optics are good, bad or mediocre.

Unfortunately I took images in TIFF format when I needed them in FITS format, the problem is that the software I used to operate the camera saves TIFF images in RBG (Red, Blue, Green) channel format, this results in the exact same data being written into all three channels.  Which lead me to have to go through a round of extracting the color channel data and then running it through WinRoddier.

Only to find that my aberrations were huge, not necessarily because the optics that were sent to me are bad but because I forgot about the first element in my optical system, the sky itself. Air pockets of different density refract light differently, and thus as you take an image the first lenses that light pass through are these air pockets in the sky, now from the above image I was able to measure the seeing, or the ammout of distortion caused by the atmosphere, its 2.68 arcseconds, which is not aweful (>5 arcseconds) but it sure as heck isn't good. (<1.5 arcseconds) The humidity on Monday night was high which probably contributed to the seeing. So now I need an artificial star to test my optics in doors.

Finally the software that I used with my camera is both old, and poorly designed, so I have now taken to working on a piece of software to replace it. But since have always claimed I wanted to write a Open Astronomical Image Processing software solution, now is as good a time as any to start. The code can be found at GitHub (in the Warp_Core1 directory) if anyone is interested in my next steps. It currently uses Visual Studio 2013 to compile.