A New Video Method to Measure Double Stars

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Introduction 

Double Star Basics

Traditional Methods to Measure Double Stars

The New Video Method

Equipment Needed to Get Started

Acquiring Videos

Procedure for Using Limovie

Reducing the Data - VidPro

VidPro Program Download

Results

Acknowledgements

INTRODUCTION

With the emergence of low cost, higher sensitivity video cameras and digital video recorders (DVR's), video astronomy has reached new levels. Along with this increase in video activity in astronomy, numerous programs to analyze videos, whether for occultation events, photometry or astrometry have appeared. This page describes a new video method to measure separations and position angles of double stars, also known as visual binary stars. From a single 20 sec - 2 minute video, this method will extract and analyze thousands of star positions for double star components and provide an accurate separation and position angle for the epoch and equator of date.

The equipment needed to get started is the same as for occultations: An equatorial mounted motor driven telescope, an optional GPS time inserter, a video camera and a DVR.

Figure 1. Position angle (PA) and separation of double star. The Black star is the primary and the red star is the secondary. "N" is in the direction of the north celestial pole (NCP).

DOUBLE STAR BASICS

The diagram above Figure 1 illustrates the position angle and separation of a double star.  The black star is assumed to be the primary (brighter) star and the red star the secondary (fainter) star. Position angles (PA) range from 0º - 360º measured positive eastward from the north celestial pole (NCP or N). In the diagram above, the PA of the secondary star is somewhere between 90º (due east) and 180º (due south) and is approximately 135º. Separations of double stars are quoted in arc-seconds (").

The Washington Double Star Catalog (WDS) maintained by the US Naval Observatory has over 125,000 entries for double/multiple stars. Measurement of position angle and separation of double stars is of prime importance in astronomy for the following reasons: 1) position angles and separations are used to compute orbits of binary stars, 2) with accurate orbits, distances to the binaries can be computed with good precision, 3) accurate distances to binaries allow the determination of the absolute physical quantities of the individual stars (luminosity, mass and sometimes their diameters), 4) this information is the fundamental basis and provides the basic calibration for expanding on the distance scale of stars, clusters and galaxies in the Universe. 

TRADITIONAL METHODS TO MEASURE DOUBLE STARS

THE NEW VIDEO METHOD

The basic concepts of this new method is as follows:

1.  The equipment needed is the same as for modern occultation observations: equatorial mounted (preferred) telescope, GPS time inserter (optional), video camera, and digital video recorder (DVR). In lieu of a DVR, older camcorders can be used for the recordings however any videos acquired will need to be in AVI format for analysis purposes.

The observer will video record a double star drift from the one (east) side of the DVR/camcorder screen to the opposite (west) side with the telescope's motor drive turned off along with GPS time insertion.  The camera/video chip's north/south edges  should be oriented fairly close to east-west, but need not be perfect. It should be within 5 degrees of true east-west direction (see Figure 2A & 2B). A few practice drifts will determine if your video camera needs to be rotated.

The GPS time inserter will overlay date and millisecond time (0.001sec) on the video for each video frame (Figure 2A).

In lieu of a GPS time inserter, you may use the known frame rate of the DVR (in frames/sec) and the no. of total frames of the drift's duration. This needs to be known precisely. The drift's duration needs to be known to better than 0.1 second.

2.  Using the freeware program Limovie, run your AVI format video choosing  2 aperture rings - one for each star - adjust them so they are tightly wrapped around each star (see Figure 4). Use the program's constraints and options as specified in the section below: "PROCEDURE FOR USING LIMOVIE - EXPLANATION OF CONTROLS".

Limovie was created by Kazuhisa Miyashita and was written for the analysis of lunar and asteroid occultation videos. It's use for double star astronomy was recognized by this author and the resultant techniques and additional software are presented here.

Limovie will record an (x,y) data point for each aperture ring (star) for each video frame as they drift. For a 60 second video and a 30 frames/sec video recording rate, this means that Limovie will generate (60 sec) x (30 frames/sec) = 1,800 (x,y) data pairs. Limovie's analysis window is 640 x 480 pixels and most f/10 optical systems will have a 0.6 - 2 arc-second/pixel scale.

                         Limovie screen shot (left) and close up of the components on Limovie's (x,y) grid (right).

3.  Once the run is completed, you will save the data to a "CSV file" (comma separated value Excel file) as per Limovie's save option.  An Excel program, VidPro, (VIdeo Drift Program ReductiOn), is available to instantly compute scale factor, position angle, separation, drift angle, and other statistical quantities from Limovie's CSV file. 

4.  Since we are only computing the relative quantities for the double star components (separation and position angle), we only need their (x,y) positions. No other stars are measured and no other stars need be visible on the video.

5.  With 1,000's of (x,y) pairs that are generated, this allows computation of 1,000's of separations and position angles from a single video. The resultant values will be averaged for a final result. A correction will be made automatically to the computed position angle for the video camera's offset from a true east-west direction.

The new video method will allow the measurement of double star separations down to about 5"- 6" (and closer using magnifying scripts) along with their position angles.

6.  The amount of data points available for analysis from this method is unprecedented compared to any other video or CCD camera technique.

EQUIPMENT NEEDED TO GET STARTED

As stated earlier the equipment needed to begin measuring double stars is the same as used for recording occultations: a motor driven equatorial mounted (preferred) telescope, a video camera (such as the Supercircuits PC-164CEX-2 camera), an optional  GPS time inserter  (AME Time Inserter, GPS Blackbox Sprite2 Time Inserter), a digital video recorder/camcorder, a means of converting the video files to AVI format and the programs Limovie and VidPro. 

Equipment needed. LEFT - Video camera attached to the prime focus of a Questar. RIGHT - Double star being recorded drifting across the field. GPS date/time info is along the bottom. Date/Time reads Oct. 06, 2010, 02h 41m 29.539sec. GPS time insertion from the AME Time Inserter unit.

ACQUIRING VIDEOS

Pick a double star whose components can be resolved on your DVR/camcorder screen. Position the double star just outside the east edge of your DVR/camcorder screen FOV.  Orient your video camera on the telescope so the top and bottom edge of your FOV is parallel to east-west, see Figure 2B. The orientation of the video chip does have to be perfectly aligned with the east-west direction but should be within 5 degrees. A few practice runs will determine if your video camera needs to be adjusted.

Turn off the telescope's motor drive and start recording.  Video record (with GPS time insertion if available) the double star drift all the way to the opposite side (west) of the FOV. Stop the recording when the stars have drifted out of the DVR/camcorder screen's FOV.  

With a typical video FOV of 15-25 arc minutes, the drift will take anywhere from 20 seconds - 2 minutes. If at all possible acquire your videos when the double stars are within 15º (1 hour) of the local meridian. As this is an astrometric method,  the less atmosphere the starlight passes through the better the results.  Always try to record your videos when the telescope has reached thermal equilibrium and the atmosphere is steady with good seeing. Poor seeing will result in fluctuating star images that may not give good results. If you cannot visually resolve the stars on your DVR or camcorder screen, Limovie won't be able to resolve them either.

A                                                                                   B

Figure 2. A: Limovie video window. The double stars (marked green) will drift across the video FOV east-west, which will likely be different than the camera/scope orientation. The drift angle a is computed automatically by the program VidPro and will vary slightly for each video in an observing session. GPS time insertion is on the bottom of the screen and date and time reads "January 28, 2011, 5h 07m 41.239sec." GPS time insertion is from the Blackbox Sprite2 Time Inserter unit. B: Attach your video camera so it's north-south edges are parallel to the east-west drift of the stars.

The video files made must in AVI format for the program Limovie to analyze them.

PROCEDURE FOR USING Limovie - EXPLANATION OF CONTROLS

Figure 3. Screen shot of the program Limovie. As the video plays the double stars begin their drift on the left ("Start") all the way to the right ("End"). The aperture rings are manually placed around the stars and drift with them across the FOV. The aperture rings have the added benefit of producing an (x,y) measurement (box labeled "3") for each video frame for each of the double stars as they drift across the FOV. The (x,y) data is in units of pixels. These (x,y) positions are stored in a Microsoft Excel CSV file for later retrieval. GPS date/time along the bottom reads February 6, 2011 3h 46m 31.266sec.

Figure 4. Limovie's 3D contour plot. This 50-pixel wide window is opened from the "Star Image 3D" button. (x,y) positions plus intensity levels of both peaks are stored in the CSV file. VidPro uses the intensity data to determine the primary star and the (x,y) positions to determine position angle and separation.

TO START: Use the "FILE" button on the far upper left of the screen to open your AVI format video. Limovie only accepts AVI format videos.

After your video is opened,  click anywhere on the screen to bring up the colored aperture rings. Anywhere you click will place the aperture rings at that spot. This 1st aperture ring will be known "Object1" in the program.  Click on either star to place it over the star.

Then "right click" on the screen and this window appears:

Click on "Object Star Add".  Select "Object2" - this creates a 2nd aperture ring and then click on the 2nd star to place it on top of it. The aperture rings need to be adjusted - see paragraph 6 below. To start the data recording, click on "START" in the area marked "5". Click "STOP" to stop the data recording. 

The controls described below are specific for double stars. The rest of Limovie's screen and controls are relevant only for occultation videos and not described here.

REMEMBER - YOU RECORD THE DOUBLE STAR DRIFT VIDEOS WITH YOUR OWN EQUIPMENT. Limovie only analyzes the videos - it does not record direct from a camcorder or DVR. 

From Figure 3 above:

1- "Current Frame" - This is the video frame number displayed

2 - These buttons start, stop and advance through the video in increments of -10sec, -1sec,  -1 frame, +1 frame, +1sec, +10sec. These controls do not start the recording of data, they merely position the video at a desired start position.

3 - Position - This is the (x,y) position of the circular apertures around the stars (only one position is displayed). The entire grid is 640x480 pixels. (x,y) values will change in real time as the stars drift. For every frame these (x,y) positions are stored in the CSV file after the run.

4 - Star Tracking options. Use the "DRIFT" option. This allows the aperture rings to follow the stars as they drift. "Radius" - this is the radius in pixels the aperture ring will search to keep centered on the star as it moves. If it's too low (like 1 or 2) it won't be able to keep up with the drifting star and will fall behind. "7" is a maximum value this author has used. When the components are very close you may have to use the "Link" feature - to the right of the box marked "3" in Figure 3. Use of the Link option will assist in keeping the aperture rings separated vs. them wanting to merge on the brighter star.  This is useful when the components are very close, as the aperture ring will want to jump to the brighter star. The "OFF" button freezes the aperture ring so it cannot move. Use the OFF option when making adjustments on the aperture ring sizes (paragraph 6 below), then switch to DRIFT to start data recording.  

"Threshold" is not used - leave at value = 50.  

5 - "START" will start the drift and begin data collection. You can see the data accumulating on the right hand portion of Limovie's window. "STOP" will stop the video and the data collection. "DataRemove" will erase the data so you can start over. "SaveToCSV-File" will open a window allowing you to save the data from the drift into a CSV file for analysis by the program VidPro or a program of your own.    

6 - Radius - Inner - Outer. Each aperture has 3 adjustable colored rings called "Radius, Inner and Outer". The sizes are in units of pixels. Ideally you want the rings wrapped around the components as tightly as possible. Set the "Radius" (inner-most ring) tightly around the star, and the "Inner" and "Outer" rings as small as they will go but not less than 2,3,3.  Typical settings for a star might be 4,5,5. Larger star disks will requires larger radii. The author recommends that the "Radius" (inner ring) never be set less than "2". Users should experiment with ring sizes/combinations to see how they affect the results.  

These rings will analyze the brightness of the star and maintain their position centered on the star using an minimum brightness/search algorithm. This algorithm is explained on Limovie's download page.

7 -   Star Image(3D) - this button opens the 3D window (Figure 3 right side, Figure 4) showing the contour peaks of the stars and their position on a 50-pixel square window.  It assists the user in placing the aperture rings over the components and seeing exactly how they are situated. When adjusting the aperture ring sizes (paragraph 6 above), watch how they change around the contour peaks. The viewing angle of the contour peaks can be adjusted by the 4 directional buttons under the "ROTATION" box on the lower right of the 3D window. The intensity (height) of the peaks is controlled by the vertical sliding lever immediate to the left of the ROTATION buttons. 

With a basic understanding of how Limovie's controls work, now make a run. Save the data to a CSV file. Use the program VidPro to compute position angle (PA) and separation.  

Reducing the data - VidPro - VIdeo Drift PRogram ReductiOn

VidPro is an Excel program written by this author to analyze the CSV file output by Limovie to determine position angle (PA), separation and other statistical quantities of double stars. Instructions for running VidPro are included with the program. VidPro has 2 versions - one for GPS time inserted videos and a second version for a video recorded with a 30 frame/second DVR.

VidPro is available from the author upon request or by free download (see below). Send your request to RNugent ”at” wt.net

VidPro is easy to use. For both versions users will input basic information marked in blue as seen below:

WDS ID of the double star,

Date,

Telescope used,

Observer,

RA and DEC.

 For the GPS version users also enter the start and stop times of the video drift where indicated. The example below shows screen shots from the 30 frame/sec version.

Optionally you may enter the "WDS PA" and "WDS sep" as they appear from the WDS catalog:

Next the user will copy the ENTIRE CSV file output by Limovie using the COPY/PASTE function into Sheet2 as illustrated below. It is recommended that before you copy the CSV file into this position, that you erase the entire old CSV file from a previous run. This prevents the carrying over of unwanted data.

THAT'S IT ! YOU'RE DONE !

OUTPUT RESULTS - Sheet 1:

Sheet1 - the position angle, separation, standard deviations, scale factor, drift duration, etc. and chart showing the relative positions of the double star components are shown below. The star info, PA, separation, etc. is on a single row for an easy copy/paste to another file.

VidPro Download

Download VidPro for your 30 frame/sec DVR here.

       Download VidPro for your unknown frame rate DVR here. (GPS Time Inserted Version).

RESULTS

This table shows results from WDS stars with little or no change in position angle and separation over a long period (120+ years). The video drift method matches them very well. The videos were made using the author's 3.5" (9cm) Questar and Meade LX-200 14" (35cm) SCT.   

WDS	video method PA°	video method  std dev	WDS PA	PA difference	video method Sep "	video method std dev	WDS sep	Separation  difference	date	No. video frames	magnitudes
00137+4934	165.2	0.9	165	0.2	20.2	0.22	20.2	0	2010.98	1093	9.34  9.25
02408+1500	312.2	1.1	312	0.2	22.5	0.49	22.7	0.2	2010.9	720	9.69   10.22
03021+0005	139.9	3.8	139	0.9	7.9	0.63	8	0.1	2010.9	701	9.78  11.1
03084-2410	217.7	1.3	218	0.3	25.8	0.56	25.7	0.1	2010.98	772	10.21  10.86
03311+2744	233	0.3	233	0	44.4	0.23	44	0.4	2011.09	1493	7.41  7.81
03313+2734	269	0.7	269	0	11.5	0.21	11.3	0.2	2010.99	1589	6.58   6.93
03383+4448	96	1.6	96	0	41.3	0.65	41	0.3	2011.09	2624	7.21  7.53
03425+0202	182.8	2.1	183	0.2	11.3	0.66	11.8	0.5	2011.09	706	9.3   9.5
04009+2312	127	2.3	127	0	7.4	0.31	7.4	0	2011.09	794	6.92   7.76
04380-1302	172.3	2	172	0.3	12.5	0.52	12.3	0.2	2011.1	740	7.33  7.85
05193-1831	18.5	1.3	19	0.5	39.4	0.93	39	0.4	2011.08	2052	6.31  6.48
06090+0230	114	1.8	114	0	29.2	0.98	29.1	0.1	2011.15	1941	5.68  6.68
08397+0546	30	0.8	30	0	26.3	0.39	25.9	0.4	2011.11	1961	7.33  8.56

Table 1. WDS stars with little or unchanged position angle and separations over long time periods (120+ years). Columns are WDS ID, video method position angle and standard deviation, WDS PA and difference, video method separation and standard deviation, WDS sep and difference, date, number of videos used for result, magnitudes of components.        

      The technique here is described in the paper published in the Journal of Double Star Observations:

Paper reference: http://www.jdso.org/volume7/number3/Nugent_50_59.pdf

Acknowledgments

Kazuhisa Miyashita wrote the video program Limovie for analyzing occultation videos. It's alternative use for measuring double stars is my own project. Ernie Iverson from Lufkin, Texas made numerous double star videos for testing and numerous suggestions.

Richard Nugent

Executive Secretary

International Occultation Timing Association

RNugent “at” wt.net

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

Here's how VidPro computes the quantities:

The brightness information is used to determine which star is the primary and secondary.  ONLY RARELY, if the double star magnitudes are very close or identical, VidPro might choose the incorrect star as the primary. This will result in the PA being 180 degrees off.  Check the WDS catalog entry for this particular double if you're not sure. Sheet2 of VidPro has a chart which displays the primary/secondary as determined from Limovie's brightness data of the individual stars. 

For each (x,y) pair the separation and PA will be found by the formulas:

The quantities x_p , x_s , y_p and  y_s are the (x,y) positions for the primary and secondary star from Limovie's CSV file.  DEC is the declination of either double star.  The formula for "Sep" is not rigorous considering we are measuring the projection of a curved celestial sphere onto a flat video chip. However this formula suffices for small separations in double star astronomy.  

The quantity "Sep" will  be converted to arc-seconds using a scale factor for your particular video. The (x,y) data points are in units of pixels. The scale factor is calculated from the GPS time inserted start time and end time of the drift and will be converted to arc-seconds per pixel ("/pixel). If there is no GPS time insertion, the scale factor is calculated by assuming a 30 frame/sec DVR recording rate (30 frame/sec version).

The PA derived will be corrected for quadrant based on which ever star is determined to be the primary.    

The PA and separations computed will be referred to the Epoch and Equator of date. To convert to a catalogued position (such as the Washington Double Star Catalog) the PA will need to be precessed to the Equator of the catalogued position and then have proper motions applied. This conversion is only needed for stars with the largest proper motions and for those doubles near to one of the celestial poles. Generally speaking, this step can be ignored.

As stated above, you'll have several hundred to several thousand (x, y) data pairs to use these formulas on. The resultant Sep and PA will be the average of all the calculated values, one for each video frame. And with a huge number of data pairs, useful information is also derived, such as standard deviations and the drift angle across the FOV. The drift angle (see Figure 2) shows how far off from a true east-west drift your camera/telescope orientation was.

The drift angle is computed from the relationship:

where "y" and "x" are the tabular values output by Limovie. This is done as a least squares adjustment of all the (x,y) data pairs in the drift. The quantity "m" is the slope of the drift line, where tan(drift angle) = m.  In the least squares calculation, the quantity "b" is not needed and can be disregarded. 

Below is a view inside a portion of Limovie's CSV file. The (x,y) position of Object 1 (1st star's aperture ring) is stored in columns Y and Z.  The (x,y) data for the 2nd star (Object 2) is stored in columns AP and AQ.                                          

Figure 5. A view inside Limovie's CSV file. The output (x,y) pairs are tabulated for both aperture rings Object 1 and Object 2. For Object 1 the (x,y) data is listed under columns Y and Z, for Object 2 the (x,y) data is tabulated under columns AP and AQ.