Measuring equatorial mount backslash through imaging

[diegop]

 

Hello All

i wonder if is it possible to measure the deviation between two images in degrees. What i am trying to do is measuring the backslash of a telescope equatorial mount. I attach a digital camera and i take two pictures,i would like if i can measure the deviation between both images using imaging software (like imajeJ or another one). 

The camera is attached this way

Best

 

[vlaiv]

Yes of course it is - provided that you have enough precision.

You need to know plate scale / your sampling rate - it can also be measured or calculated.

For calculation you need to know focal length of your lens and your camera pixel size, and this will give you arc seconds per pixel. Alternatively - take one image of the known part of the sky - identify two stars. Measure distance in pixels between two stars (in imageJ - line selection tool will give you distances. Measure distance between two stars in Stellarium using angle measure tool.

Divide two values to get arc seconds / pixels measure.

Another alternative is to upload image to astrometry.net and have it plate solved - this will give you pixel scale as well.

Now that you have pixel scale - open both images in ImageJ and create small stack out of them (stack in imagej is just sequence of images). Z-project them using max - this will give you image where you'll have stars from both images visible. Identify same star that is duplicated and measure distance in pixels it moved.

Take pixel scale and multiply with distance in pixels - this will give you arc seconds that image moved between shots.

Alternative - upload both images to Astrometry.net, have them both plate solved - it will give you centers in RA/Dec coordinates - and just calculate distance in arc seconds between those two points in RA/DEC.

By the way - welcome to SGL

 

[diegop]

58 minutes ago, vlaiv said:

Yes of course it is - provided that you have enough precision.

You need to know plate scale / your sampling rate - it can also be measured or calculated.

For calculation you need to know focal length of your lens and your camera pixel size, and this will give you arc seconds per pixel. Alternatively - take one image of the known part of the sky - identify two stars. Measure distance in pixels between two stars (in imageJ - line selection tool will give you distances. Measure distance between two stars in Stellarium using angle measure tool.

Divide two values to get arc seconds / pixels measure.

Another alternative is to upload image to astrometry.net and have it plate solved - this will give you pixel scale as well.

Now that you have pixel scale - open both images in ImageJ and create small stack out of them (stack in imagej is just sequence of images). Z-project them using max - this will give you image where you'll have stars from both images visible. Identify same star that is duplicated and measure distance in pixels it moved.

Take pixel scale and multiply with distance in pixels - this will give you arc seconds that image moved between shots.

Alternative - upload both images to Astrometry.net, have them both plate solved - it will give you centers in RA/Dec coordinates - and just calculate distance in arc seconds between those two points in RA/DEC.

By the way - welcome to SGL

Hello vlaiv,

what an awesome answer. Many thanks, really appresiated. I am a completly beginner in AP and i think that starting learning the basis should be the best.

I am just starting with what i have at home. 

Hello vlaiv, many thanks

what an awesome answer. Much appreciated. I am a completly beginner in AP and i think that starting learning the basis should be the best. I have never use ImageJ and i have try to calculate such thing as this, but i want to learn

I am just starting with what i have at home. Sorry but i am not already familiar with this concepts:

• plate scale
• sampling rate

Telescope

Refractor Skywatcher 102/1000 (i know is too slow for AP, i am using it to just start learning)

Mount

EQ3-2 helios skycan 2001

Camera

Old compact camera Nikon coolpix l15

https://www.digicamdb.com/specs/nikon_coolpix-l15/

Focal length (35mm equiv.):    35 - 105 mm

So the data i first need to know is:

pixel scale (is it the same that plate scale?) 

Seems the Astrometry.net alternative should be more easy, i'll try first the astrometry.net method and then with ImageJ because i really would like to learn measure it with the imageJ.

let's do it!

Best

 

 

 

[vlaiv]

39 minutes ago, diegop said:

let's do it!

Ok, so first - plate scale is term used for plate solving - and it represents ratio of physical distance on old film photography to angles on the sky - it can also be used for images, in that case we are talking about pixels rather than mm or whatever unit of length is used.

Sampling rate - is again the same thing only coming from different field - it is how much sky is covered by single pixel - or rather what is the distance between two adjacent pixels (but since pixels are tightly packed - it is the same as size of pixel).

Both tell you mapping in pixels versus angles in the sky, or how much sky angle each pixel contains.

43 minutes ago, diegop said:

Refractor Skywatcher 102/1000 (i know is too slow for AP, i am using it to just start learning)

No such thing as slow scope, but that is whole another story so we won't be getting into that

44 minutes ago, diegop said:

EQ3-2 helios skycan 2001

Well, that mount is going to be good for camera + lens astrophotography. Your scope is too heavy / big for that mount for astrophotograpy - it will be ok for visual (although eq5 would be better there as well).

Do you know what the backlash is?

You say you want to measure backlash, but that is going to be very hard with camera that you have. Backlash can be measured and is often measured with guiding equipment. Computer is automating the process, but you need to have it control both the telescope mount and guide camera in order to measure backlash.

Backlash in a mount is "empty movement" of one of mount axis. Say you have DEC backlash. If you move mount in DEC using slow motion controls (knobs that you turn by hand and mount tracks in that axis) and then stop and change direction and turn the same knob in other direction. Mount might not respond immediately and it might take say 1/16th or 1/8th of a turn before mount stars moving in opposite direction. That turning of your DEC knob before mount actually starts turning is called backlash and it is expressed in arc seconds - which correspond to motion of the mount around that particular axis when you turn your knob for 1/16th or 1/8th (or whatever was empty motion) when mount does track.

This is useful to know precisely in arc seconds - for computer software that operates your telescope mount. It needs to know how much to "add" to motion when changing direction - knowing that this "added" winding of knob will actually count for nothing in terms of mount motion.

Say your computer moved mount in +DEC and then you tell it to go to 30 arc seconds in -DEC direction. You have 7 arc seconds of backlash in DEC axis. In this case, computer will turn DEC axis for total of 37 arc seconds worth of turn. 7" of those will be used up for clearing the backlash and rest 30" will be used to actually move mount 30" in -DEC direction.

Makes sense?

Not sure how do you think of recording backlash with camera since actual backlash does not move mount at all - it is "empty" motion of mount axis knob (or rather whole worm mechanism - but I used term knob as it is easier to relate to).

As long as you are clearing backlash - you'll get the same images.

55 minutes ago, diegop said:

Old compact camera Nikon coolpix l15

https://www.digicamdb.com/specs/nikon_coolpix-l15/

Focal length (35mm equiv.):    35 - 105 mm

Ok, so this is for your reference only as it is good thing to know.

Coolpix L15 has 1.76µm pixel size.

It also has 1/2.5" sensor (it is actually not 1/2.5" sized sensor - it is very strange unit for sensor size - it has nothing to do with inch - 1" sensor having something like 16mm diagonal - not even close to 25.4mm). This is needed to calculate actual focal length of the lens attached to camera.

It says 35-105mm equivalent - so actual lens focal length is that much smaller as is 1/2.5" sensor is compared to 35mm sensor (or full frame).

https://en.wikipedia.org/wiki/Image_sensor_format

1/2.5" sensor has crop factor of about 6 - so actual focal length of lens on camera will be x6 smaller than is quoted as "35mm equivalent".

35/6 - 105/6 = 5.83 - 17.5

now we can calculate (approximate, as we don't actually know exact focal length of the lens - only approximate or "35mm equivalent") pixel scale / plate scale / sampling rate / arc second per pixel / "/px (all terms used for same thing).

formula is

pixel_scale = pixel_size(in µm) * 206.3 / focal_length(in mm)

Thus pixel scale ranges between

1.76µm * 206.3 / 5.83 - 1.76µm*206.3 / 17.5 = 62.28"/px - 20.75"/px

So you see why your camera is not good option to record back lash, even if there was feasible way to do it with images (and I'm sure there is somehow but it is probably rather complex - like shining laser from the mount on the wall, turning one whole revolution of axis knob in one side, then in other, then back in first - taking images, measuring distance to wall - measuring laser dot displacement on the wall and so on ... ) - you have too coarse sampling rate. You cannot possibly measure angles smaller than ~20" as image would move less than one pixel - and there is really no good way to measure between (actually there is - you can determine position of a star down to fraction of pixel - but again, that is outside the scope of this answer ).

1 hour ago, diegop said:

Seems the Astrometry.net alternative should be more easy, i'll try first the astrometry.net method and then with ImageJ because i really would like to learn measure it with the imageJ.

Ok, astrometry.net is rather simple.

Take two of your images, go to

https://nova.astrometry.net/upload

upload first image, hit "go" or whatever and wait for it to solve.

See this video for details:

https://www.youtube.com/watch?v=hz8poNTOtgw

Notice that you'll get center of the image on results page:

as well as pixel scale.

Once you have your set of coordinates - you can then calculate distance between them:

https://astronomy.stackexchange.com/questions/19287/angle-from-2-point-on-celestial-sphere/19292

To the first approximation - you subtract RA of first and second and DEC of first and second and do Pythagoras on those (square root of sum of squares - finding diagonal). This works for small distances - where curvature is close to 0 (good for values associated with backlash - like few to few dozen arc seconds).

Second method in ImageJ goes like this:

Open images in ImageJ and take first image. Adjust brightness and contrast until you can clearly see what is in the image:

Take two prominent stars and mark with line segment between them:

Then hit analyze / measure and look at length (result of measurement). In case you can't find length being displayed as result of measurement - check menu option Analyze / set measurements.

Start stellarium (Check out stellarium.org to download it - it is free planetarium software) - find your target, select angle measure tool (one of the plugins if I'm not mistaken) and measure distance between those two stars:

Now we have distance of about 6576 arc seconds there and 260 pixels - so our pixel scale in this example is 25.3"/px

Now hit Images / stacks / images to stack and you should get your two images being joined into single window with slider on the bottom (this is called stack in imagej - or just collection of similar images).

Next you can do Image / stack / z-project and choose max method:

This will create new image where there will be stars from both images:

Again set line marker joining two stars and measure distance:

I roughly measured 5.2px of distance between these two frames.

If we have 25.3"/px and 5.2px, then we have 25.3 * 5.2 = 131.56, or about 131 arc seconds of distance between these two frames.

 

[diegop]

Wow! Thanks a lot vlaiv, i am left speechless. I will try to understand everything and i'll write you back with doubts

Best regards