Determination of Focal Length from Image...

[Captain Scarlet]

Hi

You'll find below an annotated image I took with one of my scopes recently. The image is a full-frame off a Canon EOS 6D (mk1). I need to know as exactly as possible the focal length of the scope, and this image can provide that. Although a .jpeg, I believe it has all its pixels.

Can someone here kindly work out, independently of me, what FL the image was taken with please? I have already made the calculation myself but I'd like it confirmed.

Cheers, Magnus

Edited August 18, 2020 by Captain Magenta

[lenscap]

Measuring the seperation of TYC 3122-2059 and -0032 on my screen and assuming a sensor width of 35.8 mm gives a seperation of 26.85mm on the sensor.

From Skysafari those stars are 757" apart in Dec & 158 seconds ( = 2370 arc sec) in RA, which gives an angular seperation of 2488 arc sec.

F = 26.85 x 3600 x 57.3 / 2488 = 2226 mm

Probably completely wrong though. 😀

[Captain Scarlet]

42 minutes ago, lenscap said:

Measuring the seperation of TYC 3122-2059 and -0032 on my screen and assuming a sensor width of 35.8 mm gives a seperation of 26.85mm on the sensor.

From Skysafari those stars are 757" apart in Dec & 158 seconds ( = 2370 arc sec) in RA, which gives an angular seperation of 2488 arc sec.

F = 26.85 x 3600 x 57.3 / 2488 = 2226 mm

Probably completely wrong though. 😀

I think you have the angular separation a bit wrong ... the SIMBAD database shows it as 1976.64 arcsecs (J2000), using which would bring your calc to 2802mm

[Captain Scarlet]

OK seeing as nobody else is going to take the bait, my own calc is that

Separation on the sensor is 4081 pixels, between the two stars that lenscap chose, equating to 26.72mm.

The angular separation between them now (as opposed to J2000) is 1976.90 arcseconds taking account of their proper motions between 2000 and now

Leading to a focal length of 2788mm (+- 24mm) for the scope used to take the photo. I've tried all the combinations of stars and all yield the same result.

Interesting as the scope was my Skymax 180, nominal FL 2700mm, and the back-focus used to take the pic was somewhat less than that taken up by the standard visual back and diagonal, which should have meant a FL less than 2700mm for the photo.

I'm going to re-check this result as I forgot to photograph my set-up at the time I took it (schoolboy error), by taking the pic again before I update my EFLs upwards by 200mm on my big post on EFL of the Skymax 180.

M

[JamesF]

Won't astrometry.net tell you the focal length if you feed it the original image?

James

[vlaiv]

8 minutes ago, Captain Magenta said:

Interesting as the scope was my Skymax 180, nominal FL 2700mm, and the back-focus used to take the pic was somewhat less than that taken up by the standard visual back and diagonal, which should have meant a FL less than 2700mm for the photo.

I just have one question - are you sure that creating larger separation between mirrors is going to shorten focal length?

In fact - I'm even not sure if focusing closer is done by making separation between mirrors larger (it's just a hunch that I have).

[Captain Scarlet]

41 minutes ago, JamesF said:

Won't astrometry.net tell you the focal length if you feed it the original image?

James

I'd be surprised if there weren't apps that could do that, I've just not used any before. But it's such a simple exercise and calculation if you have something like photoshop and access to very precise star-coordinates that I did it myself.

[Adam J]

46 minutes ago, vlaiv said:

I just have one question - are you sure that creating larger separation between mirrors is going to shorten focal length?

In fact - I'm even not sure if focusing closer is done by making separation between mirrors larger (it's just a hunch that I have).

I agree I would think that it would not change the focal length just move the location of focus.

Adam

[JamesF]

3 minutes ago, Adam J said:

I agree I would think that it would not change the focal length just move the location of focus.

Moving the primary to focus in a Mak or SCT does definitely change the focal length.

James

[Captain Scarlet]

56 minutes ago, vlaiv said:

I just have one question - are you sure that creating larger separation between mirrors is going to shorten focal length?

In fact - I'm even not sure if focusing closer is done by making separation between mirrors larger (it's just a hunch that I have).

I've basically used two equations: one the standard 2-mirror catadioptric equation, and the other is straightforwardly derived by drawing out the geometry of what's going on.

EFL = -F1.F2/(F1 - F2 - x) is the 2-mirror equation (for 2 convex mirrors convex secondary and concave primary in mak config) where x is the mirror separation

B = -F2.(F1 - x)/(F1 - F2 - x) where B is the distance from secondary mirror to backfocus

The first immediately shows the inverse relationship between x and focal length

Edited August 20, 2020 by Captain Magenta

[vlaiv]

1 minute ago, Adam J said:

I agree I would think that it would not change the focal length just move the location of focus.

Adam

I think that it actually changes the focal length - I just don't know which way.

Here is two lens formula:

d is separation between lenses.

In mak, secondary is negative but is oriented "backwards" - so I have no idea what are the signs for focal lengths (in regular lens - positive lens is + and negative lens is -, hence the names).

[vlaiv]

3 minutes ago, Captain Magenta said:

The first immediately shows the inverse relationship between x and focal length

It's sort of not obvious to me, so I'll need a little help.

if term is (F1 - F2 - x) getting bigger in absolute value as x increases than EFL decreases, but if that term is getting smaller in absolute value as x increases then EFL increases as well.

If F1-F2 is negative then absolute value will grow with growing x, and if F1-F2 is positive then it will get smaller with growing x.

I would say that sign of F1-F2 determines what happens (if I'm not mistaken).

[Captain Scarlet]

4 minutes ago, vlaiv said:

It's sort of not obvious to me, so I'll need a little help.

Sorry. attached the diagram I drew to try to understand it:

[Adam J]

Yes it must change thinking about it in more depth.

[vlaiv]

Ok, so we have f1 to be negative, f2 to be negative and s to be negative.

f1 * f2 is going to be positive, so bottom expression also needs to be positive. Since there is minus sign in front of separation, separation contribution is positive - larger s means larger bottom expression - means less focal length.

[Captain Scarlet]

The whole point of this exercise for me was to try to establish as accurately as possible the true F1 and F2 of my two mirrors given the two equations

EFL = -F1.F2/(F1 - F2 - x)

B = -F2.(F1 - x)/(F1 - F2 - x)

I can rearrange them to be

F1 = x/(1 - B/EFL)    and     F2 = B.x/(EFL - B -x)

I can physically measure x and B by taking the scope apart and applying a micrometer, which I have done (my other thread).

The last bit was to accurately and independently measure the EFL for a given configuration, which was the whole point of the annotated star photo.

I arrived at values for F1 and F2 with error estimates for each of 2.5mm and 1mm respectively (F1 = 463.28mm and F2 = 115.71mm as it happens).

I now want to do it all again as I'm only 99% certain of the adapters and hence BF I was using, and also do it for 2 or 3 different amounts of back-focus

 

[inFINNity Deck]

According to Astrometry.net:

Size:    44.2 x 29.4 arcmin
Radius:    0.442 deg
Pixel scale:    0.484 arcsec/pixel

In fact the pixel size is (44.2 x 60)/5472 = 0.484649 "/px

The sensor has a pixel size of 6.55micron, so the focal length would then be (6.55 x 206.3) / 0.484649 = 2788.1mm

Of course I could be wrong...

Nicolàs

 

[vlaiv]

9 minutes ago, Captain Magenta said:

I arrived at values for F1 and F2 with error estimates for each of 2.5mm and 1mm respectively (F1 = 463.28mm and F2 = 115.71mm as it happens).

Shouldn't focal length of secondary mirror be longer?

[wornish]

Can I ask why you need the effective focal length? 

What will you use the information for?

 

[vlaiv]

6 minutes ago, wornish said:

Can I ask why you need the effective focal length? 

What will you use the information for?

 

a bit of reverse engineering - finding out focal lengths of mirrors and their separation.

Enables you to do calculations of telescope performance in various software and maybe design focal reducer for specific purpose (hint, hint, EEVA - large reduction, corrected field for small sensors?).

[Captain Scarlet]

11 minutes ago, vlaiv said:

Shouldn't focal length of secondary mirror be longer?

Those are the numbers that come out from the equations and measurements, and they combine to produce the following table, which accords with reality as far as how many turns of the knob gets me to focus:

[Captain Scarlet]

9 minutes ago, wornish said:

Can I ask why you need the effective focal length? 

What will you use the information for?

so I can produce a table like this:

[Captain Scarlet]

... however I want to now photograph an area of sky at 3 different amounts of back-focus just to check the numbers accord with reality.

[Captain Scarlet]

39 minutes ago, inFINNity Deck said:

According to Astrometry.net:

Size:    44.2 x 29.4 arcmin
Radius:    0.442 deg
Pixel scale:    0.484 arcsec/pixel

In fact the pixel size is (44.2 x 60)/5472 = 0.484649 "/px

The sensor has a pixel size of 6.55micron, so the focal length would then be (6.55 x 206.3) / 0.484649 = 2788.1mm

Of course I could be wrong...

Nicolàs

Bang on my number, that's a relief!

[inFINNity Deck]

I was surprised Astronomy.net managed to solve the original image with all that annotation and hand-drawn circles! 🙂

Nicolàs