Secondary Mirror replacement - Skywatcher 300p Newt

[Captain Scarlet]

In early November 2019 I ordered, from a popular European supplier, an expensive Hubble Optics 1/10 lambda 70mm secondary mirror, to replace the OEM one on my SW300p 12” newt. I ordered it in early November to ensure its arrival in time for my Christmas visit to Ireland. Ha! It was eventually delivered in early February 2020, having I guess been made to order in the US, shipped to Germany and shipped to Ireland.

Anyway, arrive it did, and I got around to starting this little project at the start of Irish lockdown, late March 2020.

Before embarking, I had of course somehow to work out precisely how, and more importantly where, to glue the mirror-holder onto the back of the mirror. Specifically I’m talking about “the offset”, and more specifically the lateral offset across from the eyepiece: the other “up-tube” offset sorts itself out in the collimation procedure. I needed to work out where to mark 4 lines on the back of the new mirror corresponding to the two sides and two ends of the 45-degree-angled face of the secondary holder.

Obviously, the two “sides” would each be symmetrical: half the holder’s diameter away from the long centre-line of the mirror. The two “ends” though would be shifted towards one end of the long axis. I needed to work out what this shift needed to be. Purely a formula for the offset itself was not especially useful. I needed formulae for how far from each end of the mirror I needed the end-points of the holder to be, which I’ve called L1 and L2 below, so that I could mark the mirror at those points and simply (carefully) plonk it down.

These calculated distances needed to take account of where along the primary’s axis I wanted the reflection; the focal ratio of the mirror; the amount by which the secondary is oversized from the light-cone minimum, and the thickness of the adhesive layer gluing the secondary onto the holder. In particular, a typical thickness of glue makes a difference in the same order of magnitude as the total offset itself, so it’s very important to account for it. I’ve left the actual equations I used and the diagrams to the end of this post, if anyone’s interested.

Both mirrors, old and new, were nominally the same size: 70mm minor diameter, whereas the minimum for the on-axis light-cone for this scope was 66mm. Laying the two mirrors side by side the difference in quality was obvious. The blank used by SW was rather coarse and lumpy around its edge, whereas the Hubble Optics one was finer, smoother and beautifully frosted. The SW mirror itself had a straight line on one edge, presumably where it was held in the silvering process, and you can clearly see this manifesting as an extra diffraction spike on bright stars. There is no such “missed silvering” on the Hubble Optics mirror.

However, carefully measuring the various dimensions of the old mirror too, to see how well SW had placed the secondary holder, I was impressed that their mirror had been positioned spot on, including their glue-thickness, and consistent too with the oversize-factor in the offset formula. Good on them.

The SW mirror was held on to its holder with a large blob of what looked like chewing gum, giving a 2mm “glue gap”, whereas I used number-plate tape (0.7mm thick).

 

Cheers, Magnus

 

Pictures and formulae below:

Old mirror and glue-flakes

 

 

 

New mirror marked and holder ready to come together...

 

Preparatory scribblings:

 

Finished, ready to re-install to scope:

 

 

 Formulae:

L1 = (a – d/2 –t) . sqrt(2)                            L2 = (b – d/2 + t) . sqrt(2)

Where                a = s / (2.F/x +1) and b = s / (2.F/x – 1)

This makes the offset itself, (b – a)/2 , equal to s / (4.(F/x)^2 -1) … multiplied by sqrt(2) if measured along the face of the mirror.

 

 

L1 is the “short” distance from the rear end of the holder to the end of the mirror;

L2 is the “long” distance from the front end of the holder to the other end of the mirror;

“s” is the distance from primary mirror focal point back along its axis to the optical bounce point off the secondary: i.e. how much of the far end of the cone’s axis is bounced off sideways;

“F” is the primary mirror focal ratio;

“d” is the diameter of the secondary-holder;

“x” is the linear factor by which the secondary is oversized from that required perfectly to intercept the on-axis light cone of the primary (this increases the area of the fully illuminated region, but also increases the CO ratio). An “x” of less than 1 implies a secondary smaller than that necessary to “catch” all the primary’s converging light (the case with my 200p, actually!);

“t” is the thickness of the adhesive layer used to glue the holder to the mirror (makes a surprisingly significant difference).

 

Edited May 6, 2020 by Captain Magenta

[markse68]

Hi Magnus, your attention to detail and maths are admirable but shouldn’t/doesn’t the mirror mount in your scope have the adjustments necessary to get the offsets right once mounted?

[John]

3 minutes ago, markse68 said:

Hi Magnus, your attention to detail and maths are admirable but shouldn’t/doesn’t the mirror mount in your scope have the adjustments necessary to get the offsets right once mounted?

The offset on many scopes is "built in" by offsetting the position that the secondary is attached to the mounting boss. So Magnus is replicating the approach that Skywatcher and others use.

 

 

[johnturley]

Quote

 

What sort of glue did you use

John

[Captain Scarlet]

Number-plate tape (double-sided)...

 

[Captain Scarlet]

15 minutes ago, John said:

The offset on many scopes is "built in" by offsetting the position that the secondary is attached to the mounting boss. So Magnus is replicating the approach that Skywatcher and others use.

Yes just so: it keeps the spider-boss totally central, and the spider vanes and diffraction spikes perpendicular

[johnturley]

3 minutes ago, Captain Magenta said:

Number-plate tape (double-sided)...

 

 

[johnturley]

Looks similar to some UniBond 'No More Nails' doubled sided tape that I have, but would be a bit nervous about relying this to hold a secondary mirror in place.

John

[Pitch Black Skies]

On 06/05/2020 at 11:20, Captain Magenta said:

In early November 2019 I ordered, from a popular European supplier, an expensive Hubble Optics 1/10 lambda 70mm secondary mirror, to replace the OEM one on my SW300p 12” newt. I ordered it in early November to ensure its arrival in time for my Christmas visit to Ireland. Ha! It was eventually delivered in early February 2020, having I guess been made to order in the US, shipped to Germany and shipped to Ireland.

Anyway, arrive it did, and I got around to starting this little project at the start of Irish lockdown, late March 2020.

Before embarking, I had of course somehow to work out precisely how, and more importantly where, to glue the mirror-holder onto the back of the mirror. Specifically I’m talking about “the offset”, and more specifically the lateral offset across from the eyepiece: the other “up-tube” offset sorts itself out in the collimation procedure. I needed to work out where to mark 4 lines on the back of the new mirror corresponding to the two sides and two ends of the 45-degree-angled face of the secondary holder.

Obviously, the two “sides” would each be symmetrical: half the holder’s diameter away from the long centre-line of the mirror. The two “ends” though would be shifted towards one end of the long axis. I needed to work out what this shift needed to be. Purely a formula for the offset itself was not especially useful. I needed formulae for how far from each end of the mirror I needed the end-points of the holder to be, which I’ve called L1 and L2 below, so that I could mark the mirror at those points and simply (carefully) plonk it down.

These calculated distances needed to take account of where along the primary’s axis I wanted the reflection; the focal ratio of the mirror; the amount by which the secondary is oversized from the light-cone minimum, and the thickness of the adhesive layer gluing the secondary onto the holder. In particular, a typical thickness of glue makes a difference in the same order of magnitude as the total offset itself, so it’s very important to account for it. I’ve left the actual equations I used and the diagrams to the end of this post, if anyone’s interested.

Both mirrors, old and new, were nominally the same size: 70mm minor diameter, whereas the minimum for the on-axis light-cone for this scope was 66mm. Laying the two mirrors side by side the difference in quality was obvious. The blank used by SW was rather coarse and lumpy around its edge, whereas the Hubble Optics one was finer, smoother and beautifully frosted. The SW mirror itself had a straight line on one edge, presumably where it was held in the silvering process, and you can clearly see this manifesting as an extra diffraction spike on bright stars. There is no such “missed silvering” on the Hubble Optics mirror.

However, carefully measuring the various dimensions of the old mirror too, to see how well SW had placed the secondary holder, I was impressed that their mirror had been positioned spot on, including their glue-thickness, and consistent too with the oversize-factor in the offset formula. Good on them.

The SW mirror was held on to its holder with a large blob of what looked like chewing gum, giving a 2mm “glue gap”, whereas I used number-plate tape (0.7mm thick).

 

Cheers, Magnus

 

Pictures and formulae below:

Old mirror and glue-flakes

 

 

 

New mirror marked and holder ready to come together...

 

Preparatory scribblings:

 

Finished, ready to re-install to scope:

 

 

 Formulae:

L1 = (a – d/2 –t) . sqrt(2)                            L2 = (b – d/2 + t) . sqrt(2)

Where                a = s / (2.F/x +1) and b = s / (2.F/x – 1)

This makes the offset itself, (b – a)/2 , equal to s / (4.(F/x)^2 -1) … multiplied by sqrt(2) if measured along the face of the mirror.

 

 

L1 is the “short” distance from the rear end of the holder to the end of the mirror;

L2 is the “long” distance from the front end of the holder to the other end of the mirror;

“s” is the distance from primary mirror focal point back along its axis to the optical bounce point off the secondary: i.e. how much of the far end of the cone’s axis is bounced off sideways;

“F” is the primary mirror focal ratio;

“d” is the diameter of the secondary-holder;

“x” is the linear factor by which the secondary is oversized from that required perfectly to intercept the on-axis light cone of the primary (this increases the area of the fully illuminated region, but also increases the CO ratio). An “x” of less than 1 implies a secondary smaller than that necessary to “catch” all the primary’s converging light (the case with my 200p, actually!);

“t” is the thickness of the adhesive layer used to glue the holder to the mirror (makes a surprisingly significant difference).

 

I'm stuck on the very first part of figuring out what "s" is for "a". How do you measure"s"? 😳

I wonder if you would be kind enough to demonstrate the whole sum from start to finish with the measurements included?

It's extremely well thought out and put together, personally I just struggle with maths.

I've bought the same double sided tape you have, and my secondary is 70mm too.

I could however just take a picture of your marked secondary. Enlarge the pic so the width is 70mm, and then measure the lines on the pic 😉 #thelazyapproach

Cheers,

Alan

[Captain Scarlet]

Hi Alan,

Imagine there is no secondary mirror, and imagine a line from the centre of the primary mirror to its focal point. Obviously the length of that line is the focal length of the mirror. Now imagine another line, along the centre-line of the focuser/eyepiece tube. In ideal circumstances, these two lines would intersect. The point of intersection is the point at which the line from the primary-mirror-centre would "bounce" off a perfectly-placed secondary along the eyepiece tube.

"s" is the distance from that "point of bounce" to the focal point of the primary mirror. It's also the (sideways) distance from the centre-line of the OTA to the focal point of the eyepiece when focussed.

You can measure/deduce it in a couple of ways.

- Assume the focal length of the primary is correct as stated by the manufacturer. Call this L.

- Measure the distance, on the outside of the main OTA, from the back of the external OTA tube to the mid-point of the focuser assembly. Call this A. (The mid point of the focuser assembly should be the same distance along the OTA as the mid-point of the actual eyepiece tube).

- Measure or deduce the distance from the back of the external OTA tube to the face of the primary mirror, by measuring the depth of the back of the mirror from the back of the OTA tube, and adjusting for the thickness of the mirror which you should know or be able to look up. Call this depth+thickness B

- the distance "s" is then L - A + B.

Worked example using random but plausible values for a 12" f/4.9:

focal length = 1500mm i.e. L = 1500

dist from focuser centre to back of OTA is 1241mm i.e. A = 1241

depth of REAR of primary mirror from back of OTA is 20mm

thickness of mirror is 36mm i.e. B = 20+36 = 56

Thus "s" = L - A + B = 1500 - 1241 + 56 = 315mm .

This pic might help too...

Edited September 14, 2021 by Captain Magenta
making numbers more plausible

[Captain Scarlet]

3 hours ago, Pitch Black Skies said:

... I wonder if you would be kind enough to demonstrate the whole sum from start to finish with the measurements included? ...

I've run out of time today, but yes I'll gladly do that.

BTW whereabouts in Ireland are you? I'm between Baltimore and Skibbereen.

[Pitch Black Skies]

Awesome, thanks so much for that Magnus. You would make a great teacher if not already, seriously.

Oh you're in Ireland?!

I'm by the Copper Coast, Co. Waterford. 

[Captain Scarlet]

... OK I can see where a difficulty lies in trying to apply those formulae. Those formulae include a term, "x", which is the ratio of the minor diamaters of the mirror you actually have, versus that of the mirror which just about and perfectly coincides with your primary mirror.

In fact the "x" is an approximate adjustment, only valid for a small difference between your actual mirror and the minimum theorectical secondary. If your actual secondary is significantly bigger than the minimum, the formulae above are wrong.

The correct formulae to determine L1 and L2 are:

Formulae:

L1 = (A – d/2 –t) . sqrt(2)

L2 = (B – d/2 + t) . sqrt(2)

Where

A = 0.5 . (s + M - sqrt(s^2 + M^2))

B = M - A

The offset itself is (B – A)/2 … multiplied by sqrt(2) if measured along the face of the mirror.

 

L1 is the “short” distance from the rear end of the holder to the end of the mirror;

L2 is the “long” distance from the front end of the holder to the other end of the mirror;

"M" is the minor diameter of your actual mirror; you either know or measure this

“s” is the distance from primary mirror focal point back along its axis to the optical bounce point off the secondary: i.e. how much of the far end of the cone’s axis is bounced off sideways; you measure this.

“d” is the diameter of the secondary-holder;

“t” is the thickness of the adhesive layer used to glue the holder to the mirror (makes a surprisingly significant difference).

Edited September 14, 2021 by Captain Magenta

[Captain Scarlet]

... worked example still to come ... I've attached an Excel spreadsheet which allows you to calculate it.

I'll do a worked example in text format too

Cheers, Magnus

SecondaryMirrorCalculator_SGL.xlsx

Edited September 14, 2021 by Captain Magenta

[Captain Scarlet]

So, finally, a worked-through example. I’ll use values from my own customized Newtonian

“s”  = 309mm optical bounce point to focus
“d” = 32mm diameter of holder for esondary mirror
“M” = 70mm minor diameter of secondary mirror
“t” = 0.7mm thickness of adhesive tape

First we need to compute “A” and “B” as per the preliminary formula
A = 0.5 * (s + M - sqrt(s^2 + M^2))
A = 0.5 * (309 + 70 - sqrt(309*309 + 70*70))
A = 0.5 * (309 + 70 - sqrt(100,381))
A = 0.5 * (309 + 70 - 316.830) = 0.5 * 62.170
thus A = 31.085mm

Now we can compute “B” as per our other preliminary formula
B = M – A
B = 70 – 31.085
thus B = 38.915mm

Now we have enough to achieve our goal of determining L1 and L2 so we know exactly where to mark the back of the mirror for placement:

L1 = (A – d/2 –t) . sqrt(2)
L1 = (31.085 – 32/2 – 0.7)*1.414
L1 = (31.085 – 16 – 0.7)*1.414
thus L1 = 20.34mm

similarly
L2 = (B – d/2 + t) . sqrt(2)
L2 = (38.915 – 16 + 0.7)*1.414
thus L2 = 33.39mm

according to the labels in the following diagram:

I hope that's been helpful, and that you get your mirror attached safely!

Cheers, Magnus

 

Edited September 15, 2021 by Captain Magenta
Added pic

[kbrown]

Hmm... I'm by no means trying to invalidate what you've done here but I'm a little confused. I'm about to replace my secondary too on my SW 250p. I used this to calculate the offsets: http://www.deepskywatch.com/Articles/replace-offset-collimate-secondary.html

I'm getting quite different results from your spread sheet vs the method in the above article. I'm getting these values using the above article:

• L1 = 29.89mm
• L2 = 41.11mm

With your spreadsheet I get:

• L1 = 21.28mm
• L2 = 35.28mm

Also your L1 + L2 + Holder Diameter does not add up to the major axis of my secondary => 21.28mm + 35.28mm + 35mm = 91.56mm while the actual major axis of my secondary is 106mm. I'm attaching a spreadsheet I made based on the above article.

 

EDIT: Attachment removed as it had errors in it. See below...

 

Cheers,

Kari

 

Edited September 16, 2021 by kbrown

[Captain Scarlet]

1 hour ago, kbrown said:

... Also your L1 + L2 + Holder Diameter does not add up to the major axis of my secondary => 21.28mm + 35.28mm + 35mm = 91.56mm while the actual major axis of my secondary is 106mm. I'm attaching a spreadsheet I made based on the above article.

 

Cheers,

Kari

secondary_mirror_offset.ods 89.72 kB · 0 downloads

Re adding up the components you need to multiply the holder diameter by sqrt 2 to make up the major axis length, because the holder is at 45 degs to the back of the mirror

i.e. my method's values: 21.28mm + 35.28mm + 35x1.414mm = 106.05mm

but that website's quoted values for L1 and L2, when added to the oblique length of the secondary, do not add up to 106

i.e. 29.89 + 41.11 + 35x1.414 = 120.49mm

Perhaps the website is not returning L1 and L2 as I have defined them, but some other dimensions? I can't check as I can't open your spreadsheet, it's a format my computer doesn't recognize, so I don't know what input values you've used: i.e. distance of mirror-interception from focus etc.

Cheers, Magnus

Edited September 16, 2021 by Captain Magenta

[kbrown]

31 minutes ago, Captain Magenta said:

Re the adding up the components you need to multiply the holder diameter by sqrt 2 to make up the major axis length

Ah. This is because it's cut in 45 degree angle and the cross-section is an ellipse? Still don't understand why I get so different results?

 

EDIT: I think I understand now... I had the holder major axis the same as the holder minor axis in my spreadsheet... If I multiply that with sqrt 2 I get to the same ball park! New version attached to this post.

secondary_mirror_offset.ods

Edited September 16, 2021 by kbrown

[kbrown]

2 hours ago, Captain Magenta said:

Perhaps the website is not returning L1 and L2 as I have defined them, but some other dimensions? I can't check as I can't open your spreadsheet, it's a format my computer doesn't recognize, so I don't know what input values you've used: i.e. distance of mirror-interception from focus etc.

Cheers, Magnus

No, it was my error. I was using 35mm for both minor and major axis of the holder diameter. After changing the major axis to SQRT(2) * MinorAxis I get to the same ball bark as you with your values and my values add up too.

• L1 = 22.64mm
• L2 = 33.86mm
• Holder Major Axis = SQRT(2) * 35mm = 49.5mm
• L1 + L2 + MajorAxis = 106mm

I tried to save my spreadsheet as Excel file from LibreOffice Calc which I use. Attached below. Hope it works.

secondary_mirror_offset.xlsx

Edited September 16, 2021 by kbrown

[kbrown]

Just attached my new secondary. Turns out the holder was actually 32mm (not 35mm) on my SW 250P so I had to re-calculate the offset again. Drew an printed a template in LibreCAD, then cut and taped it on the back of the mirror with a hole for the holder.

 

Was a bit tricky to get the holder in the right place as I've added a heater and temperature sensor around the holder. Didn't want to take those off as it would have most certainly damaged them. Hope it's in a good enough position.

 

All done... For now..