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# Help Needed With mRad Calculations....

#### Accutronitis

##### Banned
I just got done measuring all the beam sizes focused to infinity at zero and out to 175 feet and here is what I got.....

Focused to infinity at zero feet it's 12.5mm fast axis 10mm slow axis

Focused to infinity at 175 feet the fast axis was 49mm and the slow axis was 19mm

Sooooo the....

Slow Axis mRad Is 0.1874765632328795 focused to infinity

Fast axis mRad Is 0.6842893570104003 focused to infinity
And from what many people have told me in the past numbers that low are unbelievable, Can someone please tell me what I'm doing wrong ???

##### Well-known member
It seems to me the laser has negative divergence (might not be evident). Check it at various lower distances if the dot is bigger with distance during all beam path or it is getting smaller (sign of negative divergence) with distance in some area. It might be hard to notice unless you go through the beam. My WL Inferno has negative divergence for example, I discovered it when I was testing burning abilities and at larger distance it burned much better than close to aperture, closer look and measurements of the beam than confirmed my hypothesis.

Edit: Here for example, how to measure it - http://vlab.amrita.edu/?sub=1&brch=189&sim=342&cnt=1

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#### Accutronitis

##### Banned
I walked the entire length of the beam and loked at it very carefully and it just very slowly get bigger from the laser on out........

The divergence of a laser beam can be calculated if the beam diameter d1 and d2 at two separate distances are known. Let z1and z2 are the distances along the laser axis, from the end of the laser to points “1” and “2”.

Usually, divergence angle is taken as the full angle of opening of the beam. Then, Half of the divergence angle can be calculated as
where w1 and w2 are the radii of the beam at z1 and z2.

Like all electromagnetic beams, lasers are subject to divergence, which is measured in milliradians (mrad) or degrees. For many applications, a lower-divergence beam is preferable.
I don't understand what this means ?

Usually, divergence angle is taken as the full angle of opening of the beam
Can someone explain what the full angle of opening of the beam is ?

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#### diachi

##### Well-known member
I walked the entire length of the beam and loked at it very carefully and it just very slowly get bigger from the laser on out........

I don't understand what this means ?

Can someone explain what the full angle of opening of the beam is ?
It's just the full angle divergence, instead of the half angle divergence...?

Imagine splitting the beam in half right down the middle, then measuring the divergence of one half, that'd be the half angle divergence. The full angle is both halves added together.

You'd get the half angle by measuring the radius at different distances and the full angle my measuring the diameter.

#### steve001

##### Well-known member
Forget all that technical stuff.
Ok. Now assuming 3 things and those 3 things are you adjusted the beam until the spot size at a distance of 175 feet was as small possible or if you prefer focused to infinity (I like infinite conjugate). And you measured the beam diameter at various points along the length out to where it terminates and the results where X and X. And you calculated correctly. Then that's the correct result.

#### Accutronitis

##### Banned
Forget all that technical stuff.
Ok. Now assuming 3 things and those 3 things are you adjusted the beam until the spot size at a distance of 175 feet was as small possible or if you prefer focused to infinity (I like infinite conjugate). And you measured the beam diameter at various points along the length out to where it terminates and the results where X and X. And you calculated correctly. Then that's the correct result.
Alaskan suggested I should be focusing to infinity so that's what I did, and then I sat it on the ground pointing at a wall at the end of my cul-de-sac which is 175 feet away from the front of my house, then I used dial calipers and measured the spot size on the wall which was 49mm on the fast axis and 19mm on the slow axis, Then I measured the spot size on the output lens of the beam expander which was 12.5 on the fast axis and 10mm on the slow axis.

After that I went to pseudonomen137's mRad Calculator for laser divergence website

pseudonomen137's JScript mRad Calculator

and I put in the numbers I just got and I got.......

Slow Axis mRad Is 0.1874765632328795 focused to infinity.

Fast axis mRad Is 0.6842893570104003 focused to infinity.

I can't see what I'm doing wrong ???

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#### diachi

##### Well-known member
Alaskan suggested I should be focusing to infinity so that's what I did, and then I sat it on the ground pointing at a wall at the end of my cul-de-sac which is 175 feet away from the front of my house, then I used dial calipers and measured the spot size on the wall which was 49mm on the fast axis and 19mm on the slow axis, Then I measured the spot size on the output lens of the beam expander which was 12.5 on the fast axis and 10mm on the slow axis.

After that I went to pseudonomen137's mRad Calculator for laser divergence website

pseudonomen137's JScript mRad Calculator

and I put in the numbers I just got and I got.......

Slow Axis mRad Is 0.1874765632328795 focused to infinity.

Fast axis mRad Is 0.6842893570104003 focused to infinity.

I can't see what I'm doing wrong ???

So you have fast axis correction and a beam expander on there...? If so - how much expansion is the BE providing?

##### Well-known member
A NUBM44 Laser diode using a 6 mm diameter "G2" collimating lens has under 12 mRad. From that it's easy to figure out what the divergence would be by doubling the beam diameter to get half the divergence. For example, if the beam had a divergence of 12 mRad with a 4 mm wide beam and the beam were expanded to 8 mm, the divergence would be about half or about 6 mRad, double the beam diameter again to 16 mm and about 3 mRad. At a beam diameter of 32 mm, or over an inch, about 1.5 mRad, and so on. These are very rough examples, I don't know the diameter of this diode when collimated with a G2 or similar 6 mm diameter lens at its FL.

#### Accutronitis

##### Banned
So you have fast axis correction and a beam expander on there...? If so - how much expansion is the BE providing?
I don't know as I'm using a input lens out of a camera lens and I'm using a jetlasers output lens from one of their 10X beam expanders.....

A NUBM44 Laser diode using a 6 mm diameter "G2" collimating lens has under 12 mRad. From that it's easy to figure out what the divergence would be by doubling the beam diameter to get half the divergence. For example, if the beam had a divergence of 12 mRad with a 4 mm wide beam and the beam were expanded to 8 mm, the divergence would be about half or about 6 mRad, double the beam diameter again to 16 mm and about 3 mRad. At a beam diameter of 32 mm, or over an inch, about 1.5 mRad, and so on. These are very rough examples, I don't know the diameter of this diode when collimated with a G2 or similar 6 mm diameter lens at its FL.
I posted all the numbers I got and how I got them ???

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#### diachi

##### Well-known member
I don't know as I'm using a input lens out of a camera lens and I'm using a jetlasers output lens from one of their 10X beam expanders.....

I posted all the numbers I got and how I got them ???

What's the diameters before and after the BE? Can easily calculate expansion factor from that. Depending on the level of expansion your numbers could well be correct.

##### Well-known member
It's just the full angle divergence, instead of the half angle divergence...?

Imagine splitting the beam in half right down the middle, then measuring the divergence of one half, that'd be the half angle divergence. The full angle is both halves added together.

You'd get the half angle by measuring the radius at different distances and the full angle my measuring the diameter.

Exactly. Now in case of positive divergence just forget the pic above and do your own slightly different: You can use geometry with goniometry and triangles found there to get formula as reasonable estimate. Just draw beam as paralel lines (distance between them is measurment of diameter close output aperture d1), draw lines of spreading beam to diameter far (d2 at distance l between place d1 and d2). Than you will see half angle triangle. Using tangens for angle found between paralel lines as tan alpha = ((d2-d1)/2)/l. The angle alpha you got is half angle - so multiply 2 is full angle. In tangens function there are diameters, to get right angle triangle you need to get radii difference - that's where 2 comes from. You can get angle in degrees or radians (divide by 1000 to get mrad). Hopefully I did not make mistake (just from head in pub :beer.

#### Accutronitis

##### Banned
What's the diameters before and after the BE? Can easily calculate expansion factor from that. Depending on the level of expansion your numbers could well be correct.
The beam before the beam expander size I don't know because I didn't think that needed measuring, But I do know the diameter after the BE......

Exactly. Now in case of positive divergence just forget the pic above and do your own slightly different: You can use geometry with goniometry and triangles found there to get formula as reasonable estimate. Just draw beam as paralel lines (distance between them is measurment of diameter close output aperture d1), draw lines of spreading beam to diameter far (d2 at distance l between place d1 and d2). Than you will see half angle triangle. Using tangens for angle found between paralel lines as tan alpha = ((d2-d1)/2)/l. The angle alpha you got is half angle - so multiply 2 is full angle. In tangens function there are diameters, to get right angle triangle you need to get radii difference - that's where 2 comes from. You can get angle in degrees or radians (divide by 1000 to get mrad). Hopefully I did not make mistake (just from head in pub :beer.
Say what, who, where ??? lol

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##### Well-known member
I believe RedCowBoy did a divergence measurement using a 6 mm diameter G2 type of lens, maybe he will chime in with all his figures and we can extrapolate the expected divergence at a given beam diameter.

#### steve001

##### Well-known member
The beam before the beam expander size I don't know because I didn't think that needed measuring, But I do know the diameter after the BE......

Say what, who, where ??? lol
You only need to know that if you want to know the beam expander power. If not don't concern yourself.

You said your are using a lens from a JL expander. That implies you took one apart. I have one too. How did you ?

#### steve001

##### Well-known member
I believe RedCowBoy did a divergence measurement using a 6 mm diameter G2 type of lens, maybe he will chime in with all his figures and we can extrapolate the expected divergence at a given beam diameter.
For any beam expander.
If you know the focal lengths of the lenses then divide the longer focal length by the shorter focal length will give the expander power.

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#### diachi

##### Well-known member
The beam before the beam expander size I don't know because I didn't think that needed measuring, But I do know the diameter after the BE......

Say what, who, where ??? lol
It doesn't need measuring for divergence calculations, but it's good to know anyway. If it's a very large expansion that'd explain your rather low divergence.