What are the physics of an optical snoot & gobo?

TheAthenA714 wrote:

Hey everyone!

So since I've heard about optical snoots and gobos I've been wanting to try and build one on my own. I have an old 55mm/f1.4 M42 manual lens, a few adapters and extensions tubes and a basic Godox non-optical snoot with a bowens mount for my light.

From my basic testing I think I understand the following :

• I need to place the gobo in between the light and the lens
• The smaller the distance between the gobo and the light, the bigger the projected image will be
• The closer the lens is to the light, the further away the projected image will be focused
• I can fine-tuning the focusing with the focusing ring on the lens, but it only allows very minor adjustements. So if I want to move the focus plane a few inches I need to actually move the lens closer/further away
• I don't know if changing the focal length (swaping the 55mm for an 85 or a 35mm) would affect the result

So assuming I'm correct in my understanding, I'm now trying to build a DIY optical snoot that would allow me to place a gobo at the end of my godox snoot (or maybe even inside the snoot itself to bring the gobo closer to the light), and then have a tube of easily adjustable length between the snoot and the lens.

The big question is: how long should that tube be? And that's where I'd like to know the physics so I can calculate some rough estimation of where the focal plane would be based on that length. Basically what I want to know is:

• If I place the gobo at X cm from the light and the lens at Y cm from the light, where will the projected image be focused?

Is there a formula to calculate that? Any other advices/resources to explore that concept?

The projected image will be focussed at a distance that depends on the lens and on the distance between the gobo and the lens.  The light needs to be sufficiently far from the gobo so that the lens is not just projecting an image of the light itself.

Imagine that the gobo is the sensor of your camera and the lens on the camera is projecting light from the gobo. For the image of the gobo to be projected at infinity, the lens should be focussed at infinity and the distance between the gobo and the lens should be exactly the same as the distance between the camera sensor and the lens.

There are various formulae that describe how to calculate the image distance and it can get very complicated if you want to do it to high accuracy.  However, provided you are happy with getting a good estimate of the distance, an easy formula to use is this one:

image distance from lens = f^2 / distance of the gobo from the infinity focus position, where f is the focal length of the lens.

So, if your lens is 55mm (i.e 5.5cm), then f^2 = 5.5 x 5.5 = 30.

To get the image distance in cm, you need to divide 30 by the distance in cm that you move the gobo from its infinity focus position.

You can find the infinity focus position for the gobo by trial and error using the far wall of a very large room (which will be near enough to infinity) to focus the image on.

So, moving the gobo just 1 cm from its infinity focus position will mean the image now focuses only 30 cm from the lens (approximately). Make sure that you don't change the focus scale on the lens itself (which will mess up these calculations).

Alternatively, it may be easier to leave the gobo fixed and focus use the focus adjustment on the lens itself.

Thank you very much, I'm gonna experiment with all that and do some calculations.

Quick follow up questions:

For the image of the gobo to be projected at infinity, the lens should be focussed at infinity and the distance between the gobo and the lens should be exactly the same as the distance between the camera sensor and the lens.

If I'm understanding this correctly I should look up the flange distance of the specific lens mount I'm using and use that as the space between the lens and the gobo right?

The 55mm lens I'm using now is an M42 lens, but that means if I were to switch it to an EF lens or something else, I would have to change the spacing right?

• You can find the infinity focus position for the gobo by trial and error using the far wall of a very large room (which will be near enough to infinity) to focus the image on.

Sounds simple enough to do, but just out of curiosity is there a formula to calculate that? What would be the variables that impact that value?

TheAthenA714 wrote:

Thank you very much, I'm gonna experiment with all that and do some calculations.

Quick follow up questions:

For the image of the gobo to be projected at infinity, the lens should be focussed at infinity and the distance between the gobo and the lens should be exactly the same as the distance between the camera sensor and the lens.

If I'm understanding this correctly I should look up the flange distance of the specific lens mount I'm using and use that as the space between the lens and the gobo right?

Yes.

The 55mm lens I'm using now is an M42 lens, but that means if I were to switch it to an EF lens or something else, I would have to change the spacing right?

Yes.

• You can find the infinity focus position for the gobo by trial and error using the far wall of a very large room (which will be near enough to infinity) to focus the image on.

Sounds simple enough to do, but just out of curiosity is there a formula to calculate that? What would be the variables that impact that value?

There are various formula according to whether you measure the distance from the principal points or the pupils of the lens, but the problem with these is in determining exactly where the principal points of the lens are, or where the pupils are.  These positions can be determined, but it is not trivial to do.

Have a look at Bill Claff's Optics Primer if you want to go into more detail.

The simplest thing is to find the sensor to flange distance for your lens, as you suggest, and use that to determine the position of the infinity focus (usually just called the focal point of the lens).

Have a look at Bill Claff's Optics Primer if you want to go into more detail.

Damn, I was about to ask if you had any books or resources to recommend to dig into more details about all that, but you beat me to the punch

The simplest thing is to find the sensor to flange distance for your lens, as you suggest, and use that to determine the position of the infinity focus (usually just called the focal point of the lens).

So the M42 flange distance is about 45mm, and it just so happens that I have a M42->NEX adapter that is about 26mm, and a 16mm extension tube. Both together get me pretty close and allows me to put a gobo right at the back of the extension tube.

However I can't focus to infinity with that setup because I'm putting all of that at the end of my snoot, which is not the proper size. So now all I need to do is find some cardboard tubes and try to fashion a snoot myself.

One last question: if I get infinity focus right, am I correct in assuming that the focus marking on the lens would be accurate as well? I.e if I turn the focusing ring to 2 meters, it should focus the projected image to 2 meters right?

Thank you very much for your help!

TheAthenA714 wrote:

Have a look at Bill Claff's Optics Primer if you want to go into more detail.

Damn, I was about to ask if you had any books or resources to recommend to dig into more details about all that, but you beat me to the punch

The simplest thing is to find the sensor to flange distance for your lens, as you suggest, and use that to determine the position of the infinity focus (usually just called the focal point of the lens).

So the M42 flange distance is about 45mm, and it just so happens that I have a M42->NEX adapter that is about 26mm, and a 16mm extension tube. Both together get me pretty close and allows me to put a gobo right at the back of the extension tube.

However I can't focus to infinity with that setup because I'm putting all of that at the end of my snoot, which is not the proper size. So now all I need to do is find some cardboard tubes and try to fashion a snoot myself.

One last question: if I get infinity focus right, am I correct in assuming that the focus marking on the lens would be accurate as well? I.e if I turn the focusing ring to 2 meters, it should focus the projected image to 2 meters right?

Yes, that's correct.

Thank you very much for your help!

You're welcome.