What formula is used to create the lens focus scale?

Started Aug 31, 2010 | Discussions
john barlow Regular Member • Posts: 229
What formula is used to create the lens focus scale?

The distance focus scale on a lens must use some formula, can you point me to a resource or expalin here how to calculate the scale?

thanks

xrdbear Veteran Member • Posts: 3,949
Re: What formula is used to create the lens focus scale?

There must be more to this. Why would you need to know? The marking positions may just be derived empirically.
--
Brian
Fine Art Print sales of the Isle of Skye at:
http://www.eyeofskye.co.uk/

michaeladawson Forum Pro • Posts: 14,141
What scale are you talking about?

What distance focus scale are talking about? Are you talking about depth of field? Are you simply talking about the distance markings on the lens barrel?

If you mean DOF there are plenty of places on the web that you can find this information. Google should find you a formula pretty quickly.

I'm not sure if there is any formula for the distance scale printed on the lens barrel. Seems to me this would be based on not only the lens formula but also entirely dependent on the mechanical gearing that has been built into the lens. This gearing could even change the scale at different ends of the focus travel.

Do I misunderstand the question?

john barlow wrote:

The distance focus scale on a lens must use some formula, can you point me to a resource or expalin here how to calculate the scale?

thanks

-- hide signature --

Mike Dawson

 michaeladawson's gear list:michaeladawson's gear list
Nikon D810 Nikon D7200 Nikon D5 Fujifilm X-T2 Fujifilm X-H1 +30 more
tellurium New Member • Posts: 10
Re: What formula is used to create the lens focus scale?

With the new AF-S lenses, it appears to be a random number generator...

OP john barlow Regular Member • Posts: 229
Re: What formula is used to create the lens focus scale?

Just for clarification :

I am referring to the relationship between the rotatational movement of the focus ring and the focal distance.

The actual numbers will vary from lens to lens and from manufacturer to manufacturer , but it will be based on an algebraic formula.

for example Q = a*s/(s+b); where Q is rotation angle of the focus ring and s the focal distance (relative to MFD) and a, b are lens derived constants.

I tried Google but have obviously not tuned into the correct search word parameters

Robin Casady Forum Pro • Posts: 12,898
Re: What formula is used to create the lens focus scale?

I believe that would depend on the pitch of the threads used for the focus ring, and how much the lens element needs to be moved. Without knowing the pitch, you couldn't calculate the required angle of rotation.
--
Robin Casady
http://www.robincasady.com/Photo/index.html

SiPat Contributing Member • Posts: 928
Re: What formula is used to create the lens focus scale?

john barlow wrote:

The distance focus scale on a lens must use some formula, can you point me to a resource or expalin here how to calculate the scale?

thanks

Go and read this, and you may/may not find the info you want:

http://www.kenrockwell.com/tech/focus.htm

Ken Rockwell has some very simple explanations for photography issues that others like to complicate so that photography seems some mysterious hocus-pocus.

Alan Brown
Alan Brown Veteran Member • Posts: 5,655
exactly..

the pitch is crucial and 'perhaps' you could work it out as a rotation in degrees/ movement.

However I would expect (presuming the same FL lens is for the same application) the ratio of the markings (actual measureable distance between 5m to 3m on the distance scale engraved on the barrel) is fixed.... otherwise publshed DOF scales for a certain lens/application wouild all be wrong.

intriguing

Robin Casady wrote:

I believe that would depend on the pitch of the threads used for the focus ring, and how much the lens element needs to be moved. Without knowing the pitch, you couldn't calculate the required angle of rotation.
--
Robin Casady
http://www.robincasady.com/Photo/index.html

-- hide signature --

There is a very fine line between 'hobby' and 'mental illness.' :'!':

 Alan Brown's gear list:Alan Brown's gear list
Fujifilm X-T1 Fujifilm XF 18-55mm F2.8-4 R LM OIS
OP john barlow Regular Member • Posts: 229
Re: What formula is used to create the lens focus scale?

thats easy I know the pitch its "p"

and the formula is .... ????

Robin Casady wrote:

I believe that would depend on the pitch of the threads used for the focus ring, and how much the lens element needs to be moved. Without knowing the pitch, you couldn't calculate the required angle of rotation.
--
Robin Casady
http://www.robincasady.com/Photo/index.html

OP john barlow Regular Member • Posts: 229
Re: What formula is used to create the lens focus scale?

nothing of relevance there

SiPat wrote:

john barlow wrote:

The distance focus scale on a lens must use some formula, can you point me to a resource or expalin here how to calculate the scale?

thanks

Go and read this, and you may/may not find the info you want:

http://www.kenrockwell.com/tech/focus.htm

Ken Rockwell has some very simple explanations for photography issues that others like to complicate so that photography seems some mysterious hocus-pocus.

Robin Casady Forum Pro • Posts: 12,898
Re: What formula is used to create the lens focus scale?

The point is that you are unlikely to find the numeric values for the pitch and details of the optical design. So, you are SOL with or without a formula.

What, exactly, are you trying to achieve?

john barlow wrote:
thats easy I know the pitch its "p"

and the formula is .... ????

Robin Casady wrote:

I believe that would depend on the pitch of the threads used for the focus ring, and how much the lens element needs to be moved. Without knowing the pitch, you couldn't calculate the required angle of rotation.
--
Robin Casady
http://www.robincasady.com/Photo/index.html

-- hide signature --
gonzalu
gonzalu Forum Pro • Posts: 10,398
It may not be a formula at all, it may be measured

Manufacturer may actually measure the focal length/subject distance at each particular point on the focus scale and then create the plates accordingly.

Or I could just be talking out my $%&
--
Manny
http://www.pbase.com/gonzalu/
http://www.mannyphoto.com/
FCAS Member - http://fcasmembers.com/

 gonzalu's gear list:gonzalu's gear list
Sony RX100 VII Nikon D500 Nikon AF-S Nikkor 14-24mm f/2.8G ED Nikon AF-S Nikkor 50mm F1.4G Nikon AF-S Nikkor 70-200mm f/2.8G ED VR II +15 more
OP john barlow Regular Member • Posts: 229
Re: What formula is used to create the lens focus scale?

In the example formula I gave earlier; the requirement is to calculate 'a' and 'b' from measurement of Q and s on two points on the scale to give 2 simultaneous equations and therefore calculate Q versus s for the whole range. Simple math 101

Specific lens characteristics are constants and can be lumped together and derived from measurement.

Knowing the true formula enables me to group lens constants together this way.

If you have not seen such formula it is unlikely you can make a positive contribution to this thread.

Robin Casady wrote:

The point is that you are unlikely to find the numeric values for the pitch and details of the optical design. So, you are SOL with or without a formula.

What, exactly, are you trying to achieve?

john barlow wrote:
thats easy I know the pitch its "p"

and the formula is .... ????

Robin Casady wrote:

I believe that would depend on the pitch of the threads used for the focus ring, and how much the lens element needs to be moved. Without knowing the pitch, you couldn't calculate the required angle of rotation.
--
Robin Casady
http://www.robincasady.com/Photo/index.html

mblg Regular Member • Posts: 392
Unless...

You have some real passion in optics design, I simply don't get what you really want to grab for this hobby. However, just to satisfy partly your question, there is no simple answer to your question.

What you actually get into is very complex optimization calculus (unless you don't start from the paraxial oversimplification which might give a relative solution). I suppose that you are not interested in the complexity of real-life approximation and calculus, but, probably, a simplistic focal-plane relationship between movement of a simple meniscus mounted on a threaded element that rotates.

Thus, if you really have a catch for kind of physics that I've learned (don't know about your country's curricula) in tenth grade, start from the lensmaker's equation and approximate the camera lens with a simple convergent lens of focal length f.

Then calculate the x-x' movement of lens for various focus distances and calculate threads by this link:

http://www.sherline.com/THREAD%20CALCULATOR.xls

Good luck. It's fun. But, again it's an oversimplification. For your info, calculus of one optical element involves 9 degrees of freedom (9 dimensions). These increase enormously with any added element.

br

mblg

john barlow wrote:

The distance focus scale on a lens must use some formula, can you point me to a resource or expalin here how to calculate the scale?

thanks

Marianne Oelund Veteran Member • Posts: 7,788
Try this equation

john barlow wrote:

The actual numbers will vary from lens to lens and from manufacturer to manufacturer , but it will be based on an algebraic formula.

for example Q = a*s/(s+b); where Q is rotation angle of the focus ring and s the focal distance (relative to MFD) and a, b are lens derived constants.

Try
Q = a*{(m-d)*[1 - SQRT(1 - 4f/(m-d))]/2 - f},

where f is the lens focal length, d is the distance (separation) between the lens front and rear nodal points, and m is the distance marked on the focus ring (which is actually the distance from image plane to subject). Here, Q is ring rotation measured from the infinity-focus position, that is Q=0 when m is infinity. Note that d is typically negative for telephotos, positive for wide-angles, and may be small enough to ignore for moderate focal lengths.

You need to determine the proportionality constant, a, empirically using one of the markings on the focus ring, then you can check the accuracy of the formula against other markings. This is derived from a modified thin-lens equation, thus cannot be expected to be exact for complex lenses.

The difficulty is that f often varies with focus ring position, in a manner determined by the lens internal design, so you will only be able to obtain accurate results for lenses that have zero focus breathing. Also, d may be tricky to determine, will likely change with focal length on zoom lenses, and may also change with focus distance.

The bottom line is that without access to lens design details, there isn't an accurate way to determine the precise relationship you are looking for, and in general, it will not be a simple algebraic formula. The lens manufacturers can determine the focus ring markings from the design models they run on their supercomputers. It's unlikely that they do it empirically, or via any simple formulas.

If you are only interested in a relationship between Q and subject distance, for subjects that are relatively distant, you can use the approximation Q = b/(m - d - 2f) where b is a proportionality constant to be determined empirically.

Mark Hollister Regular Member • Posts: 388
Well, of course

What I meant to say was whaaaat? Marianne, your level of knowledge greatly impresses me. Sometimes I wonder if you are really Thom, or Thom is you. Or maybe you taught Thom.

I've got a lot of photography books, and I'll admit I haven't read all of them. But even if I did, I know full well I still wouldn't know squat compared to you. If you don't mind me asking, where did you get your extensive knowledge?

dwight3
dwight3 Senior Member • Posts: 2,783
Re: What formula is used to create the lens focus scale?

john barlow wrote:

Just for clarification :

I am referring to the relationship between the rotatational movement of the focus ring and the focal distance.

The actual numbers will vary from lens to lens and from manufacturer to manufacturer , but it will be based on an algebraic formula.

for example Q = a*s/(s+b); where Q is rotation angle of the focus ring and s the focal distance (relative to MFD) and a, b are lens derived constants.

You are making an unwarranted assumption here: that the motion of the lens is linear with rotation of the focus ring. That is not necessarily the case. The lens is moved by a cam that is operated by the focus ring. The cam can have any shape the manufacturer desires. It might be desirable to have the motion slow down at the infinity end of the travel in order to have more resolution in the distance scale.

 dwight3's gear list:dwight3's gear list
Nikon D4 Nikon D800E Nikon D5 Nikon AF-S Nikkor 70-200mm f/2.8G ED VR Nikon AF-S Nikkor 14-24mm f/2.8G ED +10 more
Marianne Oelund Veteran Member • Posts: 7,788
When is it linear?

dwight3 wrote:

You are making an unwarranted assumption here: that the motion of the lens is linear with rotation of the focus ring. That is not necessarily the case. The lens is moved by a cam that is operated by the focus ring. The cam can have any shape the manufacturer desires. It might be desirable to have the motion slow down at the infinity end of the travel in order to have more resolution in the distance scale.

It's a safe assumption for any lens which has a DOF scale on it; otherwise, the scale would be invalid over part of the focusing range.

Many newer lenses lack DOF scales, but it's rare that the focusing helicoid is nonlinear. For one thing, it would cause unnecessary complications for the AF system. Nonlinear cams are almost exclusively employed for moving the zoom groups.

OP john barlow Regular Member • Posts: 229
Re: When is it linear?

@Marianne

Brilliant, once again many thanks

viking79
viking79 Forum Pro • Posts: 14,156
Re: What formula is used to create the lens focus scale?

john barlow wrote:

The distance focus scale on a lens must use some formula, can you point me to a resource or expalin here how to calculate the scale?

thanks

The only reason I can think of needing information like this is if you plan to make a device to focus the lens automatically (say for video) and wanted to calculate how much to turn the lens? In which case I would just assume use look up tables in software for each lens determined by measuring a lens individually, and not try to calculate the focus point.

To make matters more difficult, a lens with spherical aberration has more than one focus point, that changes with various apertures. The focus shift between f/1.4 and f/4 can be extremely large in lenses like the Rokinon 85mm f/1.4, or even the Sigma 30mm f/1.4 has pretty significant focus shift.

I don't think you are going to find an easy one solution that will work for every lens, so it might be easier as I said to profile each lens individually and make a look up table in your software that corresponds to each lens.

Also, each camera can have some mount positioning error that will throw off your data a little as well. If the camera mount is positioned a fraction of an inch off your focus scale is all wrong anyway.

I think any open loop focus system for a DSLR would be very difficult to implement in a way that gives good results. You really need closed loop if you want any sort of precision.

Eric
--
I never saw an ugly thing in my life: for let the form of an object
be what it may - light, shade, and perspective will always make it
beautiful. - John Constable (quote)

See my Blog at: http://viking79.blogspot.com/ (Weekly)
Flickr Photostream: http://www.flickr.com/photos/28177041@N03/ (updated daily)
See my PPG Shots: http://www.pentaxphotogallery.com/erictastad (8/31/09)

 viking79's gear list:viking79's gear list
Sony a7R Samsung NX1 Samsung NX 30mm F2 Pancake Samsung NX 85mm F1.4 ED SSA Samsung NX 60mm F2.8 Macro ED OIS SSA +5 more
Keyboard shortcuts:
FForum MMy threads