# Thread: The maths of how to achieve accurate focusing.

1. ## The maths of how to achieve accurate focusing.

Hi,

I wondered if anyone out there could explain how to ensure accurate focusing. I am using a Cambo Legend 10" x 8" with a Rodenstock 210mm macro lens.

I'm shooting at F:22, which is as deep as I can go with the depth of field before losing clarity.

I am finding that when the image appears to be in focus at the point I want on the object i am shooting, the results are slightly out. I seem to recall something about not focusing on the plane that you want but focusing deeper and the results will mean that the original desired plane of focus is achieved.

Do I sound confused? I am!

If anyone out there knows an accurate solution to this that would be great, thanks!

Danny.

2. ## Re: The maths of how to achieve accurate focusing.

Before the maths, may be some additional information can be useful

- do you focus with your lens wide open ? With some old lenses, the best focus is slightly different between wide open and stopped down to the working aperture (here, f/22)
- are you absolutey sure of the mechanical / optical setting of your ground glass ?

if:
- the lens is modern and no focus shift can be invoked,
- the ground glass is properly set including all required corrections due to Fres1el lenses in front,
- the film holder is OK and the film plane position inside is not offset,
- when locking the focusing stage, be sure that nothing moves even a tiny bit;

then, the proper focus ON FILM should be... where you see it is on the ground glass.
If not, we are probably missing something.

A satisfactory way to focus in low light levels by moving the rear standard (this is valid even in close-up) is to find "on both sides" of the best focus the position of the focusing stage that gives an identical blur ; and eventually set the focus in between as the best possible position.
This is consistent with the smiple geometrical diagram of defocusing, the depth of of focus problem, the plane of best focus is located in the middle of two positions where the image of a point is projected as a small circle.

3. ## Re: The maths of how to achieve accurate focusing.

Hi,

yes I focus wide open, I think the lens is not classed as 'old' its a macro sironar N MC 5:6.

I am sure the gg is fine as with a standard lens it has been great.

As a final check when my focus is locked I slightly push the gg screen to check that it settles back to its original optimum focus position and it always does.

There is no fresnel lens.

very strange...

4. ## Re: The maths of how to achieve accurate focusing.

Are you at medium or long distance? That is a macro lens. And even modern lenses will often have some focus shift when used outside the range they are corrected for.

5. ## Re: The maths of how to achieve accurate focusing.

Originally Posted by Danny Treacy
Hi,
I am sure the gg is fine as with a standard lens it has been great.

Well, to be fair, most normal situations may not be sensitive enough to have the error noticeable. For a very small error in GG placement, you would need exceedingly small DoF to notice it; Macro meets that nicely.

Incidentally, I don't see how staying F/22 or under for clarity is going to help you if you don't have sufficient DoF for your subject. Just saying, is all.

6. ## Re: The maths of how to achieve accurate focusing.

I'm very close to the subject (still life).

My F:22 DoF is not a problem, I'm actually happy with it as it gives a beautiful fall off, the problem is more that what appears sharp on the gg does not come back as sharp on the transparency.

I guess it could be mis-aligned, any suggestions on how to resolve this if this is the problem?

7. ## Re: The maths of how to achieve accurate focusing.

I'm not sure I can be helpful, but I can tell you some things about the math.

First, it is impossible to focus exactly. There is a range along the rail, called the depth of focus, in which everything looks equally in focus. There is a formula for it, but it is best to measure what it is for you, given the way you focus. To do this, you need to be able to measure small displacements on the rail. If your camera has a fine focusing knob, it is not too hard to do this. Make one complete turn of the knob and see how far the standard moves on the rail. (It is best to do this using a metric taped marked in mm.) Measure the circumference of the knob, and divide the first length by the second. The resulting ratio tells you how to convert distance along the focusing knob into distance along the rail. (You can find an explanation of how I did this for my Toho FC-45X at
http://www.math.northwestern.edu/~le.../dof_essay.pdf.)

Depth of focus is not the same as depth of field, so don't confuse the two.

To measure your depth of focus, pick some detail at a convenient distance, see where it just comes into focus, noting the position on the rail, and then continue until it just goes out of focus and again the note the position. Subtract to determine the distance on the rail between them.
Do this the way you usually focus using whatever power loupe you use. If you do it several times, you will get different answers since it is hard to determine exactly when you think you have just gone into focus or just gone out of focus. Average the values you get to get an estimate of your personal depth of focus with that lens at the given subject distance.

For example, suppose are using an f/5.6 lens, the subject distance is such that reproduction ratio is 1:2 or 0.5, you don't use a loupe ,and you put your eye about 12 inches from your 8 x 10 gg, My guess is that you would find the depth of focus was not much less than about 0.6 mm and probably greater than that. On the other hand, if you used a 2 X loupe it would be half that and for a 4 X loupe it would be one quarter of that. (There is not much point in increasing the power much beyond 4 X since then the surface texture of the gg will start playing a role.)

If you use a different f-stop, you have to multiply by the ratio of the f-numbers. For example, focusing at f/8 instead of f/5.6 would require multiplying by 1.4. To determine what the depth of focus would be if you focused on an object at a different distance is a bit more complicated. For each distance, find the reproduction ratio--see the PS below---and then add one to it. Then take the ratio of the resulting numbers and that is the factor to use to find the depth of focus at the new distance. For example, at infinity the reproduction ratio is 1:infinty = 0.0. Adding 1 yields 1 + 0 = 1.0. For reproduction ratio 1:2 or 0.5, adding 1 yields 1.5. So to find the depth of focus when focusing at infinity, multiply by 1/1.5 = 2/3 ~ 0.67. If the depth of focus at 1:2 were 0.6 mm, at infinity it would be 0.4 mm.

You will note certain things from this discussion. First, as you probably knew, the depth of focus gets larger if you focus at a smaller aperture. It also gets smaller if you use a higher power loupe. Finally it is larger if the subject is closer than if it is at a great distance.

For perfect lenses, depth of focus doesn't depend on focal length, but clearly if there are significant aberrations, that will increase it. Since you say you have no trouble focusing with another lens, that could be the case for for your 210 mm lens.

So, is there anything you can do to focus better? The theory behind the formulas for depth of focus in essence says that you can't focus any better than you can see. But there are some tricks to use to improve focusing. For one thing, you can make several attempts to focus, noting in each case the position on the rail. If you then take an average of all these positions, you may be able to reduce the focus error by a significant amount. For example, if you average 5 measurements, the focusing error will be reduced by about a factor of 2. Also, experienced photographers will develop a feel for how far to go beyond just where the image goes into focus so it is midway in the depth of focus.

PS the easiest way to find the reproduction ratio is to determine the distance from the subject to the lens in mm, divide it by the focal length, subtract 1 and take the reciprocal. For example, suppose your focal length is 1040 mm and your focal length is 210 mm. then 1050/210 = 5. Subtract 1 to get 5 - 1 = 4, and take the reciprocal to get 1:4 = 1/4 = 0.25.

In measuring the distance to the lens, you have to use the front principal point, which for most lenses is at the front of the lensboard. For telephoto and some wide angle lenses, you have to look up the flange focal length and make some calculations.

8. ## Re: The maths of how to achieve accurate focusing.

Originally Posted by Danny Treacy
I'm very close to the subject (still life).
But that does not tell us what magnification ration you are using.

If you don't know your ratio simply measure the objects width and then measure its' width on the ground glass. That is what determines the magnification ratio. If they are the same width you are at 1:1. If the object is twice the width on the ground glass you are at 1:2. If the width on the GG is twice as wide as the object you are at 2:1.

Then how are you lens elements assembled? Wider group in front or narrower group in front?

9. ## Re: The maths of how to achieve accurate focusing.

Leonard, isn't depth of focus the distance around the film plane within which the image is acceptably in focus? I think that's the term's usual meaning.

Also, without knowing details of the lens' design it is impossible to know where its principal planes are. We all use the diaphragm's position as an approximation, but it isn't exact or always even close.

In principle one can locate the rear principal plane by focusing the lens on a very distant subject, in which case the rear pp is one focal length from the film plane. Similarly, with the lens reversed, to find where the front pp is. But this assumes actual focal length equals nominal, and this is rarely true. Whence custom RF cams for Linhofs with rangefinders, all those Super Graphic RF cams for lenses of the same nominal focal length, ...

Danny, FWIW, I sometimes have great difficulty focusing well on the GG using a roughly 3x loupe. I do better with a 12x and a lot of focusing back and forth through the desired plane of best focus.

Also, if you're shooting at nominal f/22 and the subject is close, the effective aperture will be smaller than f/22 and diffraction can indeed be a problem. The magic formula is effective aperture = aperture set * (1 + magnification). So at 1:1, the effective aperture is f/45. This limits enlargements to ~ 4x.

Which raises the next question. Why do you care about on-film sharpness? IMO, what matters is sharpness in the final print. How much fuzz you can allow in the negative depends on how much you want to enlarge.

Cheers,

Dan

10. ## Re: The maths of how to achieve accurate focusing.

Originally Posted by Dan Fromm
Leonard, isn't depth of focus the distance around the film plane within which the image is acceptably in focus? I think that's the term's usual meaning.
There is more than one way to define depth of focus. With your definition, we assume the ground glass surface (which we identify optimistically with the eventual position of the film plane) has been placed in a particular in a particular spot. We then ask how far off on either side the exact image could be and still appear in focus on the ground glass. The total range of such positions is the depth of focus. The way I stated it is a bit different. I assume the image is formed at a specific location, and then I ask how far from that position on either side can you put the gg and still have the image look in focus. I believe my definition is closer to what you are actually interested in since with the subject fixed, so is the image, and you are changing the position of the gg.

The two formulas give essentially the same formula for the depth of focus 2Nc(M+1) where N is the f-number, c is the relevant circle of confusion on the gg, and M is the magnification. My method gives this formula exactly and yours gives it to a very high degree of approximation. There is one further subtle difference. With your method, M is the magnification which would hold if the subject were such that it came to focus exactly on the ground glass, which it doesn't. So it is not actually the magnification for the subject being focused on, but for a subject displaced from it. With my method, M is the actual magnification for the subject being focused on, and it stays fixed wherever you put the gg. However, the different values of M are so close together in practice that you need not worry about the difference.

Also, without knowing details of the lens' design it is impossible to know where its principal planes are. We all use the diaphragm's position as an approximation, but it isn't exact or always even close.

In principle one can locate the rear principal plane by focusing the lens on a very distant subject, in which case the rear pp is one focal length from the film plane. Similarly, with the lens reversed, to find where the front pp is. But this assumes actual focal length equals nominal, and this is rarely true. Whence custom RF cams for Linhofs with rangefinders, all those Super Graphic RF cams for lenses of the same nominal focal length, ...
All that is true, but for normal lens and normal subject distances, even in close-up photography, it is usually good enough to assume the principal plane is at the front of the lensboard because it will differ from that by just a few mm.

Danny, FWIW, I sometimes have great difficulty focusing well on the GG using a roughly 3x loupe. I do better with a 12x and a lot of focusing back and forth through the desired plane of best focus.
As I mentioned previously, with a 3 X loupe you have about 4 times as much depth of focus as you would with a 12 X loupe, provided the screen is fine enough that its surface texture doesn't interfere with seeing the image.

Also, as I noted, many of us have learned intuitively just where to put the ground glass as we focus without having to think about it. But it is hard to tell someone how to do something you do instinctively.

Myself, I find I can focus my Toho FC-45X with a Maxwell screen reasonably well with 2 X power and better with a 3.6 X loupe. I can also sometimes do it even better with a 7 X loupe, but surface features of the screen such as Fresnel rulings can interfere.

[QUOTE}
Also, if you're shooting at nominal f/22 and the subject is close, the effective aperture will be smaller than f/22 and diffraction can indeed be a problem. The magic formula is effective aperture = aperture set * (1 + magnification). So at 1:1, the effective aperture is f/45. This limits enlargements to ~ 4x.

Which raises the next question. Why do you care about on-film sharpness? IMO, what matters is sharpness in the final print. How much fuzz you can allow in the negative depends on how much you want to enlarge.

Cheers,

Dan[/QUOTE]

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