The hyperfocal distance is the distance at which you focus a lens to obtain the greatest depth of field (DOF). Viewed another way, the hyperfocal distance is the minimum distance at which the objects at infinity are acceptably sharp.
The formula for calculating the hyperfocal distance of a lens is:
H = L x L / F / CoC / 1000, where:
H is hyperfocal distance in meters.
L is the focal length of the lens.
F is the F-Number of the lens.
CoC is the diameter of the Circle of Confusion in mm.
As I had explained earlier, riflescope makers do not divulge the focal length of their riflescopes; some consider it a trade secret as part of their design. Without the focal length, we cannot use the formula.
However, we can guestimate the focal length and work from there. For this, you will need a ruler or a caliper that measure in metric or just convert the measurements to metric. As I said, you will need a ruler or caliper, a pencil, paper, eraser, rubber band, fork and a beer.
A riflescope is essentially three parts: the objective lens group, the erector assembly, and the eyepiece. The magnification range of a riflescope is calculated by dividing the focal length of the objective group by the focal length of the eyepiece and then multiplying by the zoom ratio of the erector set.
The focal length of the objective lens is the distance between the objective lens group and the first focal plane, regardless if the scope is FFP or SFP. I believe that FFP is usually located in the middle of the elevation knob, where there is the greatest range of movement for the FFP. Again, that’s irrespective of FFP or SFP design.
Now if you look at the objective lens from the front, you can see that sometimes it’s close to the front edge and sometimes is further in. There are more than one lens in that objective lens group. This makes it difficult to find out exactly where to measure from, but I would think that where the objective starts to taper towards main tube size is near the lenses. I can’t imagine that there would be a big gap between the back of the lenses and the start of the taper. So I measure about a half inch forward of where the taper starts to the middle of the elevation dial. You also need to do measure parallel to the riflescope body.
1- place the rubber band tightly around the wrist of the hand holding the riflescope.
2- Pick up the riflescope and identify the objective part of the scope. That’s usually the big end of the riflescope, but on LPVOs that will be the small end of the riflescope.
3- In your other hand take the measuring instrument and place one end on the objective part about a half inch in front of the start of the taper. On an LPVO, you have to be a little imaginative; just remember that the diameter of the lens is small and so is the thickness, but there are a couple of lenses in the objective group.
4- Measure the straight distance to the middle of the elevation knob.
5- Record that measurement on the paper using the pencil.
6- Measure it is again and mark down the second reading below the first one.
7- Compare the two measurements.
- If the measurements are substantially different place the riflescope down on the table, pick up the fork and stab the hand that held the riflescope. Use the eraser to get rid of your mistake, then go back to step 3.
- If the measurement are essentially the same, add them up and divide by two. Then drink the beer to celebrate. You can remove the rubber bad from your wrist.
You now have the focal length of the objective lens group. Let’s calculate the F-number of the lens. Divide the focal length by the diameter of the objective lens. That number will be dimensionless; it’s just a number.
The Circle of Confusion (CoC) is going to be a number of your choosing. To my mind, this number would vary between .03mm and .01mm. The larger the number, the less picky you are about what looks in acceptable focus. I think it should vary with the magnification that you want to use. So, let’s say your zoom ratio is 10X, like in that March 1-10X24 discussed in this thread. I would say that if I am going to stay between 1-3X, I would choose a CoC of .03mm. If I’m going to go up to 7X, I would choose a CoC of .02mm. If I want the whole 1-10X without having to touch the side focus, I would choose a CoC of .01mm. This is something that you will have to decide for your needs.
Now plug in the three numbers that we have identified into the formula and we are ready to calculate the hyperfocal distance for that riflescope.
So let’s say the focal length is 48mm and the diameter of the lens is 24mm, the F-number of the lens is 48/24=2.
H= (48 * 48) / 2 / .03 / 1000 H= 38.4 meters
H= (48 * 48) / 2 / .02 / 1000 H= 57.6 meters.
H= (48 * 48) / 2 / .01 / 1000 H= 115.2 meters.
Of course, you can reduce this further by doing: (48*48)/2/1000 and then divide the result (1.152) by whatever CoC you want. That number (1.152) only applies to the riflescope that you measured to get the numbers.
But that number is sterile, it only tells us at which distance everything behind it will be in focus. What about in front of that distance?
I will give you the numbers for each and then we will explore how that’s done and how to take it further.
At H = 38.4, CoC = 0.03, the near limit is 19.2 meters.
At H = 57.6, CoC = 0.02, the near limit is 28.8 meters.
At H = 115.2, CoC = 0.01, the near limit is 57.6 meters.
Now, let me introduce you to the DOF Master calculator. This is the site I use to calculate DOF coverage and other such things.
Online Depth of Field Calculator (dofmaster.com) It requires 4 pieces of data to calculate and produce great information.
The first one is Camera, film format, or circle of confusion. For our purposes, we use CoC. So drop down the list and go to the end to find the CoC values. Be careful with the decimal point. We are looking at values between 0.010mm and 0.030mm. As I explained earlier, the bigger the CoC, the larger the DOF.
The second number is the Focal length. This is the value we (painfully) measured on the riflescope earlier. The numbers are a little wonky, but remember this is a camera site.
The third number is the Selected f-stop (or f-number). Again, the numbers may be a little wonky, just select the one that is closest to your calculated one.
The fourth and final number is the Subject distance and its associated unit of measure.
So let’s say I would like to know where to focus my riflescope to have an acceptable DOF from say 20 meters to 200 meters at up to 7X. For that, I select a CoC of 0.020. Next. I select the hyperfocus distance of 57.6 meters to see what this produces. I get a near limit of 29m and, of course, infinity. Remember, this is the hypefocal distance. That quite close to what I’m looking for. Let’s bring it down to 40 meters. Remember, the near limit DOF is much shallower than the far limit. At 45, I get a near limit of 25 and a far limit of 205 meters. That’s pretty good. I can tweak it a little further towards the near limit but every meter I subtracts I lose s significant chunk at the other end and the near limit crawls.
This is where you start making your own decisions and figure out what is “acceptable sharpness” for you and what distances and magnifications are right for you. This is where the riflescopes with the side focus provide you with the flexibility to customize them for your needs if you so desire.
Of course, if your riflescope does not have a side focus, the DOF Master will show you what the DOF parameters are and you can certainly play with the CoC values to go along with the magnification.
This is all meant as a guide, and to help understand how to use a side focus. The focal length numbers I used above are approximations only.