Introduction | Table | Determining the "Allowable" Minimum Distance | Procedure | How to Use the Tables for Finite Distances | Conclusions | References
On this page, I present a table of "Merklinger apertures" for the Leica X Vario that was calculated using Excel. The calculations are based on formulae from Harold M. Merklinger's paper The INs and OUTs of Focus - An Alternative Way to Estimate Depth-of-Field and Sharpness in the Photographic Image (Internet edition).
Note: For more information, see my general page Merklinger's Approach to Estimating Depth of Field. |
In his article Hyperfocal distances and Merklinger's method in landscape photography, Kevin Boone discusses hyperfocal distance versus Harold M. Merklinger's approach to estimating depth-of-field in landscape photography. Boone's briefly describes Merklinger's method for scenes with distant objects as follows:
For those, who just want to use this approach, Boone's article provides already the most important things that you need to know. There, you can find tables that help you employ the method (including added minimum distances from conventional DOF tables), as well as a discussion about the traditional approach to depth of field and hyperfocal distance calculations versus Merklinger's approach.
This page is directed at those, who want to use this approach with the Leica X Vario. I list a table of so-called "Merklinger apertures" that I calculated for this camera at various focal lengths and point to the table of hyperfocal distances for determining the corresponding "allowable" minimum distances. Finally, I list a simple procedure how the table can be used.
The following table lists disks of confusion (distance set to infinity) for the Leica X Vario at different focal lengths.This allows you to find the suitable "Merklinger apertures" in steps of one-third f-numbers.
Focal Length | f-Number |
|||||||||||||||
Actual | Equiv. | Nominal > |
3.5 | 4 | 4.5 | 5.1 | 5.6 | 6.4 | 7.1 | 8 | 9 | 10 | 11 | 12.7 | 14 | 16 |
Exact > |
3.56 | 4 | 4.49 | 5.04 | 5.66 | 6.35 | 7.13 | 8 | 8.98 | 10.08 | 11.31 | 12.70 | 14.25 | 16.00 | ||
18 |
28 |
Diameter of Disk of Confusion (mm) > |
5.05 | 4.50 | 4.01 | 3.57 | 3.18 | 2.83 | 2.53 | 2.25 | 2.00 | 1.79 | 1.59 | 1.42 | 1.26 | 1.13 |
23 |
35 |
6.45 | 5.75 | 5.12 | 4.56 | 4.07 | 3.62 | 3.23 | 2.88 | 2.56 | 2.28 | 2.03 | 1.81 | 1.61 | 1.44 | |
33 |
50 |
9.26 | 8.25 | 7.35 | 6.55 | 5.83 | 5.20 | 4.63 | 4.13 | 3.67 | 3.27 | 2.92 | 2.60 | 2.32 | 2.06 | |
46 |
70 |
12.91 | 11.50 | 10.25 | 9.13 | 8.13 | 7.24 | 6.45 | 5.75 | 5.12 | 4.56 | 4.07 | 3.62 | 3.23 | 2.88 |
Note: I determined the following maximum aperture values (equivalent focal lengths) for the Leica X Vario: 28 mm: f/3.5, 35 mm: f/4.5, 50 mm: f/5.1, 70 mm: f/6.4 (f/6.4 starts between 50 mm and 70 mm).
The diameters were calculated according to the formula d = f / N (d = diameter of disk of confusion = diameter of working aperture; f = focal length; N = f-number), which is valid for distance set to infinity. The exact f-numbers were used in the calculations.
Further down, I present a simple procedure how the table can be used.
You can determine the "allowable" minimum distance on the basis of traditional calculation tables (or the DOF markers on the lens - but the Leica X Vario has none...). As Merklinger shows for the traditional DOF calculations (p. 15) and I found out myself independently using Merklinger's approach, the hyperfocal distance (HFD) is the minimum distance (based on the CoC criterion) for a given "Merklinger aperture", when the lens is focused at infinity.
Thus, for determining the minimum distance for the Leica X Vario, just look at my table for hyperfocal distances for this camera. Also note that at half the hyperfocal distance, the disk of confusion is half the size of the diameter of the working aperture, meaning the CoC is about double the "allowed" size. This leads to a decrease in resolving power in the object field and a decrease in conventional sharpness in the image (CoC and DoC are proportional to each other*).
*) The formula is: Sx = c * X / f (focus D on infinity, X = object distance; c = diameter of circle of confusion; Sx = diameter of disk of confusion; f = focal length of lens)
In short: When focusing at infinity and setting the "Merklinger aperture", the CoC has its "nominal" (= allowable) size at HFD and double its "nominal" size at HFD/2.
With distance set to infinity, you can employ a "special case" of the "Merklinger approach" suitable for landscape photography (no important objects in the close foreground) by following these steps:
*) For my tables, I used fixed f-numbers, as given by the cameras, and the most important focal lengths of my cameras to calculate tables of d-values. When you use these tables, you first have to decide on a value of d based on the scene to be photographed and a focal length and then search the table for a suitable d-value and extract the corresponding f-number for that focal length. Often, you will not find the exact d-value in the table and have to decide for one that comes close. Choose the f-number conservatively in this case, that is, select the next larger f-number to be "on the safe side".
Can you use the f-numbers that I calculated for the infinity condition also for finite distances? The answer is "yes" if you are willing to do some simple calculations - in your head or using a calculator: Just calculate or estimate (X - D) / D and multiply the f-number for infinity with it - voila! It's even simpler for fractions of D. Here are the formulae:
Examples:
Using the table of "Merklinger apertures" on this page and the table of hyperfocal distances for the Leica X Vario, you can employ a "special case" of Merklinger's approach where distance is set to infinity, which is well suited to landscape photography. But you can also use the table for finite focus distances.