### Costruire un veloce misuratore della DOF

13 aprile 2007  Pier-Luigi  Fotografia (0)
Making a DOF calculator for your camera
This document explains how to make a DOF calculator. One actual example for a geared focus knob on the Arca Swiss F-line Classic 4x5 is worked out for your reference. The step-by-step instructions which follow can be applied to any camera.
Contents

The whole reason I do this is to make LF techniques quick and fast, so I can spare the precious moment to concentrate on the image and aesthetics of the subject.
The calculator tells you the minimum f-number required to include all the subjects you want to be sharp. It is the quickest way I know to determine depth of field (DOF). Some cameras come with such a device: an example is Sinar's step 3.
This document explains how you can build such a device for your own camera.
Example using Arca Swiss F-line Classic camera
The drawing for C-ring is available in gif file. All units are in inches unless otherwise noted. All dimensions listed are mere examples I used.
The focus knob of Arca F-line is covered with rubber piece. First, decide how much width to leave for focusing and give space for the DOF C-ring. Leave 52% or .290" of the total width .561" to the rubber. The rest .271" is cut away based on two set screw holes .167" off from the side and on how much rubber piece is necessary for focusing without sacrificing the comfort (Figure 1).
Figure 1 (the other hole is not visible in this picture)
The width of ring has to cover the holes to ensure the ends of C-ring not getting caught by the holes, which may prevent smooth turns of the ring. The dimension of the ring is then determined: Inner diameter = .950", Outer Diameter = 1.09", Width = .235". The outer diameter takes into account the thickness of laser paper (.004") for DOF scale, so that the final outer diameter is slightly less than that of rubber piece. This avoids unintentional turns of ring.
The ring is lathed from a chunk of cylinder plastic, then cut in the ring by bandsaw to make it C-ring. The surface is cleaned, the C-ring is snapped onto the knob, then checked if it is acceptable to do the job.
Mark a line (here piece of pink tape) on the closest part of the camera to the ring (Figure 2a) as explained below. This mark corresponds to a reference point for zeroing the DOF scale when focusing either near or far at the beginning of DOF calculation.
Find a comfortable working angle where you can see the reference point by pretending as if you are taking pictures; check focus on ground glass, uncover darkcloth and look into the knob. That's where your working angle is. Mark that reference point on the closest part of camera to the focus knob. Check the working angle again and look into the reference mark. Mark that point permanently.
Note: Here the reference point is on the tension control knob for focusing. Tighten the tension knob all the way then mark the reference point, for backlash causes error in calculation.
Glue a strip of paper on the ring, mark a parallel line on the closer side of the strip to the reference point. Here the line is black in Figure 2a.
Figure 2a
Rotate the focus knob while making sure the ring is turning with the knob until reading the delta on the rail 8.1mm for the corresponding min. f-number N = 45 for 4x5 as shown in Table 1 below. Then mark the corresponding point on the strip (Figure 2b).
Figure 2b
Take off the strip and measure the difference 37.6mm. Calculate the conversion factor D = (delta on ring)/delta, or D = 37.6/8.1 = 4.67. This D is used in the the fourth column in Table 1 to calculate delta on ring = D*delta.
 Table 1 film size       CoC(mm)         delta(mm) at N=45       delta on ring(mm) at N=45 MF             .05             4.5                     21.1 4x5             .089            8.1                     37.6 5x7             .12             10.9                    50.7 8x10            .18             16.3                    76.0
delta = 2*c*N, delta on ring = D*delta.
Print DOF strip. Set the printer scale option based on the table above. The following example describes how to rescale the strip.
Example: For my 4x5 camera, printing with default setting gives [delta on ring at N=45] = 115.2mm while I need to scale it down to 37.6mm according to the table. Calculate %rescaling factor = 100*37.6/115.2. The calculation gives about 32.6%. Set the rescaling factor to 32.6% of the default print size setting (normally 100%). Then print and check if the scale printed at N =45 is equal to 37.6mm.
Note: DOF strip with no mm scale is valid for any format, circle of confusion c and conversion factor D (which is specific to each camera). The strip only requires a different rescaling when printed. Strips with mm scale for different formats are also available at your choice.
Completed picture 1 (mine does not have mm scale used to calculate tilt/swing)
Completed picture 2
Step by step instructions to make a DOF calculator for your camera
1. If your camera has both front and rear geared focus knobs, then pick the rear. Figure out how much portion of the width you need to reserve for focusing and to give a space (at least .15") for DOF calculator.
2. Lathe the portion of knurl closer to the camera body but leave the end width about 50/1000". This will give a ditch for the DOF calculator ring and keep it in place. You need a smooth surface for the ring to turn freely on the knob.
3. Make the ring that DOF strip glues on. Use durable plastic such as Teflon. The width of the ring should be at least 10/1000" less for the play than the ditch of the knob you just made. Ideally, the outer diameter of the ring should be smaller than that of knob you saved for focusing. But the outer diameter should be bigger if numbers and scales on the strip are going to be too small to read (Important!). It is adviced to check that you are happy with the size of scales by a trial dimension of the outer diameter of ring. The inner diameter of ring should be about 20/1000" less than the ditch diameter of the knob, but not too much. If the inner diameter of the ring is too small, not only is the ring too tight on the ditch but also the ring deviates from the ideal circular shape.The ring must be dimensioned such that it turns freely by hand without turning the focus knob, else it stays together and turns with the knob while you focus near and far. The right dimension primarily depends on the thickness and material of the ring. If the ring is too tight for the purpose, then for the next try, increase the inner diameter, rather than decreasing the outer diameter.
4. Now you have made the ring. Cut in the ring with bandsaw to make it C-ring. Clean up burs on the surface. Snap it on to the knob, check if the ring does the job satisfactory. If not, repeat step 3 until you get it right.
5. Mark a line (here piece of pink tape) on the closest part of the camera to the ring explained below. This mark corresponds to a reference point for zeroing the DOF scale when focusing either near or far at the beginning of DOF calculation.
Find a comfortable working angle where you can see the reference point by pretending as if you are taking pictures; check focus on ground glass, uncover darkcloth and look into the knob. That's where your working angle is. Mark that reference point on the closest part of camera to the focus knob. Check the working angle again and look into the reference mark. Mark that point permanently.
1. Glue a strip of paper on the ring, mark a parallel line on the closer side of the strip to the reference point.
2. Rotate the focus knob while making sure the ring is turning with the knob until you read the delta on the rail for the corresponding min. f-number N = 45 for your format size as shown in Table 2 below. Then mark the corresponding point on the strip. Take it off and measure the difference (delta on ring at N=45). Calculate the conversion factor D = (delta on ring)/delta. Use this D to calculate the delta on ring = D*delta in the fourth column in Table 2 for your format size.
 Table 2 film size       CoC(mm)         delta(mm) at N=45       delta on ring(mm) at N=45 MF              .05             4.5                                     4x5             .089            8.1                                     5x7             .12             10.9                                    8x10            .18             16.3
Or if you want to use a different CoC, then use Table 3 below and crank up the math using delta = 2*c*N, delta on ring = D*delta.
 Table 3 film size       CoC(mm)         delta(mm) at N=45       delta on ring(mm) at N=45 MF                                                              4x5                                                      5x7                                                             8x10
1. Follow the example above for rescaling. Print DOF strip. Set the printer scale option based on the table above. Then print, cut and paste the DOF strip on the ring. The strip with no scale is valid for any format, circle of confusion c and conversion factor D (which is specific to each camera). The strip only requires a different rescaling when printed. DOF strips with optional mm scale for calculating tilt/swing angles are available for MF, 4x5, 5x7, 8x10 and 10x12.
2. Double check if you read corresponding min. f-numbers on the ring to deltas on rail.
3. You have just made a DOF calculator for your focus knob.
And do the rest starting from Step 5 above.
DOF card is for any camera whether or not it has a geared focus knob.
This is a little bit slower than the ring version, but much easier to make. What you need is to print DOF card strip. Rescale and print so that f-numbers match to corresponding real-scale mm deltas. Refer to Table 4 below to match up a f-number N (N = 45 here) to the corresponding delta (mm).
 Table 4 film size       CoC(mm)         delta(mm) at N=45 MF              .05             4.5 4x5             .089            8.1 5x7             .12             10.9 8x10            .18             16.3
Or if you like to use a different CoC, then use Table 5 below and crank up the math using delta = 2*c*N = 2*c*45 = 90*c.
 Table 5 film size       CoC(mm)         delta(mm) at N=45 MF              4x5             5x7             8x10
Cut the paper in a convenient size, laminate the strip. Now you have a DOF card.
Buy a type of document holder that comes with a long plastic piece on one end that pinches sheets of paper, available from any office supply store. The plastic piece can be used as a rail to hold the DOF card. Attach the piece on a side of the main body of the camera that does not move while focusing. This way you don't have to hold the card anymore.
Editor's note: On my Canham KBC (the wooden one), I have glued to the outside of the front left focussing rail a strip which has a metric scale and a DOF scale (postcript file, source xfig file). I like CoC=0.1 for 5x7. It makes also calculations simpler. The DOF scale is used in the following way:
• Align the front focussing rail with the zero mark of the DOF scale
• Focus on the farthest object using the real focussing rail
• Focus on the nearest object using the front focussing rail
• Read the f-stop and back off two stops
Without tilt/swing:
1. Focus on the farthest [nearest] object you want to be sharp
2. Set 0 scale on the ring* to the reference point
3. Focus on the nearest [farthest] object you want to be sharp
4. Read the scale on the ring next to the reference mark. That's the min. f-number you need
5. Back off two stops towards 0. The camera is at the optimum position.
6. Set time and aperture based on the min. f-number and take a picture.
With tilt/swing:
1. Set the optimum plane of focus so that the farthest and nearest objects lie about equal angles apart from the optimum plane of focus. There're at least two ways to acheive this goal: Pick one (or both) based on your preference.
• Trial and error: Guess where the optimum plane of focus and try to get two sharp points lie on the plane.
• Caluculating the tilt/swing angle phi:
• Use Wheeler's rule phi = 60*delta/difference on GG. The difference on GG is defined as the perpendicular distance between two points on the optimum plane of focus, imaged on GG before you tilt/swing the camera.
• Use Rodenstock Calculator. Don't get bothered with alpha and beta** on the Rodenstock. Just set them both zero.
The phi calculated in both two ways assumes the optical center of lens does not move. But whether you have center tilt or base tilt camera, phi will be about the same. So no worry. DOF strip includes delta to calculate phi for your convenience.
1. After setting the optimum plane of focus, follow Step 1 through 6 above.
* For DOF card, replace the word "ring" by "card". The reference point can be anything that moves while focusing. For example, a good reference point would be an bottom edge of the standard.
**beta is for macro.
Optional: Add stops for bellows extension as necessary. (I prefer no compensation first and consider it as a part of bracketing [underexposure], unless I'm doing macro work.)
Note: With no tilt/swing (only shift/rise), the plane of focus is perpendicular to the optical axis. So the nearest and farthest points lie in the planes perpendicular to the axis. Think Scheimpflug and Hinge points converge at infinity, as a special case when using tilt/swing. In this sense, you focus on the two farthest angle planes from the optimum plane of focus. So when tilt/swings are used, focus on the two farthest angle planes where the corresponding objects lie.
Comment: Regarding to the two ways to determine tilt/swing angle phi, My experience tells me that the trial and error way is the quickest as long as I can find two points in focus (i.e. then I know where the plane of focus is and know which way I need to tilt/swing to get to the assumed optimal plane of focus, based on Scheimpflug and Hinge Rules). Well, if I can't find the two points, then I know I tilted/swung too much or too little.
Good things to know
The min. f-numbers calibrated are correct at magnification M = 0, infinity focus. However, at any magnification, the min. f-number required for a given delta will be less than that at infinity focus. Therefore you're always guaranteed to get min. DOF for a given delta at any magnification.
At magnification M = 1 (life-size, 1:1), the min. f-numbers N on scale are half. At any magnification in between 0 and 1, the min. f-number required will fall in between the f-number scales and their corresponding halves. For an arbitrary N, use N(M) = 1/(1+M)*N(M=0) to figure out exact min. f-number required at M. For example, at M = 0.5, N(M=0.5) = 2/3*N(M=0). So multiply the f-numbers on scale by 2/3.
For example, if the scale is made for 4x5, the ring can be used for 8x10 as well by dividing a min. f-number by half, provided the circle of confusion for 4x5 is simply doubled. But one may want to have more than one ring for different formats to avoid confusion and mistakes.
Details
The min. f-numbers in DOF strip are calibrated in both directions. This allows you to focus in either order: nearest and farthest, or farthest and nearest, without loosing intuitiveness.
The ring makes your life easy. The min. f-number will always be at the reference point where you called it as the working angle.
Regarding Step 5, backing off 2 stops is equivalent to setting the standard at the optimum plane of focus, delta/2.
Math behind the scale for those interested; also partially explained in Sheet 1, Excel file and Static html file for Sheet 1.
Limitations
Because of some magnification and you rarely set the camera at infinity for a delta/2 position, you're always getting a min. f-number more than you need, although the depth of field calculator you made contains essentially all the information you need at any magnification.
If you want to know the precise min. f-number, figure out the magnification at the delta/2 position. Use one of the methods described here. I like Quick disk.
If your reference point and the scales on the ring are separated too far, it is hard to match lines to read min. f-numbers due to parallax problem.
There is also some error produced by backlash of the focus knob. The DOF card has the advantage in this regard since it does not involve any backlash.
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