I 've asked a question about the diffraction of small f-stop diameter in my last post. And, now I'd like ask about caluculating DOF for my particular shooting situation. As I mentioned before, I am shooting 6 people, who are standing very closely each other in front of black seamless, in the studio using 8x10 with a 165mm super angular lens. Because I want to make people just fit in the frame, the lens is very close to them. (about 30 in.) Then, to make everything in focus I think I have to stop down to f64 . (Near distance 30in. Far distance 70in) Then, I'm going to make at least 30in x 40in prints from the neg. Now, I am wondering where to focus. I know that I have to fucus 1/3 of the point in the area where to be focused and depends on circle of confusion. Since as we know, in the large format, when we move the focusing nob, the size of image changes a lot, I 'd like to know the exact point to be focused to get everything in focus. Is there any fomula which I can caluculate the DOF in this particular situation. Thanks Joe

-- Joe (joe266@aol.com), January 06, 2001

Answers

The Rodenstock DOF/Scheimpflug rotary calculator will fit in your shirt pocket and easily calculate this for you.

Many cameras let you focus the lens which does not change the film to subject distance. Some let you focus the film which does change the film to subject distance.

To keep a given extension when focusing Linhof makes some heavy duty focus rails that will let you move the camera front and back to obtain focus while keeping a lens to film distance at a constant. These will easily support an 810 camera.

We even set up the Smithsonian with one of these to move a very large and heavy IR video camera for use in restoring old paintings.

BTW, I trie to email this to you but your address bounced back.

-- Bob Salomon (bobsalomon@mindspring.com), January 06, 2001.

Joe, please read http://www.cs.berkeley.edu/~qtluong/photography/lf/how-to-focus.html and use II.3 without any movement. The formulas are much simpler on your rail (image space) than if applied in the scene (object space). Also, try to provide us with a valid email.

-- Q.-Tuan Luong (qtl@ai.sri.com), January 06, 2001.

I found this long and helpful article and reproduce it here. It argues that as the format increases, depth of field and diffraction decrease at an equal rate. This means that an 8x10 camera can use much smaller apertures than a 35mm before diffraction becomes a problem. When you get to the end of the article, you will see that there is a 6-stop difference between 8x10 and 35mm: f64 for an 8x10 camera is equivalent to f8 for a 35mm. You won't have a diffraction problem when using f64 with 8x10. This may even be the optimum aperture, just as f8 is about optimum for 35mm. Where else does the f64 Group get its name? I stop down to f45-f64 with 8x10 as a matter of course. I bet this article with spark some controversy.

Title: Dof is Squelched by Diffraction Author: Michael Davis Date: 1998/08/15 Newsgroup: rec.photo.misc Diffraction is the only aberration suffered by pinhole cameras. It is an image degrading phenomenon for which there is no means of correction. The smaller the aperture through which light must pass, the greater the effect and the more an image at the film plane must be magnified to create a print of a given size, the more visible the degradation in that print.Small formats are proportionately more vulnerable to the effects of diffraction than larger formats, so much so, that the smallest formats, APS and to a lesser degree, 35mm, can not exploit the Depth of Field advantage they have over large formats at their smallest available apertures. They are diffraction-limited to using wider apertures than those which can be used by the larger formats. Depth of Field is squelched by diffraction and the point at which this happens moves to smaller f-number values (wider apertures) as the format diagonal decreases. The good news is that at the diffraction-limited apertures for each of the formats, the exact same depth of field can be achieved, with the larger formats having a disadvantage of longer exposures. Let's look at why this is true. John B. Williams authored a book called *Image Clarity, High- Resolution Photography* that has a discussion of diffraction. He gives the following formula that calculates the radius (r) of an Airy disk. (G.B. Airy is the astronmer who discovered diffraction in 1890 and diffraction's disks are named after him, Airy, not airy.) I can't type a lamda, so I have substitued a "w" in the formula below, for wavelength. "f" is for focal length and "a" is for diameter of the aperture. r = 1.22w(f/a) OK, f/a can be renamed N where N is the familiar f-number that describes the ratio of focal length to aperture diameter. That gives us this: r = 1.22wN In his book, Williams selects 0.0005 mm as an average wavelength of light, but I prefer 0.000555 mm, or 555 nanometers as being the wavelength that is dead center in the spectrum of sensitivity. It happens to be a nice yellow-green, not far from William's choice anyway. OK, moving on, that gives us this formula, using 555 nanometers for all future calculations: r = 1.22 * 0.000555 * N r = 0.0006771 N To convert this formula to diameter (d) instead of radius (r): 2 * r = 2 * 0.0006771 N d = 0.0013542 N This is the diameter in millimeters. It was at about this point that I decided I didn't like the fact that William's formula had so few significant digits in the constant 1.22, so I went searching and found a longer, more accurate version of it and here it is -- infinitely accurate: __ 1.21966 (66 repeating) Not much different from 1.22, but it does change my formula for diameter of an Airy disk to this: d = 0.00135383 N Previously, I introduced a bit of myself, so to speak, when choosing 555 nanometers as the average wavelength for calculating the diameter of Airy disks and now I would like to state that I believe 1/175-inch is a good, aggressive choice for maximum permissible circles of confusion when doing depth of field calculations and thus, it is also my choice for the maximum permissible diameter of Airy disks. The reason this is expressed in fractions of an inch instead of millimeters is because that is the convention for discussions of circles of confusion and that convention also adheres to stating such diameters not at the film plane, but rather at the print, after magnification from a negative, and that print size is a print with a 10-inch diagonal that is expected to be viewed at a distance of ten inches. More specifically, the viewing distance is measured from the eye to any equidistant corner, while centered over the print, not from the eye straight down a line perpendicular to the plane of the print. If the two of us are discussing circles of confusion and are both adhering to this convention, we will be comparing apples to apples even if you use 8x10 and I use 35mm and better still, if you decide to make a 16x20 print and I decide to make a 32x40 print, as long as viewing distances are equal to the print diagonals in each case, they will both have the same perceived sharpness (in so far as depth of field can effect sharpness) if we have both chosen the same value (i.e. 1/175-inch) as the maximum permissible diameter for circles of confusion for a 10-inch diagonal print to be viewed at 10 inches. Our mutual decision to limit circles of confusion to 1/175-inch in a 10- inch diagonal print would limit CoC's at the film plane to 0.024724 mm for my 35mm, but your 8x10 could permit CoC's at the film plane that are much larger, 0.185874 mm. Both formats would however, deliver the same illusion of depth of field after magnification to a given print size, at a given viewing distance. Quoting page 131 of "Basic Photographic Materials and Processes" by Stroebel, Compton, Current, and Zakia (c1990 Focal Press): "Permissible circles of confusion are generally specified for a viewing distance of 10 inches, and 1/100 inch is commonly sited as an appropriate value for the diameter. A study involving a small sample of cameras designed for advanced amateurs and professional photographers revealed that values ranging from 1/70 to 1/200 inch were used -- approximately a 3:1 ratio." It's somewhat subjective, but I like 1/175 inch, toward the more critical end of the range used by manufacturers. The larger the value you specify for the denominator, the more conservative your calculated depths of field will be. The rotating-disk Depth of Field calculators published by Kodak in their Photoguides use a generous, less critical value of 1/100 inch. Using 1/175 inch, the maximum tolerable diameter of circles of confusion for a given format can be calculated as the format diagonal divided by 1750. (There would be 1750 circles set end to end along a print diagonal that is 10 inches in length.) As discussed above, the diameter of Airy disks is calculated as 0.00135383 * f-number. If we can calculate the aperture at which Airy disks become 1/175 inch diameter when the format is enlarged or reduced to a 10-inch diagonal print, we will know the aperture at which it is pointless to make circles of confusion any smaller than 1/175 inch. This will be the aperture at which a quest for more Depth of Field should be conducted using techniques other than going to a smaller aperture (increasing the subject distance, using tilts and swings, etc.) Here we go: To set the size of the Airy disks equal to (and no larger than) the tolerable diameter for circles of confusion for any format after magnification or reduction to a 10-inch diagonal print to be viewed at 10 inches, I just have to equate to 1 the quotient had when circles of confusion diameter is divided by Airy disk diameter, then reduce. 1 = (Format Diagonal mm / 1750) / (0.00135383 * f-number) or f-number = Format Diagonal mm / 2.36920501777 Tah-dah! My formula makes two assumptions. This constant is specific for yellow-green light at 555 nanometers and we don't want our Airy disks to exceed 1/175-inch on a 10-inch print viewed at 10 inches. You may modify the constant proportionately if you want to change the values 0.000555 for wavelength or 1750 for the number of Airy disks set end-to-end along a 10-inch diagonal print. Here's the formula modified to allow specification of a diameter other than 1/175-inch: f-number = (Format Diagonal,mm / 0.01353831438675) * Max. Disk Diam.,in. But for the remainder of this disuccsion, let's stick with 1/175-inch as our maximum permissible diameter in a a 10-inch diagonal print to be viewed at a distance of 10 inches. So, this calculated f-number is the aperture at which diffraction's Airy disks would have a diameter of 1/175th inch in a 10-inch diagonal print. As long as the viewing distance is equal to or greater than the print diagonal, there would be no visible evidence of diffraction, no matter how large the print is. If however, the viewing distance were to be cut to one half the print diagonal -- say a viewing distance of 12.5 inches for a 16x20 print, then the aperture number would have to be cut in half. For example, using the formula above, the f-number at which the 8x10 format would begin to show evidence of diffraction in a print viewed at a distance equal to its diagonal is: 312.51 mm / 2.36920501777 = 132 So, according to the math, we can use f/90, but not f/128 (very near f/132). If we know in advance that we'll be viewing the final print at half the print diagonal, we have to cut the f/number in half -- in this case, from f/128 to f/64 -- a two-stop difference. In this case, f/45 would be acceptable, but not f/64. Another easily overlooked point is that since this the formula uses format diagonal, if you know in advance that you will be cropping to use only a portion of the full image area, you should use the resulting cropped diagonal to calculate the f-number at which diffraction effects become visible! The smaller the diagonal, the greater the effects of diffraction because of the increase in magnification necessary to yield a given print size. Format diagonal and maximum permissible diameter for the Airy disks are the only variables for determining the f-number at which the effects of diffraction become visible. Using the formula given above, where Airy disks will be limited to a diameter of 1/175 inch in a 10- inch diagonal print, and which will be found equally acceptable in any size print as long as the viewing distance is equal to or geater than the print diagonal and where the full format diagonal is used, without cropping, I get the following values for these formats: Format Full Diagonal Diffraction No Diffraction Visible at Visible at APS 34.51 mm f/14.56 f/11 35 mm 43.27 mm f/18.26 f/16 4.5x6 cm 69.70 mm f/29.42 f/22 6x6 cm 77.78 mm f/32.83 f/22 + 1/2 stop 6x7 cm 87.46 mm f/36.92 f/32 6x9 cm 102.08 mm f/43.09 f/32 + 1/2 stop 4x5 in 153.67 mm f/64.86 f/45 + 1/2 stop 5x7 in 208.66 mm f/88.07 f/64 + 1/2 stop 8x10 in 312.51 mm f/131.9 f/90 + 1/2 stop 10x12 in 383.47 mm f/161.9 f/128 11x14 in 447.78 mm f/189.0 f/128 + 1/2 stop Now let's generate the same table, but this time using the cropped image diagonals that would be used to produce 4:5 aspect ratio prints, (8x10, 11x14, 16x20, etc.) instead of the full format diagonals. Since the diagonals are smaller in some cases, where the full format diagonal is not already a 4:5 aspect ratio, the resulting diffraction limits occur sooner, at wider apertures! Format 4:5 Cropped Diffraction No Diffraction Diagonal Visible at Visible at APS 26.73 mm f/11.28 f/8 + 1/2 stop 35 mm 38.42 mm f/16.22 f/11 + 1/2 stop 4.5x6 cm 66.43 mm f/28.04 f/22 6x6 cm 70.43 mm f/29.73 f/22 + 1/2 stop 6x7 cm 87.08 mm f/36.75 f/32 6x9 cm 88.04 mm f/37.16 f/32 + 1/2 stop 4x5 in 153.67 mm f/64.86 f/45 + 1/2 stop 5x7 in 193.69 mm f/81.75 f/64 8x10 in 310.55 mm f/131.1 f/90 + 1/2 stop 10x12 in 377.78 mm f/159.5 f/128 11x14 in 442.18 mm f/186.6 f/128 + 1/2 stop If viewing distance is one half of print diagonal, open up two more stops. An acceptable aperture of f/16 for uncropped 35mm must be opened to f/8 if the print will be viewed at a distance equal to half its diagonal! At the top of this article I stated that at the diffraction-limited apertures for each of the formats, the exact same depth of field can be achieved, with the larger formats having a disadvantage of longer exposures. We've got the foundation to look at that, now. Everybody laments that an 8x10 has less Depth of Field than a 4x5, than a 6x7, etc., assuming they are using equivalent focal lengths and people argue that tiny formats like APS offer more depth of field, but thanks to diffraction, the small format DoF advantage is squelched. The achievable diffraction-limited Near Sharp distances are IDENTICAL for all formats, given that the ratio of focal length to image diagonal is the same from one format to the next. In other words, if several formats are using focal lengths that are equivalent in their ratio to the format diagonals, the effects of diffraction will limit each format to a unique minimum aperture at which diffraction becomes visible AND it turns out that if you calculate the Depth of Field for each focal length/image diagonal pair AT THOSE UNIQUE APERTURES, you'll find that ALL the formats can achieve the SAME Near Sharp (without movements and at different f/stops, course). The only disadvantage had by the larger formats is the longer exposure times necessary to reach their diffraction-limited apertures. The smallest formats, can not use their smallest apertures, but they too can achieve the same Near sharps had by the larger formats using the apertures that aren't diffraction limited for them. They have no depth of field advantage, only the advantage of shorter exposures to get the same depth of field larger formats have with longer exposures. (I'm compelled to mention here, that aside from the issues of depth of field and diffraction, the larger formats benefit by all that comes with having less magnification to get to a given print size and until someone makes a 35mm with full movements, the larger formats also benefit by using movements to control the position of the focus plane and perspective.) In the table below, the third column (Near Sharp at f/22) was calculated using a maximum permissible diameter for Circles of Confusion of 1/175th of an inch. The fourth column (Largest Aperture with Visible Diffraction) was calculated with aerial disk diameters of 1/175th of an inch, also. This reduces to the equation: Format Diagonal in mm / 2.36920501777 = Aperture where diffraction becomes visible. Focal length is not a variable for this calculation. Format, Focal Near Sharp Largest Near Sharp at Using 4:5 Length Distance Aperture Largest Aperture Aspect Ratio (mm) at f/22 With Visible With Visible Diagonal (feet) Diffraction Diffraction (f/stop) (feet) APS 24.6 3.0 11.3 5.7 35mm 35.3 4.2 16.2 5.7 6x7cm 80.0 9.6 36.8 5.7 4x5in 141.2 16.9 64.9 5.7 8x10in 285.3 34.2 131.1 5.7 11x14in 406.2 48.7 186.6 5.7 First, notice that at f/22, the Near Sharps are much closer for the smaller formats. (The Far Sharps are all nominally at infinity.) So you can see that 8x10 has half the Depth of Field enjoyed by 4x5, with a resulting Near Sharp that's twice as far from the camera. But, also notice that the last column calculates the Near Sharp distances for each format at each format's largest aperture with visible diffraction. The Near Sharps at THESE apertures all work out to be exactly the same! For these focal lengths, they are all 5.7 feet. And notice that thanks to diminished diffraction, the larger formats can bring their Near Sharps to that had by APS and 35mm, just by stopping down to apertures where small formats should not follow. Diffraction limits them all to the SAME Near Sharp. Large Format can get just as much Depth of Field as small format because diffraction is getting out of the way exactly in proportion to the loss of Depth of Field! Guess what? At the diffraction-limited apertures for each format, the size of the hole the light passes through is identical in proportion to the format diagonals! That's why this whole discussion is true. The above chart illustrates the fact that the impact of diffraction is diminished linearly just as the Depth of Field diminishes with increase in format diagonal. So, to avoid diffraction, the astute 35mm photographer stops down no further than f/16, the APS photographer no further than f/11, etc. and the depth of field promised at apertures smaller than f/16 can never actually be enjoyed. With a focal length of 35.3mm, the 35mm format can not enjoy a Near Sharp closer than 5.7 feet. BUT, this figure holds true for EVERY format using equivalent focal lengths, at the diffraction-limited minimum apertures for each format. They can all achieve a Near Sharp of 5.7 feet when stopped down to their respective diffraction-limited minimum apertures. Obviously, the larger formats will need longer exposures to achive this Depth of Field (independent of movements) and the 11x14 format would be hard pressed to find a lens with f/180. So, in summary, I contend that even without their movements, large- format cameras CAN achieve the exact SAME Depth of Field had by the smaller formats (with longer exposures.)

-- William Marderness (wmarderness@hotmail.com), January 06, 2001.