Diffraction Effects (Example Photos)
(...Continued from above)
For calculating either the CoC diameter that you can specify in your choice of DoF calculator (of those that permit user-specification of max. CoC) or for calculating the f-Number at which diffraction will begin to inhibit a desired final image resolution at an anticipated enlargement factor, here are some definitions of the two variables used in each equation:
Enlargement factor is simply the ratio of the final image dimensions to your sensor or film dimensions. (Divide print diagonal by sensor diagonal, or print width by sensor width, for example.)
For your desired final image resolution, I recommend a value of 4- to 8-lp/mm when you want the print to survive scrutiny at a viewing distance of 10 inches. 4 lp/mm will satisfy most people at that viewing distance and anything greater than 8 lp/mm would be overkill (despite Ctein saying that some people can appreciate resolutions as high as 25 lp/mm in a print viewed at 25cm). If you only want to satisfy a viewing distance of 20 inches, you can cut my recommendation for desired resolution (at 10 inches) in half.
A desired final image resolution of 2 lp/mm requires an unresampled image file resolution of 100 dpi (for a sensor that lacks an AA filter) or 144 dpi for a typical CMOS sensor, due to a 30% loss of resolution typically imposed by the RGBG Bayer algorithm and AA filter.
A desired final image resolution of 3 lp/mm requires an unresampled image file resolution of 150 dpi (no AA filter) or 216 dpi (with 30% Bayer and AA losses).
A desired final image resolution of 4 lp/mm requires an unresampled image file resolution of 200 dpi (no AA filter) or 288 dpi (with 30% Bayer and AA losses).
A desired final image resolution of 5 lp/mm requires an unresampled image file resolution of 250 dpi (no AA filter) or 360 dpi (with 30% Bayer and AA losses).
A desired final image resolution of 6 lp/mm requires an unresampled image file resolution of 300 dpi (no AA filter) or 432 dpi (with 30% Bayer and AA losses).
A desired final image resolution of 7 lp/mm requires an unresampled image file resolution of 350 dpi (no AA filter) or 504 dpi (with 30% Bayer and AA losses).
A desired final image resolution of 8 lp/mm requires an unresampled image file resolution of 400 dpi (no AA filter) or 576 dpi (with 30% Bayer and AA losses).
Before you can select a "desired" final image resolution, you have to be realistic when selecting an enlargement factor.
For example, the Nikon D300's 15.7 x 23.7mm sensor captures 4288 x 2848 pixels (12.21 MP) at a moderate pixel density of 181 pixels/mm.
Taking into account the loss of resolution caused by the RGBG Bayer algorithm and AA filter, typically a 30% loss relative to actual pixel count, if you "desire" to record subject detail in the final image at a resolution of 5 lp/mm, you'll be limited by pixel count to the following print dimensions:
Max. 5 lp/mm Width: 4288 pixels / 360 dpi = 11.91 inches
Max. 5 lp/mm Height: 2848 pixels / 360 dpi = 7.91 inches
Assuming you plan to make 7.91 x 11.91-inch prints (where the Pixel Count will support a desired print resolution of 5 lp/mm), your enlargement factor (without cropping) would be 11.91 inches / 23.7mm = 302.54 mm / 23.7mm = 12.8x
Now let's run the two equations for an anticipated viewing distance of 25cm (9.84-inches):
FOR CONTROLLING DEFOCUS:
CoC (mm) = 1 / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement factor
CoC (mm) = 1 / 5 / 12.8 = 0.0156 mm
Your largest CoCs, which will occur at the near and far limits of DoF, must not exceed 0.0156 mm at the sensor, before enlargement. Plug this CoC diameter into your choice of DoF calculators (www.dofmaster.com, for example), then follow the calculator's recommendations for setting both your working aperture and your focus distance.
FOR CONTROLLING DIFFRACTION:
N = 1 / desired print resolution (lp/mm) / anticipated enlargement factor / 0.00135383
N = 1 / 5 / 12.8 / 0.00135383 = 11.54 (or f/11.54)
Thus, even when your DoF requirements indicate that you should use an f-Number larger than f/11.54, doing so would cause diffraction to inhibit your desired goal of 5 lp/mm in prints that require an enlargement factor of 12.8x.
(...Continued from above)
Unfortunately, the loss of subject detail caused by diffraction impacts the entire image uniformly, where loss of subject detail caused by defocus occurs only at the near and far sharps of DoF. Thus, it's more difficult to discern a loss of resolution that impacts the entire print vs. a loss of resolution that occurs only at the nearest or farthest distances in the subject space, unless you make a side-by-side comparison of two prints.
Any print can be made "sharp" by enhancing its acutance (edge sharpness), through the use of tools like unsharp mask in PS, but rendering actual subject detail at resolutions that cause people to gasp in appreciation, requires that you control both defocus and diffraction, to ensure that both the circles of confusion caused by defocus -and- diffraction's Airy disks are kept small enough, after enlargement, to satisfy your desired print resolution (which should have been chosen with consideration for an anticipated viewing distance).
For a better understanding of the difference between acutance and resolution, see Sean McHugh's tutorial on "sharpness" at http://www.cambridgeincolour.com/tutorials/sharpness.htm
Remember that if the DoF calculator calls for an f-Number that you can't use (because the corresponding shutter speed would be too slow, or because that f-Number is larger than the f-Number at which diffraction will become visible, or because your lens simply doesn't offer that f-Number), all you have to do is....
Back away from the nearest subject until you're far enough away to use a viable f-Number (you'll have to recalculate DoF for this new range of subject distances).
Go to a shorter focal length without moving the camera (you'll have to recalculate DoF for this new focal length).
Resign yourself to making a smaller print: Reducing the enlargement factor by 1.414x (making a 10-inch print instead of a 14-inch print) allows you to open up one stop and get the same apparent resolution. Reducing the enlargement factor by 2x (making a 7-inch print instead of a 14-inch print) allows you to open up two stops and get the same apparent resolution).
Resign yourself to hanging the print in a location (over a piano?) where people can't examine it at your originally anticipated viewing distance: Increasing the viewing distance by a factor of 1.414x allows you to open up one stop. Increasing the viewing distance by a factor of 2x allows you to open up two stops. (This last solution is difficult to enforce, so it's not practical.)
Sometimes, in the interest of maintaining your intended composition (as defined by your original choice of camera position and focal length), it's best to just go for a smaller print (an enlargement factor lower than that specified when you calculated the Circle of Confusion diameter used to produce your DoF calculators) rather than backing away from the nearest subject or selecting a shorter focal length - both of which can change the composition drastically. But you've got to remember that you made this choice, in the field, to go with a smaller print. Don't cop out later and produce the full sized print only to suffer visible degradation caused by defocus and/or diffraction. Stay the course.
Lastly, please realize that there are many factors other than available pixel count, defocus and diffraction that can prevent you from achieving a "desired" final image resolution. What I've written here only describes an approach to controlling defocus and diffraction, with no attention given to lens resolving power at various apertures, the smearing caused by subject or camera motion at inadequate shutter speeds, film resolution and in-camera flatness (for those who are still shooting film), etc. Defocus and diffraction are, however, among the most controllable of factors affecting final image resolution, if you're willing to exercise that control instead of just rolling the dice every time you make an exposure.
For more on how I approach landscape photography (only one of many ways to boil the proverbial egg), read these five posts (or the entire thread) from the Canon Digital Photography Forum:
The complete thread starts here:
Mike Davis wrote:
You've made an excellent point here, Lance, regarding viewing distance, which like enlargement factor, should always be declared when drawing conclusions about the impact of diffraction or defocus on one's ability to achieve a desired resolution (another varriable that should always be declared).
Again, I thank you for seeing the light, Mike! As I replied in the other thread with regards to your brilliant post:
"This has partly been where I have been coming from with regards to the 36Mp sensor and it being desriable, may be not to all, but to plenty of us. Others have gone off in tangents explaining how a FF 36Mp sensor will not assist us, will actually be a step backwards and that all we need is FF 12 or 16MP or whatever, but they miss this very vital point that I pointed out and that you have written about in your long and very interesting very detailed dissertation.
Again, I thank you for being another light of reason!" emoticon - smile