...
Aberrations tend to be worse at large apertures (small f-numbers), while diffraction gets worse at small apertures (large f-numbers). As a result, lenses tend to have an optimum aperture where they are sharpest, typically around 2 to 3 f-stops below a lens’ maximum aperture (often less for premium lenses). The optimum is fairly broad. |
You You can find the optimum aperture by running a batch of images (Imatest SFRplus or eSFR ISO recommended) taken at different apertures, then entering the combined output (a CSV file) into Batchview (Figure 1).
...
Figure 1. Set of images taken at f/4.5 to f/22In Figure 1, bars show MTF50 in line widths per picture height (LW/PH) for the weighted mean (black), center area (red), part-way area (green), and corners (blue). The procedure is described in detail here. For the lens results in Figure 1, the optimum aperture (f/8 to f/11) is 2 to 3 stops from the maximum and edge sharpness is unimpressive.
In Figure 2, diffraction-limited MTF is displayed as a pale brown dotted curve in the MTF figures produced by SFR, SFRplus, and eSFR ISO when the pixel spacing (usually in microns) has been manually entered in the appropriate dialog box and the aperture (f-number) is known (it's normally retrieved from the EXIF data, but can be entered manually).
...
Figure 2. MTF plots showing diffraction-limited MTF (as a pale brown dotted line)In this figure, the curve on the left is for the Canon EOS-40D (5.7-micron pixel spacing) with the lens set at f/22, which is a small aperture that should only be used when large depth of field is required and sharpness can be sacrificed.
...
| Eazy math inline | ||
|---|---|---|
|
...
The equation for diffraction-limited MTF can be found below and in Diffraction Modulation Transfer Function from the SPIE OPTIPEDIA, David Jacobson’s Lens Tutorial (older version), and normankoren.com. The diffraction cutoff frequency is
| Eazy math inline | ||
|---|---|---|
|
...
λ is typically 0.555 microns (0.000555 mm) for visible light (yellow-green; the approximate wavelength where the eye is most sensitive), but it can be changed for cameras with different spectral response (such as Infrared).
...
The full procedure explained and illustrated for a 108MP sensor with tiny 0.7 μm pixels and an f/2 aperture, in Test chart suitability for MTF measurements.
Diffraction, pixel response limits, and Q
The question naturally arises, "When is a camera's resolution limited by the optics, and when it it limited by the sensor pixel size?" In other words,
What is the boundary between diffraction-limited and sensor pixel size-limited optical systems?
The question can be addressed with the concept of Q, presented in "Modeling the Imaging Chain of Digital Cameras" by Robert Feite, SPIE Digital Library, 8.3., (Special thanks to J. Gordon Arkenberg for pointing this out to me.)
...
In the old days, DoF was defined as the range of object distances where the circle of confusion in an 8x10 inch print was under 0.2 mm. This definition was useful in the age of film, where lenses were often not as good as they are today (with a few exceptions), big enlargements were difficult to make, and the film itself did not stay flat: its position could vary. Stopping down the lens (increasing the f-number) increases the depth of field, but often at the expense of sharpness where the lens is in good focus (thanks to diffraction). Some applications, like landscape photography, look best with large DoF, but others, like portraits and cinema, look better with small DoF (which can blur out cluttered, distracting backgrounds). As we said, this can be a big subject.
Fixed focus lenses
...
Most consumer cameras have autofocus (or focusable) lenses, but we have recently encountered cases where the focus is fixed, usually either at infinity or the hyperfocal distance — where the lens is focused so so the far DoF limit (however it happens to be defined) is at infinity. These lenses are primarily used in the automotive industry or for aerial photography. When we encounter them, we have to determine if we can effectively test them in the limited space of our facility.
...
[caption id="attachment_47901" align="alignright" width="400"]
...
MTF for defocus
Going back to the Jacobson lens tutorial and noting that MTF = |OTF| (the modulus of the Optical Transfer Function, which includes phase): a negative value of OTF indicates a phase shift,
...