Resolution
by Makoto Honda
Updated February 9, 2005
General
The resolution is defined in terms of "line pairs per millimeter", or lp/mm for short. We are interested in determining how many lines are discernable in the distance of 1 mm. One line pair consists of a black line and the adjacent white line of the equal thickness. The better the lens resolution, the greater the number of lines you can resolve. You need a film to capture the image created by the lens. The better the film resolution, the more you can capture on the film. The final resolution of the resultant picture that you see is the accumulative effect of the lens resolution, the film resolution, and the resolution of other optical/non-optical systems involved in the entire photographic process. The overall resolution, sometimes referred to as the system resolution, is given by the following approximation.
1
System Resolution: Rs =
----------------------------
1 1
---- + ---- + .........
Rl Rf
where Rl is the lens resolution and Rf is the film resolution.
For instance, if your lens resolution is 100 lp/mm and the film resolution is also 100 lp/mm, the system resolution you get is 50 lp/mm. If you use the lens having 200 lp/mm resolution, with the same film, your system resolution will improve to 67 lp/mm.
Lens Resolution
We often use the term "aerial
resolution" in reference to the lens resolution to emphasize the fact that it is
a resolution measure of the aerial image formed by the lens at its focal
plane. Typically a microscope is precisely focused on the aerial image created
by the lens being tested. The lens aerial resolution varies widely depending on
the lens. To give some frame of reference, some high quality
35mm SLR camera lenses, often
associated with the lens manufactured by major camera manufacturers for their
own brand of cameras, yield 600 lp/mm or more, at optimal conditions. (The
resolution is often optimized for a given lens when the setting a
couple of
stops down
from the widest aperture is used for many lenses, though this is
not always the case. Also see theoretical maximum below.) The less pricey lenses, often from the third-party lens
manufacturers, may yield 300 lp/mm. There are, of course, exceptions, on both
sides of the fence. Also, zoom lenses are generally harder to design,
often involving greater number of elements, and
therefore, tend to yield lower resolution relative to their fixed focal length
counterpart. This explains why many professionals shy away from zoom lenses
(though some latest zoom lenses
offer uncompromising optical quality matching that of
prime lenses).
Theoretical Maximum Resolution
The laws of physics impose maximum resolution on the image formed by the lens. This is a theoretical limit due to the diffraction of light. As such, this is the absolute maximum an ideal lens can achieve. The theoretical resolution is dependent on the lens aperture used as well as wavelength of the light, as shown below.
1
Theoretical Maximum Resolution: Rmax =
----------------------------
1.22 x W x Feff
where W is the wavelength (in mm) and Feff is the effective f-stop. (In high magnification photomacrography, the exposure factor often pushes the effective f-stop higher than the f-stop marked on the lens, but in normal shooting situations, it is the same as the f-stop on the lens.) The wavelength of light we human can perceive lies around 0.0004 - 0.0007mm range from blue to red in the spectrum of visible light. Using the mid point of 0.00055mm (monochromatic green), the resolution equation is reduced to :
1500
Theoretical Maximum Resolution: Rmax =
-----------
Feff
The resolution values thus derived are shown in Table I for various f-stops. Again, this is the maximum resolution any lens can possibly achieve. Generally, only at larger f-stops (smaller apertures) does the lens perform anywhere close to these theoretical limits.
Table I
* f-stops below f45 may be only meaningful in photomacrography
Film Resolution
The film resolution is often described for two situations: One is for the test subject having a contrast of 1000:1, and the other of 1.6:1. The first 1000:1 contrast represents a high contrast situation in the testing laboratory, and the 1.6:1 is the average contrast of real-world subjects around us. Expectedly, the film performs much better for the 1000:1 contrast condition than in the real world. Note that the 1000:1 contrast is only achievable in a back-lit projection setup of the test pattern. Even a black and white test chart well lit by a 45 degree illumination only achieves a fraction of this contrast. Therefore, a resolution value measured at 1000:1 contrast is for comparison purposes only among different films, and is meaningless when applied to a real world situation. Here are some examples of film resolution. Generally, a B&W film yields better resolution than color. A color transparency (slide) film typically scores much better than a color print (negative) film. Also, a slower film (lower ISO rating) tends to be superior than a faster film in resolving power.
Some numbers
ISO 1000:1 1.6:1
RMS*
Fujichrome Velvia RVP
50 160
80 9
Fujichrome Velvia 100F Professional 100
160 80
8
Fujichrome Sensia 100
100 160
80 8
Fujichrome Provia 100F Professional 100
160 80
8
Kodachrome 25 / 25 Professional
25 100
63 9
Kodachrome 64 / 64 Professional
64 100
63 10
Kodachrome 200 / 200 Professional 200
100 50
16
Kodacolor
B&W
*Diffusive RMS granularity value
(source: www.fujifilm.co.jp,
http:\\medfmt.8k.com )
Film Is Limiting
Typically, the resolution of the film available in the consumer market today is much lower than the lens resolution. This often makes the film the ultimate bottleneck of the photographic process in the overall resolution equation. This explains why an expensive lens from the camera manufacturer does not drastically improve the picture quality of your family picnic when viewed side-by-side against the picture taken by a much less expensive lens.
A chart below shows the overall resolution (system resolution) for various combinations of lens and film resolutions. If you use a typical color print film of 50 lp/mm resolution, your final resolution is 43 lp/mm with a 300 lp/mm lens. If you spend a top dollar to invest in a top quality lens of 600 lp/mm resolution, your combined resolution improves to 46 lp/mm, a mere 7 % increase. Using the same 300 lp/mm lens, on the other hand, if you change your film from 50 lp/mm to 80 lp/mm, your final resolution jumps to 63 lp/mm - near 50 % improvement!
Good Lenses
High quality lenses are often
found among expensive lenses from major camera manufacturers. The
third-party lenses tend to perform less, for a lesser price. It is also
worth noting that many major 35mm SLR camera manufacturers offer two lens lines,
high-quality lenses for those who need them, and the lesser ones for
"cost-performance", which are sometimes designated as such (a la, Nikon's "XXX"
series). The differentiation is sometimes implicit, seen in the
price. For instance, a compact-size zoom lens, conveniently covering a good
focal length range, at a very reasonable price tag - an ideal lens for everyone
- is not likely to create a highest quality image. This is, by
no means, a negative endorsement on my part for such a lens. If it's suitable for
you, go for it. Just remember the limitations.
Other Factors Affecting Image
Sharpness
Now that you got the best
lens the money can buy (or at least your budget allows for), what should you do
to get the most out of your lens? To put things in perspective, if the
largest picture you ever want is a 3x5 print to put in your family album, all
the discussion we are having has little bearing to you. Even an
inexpensive lens will serve your purpose pretty well. So, let us focus
here on the highest quality image we can possibly achieve in today's
photography.
Things To Do To Achieve The Best Result
1. Use a tripod. Although cumbersome to use and time-consuming to set up (have to carry the darn thing along the way, too) the tripod does make a difference in the image quality. A tripod comes in different sizes and weight. The sturdier the better, of course, but likely the heavier. The tripod is important because the slightest camera movement might wipe out the image quality difference between an expensive lens and a cheapy you paid additional $1000 for. One more thing: If you have taken your time and effort to use a tripod, you should use a shutter release as well.
2. Mirror-lock for SLR cameras. Just like a tripod, this will reduce the camera movement. The use of mirror-lock is recommended by some people in connection with improving image resolution. This, of course, assumes the use of a tripod. In a critical shooting, such as using a long telephoto lens, the camera vibration due to a mirror flipping is not negligible. I have personally used mirror-locking during high magnification photomacrography: With the bellows extended all the way, the field of view is as narrow as a telephoto shot, which makes the image sharpness highly sensitive to camera movement.
3. Vibration-reduction Lenses. Vibration-reduction technology is relatively new. I have heard positive comments, though I have not tried one myself. The lens tends to be bulkier and heavier, but the technology appears to do the magic. Major manufacturers, such as Nikon and Cannon, offer several lenses with vibration-reduction designation.
4. Lend hood. This is very important especially in outdoor photography. You should always try to avoid the sun from hitting the lens. Even with today's advanced lens coating technology, there is often a visible image quality deterioration if a strong light hits the lens. A so-called "ghost image" is one manifestation. I often carry a piece of black cardboard to use as a lens shade in order to avoid the sun, especially for a wide-angle lens, because the attached lens hood is often not enough. The only time I allow the sun to hit my lens is when I am intentionally including the sun in my photograph.
5. Optimal lens aperture. As various tens tests show, it is known that many lenses tend to yield their highest resolution (at the image center) when used at the aperture a couple of stops down from wide open (though this could obviously vary depending on the lens). By stopping down one or two additional stops, you may increase the overall image resolution of the entire frame area due to the improvement of the resolution at the image corner, though the image center resolution may decrease. So, there is such a thing as the "best" aperture for a given lens. Obviously, this is the aperture you should use if the resolution is the only thing you are after. Personally, I decide on which aperture to use, first and foremost, to control the depth of field; the resolution consideration is often secondary.
6. Use a good film. This goes without saying. Even if your lens is forming a perfect image on the focal plane, if the film is not capable of capturing it, what's the point? As discussed earlier, the lens tends to perform much better than regular films commercially available today. That is, the film is limiting in the overall resolution equation. Any improvement on the choice of film, therefore, is likely to have a direct impact on your final photograph. Generally, a slide film (transparency) scores better than a print (negative) film. A slower film speed often means better resolution. (ISO 400 films have far larger grains than ISO100 films.) The highest resolution film is found in BW.
Other Negative Causes For Image Sharpness
There are some other causes to reduce the sharpness of your photographic image, that may not be under your control.
1. SLR camera mirror misalignment. If the mirror does not return to the precise mid-point (at 45 degree angle) between the film and the focusing screen, however carefully you focus, manual or auto, the film is not getting the focused image.
2. Film flatness. This is more of a problem for the film format larger than 35mm.
3. The focus changes as you stop down the aperture. This is a bad lens. If the lens exhibits this tendency, the only remedy is to re-focus at the aperture you intend to use. The only time I consistently do this is when I do high magnification photomacrography. I use Zuiko Macro 20mm F3.5 lens (Olympus) and Minolta Macro 12.5mm F2 lens, both specifically designed for use with a bellows extension. Since the focus tends to move as I stop down, I always set the aperture to f5.6 - f8 (no auto aperture for these lenses) and then focus very, very carefully before firing.
What Eyes Can
See
The unaided eye cannot
resolve more than 4 lp/mm on the print viewed at the distance of one foot. (Ref.
Ronald W. Harris. Understanding Resolution. Darkroom & Creative Camera
Techniques, pp.26-66. Mar-Apr. 1991).
One line pair comprises one white line and one black line. So, 4 lp/mm is equivalent to 8 dots/mm. This is what the unaided eye can discern on the print. The table below shows how many dots are needed on the photographic print to look sharp to the eye based on this unaided eye's maximum resolving capability. These dots, of course, must ultimately come from the image captured on the film (chemical or digital).
Print Size (inches) Short-side (mm) Total Pixel Number Needed on the Film (chemical/digital) *
3 x 5
75 mm x
0.5 M pixels
5 x 7
125 mm x
1.4 M pixels
8 x 10
200 mm x
3.6 M pixels
10 x 14
250 mm x
6.0 M pixels
16 x 20
400 mm x
15 M pixels
20 x 30
500 mm x
24 M pixels
30 x 40
750 mm x
54 M pixels
40 x 60
1000 mm x
96 M pixels
* Total pixel number is computed as (S x 8) x (S x 1.5 x 8) where S is the short side length of the print (expressed in mm). The longer side of the print is assumed to be 1.5 time the shorter side. If the print's aspect ratio is closer to square than 1:1.5 as in film format, it simply means the print is not taking the full advantage of the film real estate, and some pixels are thrown away. Still, for the purpose of pixel number calculation on the film, it is appropriate to use 1.5 aspect ratio.
Table - How many pixels are minimally needed on the image in order to produce a print of various DPIs - provided no pixels are lost during the printing (from the image to print).
Print DPI (dots-per-inch) 100 200 300 400 500 600 700 800
Print Size (inch)
3 x 5
300x500 600x1000
150K 600K
5 x 7
500x700 1000x1400
350K 1400K
8 x 10
10 x 14
16 x 20
20 x 30
30 x 45
40 x 60
Angular
resolution of the eye
Viewing distance, to see the whole picture - not scanning
Necessary print resolution
Max print size from various format film, resolution at the film
Large Format
Cameras
The photography world seems
to be sharply divided into two groups: 35mm photographers and
"large-format" followers. Each group religiously insists on the superiority of
their belief. I belong to the 35mm camp. As we are exploring the issue of
resolution, there is no doubt the large-format films offer far greater number of
dots on the film image, simply because of their spacious real estate, thus
allowing a larger photographic print of undeniable sharpness.
If I came up with an image I really like, and if I can reproduce the shot, I
would certainly love to re-shoot the subject with a large-format camera.
One lesson I learned in photography, which, in my opinion, is the most important and valuable lesson, more than any thing else, is the following realization. And I will let you in on it. It may shock you, or it may not.... Over many years of picture taking, I came to this realization. That is: Photography is not easy! Yes, it is difficult. How difficult? I can give some quantitative measure as to how difficult photography is. It's difficult to make a "good" photograph. Granted, what constitutes a good photograph is debatable, and subjective. But, regardless of your evaluation criterion, making a good photograph is difficult. So difficult indeed that you have to take "many" pictures, in order to get one good shot. For quite some time I had some idea as to how many pictures I have to take to make one good photograph. I recently got a clear number when I was reading an article in National Geographic Magazine. The number sited was one thousand. Yes, in order to make one photograph used in the National Geographic, the photographer shoots, on average, 1000 frames of pictures.
I personally do not have any experience of large format cameras. But I reckon it would take a fair amount of effort to shoot 5000 frames of 8x10 film. Not only that, there are many subject areas where only the versatility of 35mm systems can exploit the subjects. This would explain why the superb images appearing in the National Geographic are taken by 35mm cameras, 90%, and the rest probably 6x6cm or smaller.
Modulation
Transfer Function (MTF)
Until now, we have been
discussing the subject of resolution as it relates to the image sharpness.
However, the true measure of sharpness involves image contrast as well as
resolution. In reality, you can have a lens with an excellent resolution but a
poor contrast, and vice versa. In either case, the final picture sharpness is
compromised. Resolution and contrast must go hand-in-hand.
A graph of contrast transfer (i.e., how well the subject's contrast is retained
in the image) for a given spatial frequency (in line pairs/mm) is called the
Modulation Transfer Function or MTF. This measures the image/subject contrast
transfer in the normalized range of 0.0 to 1.0, with 1.0 being 100% transfer.
Often, the values of contrast transfer for a given spatial frequency are plotted
for different locations on the film away from the image center. MTF graphs
assume radial symmetry of the lens. MTF graphs are also created for various lens
apertures, often for lens wide open, and for some stopped-down apertures. To be
useful, the test target chart (comprising parallel lines) should be rotated at
various angles to see the effect of aberrations. Typically, for simplicity, only
two angles are used. One with the target lines parallel to the outward line from
the image center, called sagittal lines, and the other tangent to the outward
line, called tangential lines. MTF graphs are generally prepared for white
light, but can be measured for a specific monochromatic light as well.
MTF is useful to describe the quality of the lens accurately. Unfortunately, not all manufacturers provide MTF data for their lenses. Unlike resolution testing, MTF data are not readily derived outside of testing laboratories. To truly describe a given lens, many MTF graphs are needed, depending on lens apertures, spatial frequencies, and the light used. It is even possible to measure MTF for differing subject distances. Such is the case, MTF data from different sources cannot be directly compared without noting the conditions under which MTF data are derived.
How To Read MTF
To help interprete the MTF data, sample MTF graphs are given below for a fictitious 50mm f2.8 lens for 35mm format camera. The upper graph shows MTF data at lens wide open at f2.8. The lower graph shows MTF data for the same lens at f8. Each graph shows MTF curves for three different spatial frequencies: 10 lp/mm, 20 lp/mm, and 40 lp/mm. For each spatial frequency, a pair of MTF curves is given, one for the sagittal target lines (green) and one for the tangential target lines (red). Contrast always drops off as the spatial frequency increases. Recall from the discussion of theoretical maximum resolution that the f-stop limits the maximum resolution. For a given f-stop, contrast drops to zero at that spatial frequency. Of three pairs of curves on each graph, the MTF values for the lower spatial frequency (10 lp/mm in this example) are indicative of the overall contrast of the lens. The higher the curve throughout the distance range to the corner of the image (towards right in the graph), the better contrast the lens exhibits. The MTF values for the higher spatial frequency (40 lp/mm here) are more indicative of the resolution of the lens. Comparing the two MTF graphs below, both contrast and resolution are seen to move up as the lens aperture was stopped down to f8. General improvements toward the image corner are also seen.
Nikon site provides MTF data for various lenses at the end of each page.