In Chapter 3, the idea of resolution was introduced briefl y. In this chapter we will develop the means to calculate the resolution we can get with a given
camera. In the case of fi lm cameras, the resolution can be changed by the choice of fi lm. But in digital cameras the sensor is a physical part of the camera and so is not adjustable. (Many digital cameras allow the photog- rapher to save images at a lower resolution than the full capability of the sensor chip, but not higher.) Another important factor is the lens quality. For most of this chapter, it is assumed that the quality of the lens is so good that it is not really a factor. But beware, some aftermarket lenses are fairly poor and can have an impact on the resolution you can achieve with a given camera.
The place to start is with some basic phenomena and the terms associ- ated with them. First there is the issue of spatial frequency. To understand this, assume a repeating pattern such as the bar charts or sine wave charts in Figure 6.1 , which show two common implementations.
Basically, as the feature size gets smaller, the spatial frequency gets higher. In the case of sine waves, the wavelength λ is the distance from one peak to the next. The frequency ν is the reciprocal of the wavelength, as follows:
λ⫽1 /ν
The wavelength is in units of distance such as inches or millimeters, and the spatial frequency is in reciprocal distance such as per inch or per mil- limeter. Low frequency information has a long wavelength and corresponds to the broad portions of the image. High frequency information has a short wavelength and corresponds to the fi ne markings in the image.
In the test targets, selected frequencies are presented and the results in the photograph are compared with the original target, frequency by fre- quency. In general, as the frequency increases, there will be an even, high level of ability to reproduce the target up to some point. Beyond this point, the ability of the system to reproduce the target will decrease.
FIGURE 6.1 Two Commonly Used Test Targets. There are many test targets in regular use. These two are common and very different. The sine wave pattern is used to measure the Modulation Transfer Function and the three-bar USAF pattern is used to measure line pairs per millimeter that are resolved. C H A P T E R 6 : Resolution
The tendency is to think in terms of the rows and columns of the pixels. But the real world is more complicated than that. The object might be composed of lines, but they are probably not aligned with either the rows or the columns. The processes involved work about the same in both the rows and columns (except in certain video applications where the pixels are not square). So if the angle is known, we can estimate the resolution with Pythagoras’ Theorem. This implies that the best result we might hope for is that the lines are parallel to either the rows or columns since the hypotenuse is greater than either of the other two sides of a right triangle.
Note the two images in Figure 6.2 : the top one is missing high frequency information and the bottom one is missing low frequency information. The original did not have patches with discrete frequencies, however. What the fi gure demonstrates is that the various frequencies behave as though they were built into all the features in the image, and that they add together in special ways to form more complex structures. For example, sharp edges of even broad elements such as the block letters are built up of a large number of high frequencies all added together (Fourier ’s Theorem). When the higher frequencies are selectively decreased or eliminated, the edges become blurry.
FIGURE 6.2 Attenuation of High or Low Frequencies. The upper rendition shows the loss of high frequency information and how it makes edges soft and fi ne lines disappear. The lower rendition shows the loss of low frequency information and how it hollows out solid areas and makes broad sine wave bars disappear.
C H A P T E R 6 : Resolution
92
The higher frequencies are not presenting the broad, fl at areas, however, and so these are unaffected. The broad fl at areas are comprised primarily of lower frequencies, and when these are attenuated or blocked, the broad areas become hollowed out.
With traditional fi lm photography, where the photographer can change fi lms, the important factor (again assuming a very good lens) is the fi lm. Accordingly the ability to reproduce detail is stated in terms of distances on the fi lm . It might be stated as 100 line pairs per millimeter on the fi lm. With digital cameras, this is not the case. There is no fi lm that can be changed to give a higher resolution and we will never work directly with the image on the sensor chip, so such a rating is of no interest. Instead, we must be con- cerned with distance on the object. So the limit will be in terms of, let’s say, line pairs per millimeter on the object . An alternative is to work in line pairs per frame width. Then assuming knowledge of the frame width in millime- ters, for example, it is simple to compute the number of line pairs per mil- limeter on the object. The real question is, “ If I take a photograph of a full shoe impression, will I be able to resolve the fi ne details and make a unique identifi cation? ” If the shoe is a small size and the details are of a goodly size, the odds are good. If the shoe is much larger and has the smaller detail, the odds will decease.