The resolving power of a camera is measured by the size of the fi nest details that are separate entities in the object and can be represented as separate entities in the image. The modulation transfer function (MTF) does not give a set limit, but rather portrays the degree to which the camera represents sine wave objects in the image. Other related terms are acutance and acuity; these will not be discussed here.
As one records higher and higher frequencies, the ability of a sensor to reproduce detail decreases, and sooner or later it will reach a point where the detail is either not reproduced, or it is reproduced so poorly that we can consider the feature not reproduced. The point just before this complete failure typically is cited as indicative of the power of the sensor to resolve detail. The standards for determining the resolving power cut-off point vary depending upon the target being used, the criterion the investigator chooses to use, and the way in which the sensor performance deteriorates. They are:
Loss of modulation. This typically is used when measuring sine wave responses. The modulation of the original is the peak density of the chart minus the trough modulation of the chart. Similar measurements are made on the image and the ratio of the two is given, usually in log base 10 values (audio devices are measured in decibels, which is also a log base 10 measure). When the log loss in modulation is equal to 0.3, the
actual modulation has dropped by half. Sometimes this is used as the cut-off point. A more generous analysis results if we compare the modulation due to the image to the modulation that is the result of random noise. When the noise level is 0.3 log units lower than the target-induced modulation, then the signal-to-noise ratio is 2:1, and this might be used as a cut-off point as well.
When using this approach, we speak of the modulation transfer function, or MTF of the “ system. ” To obtain this, we measure the log modulation compared to that of the target at several frequencies. The result is a curve that is fl at up to a point and then starts to slope downward. Figure 6.3 shows a MTF curve. As it turns out, the MTF for a full system is the product of the MTFs of the elements: the sensor, the lens, the printer, and whatever else is in the system. On a log scale, the values for all the elements can be added and then normalized to get the overall response since this is the equivalent of the product of the values in linear space for each of the elements. The result is that we can measure the various components of the system and compute the system MTF, or we can infer the MTF of one of the elements if that of the system and the other elements is known. In practice, MTF is useful for engineers designing elements of a system, but not very practical for the camera user.
FIGURE 6.3 MTF Response. In unfi ltered images, there is a tendency for low frequency information to be reproduced at 100%. For higher frequencies, the response rate drops off. MTF curves for the elements of an imaging chain can be multiplied together to give the overall response function of the system.
Increase of Noise . In portions of an image with low levels of light, the signal generated by detail in the object will result in small levels of response from the sensor. It is also at these points where pixel-to-pixel variation due to random noise is most noticeable (due to dark current). The noise results in a colored version of salt-and-pepper patterning. At some point, the average level of the noise is comparable to that of the signal, at which point it is not possible to know whether a given feature in the image is due to signal or noise. Typically we look for a signal-to- noise level (averaged over a small area) of 2:1 or better. Whether we are looking at sine wave or bar chart test targets, the result is the same: we cannot determine what is being shown in the image.
If the image is on a print, then typically there is a problem at the high-brightness areas of the image. The noise level goes up in fi ne detail areas due to random fl uctuations in the printing device and the level of modulation is down. The result is that we cannot determine whether the areas between the supposedly separate dark areas on the test target are being seen as separate or not. Figure 6.4 shows this effect. In any event the system has failed to clearly show the separate features in the input as separate in the output.
Pixelization . In digital images, the picture comprises millions of small picture elements, or pixels, each of which has a single color. If the image is enlarged multiple times on a computer screen, it is often possible to see the separate pixels. There is no detail smaller than a pixel. But any feature in an image has more than a single color. A yellow spot on a brown background might comprise a feature. Without a background of a different color, the feature is merely another spot among many that are all the same. Typically the smallest feature is portrayed as a dark line adjacent to a light line, or a line pair.
FIGURE 6.4 Some Resolution Failure Modes. Photomicrographs of three-bar resolution test targets at points close to failure. The silver halide image shows typical MTF roll-off in the form of a blurring of edges. The Pro Ink Jet printer shows high density areas blocking and merging across the space between bars. The Desktop Ink Jet printer shows the generation of a lot of random noise, making it hard to know which spots go with which bars.
C H A P T E R 6 : Resolution
Clearly a number of line pairs can be lined up so that the dark and light lines alternate. The result is a grid of lines. The United States Air Force chart has such a pattern. There are three line pairs in each patch and there are pairs of such patches near each other but laid out so that they are perpendicular to each other. The patches vary systematically in size, and we look for the smallest pair of patches where both sets of lines are all separate and distinct. The size that corresponds to this set of patches is what is used for stating the resolution of the system under test.
Combinations of criteria . A typical combination of problems might occur in photographing a shoe impression. The fi ne accidental cut details will be on the edge of pixelization problems with most cameras. And you will be hard pressed to fi nd a printer capable of making full life-sized images without also having either noise problems or blocking between adjacent dark areas. If the lens is not a top-quality lens, there will be diffi culty due to its MTF drop-off as well.