Discrete Effect Analysis of Printed Images

According to communication theory, it is known that when using a discrete method, under ideal filtering conditions, if the reading frequency is two times higher than the band limit of the signal, then any signal can be accurately transmitted. But in actual work, the filtering situation will not be very satisfactory, so the reading frequency must be higher. Then, if the reading frequency is particularly high, a higher system speed and a larger storage capacity are required. Decreasing the reading frequency will cause distortion in the high frequency band of the signal.

When copying a printed image with a scanning device having an information digital processing function, one can see these distortions in the blurred contour of the detail and in the resulting quantized image. This is because in a certain discrete reading frequency L, if the spatial frequency is higher than a certain limit value corresponding to the image density resolution value R, the spatial frequency cannot be reproduced on the printed matter. The L/R ratio is now referred to as discrete/coefficient Kd.

When selecting discrete parameters, the main decisive factors are the resolution of the synthesized printed image and the spatial frequency of the original image. The density resolution of the synthesized printed image determines the minimum frequency of readings on the copied image.

The discrete reading frequency obtained on the manuscript should be different by M times the discrete reading frequency obtained on the copy (M is the reproduction ratio). This relationship holds true when the density resolution of the original is at least M times greater than the resolution of the replica. When this relationship cannot be achieved, the discrete reading frequency obtained on the manuscript and the discrete reading frequency obtained on the synthesized replica can be reduced proportionally.

In practice, it mainly involves the quantitative relationship between the discrete reading frequency obtained during the digital processing of the printed image and the resolution of the synthesized printed image and its measurement method.
Methods as below:

We used a roller-type scanning device to decompose and synthesize a line test chart. The line width and line spacing of this test chart are equal and range from 15 lines to 100 lines per cm.

The position of each line pattern group and the scanning direction are in the form of parallel, vertical and 45° angles, respectively.
We used a visual test to determine the sets of line drawings that can be clearly observed and that are easy to calculate on the screened replica. The number of lines per centimeter of these line graphs can be considered as the resolution of the image density. For comparison, these test charts were also reproduced using conventional photocopying methods. In both cases, the 60 line/cm screen position is at a 45° angle to the line perpendicular to the scanning direction.

The results of the study are as follows:

The distortion exhibited by the reproduction of the test chart is caused by two factors. Under the condition of high-frequency discretization, the loss of resolution is seen on the portion where the main line and the line direction are at a 45° angle. The resolution is equal to 33 lines/cm. Similar resolutions can also be achieved with replicated replicas using conventional methods.
With a lower discretization frequency, distortion begins to appear with fewer lines per centimeter and the resolution decreases accordingly.

The reduction in resolution is more clearly seen on the line graph with the 90[deg.] angle of the scan line.

From the results of this experiment, we found that the coefficient of dispersion Kd=2.6. Using an example method, it can be shown that on the condition of screen-synthesizing with a 60-line/cm screen, the image obtained by the digital image processing method is obtained on a replica. The discrete reading frequency should not be less than 33 x 2.6 = 86 readings/cm.
In the case of Kd=2.6, when the digital signal is sent to the recording device, the encoding frequency can be expressed by the following equation:

Fd=2.6LsV;
Where Ls is the screening resolution; V is the linear scan speed.

This article examines the various conditions that avoid the quantification and discretization of visual effects in individual cases. The quantification effect on the image portion of the ordered gradation range and the discretization effect of the test pattern on the ordered line element set were studied. In the actual print, the ratio of the ordered portion to the detailed portion is not the same. It is now known that printed image frequencies have very strong effects at low frequencies and very weak effects at high frequencies.

In summary, we can clearly see that only those devices whose quantitative series can automatically adapt to discrete readings are the most effective. However, the small number of quantization steps in the image details can meet the needs, but discrete readings require high frequencies, but in the ordered part, this condition is exactly the opposite. When developing an actual device for image conversion, it is necessary to consider the problem of excess information existing in the digital processing of the printed image. The reason is also here.

In selecting the discretized discretization frequency, we have determined various conditions that avoid deleterious effects on the reproduction of details. However, the screening process itself enhances the discretization of the image. Considering the printing method and printing paper used, a thicker screen should be used. Therefore, in general, the band limit of the original image should be much higher than the discretization frequency of the screen. This means that whether you use digital processing methods in the production of halftone images, or use any of the other conventional methods, will certainly produce distortion. In spite of this, practical experience still shows that print copies are generally of satisfactory quality. This is due to the fact that the highest spatial frequency is only a fraction of the frequency band of the printed image. If the printed image has a large part of the high spatial frequency band, it is advisable to use a filter in the input part. This filter must be used when copying an image original with a dot.

Source: "Printing World" Author: Lin Yingui Nie group