System MTF data measurement and processing

A. Blade scanning

When scanning with a knife edge, it is required that the scanning hole must completely reflect the density distribution rule or the light intensity variation rule of the linear image, and the slit light hole scanning blade can meet the above requirements:

If the slit width is d, the slit S (x) with the slit height h is used as the scanning aperture. When h>>d, the slit height is greater than the slit width, but smaller than the length of the scanning blade; the slit width is as much as possible. Small, and at least less than the line width of the system's limit resolution, can fully reflect the linear image density distribution. Because for a slit of width d, the slit function is

The spectrum function takes S(0)=d=1 when f=0, and it is treated as naturalization:

From S(ξ) and S(f) in Figure 7.5, S(f) is negative in the interval. This is because the slit width causes the pattern to be inverted in black and white. Therefore, if the gap between the slit width d and the maximum effective frequency component f of the system signal is satisfied during the purchase measurement, black and white inversion can be avoided. The image produced in the electronic platemaking system is mainly used for visual interpretation. If it satisfies (R is the resolution of the system) that the line width is not greater than the line width of the limit resolution, the black and white reversal phenomenon can be eliminated. Therefore, the measurement slit width can be selected as 2.5×100μ. When the scan interval is Δx.

According to the discrete density points obtained by the sampling, the variation law of the blade density function D(x) can be correctly expressed, and the spectrum can be determined from the discrete density points.

According to the relationship between Δx and d, the scanning method is divided into two types:

1 Normal sampling:

2 Overlap sampling:

Since the blade density function is a very complex function, its f is determined in advance due to difficulties, and there are many types of electronic color separation machines currently in use, and the cut-off frequency is not the same. According to relevant data, the maximum cut-off frequency is indicated. Calculated by. The actual sampling interval is:

Second, the line diffusion function L (x) to obtain

In order to obtain L(x), a sensitometric measurement is first performed and H=f[D(x)] is determined. According to the principle of MTF, the system's line spread function L(x) is the first derivative of the knife function L(x):

If the Fourier transform is performed on L(x), MTF can be obtained. The light intensity distribution I(x) at any point x of the blade curve shown in Fig. 7.6 is the sum of the line spread function values ​​at each point of the image:

Therefore, the wedge plate of the image negative film must be placed on the PDS micrometer and the blade scan must be performed under the same conditions to establish the mathematical model of H=f[D(x)] and find H(x). .

Third, the pretreatment of scan data

All scans were performed on a PDS micrometer. For data accuracy, each blade continuously scans 15 (see Figure 7.7), then takes the average value as the data for the calculation of the blade function, and at the same time weakens the photoelectric noise and emulsion particle noise of the PDS during scanning:

Selecting the blade from the actual image makes it difficult to find the ideal straight edge. The following conditions often occur:

1 the length of the straight edge of the image is limited;

2 image straight edges are not "absolute" straight.

Therefore, there is a large deviation in certain conditions for the data obtained from the scan, as shown in Figure 7.8. This requires manual intervention. Check the original data, remove the large deviations and take the average.

Fourth, D (x) filter processing

During the sampling of any image signal, the measurement data inevitably carries errors. The image signal always has an upper cut-off frequency, and the sampled frequency and the signal that is always greater than f are mostly noise signals. In this way, the signals obtained after sampling are all with noise, and the noise appears as high-frequency components.

The D(x) curve obtained by the PDS has sharp curve jitter due to the influence of scanner photoelectric noise and sensitized emulsion particle noise. Although the average pre-judgment is still obvious after taking the average value, it is necessary to adopt a filtering method to perform certain processing on D(x) before the data operation, in order to eliminate the influence of noise.

Filtering methods mainly include spatial domain filtering and spectral domain filtering. In the filtering process, the spatial filtering method is mainly based on the use of local filtering.

The so-called local filtering method, also known as the curve moving smoothing method, is based on the principle of polynomial least-squares curve fitting, and is a moving smoothing filter method that uses an n-th order polynomial function as a filter operator, such as a five-point moving smoothing formula for:

In the MTF calculation, the local smooth derivation method is mainly applied after the spectral filtering. At this point, the noise is no longer strong because the signal is filtered several times. Using this method can obtain satisfactory results, and the algorithm is simple and the calculation speed is fast. In the calculation of L(x), it is proved that the five-times third derivative filter works best.

Spectral domain filtering is a method that attenuates high-frequency components and allows low-frequency components to pass smoothly. When filtering in the frequency domain, it is usually difficult to determine the cutoff frequency f. Under the influence of noise n(t), it is usually difficult to determine the cut-off frequency f when the spectral amplitude of x(t) is filtered. Under the influence of noise n(t), the spectral amplitude x(f) of x(t) drops to a certain extent and then jitters around a certain value. At this time, it can be considered that the spectral amplitude x(f) of x(t) is mainly determined by noise; it can also be considered that the signal at this time is noise. In the experiment, this method is used for filtering to determine f, as shown in Figure 7.9.

In filtering, how many high-frequency components need to be filtered out, in order to achieve both to keep the effective signal as much as possible and suppress the noise very well, it is also a difficult problem to solve.

When performing spatial filtering, the number of filters is usually limited by the starting point of the blade. When the starting point changes during filtering, it is difficult to determine the number of filtering times. Filtering with the spectral domain method can solve the problem of starting and end point changes in spatial domain filtering. As long as the cutoff frequency f is properly selected, noise may be effectively suppressed after one filter. As for the determination of f, the Fourier transform (FFT) can be used to determine the frequency spectrum of the discrete sampling signal of the blade, and then the frequency spectrum is analyzed to obtain the cutoff frequency f, and then a filter and an inverse Fourier transform are used to restore the filtered signal. signal of. In this way, the noise can be effectively suppressed without distorting the signal; it not only ensures the signal characteristics, but also reduces the data processing time. Figure 7.10 shows the comparison of the same data after spatial domain filtering and spectral domain wave method respectively.