Basic principle of modulation transfer function

From the viewpoint of information transmission theory, the image processing process of the electronic platemaking system is essentially an information transmission process, although G. Barnstodt, EMGran, VKBiedernann obtained the formula of the comprehensive evaluation scale through experiments:

However, the analysis based on information theory is rarely seen. However, from the performance analysis of the image, it can be proved that depending on the MTF of the image transmission and the steepness of the modulation reproduction, it is possible to express the image quality of the image with a numerical value. If the MTF including the printed dot image can be obtained, the image level of the copied image can be more accurately evaluated.

I. The concept of MTF

The development of modern information theory proves that in a linear space invariant system, any imaging series can effectively be regarded as a spatial frequency filter, and its imaging characteristics and image quality evaluation can be based on the frequency between objects. The ratio is expressed. This frequency contrast characteristic is the so-called modulation transfer function MTF. The linear space invariant system means that the impulse response function of the linear system is stable, that is, the response function has nothing to do with the selected reference coordinate position, and its function value only depends on the parameter (x-ξ) between the reference coordinates. The impulse response function of a linear space-invariant system can be expressed as:

In the linear space invariant system, suppose there is a sinusoidal signal with frequency f (as shown in Figure 7.3), and its light intensity distribution is:

The information theory defines the degree of modulation M as:

Where: for the maximum brightness signal,

For the minimum brightness signal,

For sine wave amplitude,

I is the average amplitude of the sine wave.

In the same system, the original signals with different spatial frequencies are input, and the ratio of the modulation degree M through the system and the modulation degree M without system is defined as the modulation transfer function MTF:

The range of MTF is [0,1]. In general, the MTF value decreases as the frequency f increases. When f reaches a certain value, MTF=0. The frequency at this time is the cut-off frequency. Above this frequency, the signal cannot be transmitted by the system, as shown in Figure 7.4.

With the frequency f as the abscissa, MTF as the ordinate, connecting the curve formed by the MTF values ​​of different frequencies, known as the MTF curve.

Second, point spread function and line spread function

1. Point Spread Function (PSF)

Ideal imaging requires a little correspondence between the object surface and the image surface. The deterioration of the image quality is due to the fact that dots on the original cannot be formed on the negative film. The response of the system to the point is described by a point spread function. The so-called system point spread function is the light intensity of a point source on the original crucible after the electronic platemaking system is on the film, which can be written as PSF, ie, P.

I(x,y) is the light intensity distribution function of the corresponding point on the negative film. In practice, the PSF needs to be naturalized:

2. Line spread function

It is a one-dimensional projection of the point spread function due to:

After the differentiation, the line diffusion function L(x) is obtained:

It can be considered that a line on the manuscript is essentially composed of numerous points, and the constellation after the system is also formed by numerous bright spots. Because of the transitivity of the system, its constellation is transformed into an image that spreads to both sides. Therefore, the distribution of the light intensity of the line in the X direction (or the projection of P in the X direction) L(x) is called a line diffusion function. For an ordinary system, the line spread function is usually an asymmetrically distributed function, and it is symmetrical only in linear and spatially invariant systems. In the optical transfer function of linear and space invariant systems, since the phase transfer function does not affect the sharpness of the constellation, when the corresponding change is not considered, the Fourier transform of the line spread function is MTF:

From a physical point of view, the MTF is essentially the percentage of the loss of the sine wave image of each spatial frequency through the system.

For the electronic platemaking system, the line spread function can be obtained from the edge curve:

Among them, I(x) is the light intensity distribution of the blade image.

Third, the calculation method of the dot image MTF

The dot image can be regarded as the result of passing through the image signal, similar to the carrier principle in image communication. Measure MTF of halftone dot images, except for the use of the blade edge scanning method, in order to solve the separation of halftone image signal wave, carrier wave, side wave band, and easy calculation of the average value of the area of ​​a certain part, using the Fourier transform of the optical Fourier transform. It is more effective to calculate the average MTF of halftone images by the cost diffraction method.

IV. Experimental Design of MTF Measurement in Electronic Platemaking System

Since the application of MTF must meet two conditions: the system adopted by one must be linear; the second system should have the invariance of space and time:

Only when the above two conditions are satisfied and the sine wave signal of a certain frequency f is input, the system outputs a sine wave. When the frequency f is constant, only the degree of modulation changes.

In the electronic platemaking system, since the characteristics of the photosensitive material, the characteristic curve of the photoelectric conversion element, and the transfer characteristic curve of the printing ink are not completely linear, and the materials used are not perfectly uniform, input a sine having a frequency of f Wave signals, the system often outputs a non-sinusoidal signal and becomes a harmonic with other frequencies.

Based on the above reasons, when using the knife edge curve to solve the MTF, the following requirements are imposed on the density difference ΔD of the blade:

1 Density difference should be small, generally 0.5 is better;

2 Density difference should be located in the straight line of the characteristic curve.

Such a small difference in density can reduce the generation of a boundary effect during development.

The image processed by the electronic platemaking system is often divided into two consecutive halftone halftone screens.

It should be pointed out that the density value D(x) of the knife edge curve is measured from the film, and the relationship between the intensity and the light intensity can be represented by the DH curve. Therefore, in the calculation of MTF, the processing of the film must be processed simultaneously with the optical wedge for sensitometry, and the same conditions should be used for the simultaneous scanning of the blades to establish a mathematical model of H=D(x).