Keywords

1 Introduction

Digital cameras are extremely important digital devices of digital printing technology, which capture the prepress graphic information and help make reproduction of the original; they combine the imaging technology with digital information technology, having an unparalleled advantage, the appearance of digital camera create a New Era reproduction of digital printing [1, 2]. With the increase requirements of image quality of digital printing systems, the relative performance of digital cameras have also been concerned, which attempt to analysis the modulation transfer function (MTF) of digit camera.

The development of modern information theory proved that in the linear space invariant systems, any imaging series can be effectively looked as a spatial frequency filter, which imaging features and image quality evaluation, can be indicated by the ratio of frequency between the images and originals [3–5]. This frequency comparison feature is called modulation transfer function. MTF is a quantitative measure of the imaging system and a method to represent the quality of image detail. In the optical modulation transfer function, MTF describes the transmission capacity for contrast ratio of the optical system. Now, it is very common and convenient to use the MTF to assess the imaging performance of the printing system and the printing image quality in printing area.

2 Background and Significance of the Research of Digital Cameras’ MTF

Most of the former experiences are based on black and white resolution of the beta in the process of obtaining MTF [6], and in the study, in color MTF of digital cameras, the existing research are still stay R/G/B three channels. So in this article, we explore a way expanded from the traditional “black and white” beta to the color range. To test different colored blocks on the basis of color resolution testing requirements with method of moving blade [7–9], then getting the different color responses of digital camera.

In imaging system, the quality of transferred images directly related to its frequency response characteristics. Therefore, it is critical to obtain the frequency response characteristic of the imaging system to optimize the system design and use in image correction processing.

3 Principle of MTF

Linear system theory proves that the system frequency response function contains amplitude and phase frequency response in two parts. Set the original image is a cosine wave which frequency is f, amplitude is L A0, and luminance extending transversely. Including, L AV0 is brightness average (Blue line in Fig. 37.1).

Fig. 37.1
figure 1

Luminance image of cosine wave imaging

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$$ L_{0} (x) = L_{{\text{AV0}}} + L_{{\text{A0}}} \cos \left( {2\pi fx} \right) = L_{{\text{AV0}}} \times \left[ {1 + \frac{{L_{{\text{A0}}} }}{{L_{{\text{AV0}}} }}\cos \left( {2\pi fx} \right)} \right] $$
(37.3.1)

Defined modulation M as follows:

$$ M = \frac{{L_{\text{Max}} - L_{\text{Min}} }}{{L_{\text{Max}} + L_{\text{Min}} }} $$
(37.3.2)

Form: L Max = L AV0 + L A0 and L Min = L AV0 − L A0, then:

$$ M_{0} = \frac{{L_{{\text{Max0}}} - L_{{\text{Min0}}} }}{{L_{{\text{Max0}}} + L_{{\text{Min0}}} }} = \frac{{L_{{\text{A0}}} }}{{L_{{\text{AV}0}} }} $$
(37.3.3)

So:

$$ L_{0} (x) = L_{{\text{AV0}}} \times \left[ {1 + M_{0} \cos \left( {2\pi fx} \right)} \right] $$
(37.3.4)

Original image has captured by the imaging system, there is the line shown in Fig. 37.1, the obtained image function (Subscript is 1, red line):

$$ L_{1} (x) = L_{{\text{AV1}}} \times \left[ {1 + M_{1} \cos \left( {2\pi fx} \right)} \right] $$
(37.3.5)

If there is a phase shift imaging, there is other function (Green dotted line in Fig. 37.1):

$$ L_{1} (x) = L_{{\text{AV}1}} \times \left[ {1 + M_{1} \cos \left( {2\pi fx - \varphi_{\text{P}} } \right)} \right] $$
(37.3.6)

After imaging, modulation M 1 of image becomes:

$$ M_{1} = \frac{{L_{{\text{A1}}} }}{{L_{{\text{AV}1}} }} $$
(37.3.7)

Due to certain factors, modulation turns to go down (M 1 ≤ M 0). In general, with the rise of the spatial frequency of the original image, modulation of image after imaging declines.

General condition, the ratio of M 1 which is the modulation after imaging and M 0 which is the modulation of original image is called “modulation transfer value”, namely:

$$ T = \frac{{M_{ 1} }}{{M_{0} }} $$
(37.3.8)

Relationship between spatial frequency (f) and modulation transfer value called “modulation transfer function”, written as:

$$ T(f) = \frac{{M_{ 1} (f)}}{{M_{0} (f)}} = \frac{{\left( {\frac{{L_{{\text{A}1}} }}{{L_{{\text{AV}1}} }}} \right)}}{{\left( {\frac{{L_{{\text{A}0}} }}{{L_{{\text{AV}0}} }}} \right)}} = \frac{{\left( {\frac{{L_{\text{Max1}} - L_{{\text{Min}1}} }}{{L_{\text{Max1}} + L_{{\text{Min}1}} }}} \right)}}{{\left( {\frac{{L_{{\text{Max}0}} - L_{{\text{Min}0}} }}{{L_{{\text{Max}0}} + L_{{\text{Min}0}} }}} \right)}} $$
(37.3.9)

4 Experiment Part

4.1 Experimental Equipment

Experimental materials: Top advanced semigloss HD170 photo paper; ruler; 35 × 350 mm splines used by IGTAIC2-5 type printability tester.

Experiment equipment: Profile Maker software; Photoshop CS5; digital cameras Canon 7D; IGTAIC2-5 type printability tester and supporting four-color ink: cyan, magenta, yellow, black; Color Controller transmission observation box; Matlab software.

4.2 Experiment Equipment Parameters

Digital Camera Canon EOS 7D is APS-C size which has 18 million effective pixels during the experiment, the aspect ratio sets to 3:2; there are L/M/S profile to choose for photo model, its color space is Adobe RGB, and file storage format is JPG.

4.3 Experimental Procedure

4.3.1 Make Beta

Use IGTAIC2-5 type printability tester with matching ink yellow, magenta, cyan, to print yellow, magenta, cyan color splines, totally 3 pieces of splines. Colored areas of each spline cut up with a sharp knife, to keep at least one side has a sharp blade edge, keep the same size of splines, then cling them to same white with double-sided adhesive glue, respectively. As shown in Fig. 37.2.

Fig. 37.2
figure 2

Cyan print test forme

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4.3.2 Shooting Beta

Set the camera to initial state before experiment, keep the position of camera and focal length unchanged in the experiment. Put betas in the transmission observing box and use reflected light to observe which has fixed camera angles and shooting distance, an uniform reflection light, and a fixed beta slots.

Installed the camera and adjust focus before experiment. Take one test beta and fixed it in transmission observing box, put a ruler to measure the actual shooting dimensions of the digital camera, which is 120 mm × 80 mm (Fig. 37.3).

Fig. 37.3
figure 3

The shot size of camera

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To avoid jitter, set to time-lapse shooting of camera. Shooting three colors: yellow, magenta, and cyan, the each color shoots six groups of data. Totally 18 groups of data are got.

$$ \begin{array}{*{20}l} {\text{a.}\text{. Pixel value}\left( {\text{mm} \times \text{mm}} \right) = \text{L}(5184 \times 3456)} & {\text{Aperture value } = 5.6} \\ {\text{b}\text{. Pixel value}\left( {\text{mm} \times \text{mm}} \right) = \text{L}(5184 \times 3456)} & {\text{Aperture value } = 36} \\ {\text{c}\text{. Pixel value}\left( {\text{mm} \times \text{mm}} \right) = \text{M}(3456 \times 2304)\text{ }} & {\text{Aperture value } = 5.6} \\ {\text{d}\text{. Pixel value}\left( {\text{mm} \times \text{mm}} \right) = \text{M}(3456 \times 2304) } & {\text{Aperture value } = 36} \\ {\text{e}\text{. Pixel value}\left( {\text{mm} \times \text{mm}} \right) = \text{S}(2592 \times 1728)} & {\text{Aperture value } = 5.6} \\ {\text{f}\text{. Pixel value}\left( {\text{mm} \times \text{mm}} \right) = \text{S}(2592 \times 1728) } & {\text{Aperture value } = 36} \\ \end{array} $$

4.3.3 LCH-MTF of Chromaticity Space

Since this experiment is for color images, not only black and white, so get the lightness, chroma and hue of color is very important according to color properties. It is necessary to transfer between LCH and LAB. We can obtain the frequency response characteristic of a digital camera from lightness, chroma, and hue.

The image after taken by camera should transfer into LAB mode to obtain a digital camera’s MTF of LCH, and the following formulas are conversions of chroma C and hue angle H:

$$ C = \sqrt {\left( {a^{2} + b^{2} } \right)} $$
(37.4.1)

Hue angle H should discuss the position of a* and b* values:

$$ {\text{First quadrant}},\quad {\text{when}}\;a^{*} > 0,b^{*} > 0,H = \arctan \left( {b^{*} /a^{*} } \right); $$
(37.4.2)
$$ {\text{The second quadrant}},\quad {\text{when}}\;a^{*} < 0,b^{*} > 0, \quad H = 1 80 - { \arctan }\left( {b^{*} /|a^{*} |} \right); $$
(37.4.3)
$$ {\text{Third quadrant}},\quad {\text{when}}\;a^{*} < 0,b^{*} < 0,\quad H = 1 80 + { \arctan }\left( {\left| {b^{*} } \right|/|a^{*} |} \right); $$
(37.4.4)
$$ {\text{Fourth quadrant}},\quad {\text{when}}\;a^{*} > 0,b^{*} < 0,\quad H = 3 60 - { \arctan }\left( {\left| {b^{*} } \right|/a^{*} } \right); $$
(37.4.5)
$$ {\text{At the origin}},\quad {\text{when}}\;a^{*} = 0\;{\text{and}}\;b^{*} = 0,\quad H = 0; $$
(37.4.6)
$$ {\text{Right above the }}x{\text{-axis}},\quad {\text{when}}\;a^{*} > 0, b^{*} = 0,\quad H = 0; $$
(37.4.7)
$$ {\text{Right above the }}y{\text{-axis}},\quad {\text{when}}\;a^{*} = 0,b^{*} > 0,\quad H = 90; $$
(37.4.8)
$$ {\text{Right down the }}x{\text{-axis}},\quad {\text{when}}\;a^{*} < 0,b^{*} = 0,\quad H = 1 80; $$
(37.4.9)
$$ {\text{Right down the }}y{\text{-axis}},\quad {\text{when}}\;a^{*} = 0,b^{*} < 0,\quad H = 2 70. $$
(37.4.10)

4.3.4 The Programming Calculation Process of MATLAB to MTF

After photograph all betas. Convert the image pattern into LAB mode via photoshop which stored as TIFF format, ICC color profile is Adobe RGB.

Then, Matlab software processes LAB mode image to obtain MTF curves. The following is related processes of Matlab program.

  1. 1.

    First, set the digital camera’s in horizontal and vertical dimensions, according to the size of beta in photograph.

  2. 2.

    Open the image of Lab mode, turn it into double precision, and separate it into LAB three channels.

  3. 3.

    Clear the original data and convert into chrominance values, then operate equations to get the saturation value of the image.

  4. 4.

    Convert the image into LCH mode, discuss the situation the position in 1, 2, 3, 4 quadrants, at the origin, on the axis with conditional statements.

  5. 5.

    Find out the average value of the column of L channel, then seek differential, and take absolute value of it. Find out the maximum value and position of it by the Fourier transform and take half of the data from the maximum value. Determine the spacing between each two rows of pixels and find the frequency of each frequency data between two rows of difference [10]. Set the MTF function in the position of 5 % and take frequency coordinate values [11] of this position [12].

    It’s the same process for chroma.

5 Results and Discussion

5.1 Lightness MTF Test of Canon 7D

When image lightness L = 50, and the camera pixel is set as L, after MATLAB programming, brightness MTF is shown in Fig. 37.4.

Fig. 37.4
figure 4

Relationship between different color’s MTF and frequency identification when L = 50 in experience of lightness, Cyan, Magenta, and Yellow

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Frequency coordinate values in the position of 5 % of MTF as Table 37.1.

Table 37.1 The frequency identification value to cyan, magenta, and yellow of camera when MTF value is 5 % in test of lightness
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As can be seen from the data in table: when the brightness is 50, this camera’s magenta ability resolution is best, cyan is followed, and yellow is poor.

Changing pixel and aperture value of the camera, photograph the same color under those different conditions, after MATLAB programming, the data is shown in Table 37.2.

Table 37.2 The frequency identification value to cyan, magenta, and yellow of camera when MTF value is 5 % in different situation in text of lightness
Full size table

From the pictures and tables, in the lightness MTF test, the MTF will change with the pixel and aperture value of the camera, it means the frequency identification of this camera are different in different colors, pixels, and aperture values. Wholly the MTF is better in bigger pixel values; MTF is better in smaller aperture values. And Canon 7D’s frequency identification is best in Magenta, cyan is followed, and yellow is poor.

5.2 Saturation MTF Test of Canon 7D

In the test of saturation MTF of Canon 7D, experimental procedures are similar with the lightness MTF test.

Changing pixel and aperture value of the camera, photograph the same color under those different conditions, after MATLAB programming, the data are shown in Table 37.3.

Table 37.3 The frequency identification value to cyan, magenta, and yellow of camera when MTF value is 5 % in different situation in test of chroma
Full size table

From tables, in the saturation MTF test, we can found the MTF also will change with the pixel and aperture value of the camera; wholly the MTF is better in bigger pixel values; MTF is better in smaller aperture values. Canon 7D’s frequency identification is best in magenta, cyan is followed, and yellow is poor; this is same as the test in lightness MTF test.

6 Conclusions

In conclusion, the MTF will change with the pixel value and aperture value of the camera, it means the frequency identification of this camera are different in different colors, pixels, and aperture values. Wholly the MTF is better in bigger pixel values; MTF is better in smaller aperture values. And Canon 7D’s frequency identification is best in magenta, cyan is followed, yellow is poor which means Canon 7D has the strongest colorful resolution ability in magenta, relatively weaker in cyan and yellow followed. The results indicated that different digital camera pixel value and aperture value will affect MTF, and the ability to distinguish different colors of a camera is also different. Of course, there are also some problems in using the knife edge method to get camera color MTF, such as in hue angle test showed a lot noise, this method does not accurately measure its frequency identification, which will be improved further. In short, it is a good guide to analysis color MTF of different colors; it has a very important significance for future digital camera color MTF.