You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


The present invention relates to an image display device having a display panel in which a plurality of cold cathode devices are arranged in matrix.
Up to now, there have been known two kinds of electron emitting devices, that is, a hot cathode device and a cold cathode device. In the cold cathode device among them, there have been known, for example, a surface conduction electron emitting device, a field emission device (hereinafter referred to as xe2x80x9cFExe2x80x9d), a metal/insulator/metal electron emitting device (hereinafter referred to as xe2x80x9cMIMxe2x80x9d), and the like.
As the surface conduction electron emitting device, there have been known, for example, M. I. Elinson, Radio Eng. Electron Phys., 10, 1290, (1965), and other examples that will be described later. The surface conduction electron emitting device is so designed as to use a phenomenon in which a current is allowed to flow in parallel with a film surface on a thin film of a small area formed on a substrate to cause electron emission. As the surface conduction electron emitting device, there have been reported the above-mentioned electron emitting device using SnO2 thin film by Elinson et al., as well as an electron emitting device using an Au thin film (G. Dittmer: xe2x80x9cThin Solid Filmsxe2x80x9d, 9, 317 (1972), an electron emitting device using an In2O3/SnO2 thin film (M. Hartwell and C. G. Fonstad: xe2x80x9cIEEE Trans. ED Conf.xe2x80x9d, 519 (1975)), an electron emitting device using a carbon thin film (Hisashi Araki, et al.: Vacuum, Vol. 26, No. 1, 22 (1983)), and the like.
As a typical example of the device structure of those surface conduction electron emitting devices, a plan view of the above-mentioned device by M. Hartwell, et al. is shown in FIG. 19. In the figure, reference numeral 3001 denotes a substrate; and 3004 is an electroconductive thin film made of a metal oxide formed through sputtering. The electroconductive thin film 3004 is formed into an H-shaped plane as shown in the figure. The electroconductive film 3004 is subjected to energization called xe2x80x9cenergization formingxe2x80x9d which will be described later, to thereby form an electron emitting portion 3005. In the figure, an interval L is set to 0.5 to 1 mm, and W is set to 0.1 mm. For convenience of the drawing, the electron emitting portion 3005 is formed into a rectangular shape in the center of the electroconductive thin film 3004, but this is schematic and does not faithfully represent the position and shape of the actual electron emitting portion.
In the above-mentioned surface conduction electron emitting devices including the device proposed by M. Hartwell et al., it is general that the electron emitting portion 3005 is formed by subjecting the electroconductive thin film 3004 to the energization that is called xe2x80x9cenergization formingxe2x80x9d prior to electron emission. That is, the energization forming is that a constant d.c. voltage, or a d.c. voltage that steps up at a very slow rate of, for example, about 1 V/min is applied between both ends of the electroconductive thin film 3004 to energize the electroconductive thin film 3004 to locally destroy, deform or deteriorate the electroconductive thin film 3004, thereby forming the electron emitting portion 3005 which is in an electrically high resistant state. Note that a fissure occurs in a part of the electroconductive thin film 3004 that has been locally destroyed, deformed or deteriorated. In the case where an appropriate voltage is applied to the electroconductive thin film 3004 after the energization forming has been made, electron emission is conducted in the vicinity of the fissure.
Also, as the FE type example, there have been known, for example, W. P. Dyke and W. W. Dolan, xe2x80x9cField emissionxe2x80x9d, Advance in Electron Physics, 8, 89 (1956), and C. A. Spindt, xe2x80x9cPhysical Properties of thin-film field emission cathodes with molybdenum conesxe2x80x9d, J. Appl. Phys., 47, 5248 (1976), etc.
As a typical example of the FE type device structure, a cross-sectional view of the above-mentioned device proposed by C. A. Spindt, et al. is shown in FIG. 20. In the figure, reference numeral 3010 denotes a substrate, 3011 is an emitter wiring made of electroconductive material, 3012 is an emitter cone, 3013 is an insulating layer, and 3014 is a gate electrode. This device conducts the electric field electron emission from a leading portion of the emitter cone 3012 by applying an appropriate voltage between the emitter cone 3012 and the gate electrode 3014. Also, as another device structure of the FE type, there is an example in which the emitter and the gate electrode are arranged on the substrate substantially in parallel with the substrate plane instead of the laminate structure shown in FIG. 20.
Also, as the MIM type example, there have been known, for example, C. A. Mead, xe2x80x9cOperation of tunnel-emission Devicesxe2x80x9d, J. Appl. Phys., 32, 646 (1961), and the like. A typical example of the device structure of the MIM type is shown in FIG. 21. The figure is a cross-sectional view in which reference numeral 3020 denotes a substrate, 3021 denotes a lower electrode made of metal, 3022 denotes a thin insulating layer having a thickness of about 100 xc3x85, 3023 denotes an upper electrode made of metal having a thickness of about 80 to 300 xc3x85. In the MIM type, an appropriate voltage is applied between the upper electrode 3023 and the lower electrode 3021 to conduct the electron emission from the surface of the upper electrode 3023.
The above-mentioned cold cathode device requires no heater for heating because the electron emission can be obtained at a low temperature as compared with the hot cathode device. Therefore, the cold cathode device is simpler in structure than the hot cathode device, and a fine device can be prepared. Also, it is difficult that a problem such as the heat melting of the substrate occurs even if a large number of devices are arranged on the substrate with a high density. Also, because the hot cathode device operates due to the heat from the heater, there is an advantage in that a response speed is high in case of the cold cathode device which is different from the low response speed. For that reason, a study for applying the cold cathode device has been increasingly conducted.
For example, the surface conduction electron emitting device is advantageous in that a large number of devices can be formed over a large area since the device is particularly simple in structure and easy in manufacture among the cold cathode devices. Therefore, as disclosed in Japanese Patent Application Laid-Open No. 64-31332 made by the present applicant, for example, a method in which a large number of devices are arranged for driving has been studied. Also, in the application of the surface conduction electron emitting device, for example, an image forming apparatus such as an image display device or an image recording device, an electric charge beam source and the like have been studied.
In particular, as the application of the surface conduction electron emitting device to the image display device, there has been studied the image display device using the combination of the surface conduction electron emitting device with a phosphor that emits light upon irradiation of an electron beam thereto as disclosed in, for example, U.S. Pat. No. 5,066,883, Japanese Patent Application Laid-Open No. 2-257551 and Japanese Patent Application Laid-Open No. 4-28137 made by the present applicant. The image display device using the combination of the surface conduction electron emitting device with the phosphor is expected to have the characteristics superior to that of the image display device of other conventional systems. For example, it can be said that such an image display device is superior to a liquid crystal display device that has been spread in recent years in view of the fact that backlight is not required because of a self light emitting type and the fact that an angle of visibility is wide.
Also, a method in which a large number of FE devices are arranged for driving is disclosed in, for example, U.S. Pat. No. 4,904,895 made by the present applicant. Also, as an example of applying the FE device to the image display device, there has been known a plate display device that has been reported by, for example, R. Meyer, et al. (R. Meyer: xe2x80x9cRecent Development on Microtips Display at LETIxe2x80x9d, Tech. Digest of fourth Int. Vacuum Microelectronics Conf., Nagahama, pp. 6 to 9 (1991)). Also, an example in which a large number of MIM devices are arranged and applied to the image display device is disclosed in, for example, Japanese Pat. Application Laid-Open No. 3-55738 made by the present applicant.
The above-mentioned cold cathode device has the following three characteristics with respect to the emission current Ie.
First, when a voltage equal to or higher than a given voltage (called xe2x80x9cthreshold voltage Vthxe2x80x9d) is applied to the device, the emission current Ie rapidly increases, whereas in the case where a voltage lower than the threshold voltage Vth is applied to the device, the emission current Ie is hardly detected. That is, the cold cathode device is a non-linear device having a definite threshold voltage Vth with respect to the emission current Ie.
Second, because the emission current Ie changes depending on a voltage Vf that is applied to the device, the magnitude of the emission current Ie can be controlled by the voltage Vf.
Third, the response speed of the current Ie emitted from the device with respect to the voltage Vf that is applied to the device is high.
Because the cold cathode device has the above-mentioned characteristics, the combination of the cold cathode device with the phosphor can be preferably employed for the display device.
For example, in the display device in which a large number of devices are disposed in correspondence with the pixels of the display panel as shown in FIG. 10, if the above-mentioned first characteristic is used, the display screen is sequentially scanned so as to conduct display. That is, a voltage equal to or higher than the threshold voltage Vth is appropriately applied to the device that is being driven in accordance with a desired light emitting luminance, and a voltage lower than the threshold voltage Vth is applied to the devices that are in a non-selected state. If the device to be driven is sequentially changed over, the display can be conducted by sequentially scanning the display screen.
Also, if the above-mentioned second characteristic is utilized to change the voltage Vf that is applied to the device, the amount of emitted electrons can be controlled, thereby being capable of controlling the light emission luminance of the phosphor and conducting the image display.
Further, through the above-mentioned third characteristic, the amount of charges of electrons emitted from the device can be controlled by a duration of time during which the voltage Vf is applied.
A method in which the value of voltage that is applied to the cold cathode device is modulated by using the above-mentioned second characteristic to control the amount of emission electrons for displaying the image is disclosed in, for example, Japanese Patent Application Laid-Open No. 11-288246 made by the present applicant.
Also, an example in which image data M bits (M=K+L) is divided into K-bit data and L-bit data, the K bits are modulated in pulse width and the L bits are modulated in amplitude to display the image is disclosed in Japanese Patent Application Laid-Open No. 7-181916 made by Futaba Denshi Kogyo K. K.
The subject matter of the present invention resides in that the image display is conducted by using the above-mentioned second characteristic of the cold cathode device, and as a result of the zealous study by the present inventors, there arise the following problems.
The present inventors have tried the electron emitting devices of various materials, manufacturing methods and structures including the above-mentioned conventional devices. In addition, the present inventors have studied the multi electron beam source in which a large number of electron emitting devices are arranged, and the image display device to which the multi electron source is applied. The present inventors have tried the multi electron beam source made by an electric wiring method shown in, for example, FIG. 22, that is, a multi electron beam source in which a large number of electron emitting devices are arranged two-dimensionally, and those devices are wired in matrix as shown in the figure.
In the figure, reference numeral 4001 schematically shows electron emitting devices, 4002 is row wirings, and 4003 is column wirings. The row wirings 4002 and the column wirings 4003 have finite electric resistors in fact, and in the figure, the electric resistors are shown as wiring resistors 4004 and 4005. The above-mentioned wiring method is called xe2x80x9cpassive matrixxe2x80x9d. Note that, for the convenience of the drawing, a 6xc3x976 matrix is shown, but the scale of the matrix is not limited to this, for example, in case of the multi electron beam source for the image display device, a number of devices sufficient to conduct a desired image display are arranged and wired.
In the multi electron beam source in which the electron emitting devices are arranged in the passive matrix, in order to output a desired electron beam, appropriate electric signals are supplied to the row wirings 4002 and the column wirings 4003. For example, in order to drive the electron emitting devices on one arbitrary line of the matrix, a selection voltage Vs is applied to the row wiring 4002 of a selected row, and at the same time, a non-selection voltage Vns is applied to the row wiring 4002 on the non-selected rows. In synchronism with those signals, a driving voltage Ve for outputting the electron beam is applied to the column wirings 4003. According to this method, if the voltage drops due to the wirings resistors 4004 and 4005 are ignored, a voltage of Vexe2x88x92Vs is applied to the electron emitting device on the selected row, and a voltage of Vexe2x88x92Vns is applied to the electron emitting devices on the non-selected rows. If Ve, Vs and Vns are set to the voltage of the appropriate magnitude, the electron beam of a desired intensity should be outputted from only the electron emitting device on the selected row, and if the different driving voltages Ve are applied to the respective column wirings, the electron beams of different intensities should be outputted from the respective devices on the selected line (the above characteristic is called xe2x80x9cvoltage amplitude modifying characteristicxe2x80x9d). Therefore, there are proposed various intended uses of the multi electron beam source in which the electron emitting devices are wired in passive matrix, and for example, if a voltage signal in accordance with the image information is appropriately applied, it is expected that such a multi electron beam source can be applied as the electron source for the image display device.
However, the image display device that has been tried by the present inventors in advance suffers from the following problems.
In the conventional broadcast system, when an image is displayed on a CRT (cathode ray tube), because the input/output characteristic of the CRT has the characteristic that emits light of luminance proportional to input data to the power of 2.2 (this is called xe2x80x9cinverse xcex3 characteristicxe2x80x9d), a broadcasting station side subjects image-taking data to the 0.45th power conversion (called xe2x80x9cxcex3 conversionxe2x80x9d) and thereafter transmits the data in order to set the relationship of the taken image and the final display image to 1:1.
On the other hand, the image display device according to the present invention uses not the CRT but a display panel in which the cold cathode devices are arranged in matrix as the display panel.
Up to now, as a result that the present inventors have studied the input/output characteristic of the display panel according to the present invention, in the case where the driving voltage Ve that is applied to the cold cathode device is set in accordance with the input image data as shown in FIG. 23, there have been found that the display panel has a light emitting characteristic close to the inverse xcex3 characteristic (2.2nd power) of the CRT as shown in FIG. 24. In FIG. 24, the number of bits of the image data is represented by 8 bits.
If this excellent characteristic is used, there is normally an excellent advantage that in order to emit light of the luminance proportional to the input image data to the 2.2nd power, no inverse xcex3 conversion is required by using a lookup table as in a display having the linear light emitting characteristic with respect to the input image data such as a PDP (plasma display). When the inverse xcex3 conversion is conducted by using the lookup table, there generally arises such a problem that a round error occurs due to the lookup table, and a gradation at a low gradation portion is particularly erased.
On the other hand, in the display using the cold cathode device according to the present invention, because no lookup table is employed, there is an advantage that the output can represent the same number of gradations as that of the input image data due to the inverse xcex3 characteristic of the cold cathode device if the magnitude of the driving voltage Ve is modulated linearly with respect to the number of gradations of the input image data without erasing the gradation.
Therefore, as a result that the present inventors have further studied the input/output characteristic of the display panel according to the present invention, they have found that, in the case where a voltage is set as shown in FIG. 23, the output luminance with respect to the input image data has the characteristic close to the inverse xcex3 characteristic of about the 2.2nd power, but the output luminance does not always coincide with the input image data in a portion where the input image data is small (low gradation portion), and in the case where the input image data is 0 (applied voltagexe2x88x92Vs+VL), there is a phenomenon in which the light emitting luminance does not become 0. As a result, there arises such a problem that the contrast is decreased because the luminance of the dark portion slightly rises.
The present invention has been made for solving the above-mentioned problems with the conventional devices, and therefore an object of the present invention is to realize an excellent gradation characteristic which is high in contrast and does not erase the gradation by using a display device other than a CRT.
The following invention has been devised as a result of intensive efforts by the present inventors to solve the above-mentioned problems.
That is, according to the present invention, there is provided a first image display device characterized in that the device comprises:
a display panel in which (mxc3x97n) surface conduction electron emitting devices are connected in matrix by m row wirings and n column wirings;
scan means connected to the row wirings;
modulation means connected to the column wirings; and
light emitting means disposed at positions opposite to the cold cathode devices; and
that the modulation means includes M-bit voltage amplitude modulation means and pulse width limiting means for an image data of M bits, and a modulation signal that is supplied to the surface conduction electron emitting devices is a voltage signal having an amplitude and a pulse width corresponding to image data.
Here, it is preferable that based on a predetermined threshold value, the modulation means modulates only the amplitude of a modulation signal for the image data equal to or higher than a threshold value, and modulates only the pulse width or both of the amplitude and the pulse width of the modulation signal for the image data lower than the threshold value.
Further, according to the present invention, there is provided a second image display device characterized in that the device comprises:
a display panel in which (mxc3x97n) surface conduction electron emitting devices are connected in matrix by m row wirings and n column wirings;
scan means connected to the row wirings;
modulation means connected to the column wirings; and
light emitting means disposed at positions opposite to the cold cathode devices; and
that the modulation means is amplitude modulation means having a non-linear input/output characteristic when applied to the input image data.
The amplitude modulation means is characterized in that the means has K threshold values D1 to DK (where D1  less than D2 less than  . . .  less than DK, and K is an integer of 1 or more) for, for example, input image data Data, and has a stepped characteristic having:
a first inclination at 0xe2x89xa6Data less than D1;
a second inclination at D1xe2x89xa6Data less than D2;
a K-th inclination at DK-1xe2x89xa6Data less than DK; and
a (K+l)-th inclination at DKxe2x89xa6Data.
Note that the above-mentioned first image display device is definitely different from the device disclosed in Japanese Patent Application Laid-Open No. 7-181916 described in the conventional example.
In other words, in the above-mentioned conventional example, K bits are modulated in pulse width with respect to the image data of M bits (M=K+L), and the L bits are modulated by voltage amplitude modulation, to thereby obtain the gradation characteristic of M bits. On the contrary, in the image display device according to the present invention, modulation is conducted by the voltage amplitude modulation means of M bits, and the pulse width is limited in an auxiliary manner for a lower gradation portion, which does not accord with the inverse xcex3 characteristic of the 2.2nd power, to provide the 2.2nd power characteristic.
According to the above-mentioned image display device of the present invention, there is an advantage in that not only a high contrast can be realized but also an excellent gradation characteristic without erasing the gradation can be realized.