JP2011031462A - Image rewriting method and image rewriting apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve such a problem that it is difficult to form an image which develops color continuously in the sub-scanning direction, in a photothermal conversion image rewriting method and apparatus, where an image is formed by raster-scanning on a reversible thermal recording medium with one or a plurality of laser beams. <P>SOLUTION: The image rewriting apparatus includes the reversible thermal recording medium 10 which takes a color development state or a decolorized state selectively according to the difference in the temperature and the temperature change rate of the medium, and a laser array exposure means 20 where a plurality of laser beams 21 driven independently are arranged in the direction perpendicular to the moving direction of the reversible thermal recording medium 10. The reversible thermal recording medium 10 is exposed in a predetermined pattern by the laser array exposure means 20, pixels of the reversible thermal recording medium 10 which develop color are heated on the color development conditions and, at the same time, pixels of the reversible thermal recording medium which are decolorized are heated on the decolorization conditions to form an image. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to an image rewriting apparatus using a reversible thermosensitive recording medium capable of color development and decoloration by controlling the movement of thermal energy, and more particularly to a non-contact image rewriting method for applying thermal energy by light.

  Conventionally, a colorless or light-colored leuco dye, a reversible thermosensitive recording medium using a reversible color developer that develops color by heating and cooling, and re-colors by reheating, and a minute heating element. An image rewriting method and apparatus that uses a thermal head integrated on an array to form a visualized image by moving thermal energy in contact with the reversible thermal recording medium in an image-like manner, and allows the recording medium to be rewritten many times. A reversible thermosensitive recording medium is known.

  In the apparatus using the thermal head, it is necessary to press the thermal head against the recording medium in order to obtain sufficient heat conduction. When the image is formed, the thermal head and the recording medium run in contact with each other. Surface wear was inevitable. In addition, since the recording medium is used many times, dirt and foreign matter on the surface of the recording medium during use adhere to, accumulate and adhere to the surface of the thermal head, which accelerates the deterioration of the surface of the thermal head and further deteriorates the thermal head. Deterioration of the surface of the recording medium is accelerated by the surface of the head. For this reason, maintenance and replacement of the thermal head and cleaning of the surface of the recording medium are necessary.

  As a means for eliminating the drawbacks of the image rewriting method using such a thermal head, a light absorption heat conversion layer is laminated on a reversible thermosensitive recording medium, or a recording layer containing a leuco dye and a reversible developer. Method and apparatus for forming an image in a non-contact manner by scanning a recording medium mixed with a light-absorbing heat conversion material by focusing one or more laser beams on the recording medium and converting the light energy into thermal energy. That is, a photothermal conversion type image rewriting method and apparatus are disclosed (for example, Patent Document 1).

On the other hand, conventionally, as an exposure apparatus for an electrophotographic apparatus such as an optical printer or a copying machine, an LED array or the like in which a condensing lens is combined with light sources arranged in an array is used.
Using such an array exposure apparatus, optimization conditions such as the spot diameter of a laser beam, exposure energy, and sensitivity of a photoconductor for obtaining a good image are disclosed (for example, Patent Document 2).

  In the conventional photothermal conversion type image rewriting method and apparatus in which one or a plurality of laser beams perform raster scanning on a reversible thermosensitive recording medium, it is difficult to form an image that continuously develops color in the sub-scanning direction. Specifically, when raster scanning is performed in which a single laser beam performs main scanning on the recording medium and simultaneously moves the recording medium in the main scanning direction and the sub-scanning direction, the main scanning time interval is long. Then, the pixels of the recording medium heated and melted to the color development condition by the previous laser beam are cooled by the next laser beam scanning.

  In the next laser beam scanning, since the exposure energy density distribution of the laser beam is Gaussian, the tail of the Gaussian distribution is applied to the previous color pixel, and the decolorable temperature range of the recording medium is the colorable temperature range. Therefore, the previous color pixel is erased at the large radius portion of the laser beam exhibiting a small exposure energy density. Therefore, when forming an image with a long angle of view in the main scanning direction, it is difficult to form an image that continuously develops color in the sub-scanning direction. If the exposure energy density of the laser beam is excessive, the previous color pixel may satisfy the decoloring condition due to heat conduction of the recording medium.

  In order to prevent such a phenomenon that part of the colored pixels is erased by re-exposure, there is a method in which a laser array comprising laser beams arranged in an array is used as the exposure means. In such exposure means, the laser beam corresponding to all the pixels is arranged in one line in the direction orthogonal to the moving direction of the recording medium, so that all the pixels in that one line can be exposed simultaneously.

  Therefore, the time interval until the next laser beam line exposure can be made sufficiently short, and the temperature of the pixels of the recording medium heated and melted to the color development condition by the previous laser beam is maintained in the color development condition until the next laser beam scanning. The

  However, even in a method using a laser array as an exposure means, there are some problems in forming an image by coloring and erasing the recording medium without unevenness. Since the exposure energy density distribution of the laser beam is Gaussian, if the recording medium is colored until the part corresponding to the bottom of the Gaussian distribution, the exposure energy density becomes excessive at the center of the laser beam. In some parts, the temperature rises above the coloring condition, and the cooling rate required for coloring may not be obtained, and the color may be erased.

  Further, if the exposure energy density is excessive, the recording medium such as thermal decomposition and thermal deformation may be seriously damaged, and the rewrite life of the reversible thermosensitive recording medium may be reduced. For the pixel to be decolored, if the recording medium is decolored up to the portion corresponding to the bottom of the Gaussian distribution, the exposure energy density becomes too large at the central portion of the laser beam, and the coloring condition is not satisfied. The central portion of the pixel may be colored.

  Such image quality deterioration phenomenon and performance deterioration phenomenon occur because the relationship between the spot radius of the laser beam, the exposure energy density distribution, and the coloring and decoloring characteristics of the reversible thermosensitive recording medium is not set appropriately. .

  In the method using the laser array as the exposure means, it is possible to expose all the pixels of one line individually at the same time. There is a possibility that simultaneous color erasing (erasing simultaneous writing) can be performed. Accordingly, it is said that a decoloring means for uniformly heating a recording medium such as a conventional halogen lamp or a hot air blowing device is unnecessary.

  In addition, since the spot radius of the laser beam is all the same and fixed, in order to individually control the exposure conditions for the colored pixels and the decolored pixels at the same time, the laser can be controlled by pulse width modulation control or power modulation control. It is necessary to control the exposure energy density on the recording medium surface by controlling the light emission of the beam.

However, there is no conventionally disclosed condition for simultaneously satisfying two of the color development and decoloring characteristics with many restrictions as described above, and simultaneous color erase with a laser array has not been realized.
Furthermore, since the conditions for satisfying both the coloring and decoloring characteristics must correspond to all the image patterns to be formed, it is more difficult to realize simultaneous color erasing.

  On the other hand, in the electrophotographic apparatus, use conditions and setting conditions of various array exposure apparatuses have been proposed. However, these are optimized for electrophotographic materials and processes such as the sensitivity of the photoreceptor, and are not applicable with respect to the coloring and decoloring characteristics in the reversible thermosensitive recording method under the same conditions. .

  Accordingly, an object of the present invention is to enable simultaneous color erasing (erasing simultaneous writing) using a laser array exposure means in which a laser beam is arranged in a direction orthogonal to the moving direction of a reversible thermosensitive recording medium, and a recording medium It is an object of the present invention to provide a photothermal conversion type image rewriting method capable of satisfactorily rewriting and forming an arbitrary image pattern over the entire area of a recording medium without damaging the recording medium.

The present invention relates to a reversible thermosensitive recording medium that selectively forms a colored state or a decolored state depending on a difference in temperature and temperature change rate of the medium, and a plurality of independently driven laser beams in a moving direction of the reversible thermosensitive recording medium. A laser array exposure unit arranged in an orthogonal direction, the reversible thermosensitive recording medium is exposed in a predetermined pattern by the laser array exposure unit, and the pixels to be colored on the reversible thermosensitive recording medium are heated to a coloring condition, At the same time, in an image rewriting device that performs image formation by heating pixels to be decolored on a reversible thermosensitive recording medium under decoloring conditions,
E ₀₀ [J / m ² ] is the exposure energy density at the center of the imaging spot, w ₀ [m] for the imaging spot on the reversible thermosensitive recording medium of one laser beam emitted from the laser array exposure means. ] In the exposure energy density distribution formed by the imaging spot, E ₀₀ / e ² [J / m ² ] is the distance from the center of the imaging spot indicating the exposure energy density, The spot radius on the reversible thermosensitive recording medium of the laser beam,
For a plurality of imaging spots on a reversible thermosensitive recording medium of a plurality of laser beams emitted from the laser array exposure means, r ₀ [m] is ½ the distance between the pitches of the plurality of imaging spots. , and the and 1/2 in which the pixel radius of the pitch distance between the pixels that form, and then, the characteristics of the reversible thermosensitive recording medium M _c [J / m ^2] The Minimum color density, M _cm [J / m ² ] is the maximum color density, M _d [J / m ² ] is the minimum color density, M _dm [J / m ² ] is the maximum color density Equation (1) with χ as a variable and a as a parameter, and relation (2) of χ
1-a4χ + 4χ ² + 4χ ⁴ -a8χ ⁵ = 0 (1)
w ₀ / r ₀ = 2 / log (1 / χ) ^1/2 ... (2)
In
Using χ ₁ = 0.5, the spot radius w ₁ divided by the pixel radius r ₀ is w ₁ / r ₀ = 2 / log (1 / χ ₁ ) ^1/2
age,
Furthermore, the smaller value of the two values M _dm / M _d and M _cm / M _c
Using the solution χ ₂ of equation (1) when a is assumed, the spot radius w ₂ divided by the pixel radius r ₀ is w ₂ / r ₀ = 2 / log (1 / χ ₂ ) ^1/2
When
A value obtained by dividing the spot radius w ₀ by the pixel radius r ₀ is w ₂ / r ₀ ≦ w ₀ / r ₀ ≦ w ₁ / r ₀
The image rewriting device is characterized in that it is set so as to satisfy the above relationship.

Further, the present invention relates to a variable χ defined by the relational expression (2), and equations (3) and (4) using b _c and b _cm as parameters.
4b _c χ ^3/2 / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1 = 0 (3)
b _c χ ^-1/2 (1 + 4χ ² + 4χ ⁴ ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1-b _cm = 0 (4)
In
Using the minimum coloring energy density M _c [J / m ² ] and the maximum decoloring energy density M _dm [J / m ² ]
b _c = M _c / M _dm
And when
Range of variable χ
0 <χ ≦ 0.5
Using the solution χ ₃ of equation (3) at
However, in the range 0 <χ ≦ 0.5, if there is no solution χ ₃ of equation (3), χ ₃ = χ ₁ using the solution χ ₁ and the spot radius w ₃ divided by the pixel radius r ₀ is w ₃ / r ₀ = 2 / log (1 / χ ₃ ) ^1/2
And then
b _cm = M _cm / M _dm
The spot radius w ₄ divided by the pixel radius r ₀ is expressed as w ₄ / r ₀ = 2 / log (1 / χ ₄ ) ^1/2 using the solution χ ₄ of the equation (4) when
When
A value obtained by dividing the spot radius w ₀ by the pixel radius r ₀ is w ₄ / r ₀ ≦ w ₀ / r ₀ ≦ w ₃ / r ₀
The image rewriting device is characterized in that it is set so as to satisfy the above relationship.

The present invention includes a variable χ, defined by equation (2), equations b _c for parameters (5), equation (6)
0 = log (1 / χ) · ((b c ((-1/2 · χ -3/2 + 14χ 5/2) - (χ -1/2 + 4χ 7/2) (4χ + 4χ 3 + 12χ ⁵ ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ))-(b _c (χ ^-1/2 + 4χ ^7/2 )-(1 + 2χ ² + χ ⁴ + 2χ ⁶ )) (-8χ + 16χ ³ ) / (1 + 4χ ⁴ -4χ ² )) + 1 / χ ・ (b _c (χ ^-1/2 + 4χ ^7/2 )-(1 + 2χ ² + χ ⁴ + 2χ ⁶ )) ··(Five)
ρ _rB = 2 / log (1 / χ) ・ (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ ) (6)
In
Range of variable χ using solution χ ₃ and solution χ ₄ χ ₄ ≦ χ ≦ χ ₃
Using the solution χ ₅ of equation (5) in
However, if there is no solution χ ₅ of equation (5) in the range χ ₄ ≦ χ ≦ χ ₃ ,
The value obtained by substituting the solution χ ₃ into the variable χ in equation (6) is ρ _rB3 ,
The value obtained by substituting the solution χ ₄ into the variable χ in equation (6) is ρ _rB4 ,
ρ _rB3 and ρ _rB4 , whichever is smaller, solution χ ₃ , solution χ ₄ is χ ₅ ,
The spot radius w ₅ divided by the pixel radius r ₀ is w ₆ / r ₀ = 2 / log (1 / χ ₅ ) ^1/2
The image rewriting device is characterized by being set as follows.

The present invention also sets the parameter b _c
b _c = σ _CDh / σ _D0
The conditions according to the maximum decoloration energy density M _d [J / m ² ] and the maximum decoloration energy density M _dm [J / m ² ]
M _d / M _dm <σ _CDh ≤1
M _d / M _dm ≤σ _D0 <1
When the value of b _c is adjusted in the range of and this adjusted b _c is used,
Range of variable χ using solution χ ₃ and solution χ ₄ of equation (3) and equation (4) χ ₄ ≦ χ ≦ χ ₃
Is an image rewriting device characterized by satisfying the solution χ ₅ of equation (5).

Further, according to the present invention, the minimum value E 0 _cmin [J / m ² ] of the exposure energy density at the center of the exposure energy distribution of one laser beam emitted from the laser array exposure means for the pixel to be colored is
Using the variable χ defined by the relational expression (2) and the minimum coloring energy density M _c [J / m ² ],
E _0cmin = M _c / (4χ + 8χ ⁵ )
This is an image rewriting device characterized by the above.

  According to the present invention, compared with a conventional image rewriting method using a thermal head, a reversible thermosensitive recording medium can be rewritten with a remarkably many times, and a laser capable of irradiating a plurality of laser beams in a straight line. The laser beam spot radius condition that enables simultaneous color erasing with laser array exposure means that uses array exposure means and eliminates the need for special color erasing heating means compared to conventional photothermal conversion type image rewriting methods. Accordingly, a photothermal conversion type image rewriting method with high image quality can be provided.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
1 and 2 are views showing a basic configuration of an image rewriting apparatus using the photothermal conversion type image rewriting method of the first embodiment, FIG. 1 is a schematic sectional view, and FIG. 2 is a schematic perspective view. The schematic perspective view of FIG. 2 shows only the main components for easy viewing. First, an outline of the structure and rewriting function of the image rewriting apparatus according to the first embodiment will be described.
As a specific example, an image having a width of 100 mm is formed with a medium conveyance speed of about 380 mm / sec and pixels of 0.125 mm × 0.125 mm.

  A light-heat conversion type reversible thermosensitive recording medium 10 (hereinafter referred to as recording medium 10) having a light absorption heat conversion function is recorded in a recording medium conveyance direction Y at a constant speed by a medium conveyance device 90 including a known conveyance belt or conveyance roller. It is conveyed to.

  Next, in the laser array module 20 which is an exposure means, the laser beams 21 are arranged in an array in a direction perpendicular to the medium transport direction -Y, and are individually driven and exposed. As a result, necessary portions of the recording medium 10 are colored and erased like an image. That is, in the previous recorded image 11, the part of the image formed this time is colored, and the part corresponding to the background part of the image formed this time is erased to become the requested current recorded image 12.

  The exposure erasing means will be described in detail with reference to FIGS. The exposure erasing means erasing comprises a laser array module 20 (for example, using a wavelength of 808 nm or 830 nm) having a single configuration. For example, when the image size is 100 mm and the pixel size is 0.125 mm × 0.125 mm, the laser array module 20 has a laser beam 21 in the same array integration direction Χ as the line exposure direction 0.1 and at the same 0.125 mm pitch as the pixel pitch. A laser beam array having 800 emission points is formed. However, two laser beams 21 at the left and right end portions of the laser array module 20 are used to optimize the exposure energy density distribution at the end portions, and this portion is outside the range of image formation.

  The semiconductor laser array 23 constituting the laser array module 20 includes, for example, 50 semiconductor laser chips that emit 16 laser beams per one corresponding to 800 laser beams 21. This semiconductor laser chip can be individually driven and controlled for each laser beam 21 by a laser array driver 24, and by pulse width modulation control by ON / OFF control according to the pulse width and power level control according to the power setting value. Power modulation control is possible.

  Light rays emitted from the semiconductor laser array 23 form an imaging spot having a predetermined spot radius on the recording medium 10 by a condensing optical system 22 using a lens. The condensing optical system 22 is fixed, and the predetermined spot radius on the recording medium 10 is fixed with the initial setting. Therefore, in order to variably control the exposure energy on the recording medium 10, one laser on the surface of the recording medium 10 is obtained by either one or both of the pulse width modulation control and the power modulation control described above. The exposure energy density of the beam 21 is controlled.

For example, when the light intensity of one laser beam 21 on the surface of the recording medium 10 needs to be about 50 to 200 mW, the entire laser array module 20 has a light output of about 40 to 160 W.
Alternatively, known time-division driving can be performed by the laser array driver 24. For example, the driving time of the semiconductor laser chip is set to 1/3, and conversely, the light intensity of one laser beam is set to about 150 to 210 mW. Also at this time, 40 to 56 W of the optical output of the entire laser array module 20 is maintained, and necessary energy per unit recording area is secured.

  A photothermal conversion type reversible thermosensitive recording medium used in the image rewriting apparatus of the present invention will be described with reference to a schematic cross-sectional view of the reversible thermosensitive recording medium 10.

  As shown in FIG. 3, the basic configuration of the photothermal conversion type reversible thermosensitive recording medium 10 according to the present invention is a reversible thermosensitive recording layer 14 and a protective layer 15 in which a light absorbing heat converting material is mixed on a support 13. Is formed. The reversible thermosensitive recording layer 14 used in the present invention comprises at least a leuco dye, a reversible developer, and a light absorption heat conversion material. The usable photothermal conversion type reversible thermosensitive recording medium 10 includes a reversible thermosensitive recording layer formed of a leuco dye and a reversible developer, and a photothermal conversion layer made of a light-absorbing heat converting material. It is also possible to laminate.

Also, a reversible thermosensitive recording layer 15 made of a leuco dye, a reversible developer, and a light absorption heat conversion material is formed, and a light heat conversion layer made of a light absorption heat conversion material is further laminated thereon as a protective layer 15. Is also possible.
Further, when the average transmittance of light having the absorption wavelength of the light-absorbing heat conversion material is, for example, 30% or more in the reversible thermosensitive recording layer 14 containing the light-absorbing heat conversion material, the reversible thermosensitive recording layer 14. It is also possible to laminate a light-to-heat conversion layer made of a light-absorbing and heat-converting material immediately below the surface.

The material of each layer will be described below. As specific examples of the leuco dye, those disclosed in Patent Documents 3, 4, and 5 can be used. It is not limited to this.
Japanese Patent Laid-Open No. 2001-162941 JP 2004-345273 A Japanese Patent Laid-Open No. 11-151856

  As the reversible developer, a phenol compound having a long-chain alkyl group is used and disclosed in Patent Documents 3, 4, and 5. In this invention, it is necessary to limit to the reversible color developer which has high-speed decoloring property, and use of the concrete reversible color developer currently disclosed by patent document 3 is desirable. Further, as disclosed in Patent Document 3, with respect to a reversible thermosensitive recording material produced by mixing with a leuco dye even if it is another reversible developer, a color development state obtained by heating, melting and quenching When the reversible thermosensitive recording material is changed to a decolored state without showing an exothermic peak in the temperature rising process by differential scanning calorimetry or differential thermal analysis, the reversible thermosensitive recording material is a reversible thermosensitive recording material having high-speed decoloring property. It can be used. That is, in this case, it is possible to instantaneously shift from the colored state to the decolored state with a small amount of heat energy.

  Therefore, the reversible thermosensitive recording material that can be used in the present invention is required to have high-speed decoloring properties, and is not limited to leuco dyes and reversible color developers suitable therefor.

  As the light absorption heat conversion material used in the present invention, a photothermal conversion dye is used. Specific examples include phthalocyanine compounds, metal complex compounds, polymethine compounds, naphthoquinone compounds, and the like, which can be contained in the reversible thermosensitive recording layer 14 in a dispersed state or in a molecular state. Preferred are a phthalocyanine compound and a metal complex compound from the viewpoint of photothermal conversion efficiency, solubility in a solvent, dispersibility in a resin, and light resistance to ultraviolet rays, and a phthalocyanine compound is particularly preferable.

  More specifically, those disclosed in Patent Documents 3, 4, and 5 can be used. In this embodiment, a light absorption heat conversion material having an absorption peak in the vicinity of the wavelength 808 nm to 830 nm of the laser light source 21 to be used is selected.

  Various binders, additives and the like can be used for the reversible thermosensitive recording layer 14 in order to improve performance, which are disclosed in Patent Documents 3, 4, and 5. For example, a binder such as a heat resistant resin for improving the strength of the reversible thermosensitive recording layer and uniformly dispersing each material of the composition of the reversible thermosensitive recording layer without uneven distribution by heating / cooling is mentioned. . Further, thermofusible substances for adjusting the color development sensitivity and the erasing temperature are mentioned.

  The support 13 used in the present invention not only functions to support the reversible thermosensitive recording layer 14 but also functions as a heat absorber in the cooling step after heating during color development. For this reason, a synthetic resin film such as polyethylene terephthalate or polypropylene having a predetermined thermal conductivity and specific heat is used for the support 13. Specific materials that can be used are disclosed in Patent Documents 3, 4, and 5.

  As a configuration of the photothermal conversion type reversible thermosensitive recording medium 10, it is desirable that the protective layer 15 is laminated as the outermost layer on the reversible thermosensitive recording layer 35. In the image rewriting method of the present invention, the recording medium 10 can rewrite an image without contact, and basically the recording medium 10 is not damaged except for heating and cooling. However, in the entire life cycle of the recording medium 10, after being rewritten by the image rewriting method of the present invention, it becomes a use stage that plays the original role of the recording medium 10. In this stage of use, it is subject to various damages such as rubbing, striking, bending, and ultraviolet irradiation. For this reason, the protective layer 15 which is a hard-coat layer is needed.

  In particular, since the photothermal conversion dye or leuco dye as the light absorption heat conversion material is highly likely to be damaged by ultraviolet absorption, various ultraviolet absorbers can be mixed in the protective layer 15. Patent Documents 4 and 5 disclose protective layer materials including various usable UV absorbers. In general, as the light absorption heat conversion material, a material having an absorption wavelength in the near-infrared region is used, and since the coloring wavelength region of the leuco dye is a visible region, the uppermost protective layer 15 absorbs only ultraviolet rays. Neither the light-absorbing heat converting material nor the leuco dye will adversely affect its function.

The imaging spot of the elliptical laser beam 21 on the recording medium 10 has coordinates (x, y) with the spot center as the origin, where I ₀ [w / m ² ] is the intensity at the spot center (hereinafter referred to as the center intensity). ) relative to [m], having the formula (1.1 intensity distribution I (r) of the Gaussian distribution shown ^{by) [w / m 2] (} w b ≦ w a)
_{I (r) = I 0 exp} (- (2x 2 / w a 2 + 2y 2 / w b 2)) ··· (1.1)
Here, w _a is the 1 / e ² spot semimajor axis (hereinafter referred to as spot-major axis), x = w _a, when y = 0
I (w _a ) = I ₀ exp (-2) = I ₀ / e ² (1.2a)
W _b is 1 / e ² spot short radius (hereinafter referred to as spot short radius), and when x = 0, y = w _b
I (w _b ) = I ₀ exp (-2) = I ₀ / e ² (1.2b)
Satisfies the relationship.

Furthermore, when the distance that the recording medium 10 moves within the exposure time of the laser beam 21 is sufficiently short relative to the beam radius w ₀ , the exposure energy density distribution [J / m ² ] of the imaging spot by the circular laser beam 21. Can be approximated by a Gaussian distribution. Therefore, using the pixel formation time, that is, the laser exposure time t ₀ [sec] per pixel,
I (r) ・ t ₀ = I ₀・ t ₀ exp (-2r ² / w ₀ ² )
Assuming that E ₀₀ [J / m ² ] is the exposure energy density at the center of the spot (hereinafter referred to as the center exposure energy density), the exposure energy density distribution E (r) [J / m ² ] of the imaging spot by the circular laser beam 21 is used. Is
E ₀₀ = I ₀・ t ₀・ ・ ・ (1.3), E (r) = I (r) ・ t ₀
E (r) = E ₀₀ exp (-2r ² / w ₀ ² ) (1.4)

Therefore, the imaging spot of the circular laser beam 21 on the recording medium 10 is the distance r [m] from the spot center, where E ₀₀ [J / m ² ] is the exposure energy density at the spot center (center exposure energy density). In contrast, it has an exposure energy density E (r) [J / m ² ] having a Gaussian distribution represented by the equation (1.4).
Where r = w ₀
E (w ₀ ) = E ₀₀ exp (-2) = E ₀₀ / e ²
It becomes. Therefore, the exposure energy density of the Gaussian distribution represented by the formula (1.4) indicates the exposure energy density of 1 / e ² of the center exposure energy density E _{00 at} the distance w ₀ . This w ₀ is set as a spot radius.

  In examining the relationship between the exposure energy density of the imaging spot of the laser beam 21 and the coloring and decoloring characteristics of the recording medium 10, the relationship between the energy density and the coloring and decoloring characteristics is relative. Divide by the reference value, not the absolute value of the value, and treat it as dimensionless. Thereby, even if the exposure energy density and the absolute values of the coloring and decoloring characteristics change depending on the conditions and materials used, a constant setting standard can be provided.

The pitch of the laser beams 21 arranged in an array is the same as the pitch of pixels (dots) to be formed. 1/2 of this pixel (dot) pitch is defined as r ₀ [m] pixel radius, and a variable χ (spot radius index) is introduced as an index of the spot radius with respect to this pixel radius r ₀ ,
w ₀ / r ₀ = 2 / (log (1 / χ)) ^1/2 ... (1.5)
It is assumed that there is a relationship indicated by.
The distance r from the spot center is made dimensionless with the pixel radius r _0.
γ = r / r ₀ ... (1.6)
A dimensionless distance γ (hereinafter referred to as a deviation distance) from the spot center is introduced.
Substituting Equation (1.5) and Equation (1.6) into Equation (1.4),
_{E (r) = E 00 χ} ^ (γ 2/2) ··· (1.7)
It becomes.

Here, the coloring and decoloring characteristics of the recording medium 10
M _c [J / m ² ] : Minimum coloring energy density
M _cm [J / m ² ]: Maximum coloring energy density
M _d [J / m ² ]: Minimum decoloring energy density
^{_{M dm [J / m 2]}} : maximum determined as decoloring energy density, when these are dimensionless with minimum color energy density M _c
ξ _c = M _c / M _c = 1 : Dimensionless minimum coloring energy density
ξ _cm = M _cm / M _c : Dimensionless maximum coloring energy density
ξ _d = M _d / M _c : Dimensionless minimum decolorization energy density
ξ _dm = M _dm / M _c : non-dimensional maximum erasing energy density.
Further, use _Mc to make the exposure energy density dimensionless.
ε (γ) = E (r) / M _c : Dimensionless exposure energy density at deviation γ
ε ₀₀ = E ₀₀ / M _c : Dimensionless center exposure energy density From these, equation (1.6) expresses the energy density distribution of the dimensionless Gaussian distribution
_{ε (γ) = ε 00 χ} ^ (γ 2/2) ··· (1.8)
It becomes.

  Hereinafter, unless otherwise specified, the dimensionless minimum coloring energy density or the like is simply referred to as the minimum coloring energy density or the like. Similarly, the dimensionless center exposure energy density is simply referred to as center exposure energy density.

From Patent Document 2, the power [w] of the laser beam 21 can be calculated from the set spot radius w ₀ by using the laser array module 20.
The power P [w] of one laser beam 21 is
P = 1/2 ・ I ₀ πw ₀ ² ... (1.9)
Given in. therefore
P / (πr ₀ ² ) = 1/2 ・ I ₀ (w ₀ / r ₀ ) ²
When converted to energy density by applying pixel formation time on both sides, that is, laser exposure time t ₀ [sec] per pixel
t ₀ P / (πr ₀ ² ) = 1/2 ・ I ₀ t ₀ (w ₀ / r ₀ ) ²
Using equation (1.3)
t ₀ P / (πr ₀ ² ) = 1/2 ・ E ₀₀ (w ₀ / r ₀ ) ² ... (1.10)
In order to compare the magnitude of light energy required for image formation, a value obtained by dividing the beam exposure energy of one laser beam 21 by the area (πr ₀ ² ) of a circle having a pixel radius is represented by U _r [J / m ² ]. And
U _r = t ₀ P / (πr ₀ ² )
Substituting this into (1.10)
U _r = 1/2 ・ E ₀₀ (w ₀ / r ₀ ) ² ... (1.11)
Dimensionless beam energy density ρ _r , which is made dimensionless by dividing equation (1.9) by M _c [J / m ² ]
ρ _r = U _r / M _c
With
_{ρ r = ε 00 (w 0} / r 0) 2/2 ··· (1.12)
Furthermore, using equation (1.5)
ρ _r = ε ₀₀ 2 / log (1 / χ) (1.13)
It becomes. Since ρ _r does not depend on the absolute value of the pixel area, it is used for comparing the magnitude of exposure energy required for image formation. Hereinafter, unless otherwise specified, the dimensionless beam energy density is simply referred to as beam energy density.

In the present invention, the spatial frequency is
Spatial frequency = (color generation / decoloration cycle) / (number of pixels) (1.14)
And define
Furthermore, the binary spatial frequency
Spatial frequency ν _{x in the} X direction
ν _x = (coloring / erasing cycle in the X direction) / (number of pixels in the X direction) (1.15)
Spatial frequency in the Y direction ν _y
ν _y = (coloring / erasing cycle in Y direction) / (number of pixels in Y direction) (1.16)
Using
ν = (ν _x ² + ν _y ² ) ^1/2 ... (1.17)
It is defined as
In this embodiment, the reference number of pixels is that the cumulative range 30 has a 4-pixel radius, so the pitch between adjacent cumulative ranges is 4 pixel radius × 2, so this is the size of one pixel, the pixel radius Divide by x2.
Therefore
Number of reference pixels = (4 pixel radius × 2) / (pixel radius × 2) = 4
It becomes.

In the first embodiment, the accumulated exposure energy density in an image pattern having a minimum spatial frequency and coloring or decoloring all pixels is shown.
The binary spatial frequency in this case is
ν = ((0/4) ² + (0/4) ² ) ^1/2 = 0
It is.

4 (a), 4 (b), and 4 (c), the color generation / decoloration corresponding to the entire color development or color erase image pattern in which the color development pixels or the color elimination pixels are uniformly arranged on the entire surface. An exposure pattern is shown. This image pattern has the smallest spatial frequency. In FIG. 4, the state of a spot circle 31 on which the laser beam 21 forms an image on the surface of the recording medium 10 is shown. At this time, the center exposure energy density ξ ₀₀ of the spot circle 31 is all constant and is of the following two types.

In the case of a full color pattern that colors all pixels, the spot circle 31 is a color spot corresponding to a color pixel, and the central exposure energy density at this time is the color development center exposure energy density E _0c . When the E _0c to dimensionless by M _c,
ε _0c = E _0c / M _c : Dimensionless color development center exposure energy density
The spot circle 31 is a erasing spot corresponding to the erasing pixel, and at this time, the central exposure energy density is the erasing center exposure energy density E _0d . When the E _0d dimensionless dimensionless by M _c,
ε _0d = E _0d / M _c : Dimensionless erasing center exposure energy density.

In general, the sum of exposure energy densities from all laser beams 21 that can expose the observation position at an arbitrary observation position on the recording medium 10 can be defined as a cumulative exposure energy density at the observation position. In this embodiment, a certain cumulative range is set from the observation position, and the sum of the exposure energy densities from all the laser beams 21 within the range is defined as the cumulative exposure energy density at the observation position.
When the surface of FIG. 4 as a recording medium 10 surface, FIG. 4 (a), the FIG. 4 (b), in the case in each of FIG. 4 (c), consists of spot radius w ₀ by a plurality of laser beam 21 spots £ 31 It is shown. The spot radius w ₀ varies depending on the spot radius index χ. The spot circles 31 are arranged at a pitch of 2 pixels in the vertical and horizontal directions (2r ₀ ). This corresponds to the laser beams 21 being arranged in an array at a pitch of 2 pixels radius (2r ₀ ) in a direction perpendicular to the medium transport direction Y. Observation nodes 32, 33, and 34, which are specific observation positions for calculating the accumulation of exposure energy density, are respectively set, and an accumulation range 30 indicating a radius of 4 pixels (4r ₀ ) is drawn around this observation node. ing. The sum of the exposure energy density distributions of the plurality of laser beams 21 corresponding to the spot circle 31 centered in the cumulative range 30 is defined as the cumulative exposure energy density at the observation node. Strictly speaking, the laser beam 21 affects the observation node even in the cumulative range of 4r ₀ or more, but w ₀ / r ₀ ≈2.4 is the maximum value, and the exposure energy density at this time is 0.4% of the center energy density. There is only a degree. Therefore, the exposure energy of the laser beam 21 outside the cumulative range of 4r ₀ can be ignored for the calculation of the cumulative exposure energy density of the target observation node. The observation node 32 in FIG. 4A is called the center node 32 because it is located at the center of one spot circle 31. The observation node 33 in FIG. 4B is called an intermediate node 33 because it is located between the two spot circles 31. The observation node 34 in FIG. 4C is called the face center node 34 because it is located at the center of the four spot circles 31.

Next, using formula (1.8), the cumulative exposure energy density of each observation node on the recording medium 10 shown in FIGS. 4 (a), 4 (b) and 4 (c) is calculated. In FIG. 4 (a), when the dimensionless cumulative exposure energy density dimensionless by M _c at the center node 32 and sigma _0, spot £ 31 and the surrounding eight spots £ 31 a total of nine laser corresponding to the center node 32 Since the sum of the exposure energy density of the beam 21 is taken,
σ ₀ = ε ₀₀ (1 + 4χ ² + 4χ ⁴ ) (1.18)
It becomes.
In FIG. 4B, if the dimensionless cumulative exposure energy density at the intermediate node 33 is σ _{h in the} same manner, the sum of the exposure energy densities of the laser beams 21 forming 12 surrounding spot circles is obtained.
σ _h = ε ₀₀ χ ^1/2 (2+ 4χ ² + 2χ ⁴ + 4χ ⁶ ) (1.19)
It becomes.
In FIG. 4C, if the dimensionless cumulative exposure energy density at the face center node 34 is σ _f , the sum of the exposure energy densities of the laser beams 21 forming the surrounding 12 spot circles is obtained.
σ _f = ε ₀₀ (4χ + 8χ ⁵ ) ・ ・ ・ (1.20)
It becomes.
Equation (1.18), equation (1.19), ₀₀ epsilon in the equation (1.20), when calculating the exposure energy density in accordance with the image pattern, epsilon _0c or epsilon _0d is applied. Hereinafter, unless otherwise specified, the dimensionless cumulative exposure energy density is simply referred to as cumulative exposure energy density.

When the exposure energy density ε ₀₀ = 1 is fixed in the exposure patterns shown in FIGS. 4 (a), 4 (b), and 4 (c) from the formulas (1.18), (1.19), and (1.20). cumulative exposure energy density σ _0, σ _h, the sigma _f, plotted in Figure 5 under the condition of 0 <χ ≦ 0.5.
From FIG. 5, in the condition of 0 <χ ≦ 0.5,
The cumulative exposure energy density σ _{0 at the} center node 32 takes the maximum value.
The cumulative exposure energy density σ _{f at the} face center node 34 takes the minimum value.
Therefore, the condition that the center node 32 is the maximum accumulated exposure energy density and the face center node 34 is the minimum accumulated exposure energy density is the maximum allowable exposure energy density at the two accumulated exposure energy densities σ ₀ and σ _f . This is the exposure energy density ratio condition.
Therefore, when parameter a is newly introduced as the exposure cumulative energy density ratio,
a = σ ₀ / σ _f・ ・ ・ (1.21)
Substituting the equation (1.18) indicating ξ ₀ and the equation (1.20) indicating ξ _f into this equation, and deleting ε ₀₀ ,
a = (1 + 4χ ² + 4χ ⁴ ) / (4χ + 8χ ⁵ ) ・ ・ ・ (1.22)
1-a4χ + 4χ ² + 4χ ⁴ -a8χ ⁵ = 0 (1.23)
It becomes.
The σ ₀ and σ _f minimum energy density ratio is independent of the coloring and decoloring characteristics of the recording medium 10.
σ ₀ = σ _f
a = σ ₀ / σ _f = 1 (1.24)
Can be set. Under this condition, equation (1.12) becomes
1-4χ + 4χ ² + 4χ ⁴ -8χ ⁵ = 0 ・ ・ ・ (1.25)
And this solution is χ ₁
χ ₁ = 0.5. ... (1.26)
Substituting this into equation (1.5) gives the maximum allowed spot radius w ₁
w ₁ / r ₀ = 2 / log (1 / χ ₁ ) ^1/2 ... (1.27)
Set as The value of equation (1.19) can be obtained specifically.
w ₁ / r ₀ = 2 / (log (2)) ^1/2 ≒ 2.402
On the other hand, the following coloring and decoloring characteristics of the recording medium 10
M _c [J / m ² ] : Minimum coloring energy density
M _cm [J / m ² ]: Maximum coloring energy density
M _d [J / m ² ]: Minimum decoloring energy density
M _dm [J / m ² ]: From the maximum decoloring energy density, the maximum energy density ratio is
a _c = σ ₀ / σ _f = ξ _cm / ξ _c = M _cm / M _c・ ・ ・ (1.28)
a _d = σ ₀ / σ _f = ξ _dm / ξ _d = M _dm / M _d・ ・ ・ (1.29)
There are two.
The meaning of a is the maximum allowable cumulative exposure energy density ratio indicating the width of the energy density that can be developed or the width of the energy density that can be erased as the characteristic of the recording medium 10, and therefore, a _c , a _d Extracting the smaller value from the two values of
a = min (a _c , a _d )
It becomes. Here, the function min (a ₁ , a ₂ ) is a function for extracting the smaller value from the two values a ₁ and a ₂ .
Summarizing the above, the conditional expressions to be obtained are the expression (1.23) and the following (1.31).
a = min (M _cm / M _c , M _dm / M _d ) (1.30)
1-a4χ + 4χ ² + 4χ ⁴ -a8χ ⁵ = 0
It becomes.
If the solution of equation (1.23) under these conditions is χ = χ ₂ and is substituted into equation (1.5),
The minimum allowable spot radius w ₂ is
It is set as w ₂ / r ₀ = 2 / log (1 / χ ₂ ) ^1/2 (1.31).
From the above, the setting range of χ is
χ ₂ ≦ χ ≦ χ ₁ ... (1.32)
χ ₂ ≦ χ ≦ 0.5
Therefore, the spot radius w ₀ of the laser beam 21 is
w ₂ / r ₀ ≦ w ₀ / r ₀ ≦ w ₁ / r ₀ (1.33)
w ₂ / r ₀ ≦ w ₀ / r ₀ ≦ 2.402
By setting so as to satisfy this relationship, it is possible to obtain a photothermal conversion type image rewriting method capable of forming a good image in relation to the coloring and decoloring characteristics of the recording medium 10.
Further, by using the non-dimensionalized spot radius w ₀ / r ₀ , a setting reference for the spot radius irrespective of the pixel radius r ₀ of the required image solution can be obtained.

As an example satisfying the conditional expression (1.31), an effective setting range of the spot radius corresponding to the entire color erased image pattern in which all pixels are erased is shown.
As a numerical condition
ξ _d = 0.5
σ _f = ξ _d
Set.
First formula (1.23)
a = (1 + 4χ ² + 4χ ⁴ ) / (4χ + 8χ ⁵ )
Calculate a with respect to χ.
Next, assuming that the center exposure energy density ξ ₀₀ of the formula (1.20) is the decoloration center exposure energy density ξ _0d ,
σ _f = ε _0d (4χ + 8χ ⁵ )
By substituting the condition σ _f = ξ _d into this, the minimum center exposure energy density ε _0d for χ necessary to form the entire color-erased image pattern is calculated.
ε _0d = ξ _d / (4χ + 8χ ⁵ ) ・ ・ ・ (1.34)
Using the calculated ξ _0d , σ ₀ is obtained from Equation (1.18).
_{σ 0 = ε 0d (1 +} 4χ 2 + 4χ 4) ··· (1.35)
Similarly, σ _h is obtained from Equation (1.18).
σ _h = ε _0d χ ^1/2 (2+ 4χ ² + 2χ ⁴ + 4χ ⁶ ) ・ ・ ・ (1.36)
From the above, parameter a, cumulative exposure energy density ξ ₀ , ξ _h , ξ _f
0> χ ≧ 0.5
Plotted in FIG.

Also, the specific numerical value a
ξ _dm = 0.75
a = ξ _dm / ξ _d = 0.75 / 0.5 = 1.5
And set this to equation (1.23)
1-a4χ + 4χ ² + 4χ ⁴ -a8χ ⁵ = 0
Substituting and using the well-known dichotomy and Newton method,
Solution corresponding to the smallest spot radius
χ ₂ ≒ 0.1915
Is required. This is shown in FIG.
Therefore, the effective setting range of χ is
0.1915 ≦ χ ≦ 0.5
It becomes. When this is converted into a dimensionless spot radius w ₀ / r _{0 according} to equation (1.5)
1.556 ≦ w ₀ / r ₀ ≦ 2.402 (1.37)
A specific effective setting range of the dimensionless spot radius w ₀ / r ₀ is obtained.

Above settings
1.556 ≦ w ₀ / r ₀ ≦ 2.402
The cumulative exposure energy density distribution with respect to the whole surface erasable image pattern is shown.
The maximum condition of the spot radius w ₀ is
a = 1
w ₀ / r ₀ = 2.402
χ = 0.5
It is.
Substituting χ = 0.5 and ξ _d = 0.5, which are the conditions for the maximum spot radius w ₀ , into equation (1.34), the minimum value of the decoloration center exposure energy density ε _0d
ε _0d ≒ 0.2222
Is determined.
By substituting this value into Equation (1.18), Equation (1.19), and Equation (1.20), the cumulative exposure energy density at each observation node is calculated.
σ ₀ = 0.5
σ _h ≒ 0.5009
σ _f = 0.5
FIG. 7 shows the cumulative exposure energy density distribution with respect to the entire color-erased image pattern at the maximum spot radius.

The graph of FIG. 7 shows two cumulative exposure energy density distributions on line segment AA and line segment BB shown in FIG.
In the line segment AA, the peak indicates the value at the center node, and the bottom indicates the value at the intermediate node.
In the line segment BB, the peak indicates the value at the intermediate node, and the bottom indicates the value at the face center node.
In FIG. 7, the values of σ ₀ , σ _h , and σ _f exceed the calculated values by about 1% at the maximum. This is because a more rigorous calculation is performed as confirmation. This is because the cumulative range 30 in which the exposure energy density distribution of 21 is summed is about 6 pixel radius (6r ₀ ). This is a setting for summing in a wider range than the 4-pixel radius (4r ₀ ) used for the derivation of the equations (1.18), (1.19), and (1.20).
As shown in FIG. 7, the distribution of the accumulated exposure energy density σ _d is
ξ _d ≒ σ _d
Thus, the flat erasing condition is maintained.

Next, the case of the minimum value of the spot radius w ₀ is shown.
At this time, the condition is
a = 1.5
w ₀ / r ₀ = 1.556
χ = 0.1915
It is.
Χ = 0.1915 and ξ _d = which are the conditions of the minimum spot radius w ₀ Substituting 0.5 into this equation (1.34), the maximum value of the decoloration center exposure energy density ε _0d
ε _0d ≒ 0.6511
Is determined.
By substituting this value into Equation (1.18), Equation (1.19), and Equation (1.20), the exposure energy density at each observation node is calculated.
σ ₀ = 0.75
σ _h ≒ 0.6124
σ _f = 0.5
FIG. 8 shows two cumulative exposure energy density distributions on line segment AA and line segment BB with respect to the entire surface decolored image pattern at the minimum spot radius. As shown in FIG. 8, the distribution of the cumulative exposure energy density σ _d near the decoloring center node is
ξ _d ≦ σ _d ≦ ξ _dm
And the erasing condition is maintained.
Comparing FIG. 7 for the maximum spot radius and FIG. 8 for the minimum spot radius, the exposure energy density distribution is more uniform in the case of the maximum spot radius. However, the case of the minimum spot radius is preferable for forming an image pattern having a higher spatial frequency.

Next, the effective setting range of the spot radius corresponding to the full color image pattern in which all pixels are colored will be shown.
As a numerical condition
ξ _c = 1.0
ξ _f = ξ _c
Set.
First formula (1.23)
a = (1 + 4χ ² + 4χ ⁴ ) / (4χ + 8χ ⁵ )
Calculate a with respect to χ. Therefore, the value of a is the same as in the case of the entire surface erasing pattern.
Next, assuming that the center exposure energy density ξ ₀₀ of the formula (1.20) is the color development center exposure energy density ξ _0c ,
σ _f = ε _0c (4χ + 8χ ⁵ )
By substituting the condition σ _f = ξ _d into this, the minimum color center exposure energy density ε _0c for χ necessary to form the entire color image pattern is calculated.
ε _0c = ξ _c / (4χ + 8χ ⁵ ) ・ ・ ・ (1.38)
Using the calculated ξ _0d , σ ₀ is obtained from Equation (1.18).
σ ₀ = ε _0c (1 + 4χ ² + 4χ ⁴ ) (1.39)
Similarly, σ _h is obtained from Equation (1.18).
σ _h = ε _0c χ ^1/2 (2+ 4χ ² + 2χ ⁴ + 4χ ⁶ ) ・ ・ ・ (1.40)
From the above, parameter a, cumulative exposure energy density σ ₀ , σ _h , σ _f
0> χ ≧ 0.5
Plotted in FIG.

Also, the specific numerical value a
ξ _cm = 1.5
a = ξ _cm / ξ _c = 1.5 / 1.0 = 1.5
And set this to equation (1.23)
1-a4χ + 4χ ² + 4χ ⁴ -a8χ ⁵ = 0
Substituting and using the well-known dichotomy and Newton method,
Solution corresponding to the smallest spot radius
χ ₂ ≒ 0.1915
Is required. This is shown in FIG.
Therefore, the effective setting range of χ is
0.1915 ≦ χ ≦ 0.5
It becomes. When this is converted into a dimensionless spot radius w ₀ / r _{0 according} to equation (1.5)
1.556 ≦ w ₀ / r ₀ ≦ 2.402 (1.41)
A specific effective setting range of the dimensionless spot radius w ₀ / r ₀ is obtained.
This is the same result as in the case of the entire surface erasable pattern except for the level of exposure energy density. Therefore, it is possible to form an image for both full color erasure and full color development with the same spot radius setting. This is a spot radius condition that enables simultaneous color development and decoloration for an image rewriting method in which the condensing optical system 22 is fixed, that is, the spot radii of the individual laser beams 21 are all the same and fixed. .

Above settings
1.556 ≦ w ₀ / r ₀ ≦ 2.402
The cumulative exposure energy density distribution with respect to the entire color image pattern when using is shown.
The maximum condition of the spot radius w ₀ is
a = 1
w ₀ / r ₀ = 2.402
χ = 0.5
It is.
Χ = 0.5 and ξ _c = which are the conditions for the maximum spot radius w ₀ Substituting 1.0 into the formula (1.37),
Minimum value of color center exposure energy density ε _0c
ε _0c ≒ 0.4444
Is determined.
By substituting this value into Equation (1.18), Equation (1.19), and Equation (1.20), the exposure energy density at each observation node is calculated.
σ ₀ = 1.0
σ _h ≒ 1.002
σ _f = 1.0

FIG. 10 shows two cumulative exposure energy density distributions on the line segment AA and the line segment BB with respect to the entire surface decolored image pattern at the maximum spot radius. This is the same result as in the case of the entire surface erasable pattern except for the level of exposure energy density.
As shown in FIG. 10, the distribution of the accumulated exposure energy density σ _c is
ξ _c ≒ σ _c
Thus, the flat erasing condition is maintained.

Next, the case of the minimum value of the spot radius w ₀ is shown.
At this time, the condition is
a = 1.5
w ₀ / r ₀ = 1.556
χ = 0.1915
It is.
Χ = 0.1915 and ξ _c = which are the conditions of the minimum spot radius w ₀ Substituting 1.0 into equation (1.37), the minimum value of the center exposure energy density ε _0d
ε _0d ≒ 1.302
Is determined.
By substituting this value into Equation (1.18), Equation (1.19), and Equation (1.20), the exposure energy density at each observation node is calculated.
σ ₀ = 1.5
σ _h ≒ 1.225
σ _f = 1.0

FIG. 11 shows two cumulative exposure energy density distributions on line segment AA and line segment BB with respect to the entire surface decolored image pattern at the minimum spot radius.
This is the same result as in the case of the entire surface erasable pattern except for the level of exposure energy density.
As shown in FIG. 11, the distribution of the cumulative exposure energy density σ _c near the decoloring center node is
ξ _c ≦ σ _c ≦ ξ _cm
And the erasing condition is maintained.
Comparing FIG. 10 for the maximum spot radius and FIG. 11 for the minimum spot radius, the exposure energy density distribution is more uniform for the maximum spot radius. However, the case of the minimum spot radius is preferable for forming an image pattern having a higher spatial frequency.

  With the optimized spot radius setting according to the present invention, it is possible to form an image for both full color erasing and full color development with the same spot radius setting. This is suitable for the image rewriting method using the laser array in which the condensing optical system 22 is fixed, that is, the spot radii of the individual laser beams 21 are all the same and fixed. Image formation can be realized. This simultaneous color erasing eliminates the need for a color erasing unit that uniformly heats the recording medium, such as a halogen lamp or a hot air blowing device. As a result, the image rewriting apparatus can be reduced in size and simplified, and the cost can be easily reduced.

In the exposure by the laser array, when the spot radius is set to about half of the pixel pitch, the density unevenness occurs in the image due to the uneven exposure energy density at the center and the periphery of the spot.
Due to the spot radius of about 1.5 to 2.5 times the pixel radius according to the present invention, the exposure energy density at the center and the periphery of the spot is perfectly compatible with the coloring and decoloring characteristics, so high-quality image formation without unevenness Is possible.

  The spot radius setting according to the present invention has a width of about one pixel radius. This is an optimizable range based on various image patterns to be formed. For example, as an image rewriting method suitable for printing a uniform solid image of a large area, a large spot radius is adopted, or a small image rewriting method for a wide range of applications from a fine image to a large area image is used. It is possible to finely adapt to the required printing characteristics, such as adopting a spot radius.

  According to the optimized spot radius setting according to the present invention, the exposure energy density is perfectly matched to the color development and decoloring characteristics of the recording medium 10. For this reason, while maintaining a sufficient exposure energy density at the spot periphery by the laser beam 21, an excessive exposure energy density does not occur at the center of the spot. As a result, since the recording medium material is not seriously damaged by thermal decomposition, thermal deformation, etc., the rewritable life of the recording medium can be exhibited to the original properties of the material of the recording medium itself. .

  The range of effective spot radii in the entire surface erasing and entire surface coloring pattern shown in the first embodiment is too wide and insufficient for forming an image pattern having a higher spatial frequency.
  For example, maximum spot radius condition w₀/ r₀When = 2.402 is used,
        Minimum image pattern area ≥ 3 pixel pitch x 3 pixel pitch = 6r₀× 6r₀
  The arrangement pitch of the laser beams 21 is 2r.₀Nevertheless, only a three times coarser image can be formed. Therefore, in the second embodiment, an effective spot radius range for realizing a checkerboard image pattern having the maximum spatial frequency in a square lattice is shown.
  The binary spatial frequency in this case is
          ν = ((2/4)²+ (2/4)²)^1/2≒ 0.7071
It is.

12 (a), 12 (b), and 12 (c), a color-development exposure pattern corresponding to a checkerboard image pattern in which one color-development pixel and a decolorization pixel are alternately arranged vertically and horizontally. Indicates. The setting of each observation node is the same as that in FIGS. 4 (a), 4 (b), and 4 (c).
Using equation (1.8), the cumulative exposure energy density of each observation node on the recording medium 10 shown in FIGS. 12 (a), 12 (b), and 12 (c) is calculated.
At this time, the spot circle 31 has the following two types.
Color spot 31a
ε _0c : Color development center exposure energy density
Decoloring spot 31b
ε _0d : _{Decolorization} center exposure energy density.
In FIG. 12A, when the central node 32 is in the coloring condition, that is, the accumulated exposure energy density in the case of the coloring center node 32a is σ _C0 ,
_{σ C0 = ε 0c (1 +} 4χ 4) + ε 0d 4χ 2 ··· (2.1)
Further, in FIG. 12A, if the accumulated exposure energy density σ _{D0 of} the decoloring center node 32b adjacent to the coloring center node 32a is assumed, in this case, the coloring node and the decoloring spot of the spot circle 31 are switched and the central node When 32 is a decoloring condition, that is, the position of the color developing center node 32a and the position of the decoloring center node 32b may be exchanged.
_{σ D0 = ε 0d (1 +} 4χ 4) + ε 0c 4χ 4 ··· (2.2)
It becomes.
In FIG. 12B, when the accumulated exposure energy density at the intermediate node 33 is σ _CDh ,
σ _CDh = χ ^1/2 (ε _0c (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) + ε _0d (1 + 2χ ² + χ ⁴ + 2χ ⁶ )) (2.3)
It becomes.
In FIG. 12C, when the accumulated exposure energy density at the face _center node 34 is σ _CDf ,
_{σ CDf = ε 0c (2χ +} 4χ 5) + ε 0d (2χ + 4χ 5) ··· (2.4)
It becomes.
Therefore,
Erasing ξ _0d from Equation (2.2) and Equation (2.3),
ε _0c = (σ _CDh (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2x ² + x ⁴ + 2x ⁶ ) -σ _D0 ) / (1-4χ ² + 4χ ⁴ ) ・ ・ (2.5)
Erasing ξ _0c from Equation (2.2) and Equation (2.3),
_{ε 0d = - (4σ CDh χ} 3/2 / (1 + 2χ 2 + χ 4 + 2χ 6) -σ D0) / (1-4χ 2 + 4χ 4) ··· (2.6)
Substituting the results of Equation (2.5) and Equation (2.6) into Equation (2.1)
σ _C0 = σ _CDh (χ ^-1/2 + 4χ ^3/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -σ _D0 ... (2.7)
It becomes.

In this embodiment, the condition that the exposure energy density should satisfy the checkerboard image pattern is:
The erasing center exposure energy density ε _{0d at the} erasing center node 32 is zero or more. The cumulative exposure energy density σ _{D0 at the} erasing center node 32 is the maximum erasing energy density ξ _dm or less. The cumulative exposure energy density σ _{C0 at the} coloring center node 32 is Maximum coloring energy density ξ _cm or less The cumulative exposure energy density σ _{CDh at the} intermediate node 33 is set to be the minimum coloring energy density ξ _c or more.
From this condition,
σ _D0 = ξ _dm
σ _CDh = ξ _c
In the meantime, a parameter b _c which is a new allowable cumulative exposure energy density ratio is introduced.
b _c = σ _CDh / σ _D0 = ξ _c / ξ _dm = M _c / M _dm (2.8)
As the characteristics of the recording medium 10 the meaning of b _c, erasable maximum exposure energy density with a color smallest possible exposure energy density of the width, i.e. the minimum necessary exposure energy density for obtaining a good contrast of the image Indicates the ratio.
In addition, each dimensionless central exposure energy density and dimensionless cumulative exposure energy density based on the M _dm standard are newly set.
ε _0cB = ε _0c / ξ _dm (2.9)
ε _0dB = ε _0d / ξ _dm ... (2.10)
σ _C0B = σ _CO / ξ _dm ... (2.11)
And

With these,
From equation (2.5)
ε _0cB = (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ ) (2.12)
From equation (2.6), ε _0dB =-(4b _c χ ^3/2 / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ ) (2.13)
From Equation (2.7), σ _C0B = b _c (χ ^-1/2 + 4χ ^3/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1 (2.14)
Is obtained.

At the maximum spot radius, the overlap of the spot circles 31 is maximum, and the minimum decoloration center exposure energy density ε _{0 dB} allowed at this time is zero. Therefore, in equation (2.12), ε _0dB = 0
-(4b _c χ ^3/2 / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ ) = 0 ... (2.15)
Furthermore, when 0 <χ ≦ 0.5, (1-4χ ² + 4χ ⁴ )> 0.
4b _c χ ^3/2 / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1 = 0 ... (2.16)
And this solution is χ = χ ₃ .
By the way, from Equation (1.28) and Equation (1.29), the setting range of χ is
0 <χ ≦ 0.5
Therefore, χ ₃ may not satisfy the condition of 0 <χ ≦ 0.5. in this case,
χ ₃ = χ ₁ = 0.5 (2.17)
And
Substituting this χ ₃ into equation (1.5), the maximum spot radius w ₃ allowed is
w ₃ / r ₀ = 2 / log (1 / χ ₃ ) ^1/2 ... (2.18)
Set as

At the minimum spot radius, the overlap of the spot circles 31 is the minimum, and the color development center exposure energy density ε _0cB is the maximum value. At this time, the accumulated exposure energy density σ _{C0B at the} coloring center node 32 needs to be equal to or less than the maximum coloring energy density ξ _cm .
Therefore, a new parameter b _cm , which is the allowable cumulative exposure energy density ratio, is introduced.
b _cm = σ _C0B = ξ _cm / ξ _dm = M _cm / M _dm ... (2.19)
And In equation (2.14), parameter b _cm was substituted for σ _C0B
0 = b _c (χ ^-1/2 + 4χ ^3/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1-b _cm ... (2.20)
Let χ ₄ be the solution of Substituting this solution χ ₄ into equation (1.5),
The minimum allowable spot radius w ₄ is
w ₄ / r ₀ = 2 / log (1 / χ ₄ ) ^1/2 ... (2.21)
Set as

From the above, the setting range of χ is
χ ₄ ≦ χ ≦ χ ₃ (2.22)
Therefore, the spot radius w ₀ of the laser beam 21 is
w ₄ / r ₀ ≦ w ₀ / r ₀ ≦ w ₃ / r ₀ (2.23)
By setting so as to satisfy the above relationship, there is obtained a photothermal conversion type image rewriting method capable of good image formation relating to the color development and decoloring characteristics of the recording medium 10 and good image formation of the checkerboard image pattern. be able to.

As an example satisfying the equation (2.23), an effective setting range of the spot radius corresponding to the checkerboard image pattern is shown.
As a numerical condition
ξ _d = 0.5
ξ _dm = 0.75
ξ _c = 1.0
ξ _cm = 1.5
σ _D0 = ξ _dm = 0.75
σ _CDh = ξ _c = 1.0
Set.
Formula (2.5)
ε _0c = (σ _CDh (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -σ _D0 ) / (1-4χ ² + 4χ ⁴ )
Formula (2.6)
_{ε 0d = - (4σ CDh χ} 3/2 / (1 + 2χ 2 + χ 4 + 2χ 6) -σ D0) / (1-4χ 2 + 4χ 4)
Formula (2.7)
σ _C0 = σ _CDh (χ ^-1/2 + 4χ ^3/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -σ _D0
Ε _0c , ε _0d , and σ _C0 with respect to χ are obtained by substituting the above numerical conditions into.
From these values, the formula (2.4)
_{σ CDf = ε 0c (2χ +} 4χ 5) + ε 0d (2χ + 4χ 5)
Then σ _CDf is obtained.
From the above, the values of central exposure energy density ε _0c , ε _0d , cumulative exposure energy density σ _C0 , σ _CDf are
0> χ ≧ 0.5
Plotted in FIG.

Also, specific numerical values
b = σ _CDh / σ _D0 = ξ _c / ξ _dm = 1.0 / 0.75 = _4/3 = 1.333
The formula (2.16)
4bχ ^3/2 / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1 = 0
Substituting the solution for the largest spot radius
χ ₃ ≒ 0.4015
Is required.
More specific figures
M _cm / M _dm = ξ _cm / ξ _dm = 1.5 / 0.75 = 2
And set the formula (2.17)
0 = b (χ ^-1/2 + 4χ ^3/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1-M _cm / M _dm
Substituting, the solution for the smallest spot radius
χ ₄ ≒ 0.2467
Is required.
Therefore, the effective setting range of χ is
0.2467 ≦ χ ≦ 0.4015 (2.24)
It becomes. When the effective setting range of χ shown in FIG. 13 is converted into a dimensionless spot radius w ₀ / r ₀ by the equation (1.5),
1.691 ≦ w ₀ / r ₀ ≦ 2.094 (2.25)
A specific effective setting range of the dimensionless spot radius w ₀ / r ₀ is obtained.
The value of equation (2.20) is the effective setting range equation for full color erasing (1.37), and the effective setting range equation for full color development with the same value (1.41).
1.556 ≦ w ₀ / r ₀ ≦ 2.402
Compared with, it can be seen that the effective setting range is narrow.

  A spot radius of about 1.7 to 2.1 times the pixel radius according to the present invention enables image formation with a checkerboard image pattern having a maximum spatial frequency in a square lattice. The fact that an image pattern having the maximum spatial frequency can be formed means that a spatial frequency below this can be applied to the formation of an image pattern with the same effective spot radius setting range. Show. It is only the exposure energy corresponding to each imaging spot that needs to be optimized according to each image pattern, and this can be dealt with by well-known pulse width modulation control or power modulation control.

In the laser array module 20, the maximum wattage is one of the most important specifications of the semiconductor laser chip, and it is advantageous from the viewpoint of cost that the maximum wattage is as small as possible. Therefore, when the pixel formation time, that is, the laser exposure time t ₀ per pixel is determined, the optimum spot radius condition for minimizing the maximum energy required for image formation is shown. First, the minimum value of the beam energy density is obtained.
The energy required for image formation is the beam energy density ρ _r from equation (1.13).
ρ _r = ε ₀₀ 2 / log (1 / χ)
It is.
Here, in order to obtain the minimum value of the beam energy density ρ _r , ρ _r <is differentiated by χ in the range of 0 <χ ≦ 0.5.
dρ _r / dχ = (ε ₀₀ ^' log (1 / χ) + ε ₀₀ / χ) / log (1 / χ) ² ... (3.1)
here,
ε ₀₀ ^' = dε ₀₀ / dχ
It is.
If dρ _r / dχ = 0 to obtain the minimum value of the beam energy density ρ _r , 0 <χ ≤ 0.5.
0 = ε ₀₀ ^' log (1 / χ) + ξ ₀₀ / χ (3.2)
It becomes. This is an equation for _obtaining the minimum value of the beam energy density ρ _r .

The effective setting range of χ in the checkerboard image pattern with the maximum spatial frequency in the square lattice is from Equation (2.22) and Equation (2.23),
χ ₄ ≦ χ ≦ χ ₃
w ₄ / r ₀ ≦ w ₀ / r ₀ ≦ w ₃ / r ₀
Therefore, from this range, a point that minimizes the maximum energy required for image formation is obtained.
The maximum center exposure energy density in the checkerboard image pattern is the color development center exposure energy density (2.12).
ε _0cB = (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ )
Of ε _0cB .
In addition, a new dimensionless beam energy density based on M _dm
ρ _rB = ρ _r / ξ _dm (3.3)
Then, the maximum beam energy density for the checkerboard image pattern is ρ _rB = ε _0cB 2 / log (1 / χ) (3.4) from equation (1.13).
ρ _rB = 2 / log (1 / χ) ・ (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ ) ... (3.5)
Thus, the coloring beam energy density ρ _rB is determined.
When aligning the reference dimensionless into _{M c ρ r = ξ dm 2} / log (1 / χ) · (b c (χ -1/2 + 4χ 7/2) / (1 + 2χ 2 + χ 4 + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ ) ... (3.6)
This is used to draw the graph.
Also, differentiating equation (2.5),
_{dε 0cB / dχ = (b c} ((-1/2 · χ -3/2 + 14χ 5/2) (1 + 2χ 2 + χ 4 + 2χ 6) - (χ -1/2 + 4χ 7/2 ) (4χ + 4χ ³ + 12χ ⁵ )) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) ²・ (1-4χ ² + 4χ ⁴ )-(b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) ・ (-8χ + 16χ ³ )) / (1-4χ ² + 4χ ⁴ ) ²
It becomes. Here, using equation (3.1),
_{dρ r / dχ = log (1} / χ) · (b c ((-1/2 · χ -3/2 + 14χ 5/2) (1 + 2χ 2 + χ 4 + 2χ 6) - (χ -1 ^{/ 2} + 4χ ^7/2 ) (4χ + 4χ ³ + 12χ ⁵ )) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) ²・ (1 + 4χ ⁴ -4χ ² )-(b _c (χ ^{-1 / 2} + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ )-1) (-8χ + 16χ ³ )) / (1-4χ ² + 4χ ⁴ ) ² + 1 / χ ・ (b (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1 + 4χ ⁴ -4χ ² ) (3.7)
The formula for obtaining the minimum value from this formula (3.6) is
0 = log (1 / χ) · (b c ((-1/2 · χ -3/2 + 14χ 5/2) (1 + 2χ 2 + χ 4 + 2χ 6) - (χ -1/2 + 4χ ^7/2 ) (4χ + 4χ ³ + 12χ ⁵ )) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) ²・ (1 + 4χ ⁴ -4χ ² )-(b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ )-1) (-8χ + 16χ ³ )) / (1-4χ ² + 4χ ⁴ ) ² + 1 / χ ・ (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1 + 4χ ⁴ -4χ ² )
For 0 <x ≦ 0.5
0 = log (1 / χ) · ((b c ((-1/2 · χ -3/2 + 14χ 5/2) - (χ -1/2 + 4χ 7/2) (4χ + 4χ 3 + 12χ ⁵ ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ))-(b _c (χ ^-1/2 + 4χ ^7/2 )-(1 + 2χ ² + χ ⁴ + 2χ ⁶ )) (-8χ + 16χ ³ ) / (1 + 4χ ⁴ -4χ ² )) + 1 / χ ・ (b _c (χ ^-1/2 + 4χ ^7/2 )-(1 + 2χ ² + χ ⁴ + 2χ ⁶ ))・ ・ (3.8)
It becomes.

As an effective setting of χ in the checkerboard image pattern with the maximum spatial frequency in the square lattice, one of the conditions to minimize the energy required for image formation, that is, to minimize the maximum beam energy density ρ _r First, since the beam energy density is a minimum value of ρ _r , the solution χ ₅ of Equation (3.8) is the optimum value to be obtained.

However, in the checkerboard image pattern, as a prerequisite,
Formula (2.16)
4b _c χ ^3/2 / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1 = 0
Solution χ = χ ₃
Formula (2.20)
0 = b (χ ^-1/2 + 4χ ^3/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1-b _cm
Solution χ = χ ₄
Conditional expression using (2.21)
χ ₄ ≦ χ ≦ χ ₃
Limits the range of χ.
Therefore, the solution χ ₅ in 0 <χ ≦ 0.5 in equation (3.8) is
χ ₄ ≦ χ ₅ ≦ χ ₃ ... (3.9)
It is adopted as the optimum value only when the above is satisfied.
Therefore, if conditional expression (3.11) is not satisfied,
Substituting χ ₃ and χ ₄ into χ in Equation (3.4), ρ _rB3 = 2 / log (1 / χ ₃ ) ・ (b _c (χ ₃ ^-1/2 + 4χ ₃ ^7/2 ) / (1 + 2χ ₃ ² + χ ₃ ⁴ + 2χ ₃ ⁶ ) -1) / (1-4χ ₃ ² + 4χ ₃ ⁴ ) ... (3.10)
ρ _rB4 = 2 / log (1 / χ ₄ ) ・ (b _c (χ ₄ ^-1/2 + 4χ ₄ ^7/2 ) / (1 + 2χ ₄ ² + χ ₄ ⁴ + 2χ4 ₃ ⁶ ) -1) / (1-4χ ₄ ² + 4χ ₄ ⁴ ) ... (3.11)
Of ρ _r3 and ρ _r4 , χ ₃ or χ ₄ indicating the smaller value is adopted as χ ₅ ,
Conditional expression (3.9)
χ ₄ ≦ χ ₅ ≦ χ ₃
Re-set so that
Substituting this χ ₅ into equation (1.5) gives the spot radius w ₅ that minimizes the beam energy density.
w ₅ / r ₀ = 2 / log (1 / χ ₅ ) ^1/2 ... (3.12)
Set as

As an example satisfying the equation (3.12), an example of a spot radius corresponding to the checkerboard image pattern that minimizes the beam energy density is shown.
As a numerical condition
ξ _d = 0.5
ξ _dm = 0.75
ξ _c = 1.0
ξ _cm = 1.5

σ _D0 = ξ _dm = 0.75
σ _CDh = ξ _c = 1.0
b _c = σ _CDh / σ _D0 = ξ _c / ξ _dm = 1.0 / 0.75
Set.
Formula (3.5)
ρ _rB = 2 / log (1 / χ) ・ (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ )
Is used to find the beam energy density for χ.
To align the standards of non-dimensional, beam energy density [rho _r converted from the [rho _rB using equation (3.6), equation (2.5), equation (2.6) used in the central exposure energy density epsilon _0c, the epsilon _0d
0> χ ≧ 0.5
14 is plotted in FIG.
As shown in FIG. 14, χ indicating the minimum value of the color development center exposure energy density ε _0c does not indicate the minimum value of the color development beam energy density ρ _r . This is because the beam energy density ρ _r is proportional to the spot area to be exposed.

In this condition, the equation (3.8)
0 = log (1 / χ) · ((b ((- 1/2 · χ -3/2 + 14χ 5/2) - (χ -1/2 + 4χ 7/2) (4χ + 4χ 3 + 12χ ⁵ ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ))-(b (χ ^-1/2 + 4χ ^7/2 )-(1 + 2χ ² + χ ⁴ + 2χ ⁶ )) (-8χ + 16χ ³ ) / (1 + 4χ ⁴ -4χ ² )) + 1 / χ ・ (b (χ ^-1/2 + 4χ ^7/2 )-(1 + 2χ ² + χ ⁴ + 2χ ⁶ ))
Solution of
χ ₅ ≒ 0.2059
Is obtained.
At this time, from equation (3.5)
ρ _r5 ≒ 2.604
However, this χ ₅ value is the conditional expression of the effective setting range of χ in the checkerboard image pattern (2.24)
0.2467 ≦ χ ≦ 0.4015
Does not meet.

Therefore, in χ of formula (3.5)
χ ₃ ≒ 0.4015
χ ₄ ≒ 0.2467
Substituting
ρ _rB3 ≒ 3.450
ρ _rB4 ≒ 2.632
It becomes. here
ρ _rB4 <ρ _rB3
Therefore, the condition for minimizing the beam energy density when 0> χ ≧ 0.5 is
χ ₅ = χ ₄ ≒ 0.2467
Therefore, when the optimum set value of χ ₅ is converted into the dimensionless spot radius w ₀ / r ₀ by the equation (1.5)
w ₅ / r ₀ ≒ 1.691 (3.20)
Is obtained.
However, in order to align the standard of dimensionlessness in FIG.
ρ _r3 ≒ 2.587
ρ _r5 = ρ _r4 ≒ 1.974
Is calculated and plotted.
Therefore, the maximum beam energy density is minimized when χ ₅ = χ ₄ ≈0.2467. In other words, the checkerboard image pattern can be formed with the laser array module 20 having the minimum power.

Optimal spot radius above
χ ₅ = 0.2467
w ₀ / r ₀ = 1.691
The cumulative exposure energy density distribution in the checkerboard image pattern when using is shown.
Substituting the optimum spot radius conditions into Equation (2.5) and Equation (2.6), the color development center exposure energy density ε _0c and the decoloration center exposure energy density ε _0d
ε _0c ≒ 1.381
ε _0d ≒ 0.4077
Is calculated.
Substituting the values of this decoloration center exposure energy density ε _0d and center exposure energy density ε _0c into Equation (2.1), Equation (2.2), Equation (2.3), and Equation (2.4), the cumulative exposure at each observation node The energy density is calculated.
σ _C0 ≒ 1.50
σ _D0 = 0.75
σ _CDh = 1.0
σ _CDf ≒ 0.8892
FIG. 15 shows the cumulative exposure energy density distribution in the checkerboard image pattern at this optimum spot radius.

  The graph of FIG. 15 shows two cumulative exposure energy density distributions on line AA and line BB shown in FIG.
    In line segment A-A, the peak indicates the value at the coloring center node, and the bottom indicates the value at the decoloring center node.
    In line segment B-B, the peak indicates the value at the intermediate node, and the bottom indicates the value at the face center node.
  As shown in FIG. 15, the cumulative exposure energy density σ near the decoloring center node_dThe distribution of
   ξ_d≤σ_d≦ ξ_dm
And the erasing condition is maintained.
Also, cumulative exposure energy density σ near the color development center node_cThe distribution of
                ξ_c≤σ_c≦ ξ_cm
  Thus, the coloring conditions are maintained.
As described above, as shown in FIG. 15, when the optimum spot radius is used, an optimum accumulated exposure energy density distribution for the checkerboard image pattern can be realized.

  Since the optimum spot radius of the checkerboard image pattern having the maximum spatial frequency has been obtained, the following is applied to various image patterns. Although the same spot radius is applied, the exposure energy density corresponding to each imaging spot needs to be optimized according to each image pattern.

FIGS. 16 (a), 16 (b), and 16 (c) show a color development exposure pattern corresponding to an isolated color image pattern in which color cancellation pixels are arranged all around one color development pixel. . As shown in FIG. 12, in this image pattern, the setting of each observation node is the same as in FIGS. 4 (a), 4 (b), and 4 (c).
As in the case of the checkerboard image pattern, the cumulative exposure energy density of each observation node on the recording medium 10 can be calculated using Expression (1.8).
At this time, the center exposure energy density of the spot circle 31 is set to the following two types.
Color spot 31a
ε _0c : Color development center exposure energy density
Decoloring spot 31b
ε _0d : _{Decolorization} center exposure energy density.

Optimal spot radius with checkerboard image pattern
χ ₅ = 0.2467
w ₀ / r ₀ = 1.691
Is used to indicate the cumulative exposure energy density distribution in the isolated color image pattern.
From the optimal spot radius conditions, color development center exposure energy density ε _0c , decoloration center exposure energy density ε _0d
ε _0c ≒ 1.313
ε _0d ≒ 0.5596
Is calculated.
Using the values of the decoloration center exposure energy density ε _0d and the center exposure energy density ε _0c , the cumulative exposure at each observation node shown in FIGS. 16 (a), 16 (b), and 16 (c). The energy density is calculated.
σ _C0 ≒ 1.475
σ _1D0 = 0.75
σ _2D0 = 0.7069
σ _CDh = 1.0
σ _CDf ≒ 0.7422
In FIG. 16A, the decoloring center node adjacent to the coloring center node 32 is classified into the following two types based on the difference in accumulated exposure energy density.
σ _1D0 : Decoloring center node 32b1 adjacent to the coloring center node 32a in the orthogonal direction
σ _2D0 : _Decoloring center node 32b2 diagonally adjacent to the coloring center node 32a
FIG. 17 shows the cumulative exposure energy density distribution in the isolated color image pattern at this optimum spot radius.
The graph of FIG. 17 shows two cumulative exposure energy density distributions on the line segment AA and the line segment BB shown in FIG.
In the line segment AA, the center peak indicates the value at the color development center node.
In the line segment BB, each peak indicates a value at the decoloring center node.
As shown in FIG. 17, the distribution of the cumulative exposure energy density σ _c near the color development center node is
ξ _c ≦ σ _c ≦ ξ _cm , and the coloring condition is maintained.

In addition, the distribution of cumulative exposure energy density σ _d except near the color development center node is
ξ _d ≦ σ _d ≦ ξ _dm
And the erasing condition is maintained.
As described above, as shown in FIG. 17, when the optimum spot radius in the checkerboard image pattern is used, a cumulative exposure energy density distribution that satisfies a sufficient condition can be realized even in the isolated color image pattern.

18 (a), 18 (b), and 18 (c) show the erasing / erasing exposure patterns corresponding to the isolated erasing image pattern in which the coloring pixels are arranged all around one erasing pixel. Show. The setting of each observation node is the same as that in FIGS. 4 (a), 4 (b), and 4 (c).
As in the case of the checkerboard image pattern, the cumulative exposure energy density of each observation node on the recording medium 10 can be calculated using Expression (1.8).
At this time, the center exposure energy density of the spot circle 31 is set to the following two types.
Color spot 31a
ε _0c : Color development center exposure energy density
Decoloring spot 31b
ε _0d : _{Decolorization} center exposure energy density.

Optimal spot radius with checkerboard image pattern
χ ₅ = 0.2467
w ₀ / r ₀ = 1.691
Is used to indicate the cumulative exposure energy density distribution in the isolated decolored image pattern.
From the optimal spot radius conditions, color development center exposure energy density ε _0c , decoloration center exposure energy density ε _0d
ε _0c ≈ 1.192
ε _0d ≒ 0.4421
Is calculated.
Using the values of the decoloration center exposure energy density ε _0d and the center exposure energy density ε _0c , the cumulative exposure at each observation node shown in FIGS. 18A, 18B, and 18C. The energy density is calculated.
σ _D0 = 0.75
σ _1C0 ≒ 1.454
σ _2C0 ≒ 1.497
σ _CDh ≒ 0.9607
σ _CDf = 1.0
In FIG. 18A, the coloring center node adjacent to the decoloring center node 32 is classified into the following two types based on the difference in accumulated exposure energy density.
σ _1C0 : Color development center node 32a1 adjacent to the decoloration center node 32b in the orthogonal direction
σ _2C0 : Color development center node 32a2 diagonally adjacent to the color erasure center node 32b
FIG. 19 shows the cumulative exposure energy density distribution in the isolated decolored image pattern at this optimum spot radius.

The graph of FIG. 19 shows two cumulative exposure energy density distributions on the line segment AA and the line segment BB shown in FIG.
In the line segment AA, the bottom at the center indicates the value at the decoloring center node.
In the line segment BB, each peak indicates a value at the color development center node.
As shown in FIG. 19, the distribution of the cumulative exposure energy density σ _d near the decoloring center node is
Since ξ _d ≦ σ _d ≦ ξ _dm , the decoloring condition is maintained.
In addition, the distribution of accumulated exposure energy density σ _c except near the decoloring center node
ξ _c ≦ σ _c ≦ ξ _cm
Thus, the coloring conditions are maintained.
As described above, as shown in FIG. 19, when the optimum spot radius in the checkerboard image pattern is used, a cumulative exposure energy density distribution that satisfies a sufficient condition can be realized even in an isolated decolored image pattern.

20A, 20B, and 20C, one pixel line in which one pixel line is alternately arranged as a color developing line 35a (line segment AA) and a decoloring line 35b (line segment BB). The color development exposure pattern corresponding to an image pattern is shown. The setting of each observation node is the same as that in FIGS. 4 (a), 4 (b), and 4 (c).
As in the case of the checkerboard image pattern, the cumulative exposure energy density of each observation node on the recording medium 10 can be calculated using Expression (1.8).
At this time, the center exposure energy density of the spot circle 31 is set to the following two types.
Color spot 31a
ε _0c : Color development center exposure energy density
Decoloring spot 31b
ε _0d : _{Decolorization} center exposure energy density.

Optimal spot radius with checkerboard image pattern
χ ₅ = 0.2467
w ₀ / r ₀ = 1.691
Is used to show the cumulative exposure energy density distribution in a one-pixel line image pattern.
From the optimal spot radius conditions, color development center exposure energy density ε _0c , decoloration center exposure energy density ε _0d
ε _0c ≒ 1.275
ε _0d ≒ 0.5134
Is calculated.
Using the values of the erasing center exposure energy density ε _0d and the center exposure energy density ε _0c , the cumulative exposure at each observation node shown in FIGS. 20 (a), 20 (b), and 20 (c). The energy density is calculated.
σ _C0 = 1.5
σ _D0 = 0.75
σ _CDh = 1.0
σ _CCh ≒ 1.333 (Intermediate node on the coloring line)
σ _CDf = 0.8889
In FIG. 20B, the intermediate nodes are classified into the following two types based on the difference in accumulated exposure energy density.
[sigma] _CDh : intermediate node 33 located in the middle of the coloring center node 32a and the decoloring center node 32b
σ _CCh : Intermediate 33 node 33a located on the middle of the color development center node 32a and the next color development center node 32a (on the color development line)
FIG. 21 shows the cumulative exposure energy density distribution in the one-pixel line checkerboard image pattern at this optimum spot radius.

The graph of FIG. 21 shows two cumulative exposure energy density distributions on the line segment AA and the line segment CC shown in FIG. The line segment CC is an orthogonal line that crosses the coloring line 35a (line segment AA) and the decoloring line 35b (line segment BB).
In the line segment CC (orthogonal line), the peak indicates the value at the coloring center node, and the bottom indicates the value at the decoloring center node.
In line segment AA (coloring line), the peak indicates the value at the coloring center node, and the bottom indicates the value at the intermediate node on the coloring line.

As shown in FIG. 21, the distribution of the cumulative exposure energy density σ _c near the coloring line connecting the coloring center nodes is
ξ _c ≦ σ _c ≦ ξ _cm , and the coloring condition is maintained.
In addition, the distribution of the accumulated exposure energy density σ _{d in} the vicinity of the erasing line (segment CC in FIG. 21) connecting the erasing center node nodes is
ξ _d ≦ σ _d ≦ ξ _dm
And the erasing condition is maintained.
As described above, as shown in FIG. 21, when the optimum spot radius in the one-pixel line image pattern is used, a cumulative exposure energy density distribution satisfying a sufficient condition can be realized even in the isolated decolored image pattern.

  When the setting method according to the present invention is used, the maximum beam energy density required for image formation can be minimized. In other words, the checkerboard image pattern can be formed with the laser array module 20 having the minimum power. Therefore, high light energy utilization efficiency can be maintained, which contributes to lowering the cost of the laser array module 20 and reducing the maximum power consumption.

  By using the setting method for minimizing the maximum beam energy density required for image formation according to the present invention, the same energy can be obtained by optimizing only the exposure energy corresponding to each imaging spot for various image patterns. It can be supported by the spot radius. Thereby, an image rewriting method capable of forming various images with high image quality can be provided.

Considering instability of the color erasing characteristics due to variations in spot radii formed by each laser beam 21 in the laser array module 20, variations in laser power, temperature fluctuations of the recording medium 10, and the like, a uniform and stable image In order to realize the formation, it is desirable to employ a spot radius that uses the minimum value of the beam energy density ρ _{r in} the checkerboard image pattern, which is the solution of the equation (3.8).
However, the solution χ _{5 when} 0 <χ ≦ 0.5 in equation (3.8) is the conditional equation (3.9)
χ ₄ ≦ χ ₅ ≦ χ ₃
The solution χ ₅ cannot be used in all conditions because it is adopted as the optimum value only when

By the way, the parameter b _c used in (3.8) is derived from equation (2.8).
b _c = σ _CDh / σ _D0 ... (4.1)
It is. Therefore, the accumulated exposure energy density sigma _CDh intermediate node, to adjust the cumulative exposure energy density sigma _D0 of decoloring central node, solutions chi ₅ the condition for the condition to be used (3.9)
χ ₄ ≦ χ ₅ ≦ χ ₃
It is possible to satisfy.
The adjustment range of parameter b _c is
ξ _dm <σ _CDh ≦ ξ _c ... (4.2)
ξ _dm ≦ σ _D0 <ξ _c ... (4.3)
And transforming this
M _d / M _dm <σ _{CDh ≤M c} / M _c
M _d / M _dm ≤σ _D0 <M _c / M _c
And finally
M _d / M _dm <σ _CDh ≦ 1 (4.4)
M _d / M _dm ≤σ _D0 <1 (4.5)
Is obtained.

The adjustment in equation (4.4) is a method in which σ _CDh ≦ 1 and the radius of the color pixels (dots) in the checkerboard image pattern is slightly reduced.
The adjustment in equation (4.5) is a method of slightly increasing the density of the decolored pixels (dots) in the checkerboard image pattern or slightly reducing the radius of the decolored pixels by setting M _d / M _dm ≤σ _D0. .
It is also possible to adjust both values of σ _CDh and σ _D0 .
Such fine-tuning of image quality greatly affects only the checkerboard image pattern having the maximum spatial frequency, but for image patterns having a relatively small spatial frequency other than the checkerboard image pattern, the image quality The degree of change is small.

First, an example of a method for slightly reducing the diameter of the color pixels (dots) in the checkerboard image pattern will be described.
As numerical conditions in the checkerboard image pattern,
ξ _d = 0.5
ξ _dm = 0.75
ξ _c = 1.0
ξ _cm = 1.5
Set.
Settings in the third embodiment
σ _D0 = ξ _dm = 0.75
σ _CDh = ξ _c = 1.0
b _c = σ _CDh / σ _D0 ≒ 1.333
This is adjusted with the initial value.
For example, sigma _D0 respect _{σ D0-h, σ CDh-} h against sigma _CDh, the b _ch as the adjustment value for b _c
σ _D0-h = 0.75 (4.6)
σ _CDh-h = 0.9591 <1 (4.7)
b _ch = σ _CDh-h / σ _D0-h ≒ _1.279 (4.8)
Set as follows.
At this time, the cumulative exposure energy density σ _CDh-h of the intermediate node is 0.9591 <1, which is lower than the minimum coloring energy density ξ _c = 1. Therefore, a sufficient color density cannot be obtained at the intermediate node located at the pixel radius r ₀ , and as a result, the diameter of the color pixel is slightly reduced.
Next, b _{ch is changed} to equation (3.5)
ρ _rB = 2 / log (1 / χ) ・ (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ )
Substituting for b _c , find the beam energy density for χ.

To align the standards of non-dimensional, beam energy density [rho _r converted from the [rho _rB using equation (3.6), equation (2.5), equation (2.6) used in the central exposure energy density epsilon _0c, the epsilon _0d
0> χ ≧ 0.5
22 is plotted in FIG.
Also, under the adjusted conditions, the solution χ _5-h of equation (3.8) is
χ _5-h ≒ 0.2164 (4.9)
And
At this time, the corresponding beam energy density ρ _r5-h from equation (3.5) is
ρ _r5-h ≒ 2.435
It becomes.
On the other hand, when the adjusted condition is applied to Equation (2.16) and Equation (2.20), the conditional expression of the effective setting range of χ in the checkerboard image pattern is also changed.
χ ₃ ≒ 0.4209
χ ₄ ≒ 0.2164
New effective setting range of χ
0.2164 ≦ χ ≦ 0.4209 (4.10)
Is obtained.
χ _5-h value is the effective setting range of new χ
0.2164 ≦ χ _5-h ≦ 0.4209
Meet.
Therefore, when the optimum set value of χ ₅ is converted into the dimensionless spot radius w ₀ / r ₀ by the equation (1.5)
w _5-h / r ₀ ≒ 1.617 (4.11)
Is obtained.
However, in order to align the non-dimensional standard in FIG.
ρ _r5-h ≒ 1.826 (4.12)
Is calculated and plotted.
Therefore, the maximum beam energy density is minimized and minimized at the adjusted setting. That is, uniform and stable image formation is possible with the laser array module 20 having the minimum power.

Next, an example of a method for slightly increasing the density of the decolored pixels (dots) in the checkerboard image pattern or slightly reducing the diameter of the decolored pixels will be described.
As numerical conditions in the checkerboard image pattern,
ξ _d = 0.5
ξ _dm = 0.75
ξ _c = 1.0
ξ _cm = 1.5
Set.
Settings in the third embodiment
σ _D0 = ξ _dm = 0.75
σ _CDh = ξ _c = 1.0
b _c = σ _CDh / σ _D0 ≒ 1.333
This is adjusted with the initial value.
For example, the b _{c + d} as a adjustment value for sigma _D0 respect sigma _{D0 + d,} sigma respect σ _{CDh CDh + d,} b _c
σ _{D0 + d} = 0.8094 (4.13)
σ _{CDh + d} = 1.0 (4.14)
b _{c + d} = σ _{CDh + d} / σ _{D0 + d} ≒ _1.236 (4.15)
Set as follows.
At this time, the cumulative exposure energy density σ _{D0 + d} of the erasing center node is 0.75 <0.8094, which exceeds the maximum erasing energy density ξ _dm = 0.75. For this reason, the erasing center node is exposed with an energy density higher than a sufficient erasing density. As a result, the center density of the decolored pixel is slightly higher than the initial value.
Next, b _{c + d is changed} to equation (3.5)
ρ _rB = 2 / log (1 / χ) ・ (b _c (χ ^-1/2 + 4χ ^7/2 ) / (1 + 2χ ² + χ ⁴ + 2χ ⁶ ) -1) / (1-4χ ² + 4χ ⁴ )
Substituting for b _c , find the beam energy density for χ.
To align the standards of non-dimensional, beam energy density [rho _r converted from the [rho _rB using equation (3.6), equation (2.5), equation (2.6) used in the central exposure energy density epsilon _0c, the epsilon _0d
0> χ ≧ 0.5
FIG. 23 is plotted in the range of.
Also, under the adjusted condition, the solution χ _{5 + d} of equation (3.8) is
χ _{5 + d} ≒ 0.2269 ・ ・ ・ (4.16)
And
At this time, the corresponding beam energy density ρ _{r5 + d} from equation (3.5) is
ρ _{r5 + d} ≒ 2.297
It becomes.
On the other hand, when the adjusted condition is applied to Equation (2.16) and Equation (2.20), the conditional expression of the effective setting range of χ in the checkerboard image pattern is also changed.
χ ₃ ≒ 0.4388
χ ₄ ≒ 0.2269
New effective setting range of χ
0.2269 ≦ χ ≦ 0.4388 (4.17) is obtained.
χ _{5 + d} value is the new effective χ setting range
0.2269 ≦ χ _{5 + d} ≦ 0.4388
Meet.
Therefore, when the optimum set value of χ ₅ is converted into the dimensionless spot radius w ₀ / r ₀ by the equation (1.5)
w _{5 + d} / r ₀ ≒ 1.642 (4.18)
Is obtained.
However, Fig. 23 is derived from equation (3.6) to align the standard for dimensionlessness.
ρ _{r5 + d} ≒ 1.859 (4.19)
Is calculated and plotted.
Therefore, the maximum beam energy density is minimized and minimized at the adjusted setting. That is, uniform and stable image formation is possible with the laser array module 20 having the minimum power.

The above two modified minimal spot radii
χ _5-h = 0.2164
χ _{5 + d} = 0.2269
Are compared in FIG. 24 showing the cumulative exposure energy density distribution in the checkerboard image pattern.
The graph of FIG. 24 shows the cumulative exposure energy density distribution for the two spot radii in the line segment AA shown in FIG.
The cumulative exposure energy density σ _−h shown by the solid line is an example of the diameter reduction adjustment of the color pixel, and the following values are plotted.
χ _5-h = 0.2164: Color pixel diameter reduction adjustment
σ _D0-h = 0.75: Cumulative exposure energy density at the decoloring center node is the same as the initial value
σ _CDh-h = 0.9591: Cumulative exposure energy density at the adjusted intermediate node
σ _C0 = 1.5: Cumulative exposure energy density at the color development center node is the same as the initial value

2 _rh ≈ 1.869r ₀ : Reduced color pixel diameter Cumulative exposure energy density _{+ d} indicated by a broken line is an example of density increase adjustment of a decolored pixel, and the following values are plotted.
χ _{5 + d} ≒ 0.2269: Density increase adjustment for decolored pixels
σ _{D0 + d} = 0.8094: Cumulative exposure energy density at the adjusted decoloring center node
σ _{CDh + d} = 1.0: The cumulative exposure energy density at the intermediate node is the same as the initial value
σ _C0 = 1.5: Cumulative exposure energy density at the color development center node is the same as the initial value
2 _{r + d} = 2r ₀ : Colored pixel diameter is the same as the initial value

As shown in FIG. 24, the diameter of the color pixel is reduced in the color pixel diameter reduction adjustment.
2 _rh <2 _{r + d} = 2r ₀
In addition, in the density increase adjustment of the erasing pixel, the cumulative exposure energy density of the erasing center node exceeds the maximum erasing energy density. This means that the center density of the decolored pixel is increased from the initial value.
ξ _dm = σ _D0-h <σ _{D0 + d}
On the other hand, the distribution of the cumulative exposure energy density at the color development center node is the same with either adjustment method.
σ _C0 = ξ _cm
Thus, the maximum color development energy density is not exceeded, and the recording medium 10 is not seriously damaged such as thermal decomposition and thermal deformation.

By adjusting the parameter b _c shown in the present invention, a spot radius using the minimum value of the beam energy density can be adopted, and the variation of the spot radius formed by each laser beam 21 in the laser array module 20 or the variation of the laser power. It is possible to realize uniform image formation that absorbs light.

In addition, since the beam energy density has a minimum value, stable image formation that absorbs the instability of the coloring and decoloring characteristics due to environmental fluctuations such as temperature fluctuations of the recording medium 10 can be realized.
In particular, since the color development and decoloring characteristics change due to repeated use of the recording medium 10 for a long time is unavoidable, the use of the minimum and minimum maximum beam energy density by adjusting the parameter b _c shown in the present invention is stable for a long time. This guarantees image formation. As a result, the life of the recording medium 10 is extended.

In the present invention, it has been shown that various image patterns can be dealt with by adopting a spot radius using the minimum value or the minimum value of the beam energy density ρ _{r in} the checkerboard image pattern.
Even in the setting using the checkerboard image pattern reference spot radius (for example, Equation (3.20)), in actual image formation, a relatively wide area, for example, an area of 5 pixels (dots) x 5 pixels (dots) or more is developed. In the case of forming the color development exposure pattern, the formula (1.38)
ε _0c = ξ _c / (4χ + 8χ ⁵ )
Can be used.
When you remove the dimensionless expression,
E _0c = M _c / (4χ + 8χ ⁵ ) (5.1)
It becomes.
The setting of equation (5.1) for determining the center exposure energy density in the entire color image pattern results in the minimum center exposure energy density among the various color image patterns.
Therefore, newly _setting the minimum value of the center exposure energy density in the color image pattern as E 0 _cmin [J / m ² ]
E _0cmin = M _c / (4χ + 8χ ⁵ ) (5.2)
Can be obtained.

Similarly, in actual image formation, when a relatively wide area, for example, an area of 5 pixels (dots) × 5 pixels (dots) or more is developed, it was used when forming the entire color-erased image pattern. Erasing center exposure energy density formula (1.34)
ε _0d = ξ _d / (4χ + 8χ ⁵ )
Can be used.
When you remove the dimensionless expression,
E _0c = M _d / (4χ + 8χ ⁵ ) (5.3)
It becomes.
Among various erasable image patterns, it results in the minimum center exposure energy density.
_Let E _0dmin [J / m ² ] be the minimum value of the center exposure energy density in the color image pattern.
E _0dmin = M _d / (4χ + 8χ ⁵ ) (5.4)
Can be obtained.
However, this should be applied to a decolored image pattern in a relatively large area. For example, in the case of isolated decoloring, the central exposure energy for the decoloring node is smaller than in the case of full surface decoloring. Therefore, it is not possible to set a standard such as the minimum value.

  When the setting of the full color image pattern or the full color erase image pattern is applicable, the total exposure energy in the laser array module 20 can be reduced by using the minimum value of the central exposure energy density according to the present invention. Thereby, reduction of the total power consumption of the laser array module 20 is realizable.

1 is a schematic cross-sectional view showing a basic configuration of an image rewriting apparatus using a photothermal conversion type image rewriting method according to a first embodiment of the present invention. The schematic perspective view which shows the basic composition of the image rewriting apparatus using the photothermal conversion type image rewriting method concerning the embodiment. FIG. 2 is a schematic cross-sectional view of a photothermal conversion type reversible thermosensitive recording medium according to the embodiment. State drawing of color development and exposure pattern corresponding to full color development and full color erase image pattern, (a) is a diagram showing the cumulative range of the central node and its cumulative exposure energy density, (b) is the intermediate node and its cumulative exposure The figure which shows the accumulation range of energy density, (c) is a figure which shows the accumulation range of a face center node and its accumulation exposure energy density. The relationship figure of a spot radius parameter | index and a cumulative exposure energy density at the time of fixing a center exposure energy density in a full color development and a full erasable image pattern. The relationship figure of the effective spot radius parameter | index range in a whole surface decoloring image pattern, and a cumulative exposure energy density. Cumulative exposure energy density distribution for full-color erased image pattern at maximum spot radius Cumulative exposure energy density distribution for full-color erased image pattern with minimum spot radius The relationship figure of the spot radius parameter | index and accumulated exposure energy density in a whole surface color image pattern. Cumulative exposure energy density distribution for full color image pattern at maximum spot radius Cumulative exposure energy density distribution for full color image pattern with minimum spot radius The state diagram of the erasing / decoloring exposure pattern corresponding to the checkerboard image pattern, where (a) shows the cumulative range of the central node and its cumulative exposure energy density, and (b) shows the cumulative of the intermediate node and its cumulative exposure energy density. The figure which shows a range, (c) is a figure which shows the accumulation range of a face center node and its accumulated exposure energy density. The relationship figure of the effective spot radius parameter | index range in a checkerboard image pattern, center exposure energy density, and accumulated exposure energy density. The relationship figure of the optimal spot radius parameter | index in a checkerboard image pattern, center exposure energy density, cumulative exposure energy density, and beam energy density. Distribution of cumulative exposure energy density for checkerboard image pattern at optimal spot radius The state diagram of the color development exposure pattern corresponding to the isolated color image pattern, where (a) shows the central node and its cumulative exposure energy density, and (b) shows the intermediate node and its cumulative exposure energy density. The figure which shows a range, (c) is a figure which shows the accumulation range of a face center node and its accumulated exposure energy density. Cumulative exposure energy density distribution for isolated color image pattern at optimum spot radius Fig. 2 is a state diagram of the erasing / decoloring exposure pattern corresponding to the isolated erasing image pattern, where (a) is a diagram showing the cumulative range of the central node and its cumulative exposure energy density, and (b) is the intermediate node and its cumulative exposure energy density. The figure which shows a cumulative range, (c) is a figure which shows the cumulative range of a face center node and its cumulative exposure energy density. Distribution of cumulative exposure energy density for isolated decolored image pattern at optimal spot radius The state diagram of the color development exposure pattern corresponding to one pixel line image pattern, (a) shows the cumulative range of the central node and its cumulative exposure energy density, (b) shows the intermediate node and its cumulative exposure energy density. The figure which shows a cumulative range, (c) is a figure which shows the cumulative range of a face center node and its cumulative exposure energy density. Distribution diagram of cumulative exposure energy density for one pixel line image pattern at optimum spot radius FIG. 6 is a relationship diagram of a spot radius index, a center exposure energy density, a cumulative exposure energy density, and a beam energy density in a checkerboard image pattern in a diameter reduction adjustment of a color pixel. FIG. 6 is a relationship diagram of a spot radius index, a center exposure energy density, a cumulative exposure energy density, and a beam energy density in a density increase adjustment of a decolored pixel in a checkerboard image pattern. Distribution of cumulative exposure energy density for a checkerboard image pattern with two modified minimum spot radii

10: Photothermal conversion type reversible thermosensitive recording medium (recording medium),
11 ... last recorded image, 12 ... current recorded image,
13 ... support, 14 ... reversible thermosensitive recording layer, 15 ... protective layer,
20 ... Laser array module, 21 ... Laser beam,
22 ... Condensing optical system, 23 ... Semiconductor laser array, 24 ... Laser array driver,
30 ... Cumulative range, 31 ... Spot circle, 31a ... Colored spot, 31b ... Decolored spot,
32 ... central node,
32a ... Color development center node,
32a1 ... Color development center node adjacent in the orthogonal direction, 32a2 ... Color development center node adjacent in the diagonal direction,
32b ... erasing center node,
32b1 ... decoloring center node adjacent in the orthogonal direction, 32b2 ... decoloring center node adjacent in the diagonal direction,
33 ... Intermediate node, 34 ... Face center node,
35a ... coloring line, 35b ... decoloring line,
90 ... Medium conveying device

JP 2003-246144 A JP-A-7-61036

Claims (6)

A reversible thermosensitive recording medium that is selectively colored or decolored depending on the temperature of the medium and the temperature change rate, and a direction in which a plurality of independently driven laser beams are orthogonal to the moving direction of the reversible thermosensitive recording medium The reversible thermosensitive recording medium is exposed in a predetermined pattern by the laser array exposing means, and the pixels to be colored on the reversible thermosensitive recording medium are heated to a coloring condition, At the same time, in the image rewriting method for performing image formation by heating the pixels to be decolored of the reversible thermosensitive recording medium under decoloring conditions
With respect to an elliptical imaging spot on the reversible thermosensitive recording medium of one laser beam emitted from the laser array exposure means,
Let E ₀₀ [J / m ² ] be the exposure energy density at the center of the elliptical imaging spot,
w _b [m] is a short radius of the elliptical imaging spot from the center of the elliptical imaging spot toward the moving direction of the reversible thermosensitive recording medium,
w _a [m] is the major radius of the elliptical imaging spot from the center of the elliptical imaging spot in a direction perpendicular to the moving direction of the reversible thermosensitive recording medium;
For a plurality of elliptical imaging spots on the reversible thermosensitive recording medium of a plurality of laser beams emitted from the laser array exposure means,
r ₀ [m] is a length that is half the distance between the pitches in the major axis direction of the plurality of elliptical imaging spots in the direction orthogonal to the moving direction of the reversible thermosensitive recording medium, and the pixel to be formed The pixel radius is 1/2 the distance between the pitches of
Characteristics of the reversible thermosensitive recording medium
M _c [J / m ² ] The The minimum color development energy density
M _cm [J / m ² ] is the maximum coloring energy density,
_Let M _d [J / m ² ] be the minimum decoloring energy density,
_Let M _dm [J / m ² ] be the maximum decoloring energy density,
The smaller value of the two values M _dm / M _d and M _cm / M _c is defined as parameter p ₁
Equation (1) with χ _a as a variable and p ₁ as a parameter, and relation (2) of χ _a
1- p ₁ 4χ _a + 4χ _a ² + 4χ _a ⁴ -p ₁ 8χ _a ⁵ = 0 (1)
w _a / r ₀ = 2 / log (1 / χ _a ) ^1/2 ... (2)
In
Using χ _a1 = 0.5, the spot length radius w _a1 divided by the pixel radius r ₀ is w _a1 / r ₀ = 2 / log (1 / χ _a1 ) ^1/2
age,
Using the solution χ ₂ of equation (1), let the spot length radius w _a2 divided by the pixel radius r ₀ be w _a2 / r ₀ = 2 / log (1 / χ _a2 ) ^1/2 ,
Equation (3) with χ _b as a variable and p ₁ as a parameter, and equation (4) for χ _b
1- p ₁ 4χ _b + 4χ _b ² + 4χ _b ⁴ -p ₁ 8χ _b ⁵ = 0 (3)
w _b / r ₀ = 2 / log (1 / χ _b ) ^1/2 ... (4)
In
Using χ _b1 = 0.5, let the spot short radius w _b1 divided by the pixel radius r ₀ be w _b1 / r ₀ = 2 / log (1 / χ _b1 ) ^1/2 ,
When the spot short radius w _b2 divided by the pixel radius r ₀ is set to w _b2 / r ₀ = 2 / log (1 / χ _b2 ) ^1/2 using the solution χ ₂ of the equation (3),
The elliptical spot major axis w _a, and elliptical spot divided by the short radius w _b pixel radius r ₀ of the _{w a2 / r 0 ≦ w a} / r 0 ≦ w a1 / r 0, and w _b2 / r ₀ ≦ w _b / r ₀ ≦ w _b1 / r ₀
An image rewriting method comprising exposing the reversible thermosensitive recording medium with the laser beam set so as to satisfy the above relationship. Using the minimum coloring energy density M _c [J / m ² ] and the maximum decoloring energy density M _dm [J / m ² ], the parameter p ₂ is set as follows:
p ₂ = M _c / M _dm
p ₃ = M _cm / M _dm
And when
Equation (5), equation (6) with the parameters χ _a defined by the relational expression (2) and p ₂ and p ₃ as parameters.
^{_{4pχ a 3/2 / (1 + 2χ}} a 2 + χ a 4 + 2χ a 6) -1 = 0 ··· (5)
p ₂ χ _a ^-1/2 (1 + 4χ _a ² + 4χ _a ⁴ ) / (1 + 2χ _a ² + χ _a ⁴ + 2χ _a ⁶ ) -1- p ₃ = 0 (6)
In
Range of variable χ
0 <χ _a ≦ 0.5
Using the solution χ _a3 of equation (3) in
However, in the range 0 <χ _a ≦ 0.5, when there is no solution χ _a3 of the equation (3), the solution χ _a1 is used to make χ _a3 = χ _a1 and the spot length radius w divided by the pixel radius r _{0 a3} w _a3 / r ₀ = 2 / log (1 / χ _a3 ) ^1/2
age,
Using the solution χ _a4 of equation (6), the spot length radius w _a4 divided by the pixel radius r ₀ is expressed as w _a4 / r ₀ = 2 / log (1 / χ _a4 ) ^1/2
age,
Equation (7), equation (8) with the parameters χ _b defined by the relational expression (4) and p ₂ and p ₃ as parameters.
4p ₂ χ _b ^3/2 / (1 + 2χ _b ² + χ _b ⁴ + 2χ ⁶ ) -1 = 0 (7)
p ₂ χ _b ^-1/2 (1 + 4χ _b ² + 4χ _b ⁴ ) / (1 + 2χ _b ² + χ _b ⁴ + 2χ _b ⁶ ) -1- p ₃ = 0 (8)
In
Range of variable χ
0 <χ _b ≦ 0.5
Using the solution χ _b3 of equation (3) in
However, in the range 0 <χ ≦ 0.5, if there is no solution χ _b3 of the equation (3), χ ₃ = χ ₁ using the solution χ ₁ and the spot short radius w _b3 divided by the pixel radius r ₀ W _b3 / r ₀ = 2 / log (1 / χ _b3 ) ^1/2
age,
Using the solution χ ₄ of the equation (4), the spot short radius w _b4 divided by the pixel radius r ₀ is expressed as w _b4 / r ₀ = 2 / log (1 / χ _b4 ) ^1/2
When
The elliptical spot major axis w _a and the value obtained by dividing an ellipse spot short radius w _b in pixel radius r ₀ is _{w a4 / r 0 ≦ w a} / r 0 ≦ w a3 / r 0
w _b4 / r ₀ ≦ w _b / r ₀ ≦ w _b3 / r ₀
2. The image rewriting method according to claim 1, wherein the reversible thermosensitive recording medium is exposed with the laser beam set so as to satisfy the relationship. Equation (9), equation (10) for the parameter χ _a defined by the relational expression (2) and p ₂ as parameters.
_{0 = log (1 / χ a} ) · ((p 2 ((-1/2 · χ a -3/2 + 14χ a 5/2)
-(χ _a ^-1/2 + 4χ _a ^7/2 ) (4χ _a + 4χ _a ³ + 12χ _a ⁵ ) / (1 + 2χ _a ² + χ _a ⁴ + 2χ _a ⁶ ))
^{_{- (p 2 (χ a -1/2}} + 4χ a 7/2) - (1 + 2χ a 2 + χ a 4 + 2χ a 6)) (- 8χ a + 16χ a 3) / (1 + 4χ a ⁴ -4χ _a ² ))
+ 1 / χ _a・ (p ₂ (χ _a ^-1/2 + 4χ _a ^7/2 )-(1 + 2χ _a ² + χ _a ⁴ + 2χ _a ⁶ )) (9)
ρ _ar = 2 / log (1 / χ _a ) ・ (p ₂ (χ _a ^-1/2 + 4χ _a ^7/2 ) / (1 + 2χ _a ² + χ _a ⁴ + 2χ _a ⁶ ) -1) / (1-4χ _a ² + 4χ _a ⁴ ) (10)
In
Range of the variable χ _a using the solution χ _a3 and the solution χ _a4 χ _a4 ≦ χ _a ≦ χ _a3
Using the solution χ _a5 of equation (5) in
However, if there is no solution χ _a5 of the equation (5) in the range χ _a4 ≦ χ _a ≦ χ _a3 ,
The value obtained by substituting the solution χ _a3 into the variable χ in equation (10) is ρ _ar3 ,
The value obtained by substituting the solution χ _a4 into the variable χ in equation (10) is ρ _ar4 ,
ρ _ar3 and ρ _ar4 , whichever is smaller, the solution χ _a3 , the solution χ _a4 is χ _a5 ,
Equation (11), equation (12) for the variable χ _b defined by the relational expression (2) and p ₂ as parameters.
_{0 = log (1 / χ b} ) · ((p 2 ((-1/2 · χ b -3/2 + 14χ b 5/2)
-(χ _b ^-1/2 + 4χ _b ^7/2 ) (4χ _b + 4χ _b ³ + 12χ ⁵ ) / (1 + 2χ _b ² + χ _b ⁴ + 2χ _b ⁶ ))
^{_{- (p 2 (χ b -1/2}} + 4χ b 7/2) - (1 + 2χ b 2 + χ b 4 + 2χ b 6)) (- 8χ b + 16χ b 3) / (1 + 4χ b ⁴ -4χ _b ² ))
+ 1 / χ _b・ (p ₂ (χ _b ^-1/2 + 4χ _b ^7/2 )-(1 + 2χ _b ² + χ _b ⁴ + 2χ _b ⁶ )) (11)
ρ _br = 2 / log (1 / χ _b ) ・ (p ₂ (χ _b ^-1/2 + 4χ _b ^7/2 ) / (1 + 2χ _b ² + χ _b ⁴ + 2χ _b ⁶ ) -1) / (1-4χ _b ² + 4χ _b ⁴ ) (12)
In
Range of variable χ _b using solution χ _b3 and solution χ _b4 χ _b4 ≦ χ _b ≦ χ _b3
Using the solution χ _b5 of equation (5) in
However, when there is no solution χ _b5 of the equation (5) in the range χ _b4 ≦ χ _b ≦ χ _b3 ,
The value obtained by substituting the solution χ _b3 into the variable χ in the equation (12) is ρ _br3 ,
The value obtained by substituting the solution χ _b4 into the variable χ in equation (12) is ρ _br4 ,
ρ _br3 and ρ _br4 indicate the smaller value, χ _b3 , the solution χ _b4 is χ _b5 ,
The value obtained by dividing the elliptical spot long radius w _a and the elliptical spot short radius w _b by the pixel radius r ₀ is w _a6 / r ₀ = 2 / log (1 / χ _a5 ) ^1/2
w _b6 / r ₀ = 2 / log (1 / χ _b5 ) ^1/2
3. The image rewriting apparatus method according to claim 2, wherein the reversible thermosensitive recording medium is exposed with the laser beam set so as to satisfy the relationship. Parameter p ₂
p ₂ = σ _CDh / σ _D0
As described above, the conditions according to the most erasable coloring energy density M _d [J / m ² ] and the maximum erasing energy density M _dm [J / m ² ]
M _d / M _dm <σ _CDh ≤1
M _d / M _dm ≤σ _D0 <1
When adjusting the value of p ₂ in the range of and using this adjusted p ₂ ,
Range of the variable χ _a using the solution χ _a3 and the solution χ _a4 of the equation (5) and the equation (6) χ _a4 ≦ χ _a ≦ χ _a3
The solution chi _a5 satisfies the equation (9), and the equation (7) and the range of variables chi _b using the solution chi _b3 and the solution chi _b4 of the equation _{(8) χ b4 ≦ χ b} ≦ χ The image rewriting apparatus method according to claim ₃ , wherein _b3 satisfies a solution χ _b5 of the equation (10). The minimum value E 0 _cmin [J / m ² ] of the exposure energy density at the center of the exposure energy distribution of one laser beam emitted from the laser array exposure means for the pixel to be colored is
Using the variable χ _a defined by the relational expression (2), the variable χ _b defined by the relational expression (4), and the minimum coloring energy density M _c [J / m ² ],
E _0cmin = M _c / (4χ _a + 8χ _a ⁵ )
E _0cmin = M _c / (4χ _b + 8χ _b ⁵ )
The image rewriting method according to claim 2, wherein: A reversible thermosensitive recording medium that is selectively colored or decolored depending on the temperature of the medium and the temperature change rate, and a direction in which a plurality of independently driven laser beams are orthogonal to the moving direction of the reversible thermosensitive recording medium The reversible thermosensitive recording medium is exposed in a predetermined pattern by the laser array exposing means, and the pixels to be colored on the reversible thermosensitive recording medium are heated to a coloring condition, At the same time, in the image rewriting method for performing image formation by heating the pixels to be decolored of the reversible thermosensitive recording medium under decoloring conditions
With respect to an elliptical imaging spot on the reversible thermosensitive recording medium of one laser beam emitted from the laser array exposure means,
Let E ₀₀ [J / m ² ] be the exposure energy density at the center of the elliptical imaging spot,
w _b [m] is a short radius of the elliptical imaging spot from the center of the elliptical imaging spot toward the moving direction of the reversible thermosensitive recording medium,
w _a [m] is the major radius of the elliptical imaging spot from the center of the elliptical imaging spot in a direction perpendicular to the moving direction of the reversible thermosensitive recording medium;
For a plurality of elliptical imaging spots on the reversible thermosensitive recording medium of a plurality of laser beams emitted from the laser array exposure means,
r ₀ [m] is a length that is half the distance between the pitches in the major axis direction of the plurality of elliptical imaging spots in the direction orthogonal to the moving direction of the reversible thermosensitive recording medium, and the pixel to be formed The pixel radius is 1/2 the distance between the pitches of
Characteristics of the reversible thermosensitive recording medium
M _c [J / m ² ] The The minimum color development energy density
M _cm [J / m ² ] is the maximum coloring energy density,
_Let M _d [J / m ² ] be the minimum decoloring energy density,
_Let M _dm [J / m ² ] be the maximum decoloring energy density,
The smaller value of the two values M _dm / M _d and M _cm / M _c is defined as parameter p ₁
Equation (1) with χ _a as a variable and p ₁ as a parameter, and relation (2) of χ _a
1- p ₁ 4χ _a + 4χ _a ² + 4χ _a ⁴ -p ₁ 8χ _a ⁵ = 0 (1)
w _a / r ₀ = 2 / log (1 / χ _a ) ^1/2 ... (2)
In
Using χ _a1 = 0.5, the spot length radius w _a1 divided by the pixel radius r ₀ is w _a1 / r ₀ = 2 / log (1 / χ _a1 ) ^1/2
age,
Using the solution χ ₂ of equation (1), the spot length radius w _a2 divided by the pixel radius r ₀ is w _a2 / r ₀ = 2 / log (1 / χ _a2 ) ^1/2
age,
Equation (3) with χ _b as a variable and p ₁ as a parameter, and equation (4) for χ _b
1- p ₁ 4χ _b + 4χ _b ² + 4χ _b ⁴ -p ₁ 8χ _b ⁵ = 0 (3)
w _b / r ₀ = 2 / log (1 / χ _b ) ^1/2 ... (4)
In
Using χ _b1 = 0.5, the spot short radius w _b1 divided by the pixel radius r ₀ is changed to w _b1 / r ₀ = 2 / log (1 / χ _b1 ) ^1/2
age,
Using the solution χ ₂ of equation (3), the spot short radius w _b2 divided by the pixel radius r ₀ is expressed as w _b2 / r ₀ = 2 / log (1 / χ _b2 ) ^1/2
When
The elliptical spot major axis w _a, and the value obtained by dividing an ellipse spot short radius w _b in pixel radius r ₀ is _{w a2 / r 0 ≦ w a} / r 0 ≦ w a1 / r 0
w _b2 / r ₀ ≦ w _b / r ₀ ≦ w _b1 / r ₀
An image rewriting apparatus that exposes the reversible thermosensitive recording medium with the laser beam set so as to satisfy the above relationship.

Images