1. A liquid composition comprising at least a modified siloxane compound and a polymers wherein
the modified siloxane compound is at least one selected from the group consisting of a modified siloxane compound represented by the following Formula (1), a modified siloxane compound represented by the following Formula (2) and a modified siloxane compound represented by the following Formula (3), and
the polymer is at least one selected from the group consisting of a polymer A which has an acid value of from 90 mgKOHg or more to 150 mgKOHg or less and in which a hydrogen bond parameter (\u03b4h) of the polymer that is obtained by the solubility parameters of monomers constituting the polymer is from 1.0 cal0.5cm1.5 or more to 3.7 cal0.5cm1.5 or less, and a polymer B which has an acid value of from more than 150 mgKOHg to 200 mgKOHg or less and in which a hydrogen bond parameter (\u03b4h) of the polymer that is obtained by the solubility parameters of monomers constituting the polymer is from 1.0 cal0.5cm1.5 or more to 1.5 cal0.5cm1.5 or less:
where the modified siloxane compound represented by Formula (1) has a weight average molecular weight of from 8,000 or more to 30,000 or less; in Formula (1), R1 is an alkylene group having 1 to 20 carbon atom(s), R2 is a hydrogen atom or an alkyl group having 1 to 20 carbon atom(s), m is from 1 or more to 250 or less, n is from 1 or more to 100 or less, a is from 1 or more to 100 or less, and b is from 0 or more to 100 or less;
where the modified siloxane compound represented by Formula (2) has a weight average molecular weight of from 8,000 or more to less than 50,000; in Formula (2), R3’s are each independently a hydrogen atom or an alkyl group having 1 to 20 carbon atom(s), R4’s are each independently an alkylene group having 1 to 20 carbon atom(s), p is from 1 or more to 450 or less, c is from 1 or more to 250 or less, and d is from 0 or more to 100 or less; and
where the modified siloxane compound represented by Formula (3) has a weight average molecular weight of from 8,000 or more to less than 50,000 and an HLB of from 1 or more to less than 7; in Formula (3), R5’s are each independently a hydrogen atom or an alkyl group having 1 to 20 carbon atom(s), R6 is an alkylene group having 1 to 20 carbon atom(s), q is from 1 or more to 100 or less, r is from 1 or more to 100 or less, e is from 1 or more to 100 or less, and f is from 0 or more to 100 or less.
2. The liquid composition according to claim 1, wherein the modified siloxane compound represented by Formula (1) has an HLB of from 5 or more to 11 or less.
3. The liquid composition according to claim 1, wherein the polymer A comprises at least one type of monomer selected from the group consisting of styrene, n-butyl acrylate and benzyl methacrylate.
4. The liquid composition according to claim 1, wherein the polymer B comprises at least one type of monomer selected from the group consisting of styrene and \u03b1-methylstyrene.
5. The liquid composition according to claim 1, wherein the content (% by mass) of the polymer in the liquid composition is from 2.5% by mass or more to less than 4.0% by mass based on the total mass of the liquid composition.
6. The liquid composition according to claim 1, wherein the content (% by mass) of the modified siloxane compound is from 0.5% by mass or more to less than 3.0% by mass based on the total mass of the liquid composition.
7. An image forming method comprising the step of applying a pigment ink onto a recording medium and the step of applying a liquid composition onto the recording medium, wherein the liquid composition according to claim 1 is used as the liquid composition.
8. The image forming method according to claim 7, wherein the step of applying the liquid composition onto a recording medium is carried out after the step of applying a pigment ink onto the recording medium.
9. The image forming method according to claim 7, wherein an ink comprising a pigment and a polymer having an acid value of from 90 mgKOHg or more to 200 mgKOHg or less is used as the pigment ink.
10. The image forming method according to claim 7, wherein the pigment ink and the liquid composition are applied onto the recording medium by ink jet method.
11. A cartridge comprising a liquid composition storing portion which stores a liquid composition therein, wherein the liquid composition stored in the liquid composition storing portion is the liquid composition according to claim 1.
12. A recording unit comprising a liquid composition storing portion which stores a liquid composition therein and a recording head which ejects the liquid composition therefrom, wherein the liquid composition stored in the liquid composition storing portion is the liquid composition according to claim 1.
13. An ink jet recording apparatus comprising a liquid composition storing portion which stores a liquid composition therein and a recording head which ejects the liquid composition therefrom, wherein the liquid composition stored in the liquid composition storing portion is the liquid composition according to claim 1.
14. A liquid composition comprising at least a polymer and a modified siloxane compound,
wherein the modified siloxane compound is at least one selected from the group consisting of a modified siloxane compound represented by the following Formula (1), a modified siloxane compound represented by the following Formula (2) and a modified siloxane compound represented by the following Formula (3), and the liquid composition is so constituted that reference evaluation images formed using the liquid composition in conjunction with a pigment ink may have a coefficient of dynamic friction of 0.40 or less:
where the modified siloxane compound represented by Formula (1) has a weight average molecular weight of from 8,000 or more to 30,000 or less; in Formula (1), R1 is an alkylene group having 1 to 20 carbon atom(s), R2 is a hydrogen atom or an alkyl group having 1 to 20 carbon atom(s), m is from 1 or more to 250 or less, n is from 1 or more to 100 or less, a is from 1 or more to 100 or less, and b is from 0 or more to 100 or less;
where the modified siloxane compound represented by Formula (2) has a weight average molecular weight of from 8,000 or more to less than 50,000; in Formula (2), R3’s are each independently a hydrogen atom or an alkyl group having 1 to 20 carbon atom(s), R4’s are each independently an alkylene group having 1 to 20 carbon atom(s), p is from 1 or more to 450 or less, c is from 1 or more to 250 or less, and d is from 0 or more to 100 or less; and
where the modified siloxane compound represented by Formula (3) has a weight average molecular weight of from 8,000 or more to less than 50,000 and an HLB of from 1 or more to less than 7; in Formula (3), R5’s are each independently a hydrogen atom or an alkyl group having 1 to 20 carbon atom(s), R6 is an alkylene group having 1 to 20 carbon atom(s), q is from 1 or more to 100 or less, r is from 1 or more to 100 or less, e is from 1 or more to 100 or less, and f is from 0 or more to 100 or less.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method comprising, in combination:
(a) using an illumination source to provide light that is transmitted through at least (i) a stack of polarization rotators and (ii) a polarizer; and
(b) using one or more processors
(i) to perform an optimization calculation to compute a set of polarization state rotations induced in the light at respective pixels of the polarization rotators; and
(ii) to output control signals to control the polarization state rotations induced in the light at the respective pixels;
wherein
(I) each of the polarization rotators is a layer in the stack,
(II) the polarizer is optically in front of the stack,
(III) each of the polarization rotators comprises a spatially addressable device, the device being configured to dynamically vary per pixel polarization state rotations induced in the light, and
(IV) for each respective light ray in a set of light rays, the optimization calculation includes computing a summation of changes to polarization state rotation of the respective light ray that occur as the respective light ray travels through the stack of polarization rotators.
2. The method of claim 1, wherein the optimization calculation includes computing, according to Malus’ law, an intensity of the respective light ray, the intensity being as of when the respective light ray emerges from the polarizer.
3. The method of claim 2, wherein (a) Malus’ law includes a term that is a square of a sinusoidal function; (c) the sinusoidal function has an argument; (c) the optimization calculation includes solving for the argument, using an approximation based on only a single period of the sinusoidal function.
4. The method of claim 1, wherein for at least one pair of adjacent polarization rotators in the stack, no polarizer is positioned between the pair.
5. The method of claim 1, wherein the optimization calculation does not perform operations on values that are indicative of per pixel attenuation of the light and that are for pixels in a polarization rotator other than the front polarization rotator in the stack.
6. The method of claim 1, wherein each of the polarization rotators comprises a layer of liquid crystal.
7. The method of claim 1, wherein each of the polarization rotators is monochromatic and the illumination source is a strobe backlight configured to sequentially illuminate the polarization rotators with varying colors of light.
8. The method of claim 1, wherein each of the polarization rotators, respectively, is configured to dynamically vary voltage applied at the respective pixels in order to control polarization state rotation induced in the light at the respective pixels.
9. The method of claim 1, wherein the optimization calculation is a constrained linear least squares optimization calculation.
10. The method of claim 1, wherein the one or more processors are configured to employ a SART technique when performing the optimization calculation.
11. The method of claim 1, wherein the set of polarization state rotations, which is computed by the optimization calculation, minimizes error between a light field transmitted from the polarizer and a light field that would be created by a target 3D scene.
12. The method of claim 1, wherein light emerging from the polarizer produces an automultiscopic display.
13. Apparatus comprising, in combination:
a stack of polarization rotators, each of the polarization rotators being a layer in the stack;
a polarizer, the polarizer being optically in front of the stack;
an illumination source, the illumination source being configured to provide light that is transmitted through at least the stack and the polarizer; and
one or more processors;
wherein
(a) the one or more processors are configured
(i) to perform an optimization calculation to compute a set of polarization state rotations induced in the light at respective pixels of the polarization rotators, and
(ii) to output control signals to control the polarization state rotations induced in the light at the respective pixels,
(b) each of the polarization rotators comprises a spatially addressable device, the device being configured to dynamically vary per pixel polarization state rotations induced in the light, and
(c) for each respective light ray in a set of light rays, the optimization calculation includes computing a summation of changes to polarization state rotation of the respective light ray that occur as the respective light ray travels through the stack of polarization rotators.
14. The apparatus of claim 13, wherein the optimization calculation includes computing, according to Malus’ law, an intensity of the respective light ray, the intensity being as of when the respective light ray emerges from the polarizer.
15. The apparatus of claim 14, wherein (a) Malus’ law includes a term that is a square of a sinusoidal function; (c) the sinusoidal function has an argument; (c) the optimization calculation includes solving for the argument, using an approximation based on only a single period of the sinusoidal function.
16. The apparatus of claim 13, wherein for at least one pair of adjacent polarization rotators in the stack, no polarizer is positioned between the pair.
17. The apparatus of claim 13, wherein the optimization calculation does not perform operations on values that are indicative of per pixel attenuation of the light and that are for pixels in a polarization rotator other than the front polarization rotator in the stack.
18. The apparatus of claim 13, wherein the set of polarization state rotations, which is computed by the optimization calculation, minimizes error between a light field transmitted from the polarizer and a light field that would be created by a target 3D scene.
19. The apparatus of claim 13, wherein each of the polarization rotators is monochromatic and the illumination source is a strobe backlight configured to sequentially illuminate the polarization rotators with varying colors of light.
20. The apparatus of claim 13, wherein the optimization calculation is a linear optimization calculation and the one or more processors are configured to employ a SART technique when performing the linear optimization calculation.