Optimized design method for holographic optical element and apparatus using such holographic optical element

Claim 2

An optimized design method of a holographic optical element by calculating a correction coefficient so that an evaluating amount of a reconstructed light reconstructed by the holographic optical element can be minimized, the correction coefficient determining an aspheric term included in a phase transfer function, and the phase transfer function representing a shape of an interference fringe recorded on the holographic optical element, said method comprising the steps of: expressing a wavefront aberration via a linear function of the correction coefficient by positioning a main axis point on a characteristic evaluating surface onto which the reconstructed light is projected, so that the wavefront aberration of the reconstructed light can be minimized; and calculating the correction coefficient based on said linear function so that the evaluating amount can minimized.

Claim 3

A method as in claim 1, further comprising the step of: calculating the correction coefficient again by correcting the correction coefficient if the evaluating amount calculated from the correction coefficient is not proper.

Claim 4

An apparatus using a holographic optical element designed in accordance with the method in claim 2.

Claim 5

An apparatus using a holographic optical element designed in accordance with the method as in claim 1.

Claim 6

An optimized design method of a holographic optical element by calculating a correction coefficient so that an evaluating amount of a reconstructed light reconstructed by the holographic optical element can be minimized, the correction coefficient determining an aspheric term included in a phase transfer function, the phase transfer function representing a shape of an interference fringe recorded on the holographic optical element, said method comprising the steps of: expressing the evaluating amount as an average of a weighted mean-squared wavefront aberration of the reconstructed light at a main axis point on a characteristic evaluating surface onto which the reconstructed light is projected; expressing the average of the weighted mean-squared wavefront aberration via a first linear-function, the first linear-function including a phase of an outgoing wavefront surface from the holographic optical element before an aspheric term is used, and a moving distance of the main axis point while the aspheric term is being used; obtaining an equation which defines a coordinate of a moved main point axis by means of the first linear-function and Fermat's principle; expressing, based on said equation, the coordinate of the moved main axis point via a second linear-function of the correction coefficient, so as to obtain a third linear-function; expressing the wavefront aberration of the reconstructed light via the second linear-function of the correction coefficient by substituting the third linear-function for the first linear-function; obtaining linear simultaneous equations which define the correction coefficient by partially-differentiating the third linear-function by the correction coefficient; and calculating the correction coefficient in accordance with said linear simultaneous equations.

Claim 7

An optimized design method of a holographic optical element by calculating a correction coefficient so that an evaluating amount of a reconstructed light reconstructed by the holographic optical element can be minimized, the correction coefficient determining an aspheric term included in a phase transfer function, the phase transfer function representing a shape of an interference fringe recorded on the holographic optical element, said method comprising the steps of: expressing the evaluating amount as an average of a weighted mean-squared wavefront aberration of the reconstructed light at a main axis point on a characteristic evaluating surface onto which the reconstructed light is projected; expressing the average of the weighted mean-squared wavefront aberration via a first linear-function, the first linear-function including a phase of an outgoing wavefront surface from the holographic optical element before an aspheric term is used, and a moving distance of the main axis point while the aspheric term is being used; obtaining an equation which defines a coordinate of a moved main point axis by means of the first linear-function and Fermat's principle; expressing, based on said equation, the coordinate of the moved main axis point via a second linear-function of the correction coefficient, so as to obtain a third linear-function; expressing the wavefront aberration of the reconstructed light via the second linear-function of the correction coefficient by substituting the third linear-function for the first linear-function; obtaining linear simultaneous equations which define the correction coefficient by partially-differentiating the third linear-function by the correction coefficient; and calculating the correction coefficient in accordance with said linear simultaneous equations.

Claim 8

A method as in claim 5, further comprising the step of: calculating the correction coefficient again by correcting the correction coefficient if the evaluating amount calculated from the correction coefficient is not proper.

Claim 9

An apparatus using a holographic optical element designed in accordance with the method in claim 6.

Claim 10

An apparatus using a holographic optical element designed in accordance with the method in claim 5.

Claim 11

An optimized design method of a holographic optical element with a plurality of zones, by calculating a correction coefficient so that a total of an evaluating amount of a reconstructed light reconstructed by the holographic optical element for each zone can be minimized, the correction coefficient determining an aspheric term included in a phase transfer function, and the phase transfer function representing a shape of an interference fringe recorded on the holographic optical element, said method comprising the steps of: expressing a wavefront aberration via a linear function of the correction coefficient by positioning a main axis point on a characteristic evaluating surface onto which the reconstructed light is projected, so that the wavefront aberration of the reconstructed light can be minimized; and calculating the correction coefficient based on said linear function so that the evaluating amount can minimized.

Claim 12

An optimized design method of a holographic optical element with a plurality of zones, by calculating a correction coefficient so that a total of an evaluating amount of a reconstructed light reconstructed by the holographic optical element for each zone can be minimized, the correction coefficient determining an aspheric term included in a phase transfer function, and the phase transfer function representing a shape of an interference fringe recorded on the holographic optical element, said method comprising the steps of: expressing a wavefront aberration via a linear function of the correction coefficient by positioning a main axis point on a characteristic evaluating surface onto which the reconstructed light is projected, so that the wavefront aberration of the reconstructed light can be minimized; and calculating the correction coefficient based on said linear function so that the evaluating amount can minimized.

Claim 13

A method according to claim 9, wherein an incident light onto each zone of the holographic optical element is generated from a aberration-correcting holographic optical element located at a previous stage, said method simultaneously calculating correction coefficients of interference fringes of both the holographic optical element and the aberration-correcting holographic optical element.

Claim 14

An apparatus using both the holographic optical element and the aberration-correcting holographic optical element designed in accordance with the method according to claim 10.

Claim 15

A method as in claim 9, further comprising the step of: calculating the correction coefficient again by correcting the correction coefficient if the evaluating amount calculated from the correction coefficient is not proper.

Claim 16

An apparatus using a holographic optical element designed in accordance with the method in claim 12.

Claim 17

An apparatus using a holographic optical element designed in accordance with the method in claim 9.

Claim 18

An optimized design method of a holographic optical element with a plurality of zones, by calculating a correction coefficient so that a total of an evaluating amount of a reconstructed light reconstructed by the holographic optical element for each zone can be minimized, the correction coefficient determining an aspheric term included in a phase transfer function, and the phase transfer function representing a shape of an interference fringe recorded on the holographic optical element, said method comprising the steps of: expressing the evaluating amount as an average of a weighted mean-squared wavefront aberration of the reconstructed light at a main axis point on a characteristic evaluating surface onto which the reconstructed light is projected; expressing the average of the weighted mean-squared wavefront aberration via a first linear-function, the first linear-function including a phase of an outgoing wavefront surface from the holographic optical element before an aspheric term is used, and a moving distance of the main axis point while the aspheric term is being used; obtaining an equation which defines a coordinate of a moved main point axis by means of the first linear-function and Fermat's principle; expressing, based on said equation, the coordinate of the moved main axis point via a second linear-function of the correction coefficient, so as to obtain a third linear-function; expressing the wavefront aberration of the reconstructed light via the second linear-function of the correction coefficient by substituting the third linear-function for the first linear-function; obtaining linear simultaneous equations which define the correction coefficient by partially-differentiating the third linear-function by the correction coefficient; and calculating the correction coefficient in accordance with said linear simultaneous equations.

Claim 19

An optimized design method of a holographic optical element with a plurality of zones, by calculating a correction coefficient so that a total of an evaluating amount of a reconstructed light reconstructed by the holographic optical element for each zone can be minimized, the correction coefficient determining an aspheric term included in a phase transfer function, and the phase transfer function representing a shape of an interference fringe recorded on the holographic optical element, said method comprising the steps of: expressing the evaluating amount as an average of a weighted mean-squared wavefront aberration of the reconstructed light at a main axis point on a characteristic evaluating surface onto which the reconstructed light is projected; expressing the average of the weighted mean-squared wavefront aberration via a first linear-function, the first linear-function including a phase of an outgoing wavefront surface from the holographic optical element before an aspheric term is used, and a moving distance of the main axis point while the aspheric term is being used; obtaining an equation which defines a coordinate of a moved main point axis by means of the first linear-function and Fermat's principle; expressing, based on said equation, the coordinate of the moved main axis point via a second linear-function of the correction coefficient, so as to obtain a third linear-function; expressing the wavefront aberration of the reconstructed light via the second linear-function of the correction coefficient by substituting the third linear-function for the first linear-function; obtaining linear simultaneous equations which define the correction coefficient by partially-differentiating the third linear-function by the correction coefficient; and calculating the correction coefficient in accordance with said linear simultaneous equations.

Claim 20

A method as in claim 15, further comprising the step of: calculating the correction coefficient again by correcting the correction coefficient if the evaluating amount calculated from the correction coefficient is not proper.

Claim 21

An apparatus using a holographic optical element designed in accordance with the method in claim 16.

Claim 22

A method according to claim 15, wherein an incident light onto each zone of the holographic optical element is generated from a aberration-correcting holographic optical element located at a previous stage, said method simultaneously calculating correction coefficients of interference fringes of both the holographic optical element and the aberration-correcting holographic optical element.

Claim 23

An apparatus using both the holographic optical element and the aberration-correcting holographic optical element designed in accordance with the method according to claim 18.

Claim 24

An apparatus using a holographic optical element designed in accordance with the method in claim 15.