Processing apparatus and method for calculating refractive index distribution based on light beam data, optical apparatus including the processing apparatus, manufacturing apparatus for creating optical element
According to the embodiment, a processing apparatus includes an arithmetic section. The arithmetic section is configured to calculate a refractive index distribution forming a light beam path based on an estimated output calculated by inputting light beam data indicating the light beam path to an estimation model, an updated output calculated based on the light beam data and the estimated output, and an evaluation index of the estimation model calculated from a ray equation independent of a time which the light beam path follows.
1. An optical apparatus comprising:
an illumination portion including a light source configured to illuminate an object with illumination light forming a light beam path; and
an image sensor which is controlled by a processor, the image sensor being configured to capture the illumination light with which the object is illuminated;
the processor; and
a memory that stores instructions that, when executed by the processor, cause the processor to perform processing,
wherein the processor is configured to:
obtain light beam data indicating the light beam path based on image capturing data captured by the image sensor,
obtain an estimated output by inputting the light beam data indicating the light beam path to an estimation model, the light beam data being formed by a refractive index in the light beam path, the estimation model being a neural network model,
calculate an evaluation index of the estimation model from a ray equation independent of a time which the light beam path follows, wherein
the ray equation is given by
d
P
d
t
=
c
r
∂
n
∂
Q
,
the ray equation is defined in an orthogonal coordinate space, and described as follows with one coordinate variable as an intermediary parameter:
d
(
nu
)
dz
-
l
+
q
′
·
q
′
∂
n
∂
q
=
0
,
and
the evaluation index indicates a deviation between a refractive index distribution obtained in the estimated output and an actual retractive index distribution,
calculate an updated output by inputting the light beam data to an optimized estimation model,
repeatedly execute, based on the below formula, the calculation of the evaluation index, the optimization of the estimation model, and the calculation of the updated output without training data until the evaluation index becomes smaller than a preset threshold value,
g
(
u
,
q
,
z
,
μ
)
≡
❘
"\[LeftBracketingBar]"
d
(
μ
u
)
dz
-
l
+
q
′
·
q
′
∂
μ
∂
q
❘
"\[RightBracketingBar]"
2
,
and
calculate a refractive index distribution forming the light beam path, based on the estimated output, the updated output, and the evaluation index.
2. The optical apparatus according to claim 1 , wherein
the ray equation is an evolution equation for spatial coordinate information of the light beam path.
3. The optical apparatus according to claim 1 , wherein
the light beam data is expressed using, as an intermediary parameter, a coordinate of a spatial element obtained by discretizing the light beam path.
4. The optical apparatus according to claim 3 , wherein
the ray equation is expressed using the intermediary parameter, and
the refractive index distribution is calculated as a refractive index of the spatial element.
5. The optical apparatus according to claim 4 , wherein
the coordinates of the spatial element are determined in an orthogonal coordinate space, and
the intermediary parameter is one component of the coordinates determined in the orthogonal coordinate space.
6. The optical apparatus according to claim 1 , wherein
the processor is configured to iteratively optimize the estimation model based on the evaluation index.
7. The optical apparatus according to claim 6 , wherein
the estimation model is a neural network model, and
the neural network model is optimized based on an error back-propagation model using the evaluation index as an error.
8. The optical apparatus according to claim 1 ,
wherein the processor is configured to calculate, based on image capturing data captured by the image sensor, a light beam direction of the illumination light as the light beam path.
9. The optical apparatus according to claim 1 , further comprising:
a background pattern to which the illumination light from the illumination portion is applied,
wherein the image sensor is configured to capture the illumination light reflected by the background pattern and transmitted through the object.
10. The optical apparatus according to claim 1 , further comprising:
a light beam selection portion having a plurality of color filters which is between the object and the image sensor, the light beam selection portion being configured to transmit light beams corresponding to respective wavelength regions of the plurality of color filters,
wherein the illumination light with which the object is illuminated is captured after passing through the light beam selection portion.
11. The apparatus according to claim 1 , wherein
the processor is configured to acquire a refractive index of an object based on the light beam path without the light beam path analytically expressed.
12. A processing method configured to calculate refractive index, the method comprising:
illuminating, by a light source, an object with illumination light to form a light beam path;
capturing, by an image sensor, the illumination light with which the object is illuminated;
obtaining light beam data indicating the light beam path based on image capturing data captured by the image sensor;
obtaining an estimated output by inputting the light beam data indicating the light beam path to an estimation model, the light beam data being formed by a refractive index in the light beam path, and the estimation model being a neural network model;
calculating an evaluation index of the estimation model from a ray equation independent of a time which the light beam path follows, wherein
the ray equation is given by
dP
dt
=
c
n
∂
n
∂
Q
,
the ray equation is defined in an orthogonal coordinate space, and described as follows with one coordinate variable as an intermediary parameter:
d
(
nu
)
dz
-
1
+
q
′
·
q
′
∂
n
∂
q
=
0
,
and
the evaluation index indicates a deviation between a refractive index distribution obtained in the estimated output and an actual retractive index distribution;
calculating an updated output by inputting the light beam data to an optimized estimation model;
repeatedly executing, based on the formular below, the calculation of the evaluation index, the optimization of the estimation model, and the calculation of the updated output without training data until the evaluation index becomes smaller than a preset threshold value,
g
(
u
,
q
,
z
,
μ
)
≡
❘
"\[LeftBracketingBar]"
d
(
μ
u
)
dz
-
1
+
q
′
·
q
′
∂
μ
∂
q
❘
"\[RightBracketingBar]"
2
;
and
calculating, based on the estimated output, the updated output, and the evaluation index, a refractive index distribution forming the light beam path.
13. The processing method of claim 12 , further comprising:
acquiring a refractive index of an object based on the light beam path without the light beam path analytically expressed.
14. A method for manufacturing an optical element, comprising:
the processing method according to claim 12 ; and
creating an optical element based on the refractive index distribution, the optical element having the refractive index distribution.
15. A non-transitory storage medium storing a program for calculating refractive index, the program causing a computer to implement:
controlling a light source to illuminate an object with illumination light to form a light beam path;
controlling an image sensor to capture the illumination light with which the object is illuminated;
obtaining light beam data indicating the light beam path based on image capturing data captured by the image sensor;
obtaining an estimated output by inputting the light beam data indicating the light beam path to an estimation model, the light beam data being formed by a refractive index in the light beam path, and the estimation model being a neural network model,
calculating an evaluation index of the estimation model from a ray equation independent of a time which the light beam path follows, wherein
the ray equation is given by
dP
dt
=
c
n
∂
n
∂
Q
,
the ray equation is defined in an orthogonal coordinate space, and described as follows with one coordinate variable as an intermediary parameter:
d
(
nu
)
dz
-
1
+
q
′
·
q
′
∂
n
∂
q
=
0
,
and
the evaluation index indicates a deviation between a refractive index distribution obtained in the estimated output and an actual retractive index distribution,
calculating an updated output by inputting the light beam data to an optimized estimation model,
repeatedly executing, based on the formular below, the calculation of the evaluation index, the optimization of the estimation model, and the calculation of the updated output without training data until the evaluation index becomes smaller than a preset threshold value,
g
(
u
,
q
,
z
,
μ
)
≡
❘
"\[LeftBracketingBar]"
d
(
μ
u
)
dz
-
1
+
q
′
·
q
′
∂
μ
∂
q
❘
"\[RightBracketingBar]"
2
,
and
calculating a refractive index distribution forming a light beam path, based on the estimated output, the updated output, and the evaluation index.
16. The processing method of claim 15 , wherein the program further causes the computer to implement:
acquiring a refractive index of an object based on the light beam path without the light beam path analytically expressed.